apt_key
APT KEY WORDS
Author: Arthur L. Edwards (email: xenopsbird@comcast.net).
Updated: 2006 August 4 14:10.
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.and. Boolean operation "intersection" on two machine words aptbitb
.comp. Boolean operation "complement" on a machine word aptbitb
.eqv. Boolean operation "equivalence" on two machine words aptbitb
.int. Boolean operation "intersection" on two machine words aptbitb
.nand. Boolean operation "comp. .and." on two machine words aptbitb
.nor. Boolean operation "nor" on two machine words aptbitb
.not. Boolean operation "not" on two machine words aptbitb
.or. Boolean operation "union" on two machine words aptbitb
.shl. Boolean operation "shift-left" on a machine word aptbits
.shr. Boolean operation "shift-right" on a machine word aptbits
.un. Boolean operation "union" on two machine words aptbitb
.xnor. Boolean operation "equivalence" on two machine words aptbitb
.xor. Boolean operation "exclusive or" on two machine words aptbitb
0
1-D axis, distance between two points on aptvdil
1-D cylinder, intersection with a linear track aptrkcl
1-D major plane, intersection with a linear track aptrksl
1-D sphere, intersection with a linear track aptrkrl
2-D (see "major plane")
3 by 3 determinant, value of aptrips, aptdet3
3 by 3 matrix, determinant of aptdet3
4 by 4 determinant, value of aptdet4
4 by 4 matrix, determinant of aptdet4
A
absolute precision, round-off floating point data to aptrnds, aptnint
accelerated trajectory, parabolic, given points on vs time aptpart
accelerated trajectory, parabolic, intersection with line aptparl
accelerated trajectory, parabolic, intersection with plane aptparp, aptparq
accelerated trajectory, parabolic, intersection with point aptparh, aptpars
accelerated trajectory, parabolic, intersection with quadric aptparq
accelerated trajectory, parabolic, path length vs time aptparb
accelerated trajectory, parabolic, points on vs time aptparb, aptpart
accelerated trajectory, parabolic, proximal point to line aptparl
accelerated trajectory, parabolic, proximal point to plane aptparp
accelerated trajectory, parabolic, proximal point to point aptpars
accelerated trajectory, parabolic, proximal to quadric aptparx
accelerated trajectory, parabolic, velocities vs time aptparb
accelerated trajectory, time-dependent acceleration on aptacct
acceleration on a parabolic trajectory, uniform aptparb, aptpart
acceleration on a trajectory, time-dependent aptacct
add two big integers (one digit per word), any number base aptbadd
add vectors aptvsum, aptvadd
add vectors (major plane) aptvadc
adjust values of floating point data near 0 and 1 aptfdad, aptfdav
adjust values of floating point data, by round-off aptrnds, aptnint
adjust values of vector components aptvlim, aptvtol
adjust values of vector components (major plane) aptvlic, aptvtoc
aliased PDF bins, generate aptalin
aliased PDF bins, randomly sample aptalsb, aptalst
alphabetic characters, increment or decrement aptchin
alphabetic characters, random, put into a character string aptchrn
alphanumeric characters (see "character", "string")
alphanumeric characters, random, put into a character string aptchrn
alphanumeric characters, squeeze out of a character string aptchsq
alternate geometric representations (see "line", "plane")
altitudes of a triangle, orthocenter apttrig
analyze a reflection operator to find axis aptrefq
analyze a rotation operator to find rotation angle, axis aptrotq
and, Boolean operation "intersection" on two machine words aptbitb
angle (see also "cosine", "sine", "bisector")
angle (see also "parallel", "perpendicular")
angle and axis, rotate with a specified aptrota
angle between unit vectors, cosine of aptvdos, aptvdot
angle between unit vectors, cosine of (major plane) aptvdoc
angle between unit vectors, sine of aptvaxb, aptvxun
angle between unit vectors, sine of (major plane) aptvaxc, aptvxuc
angle bisector aptbang, apttrig
angle bisector (major plane) aptbanc
angle bisectors of a triangle, inscribed circle apttrig
angle interval, randomly sample direction vectors within aptscar
angle of intersection of a track with a cone aptrkis
angle of intersection of a track with a cylinder aptrkis
angle of intersection of a track with a plane aptrkis
angle of intersection of a track with a quadric surface aptrkis
angle of intersection of a track with a sphere aptrkis
angle of intersection of a track with an axisymmetric quadric aptrkis
angle of intersection of a track with an ellipsoid aptrkis
angle of rotation of a specified rotation operator aptrotq
angle of rotation, operator for a specified axis and aptrota
angle, conversion to degrees, grads, radians, arc deg, min, sec aptcang
angle, cosine and sine of (major plane) aptvanc
angle, cosine of, between two vectors aptvang
angle, cosine of, between unit vectors aptvdos, aptvdot
angle, cosine of, between unit vectors (major plane) aptvdoc
angle, operator to rotate around an axis by a specified aptrota
angle, rotate a vector by a specified (major plane) aptrotc
angle, scattering, fixed, randomly sample azimuth angle for aptscan, aptscaz
angle, scattering, fixed, randomly sample azimuth angle for aptscma, aptscmz
angle, sine of, between two unit vectors aptvaxb, aptvxun
angle, sine of, between two unit vectors (major plane) aptvaxc, aptvxuc
angle, vector bisecting aptbang, apttrig
angle, vector bisecting (major plane) aptbanc
angles from two other lines, line at specified aptetrv
angles from two other vectors, vector at specified aptetru, aptetrv
angles of a triangle apttrig
angles, rotation operator to rotate around major axes by 3 aptrots
annular disk, randomly sample points on (any plane) aptlocd
annulus of a circle, randomly sample points in aptlocd
annulus of a conical frustrum, randomly sample points in aptscnv
annulus of a cylinder, randomly sample points in aptlocy
annulus of a sphere, randomly sample points in aptlocs
approximate distance from a point to a quadric surface aptquad
approximate distance from a point to a quadric surface (OBS) aptqprr, aptqprt
arc degrees, minutes, seconds, convert an angle to aptcang
arc minutes, seconds, degrees, convert an angle to aptcang
arc seconds, degrees, minutes, convert an angle to aptcang
area between two lines aptvaxb, aptvxun
area between two lines (major plane) aptvaxc, aptvxuc
area between two vectors aptvaxb, aptvxun
area of a regular polygon aptpoly
area of a regular polygon (major plane) aptpolc
area of a triangle apttrid, apttrig
area of a triangle aptvpln
area of a triangle (major plane) apttric
area of a triangle, extend two sides to double aptrext
areas of faces of a brick (bounded by coordinate surfaces) aptbrkv
areas of vertices of a quadrangle (major plane) aptqvac
areas, equal, straight line that cuts a triangle into aptrabc, aptrcab
areas, equal, straight line that cuts a triangle into aptrcut, aptrext
arithmetic, modular, multiplicative inverse of an integer in aptmord
arithmetic, order of an integer in modular aptmord
array, delete rows containing duplicate values aptdeld
array, maximum and minimum, positive values and indices aptmnlg
array, maximum and minimum, values and indices aptmnlg, aptmnmx
array, mean value and standard deviation of aptmean
array, minimum and maximum, positive values and indices aptmnlg
array, minimum and maximum, values and indices aptmnlg, aptmnmx
array, randomly reorder an aptrand
array, reverse the order of the digits of a big integer aptbrev
array, sort, any direction or mode (one column) aptsort
array, sort, any direction, mode, or number of columns aptsorm
array, type integer*1, contract bits from into machine words aptbitp
array, type integer*1, expand bits from machine words into an aptbite
ascending order, reorder data (multiple columns) aptsorm
ascending order, reorder data (one column) aptsort
ASCII characters (see "character", "string")
ASCII characters, increment or decrement aptchin
ASCII characters, move from one string to another aptchmv
ASCII characters, replace with other characters aptchrp
ASCII characters, translate binary integer numbers into aptchia
ASCII characters, translate into integer (oct, dec, hex) aptchai
ASCII characters, translate into integer and floating point aptchtp
ASCII characters, translate into integer and floating point aptffip, aptchap
ASCII characters, translate into integer and floating point aptsubs, aptsubm
ASCII strings longer than eight characters, parse aptchtp
ASCII strings longer than eight characters, parse aptffip, aptchap
ASCII strings longer than eight characters, parse aptsubs, aptsubm
ASCII subscript, form subscripted variable from a stem and aptsuba, aptsubb
ASCII subscript, form subscripted variable from a stem and aptsuba, aptsubb
average coordinates, edge lengths, face areas of a brick aptbrkv
average value of an array aptmean
axes and center of symmetry of a quadric surface aptaxis
axes of two circular cylinders, proximal points on, parallel? aptcycy
axes, randomly sample direction vectors relative to aptscav
axes, rotation operator for 3 angles around 3 major aptrots
axial position, rotate points around axis depending on aptwist
axis and angle, rotate with a specified aptrota
axis and radius, equation of a cylinder with a specified aptclis, aptcyis
axis intercepts of a quadric surface, major and symmetry aptqupt
axis of a cylinder, distance from the center of a sphere aptspcy
axis of a cylinder, proximal point on, to a sphere aptspcy
axis of rotation of a specified rotation operator aptrotq
axis of rotation, operator for a specified angle and aptrota
axis, major, equation of a cone on aptcnis, aptcois
axis, major, equation of a cylinder on aptcyis
axis, major, equation of a hyperboloid on aptelis
axis, major, equation of an ellipsoid on aptelis, aptesis
axis, major, randomly sample directions at fixed angle from aptscma, aptscmz
axis, project toward aptprcy, aptprsp
axis, randomly sample direction vectors at fixed angle from aptscan, aptscaz
axis, randomly sample direction vectors at fixed angle from aptscma, aptscmz
axis, randomly sample direction vectors relative to aptscap, aptscar
axis, randomly sample direction vectors relative to aptscav
axis, rotate points around, depending on axial position aptwist
axis, rotate points around, depending on radial position aptwirl
axis, rotation operator for a specified angle and aptrota
axis, scale cylindrically around a specified aptsclr
axis, sphere on a specified, and through two specified points aptspha
axis, z, equation of a cone on, through two specified points aptcniz
axisymmetric coordinates, effects of linear motion in aptmove, aptmvcy
axisymmetric coordinates, intersection of a linear track in aptrkcy
axisymmetric surface (see also "quadric surface")
axisymmetric surface, distance from a plane to, intersection aptplqu
axisymmetric surface, intersection of linear track with aptrkcy, aptrkis
azimuth angle, randomly sample, for a fixed scatter angle aptscan, aptscaz
azimuth angle, randomly sample, for a fixed scatter angle aptscma, aptscmz
B
backslash, use as an escape character aptfbrk
base, find the value of a big integer in a specified number aptbasb
base, find the value of a decimal number in a specified number aptbase
basic matrix operations (see "matrix", "product")
basic symmetry operations (see "reflect", "rotate")
basic symmetry operations (see "reflection", "rotation")
basic symmetry operations (see also "inversion", "translation")
basic symmetry operations (see also "invert", "translate")
basic vector operations (see "sum", "difference", "product")
big integer (any base), convert from decimal integer into a aptdtob
big integer (any base), convert from floating point into a aptftob, aptltob
big integer (any base), convert into decimal integer aptbtod
big integer (any base), convert into floating point aptbtod
big integer (any base), count the occurrences of each digit in aptbsum
big integer (any base), find a power of a aptbpow
big integer (any base), find a root of a aptbrtn
big integer (any base), find in any other number base aptbasb
big integer (any base), find the exponential of a aptbexp
big integer (any base), find the factorial of a aptbfac
big integer (any base), find the log (base 10) of a aptbtod
big integer (any base), find the prime factors of a aptpfab
big integer (any base), reverse the order of the digits of a aptbrev
big integers (any base), find the difference of two aptbsub
big integers (any base), find the modulus of two aptbmod
big integers (any base), find the product of two aptbmul
big integers (any base), find the quotient of two aptbdiv
big integers (any base), find the remainder of division of two aptbdiv
big integers (any base), find the sum of two aptbadd
big integers, nonzero, concatenate the digits of two aptbcat
bin values, equal-probability PDF, randomly sample apteqxs, aptrans
binary Boolean operations "and", "int", "nand", "or", "un" aptbitb
binary Boolean operations "nor", "xor", "xnor", "eqv" aptbitb
binary search table look-up, ascending or descending order aptlook
bins, aliased PDF, generate aptalin
bins, aliased PDF, randomly sample aptalsb, aptalst
bins, cumulative PDF, generate aptcump
bins, cumulative PDF, randomly sample aptcums, aptcumt
bins, equal-probability PDF, generate apteqin, apteqxn
bins, equal-probability PDF, randomly sample apteqsb
bins, randomly sample, aliased aptalsb, aptalst
bins, randomly sample, cumulative probability aptcums, aptcumt
bins, randomly sample, equal-probability apteqsb
bins, specified, randomly sample from linear PDFs in aptalsl
bins, specified, randomly sample from uniform PDFs in aptalsh
bisector of a line (major plane) aptpblc
bisector of a vertex angle of a quadrangle (major plane) aptbanc
bisector of a vertex angle of a quadrangle, vector aptbang
bisector of a vertex angle of a triangle, vector aptbang, apttrig
bisector of a vertex angle of a triangle, vector (major plane) aptbanc
bisector of an angle aptbang, apttrig
bisector of an angle (major plane) aptbanc
bisector of edge of a quadrangle, perpendicular (major plane) aptpblc
bisector of edge of a quadrangle, perpendicular plane aptpbln
bisector of edge of a triangle, perpendicular (major plane) aptpblc
bisector of edge of a triangle, perpendicular plane aptpbln
bit operations "comp", "not", "and", "int", "nand", "or", "un" aptbitb
bit operations "nor", "xor", "xnor", "eqv" aptbitb
bit string, find in a machine word aptbitf
bit string, move from one machine word to another aptbitm
bit string, put random bits into aptbitr
bits from a type integer*1 array, contract into machine words aptbitp
bits, randomly sample and put into a bit string aptbitr
bits, shift right or left, wrap-around or pull aptbits
blank-delimited (see "data fields", "delimited")
blank-delimited character string, parse into symbols aptfbrk
blank-delimited character string, parse into symbols aptffip, aptchap
blank-delimited character string, read and parse into symbols aptfbrk
blank-delimited character string, read and parse into symbols aptffip, aptchap
blanks, imbedded, translate data fields with aptchtp
blanks, imbedded, translate data fields with aptsubs, aptsubm
blanks, multiple, reduce to a single blank in character string aptblsq
blanks, remove leading and/or trailing from a character string aptrmbl
blanks, squeeze out of a character string aptchsq
body, geometric (see "cylinder", "sphere", "polyhedron")
body, geometric (see also "ellipsoid")
Boolean operations "and", "int", 'nand", "or", "un", "nor" aptbitb
Boolean operations "shift-right" and "shift-left" aptbits
Boolean operations "xor", "xnor", "eqv", "comp" and "not" aptbitb
boomerang quadrangle, test for (major plane) aptqvac
bowtied quadrangle, test for (major plane) aptqvac
brackets, use as field delimiters (square [] or curly {}) aptfbrk
brick, bounded by surfaces of the coordinate system aptbrkn, aptbrkp
brick, bounded by surfaces of the coordinate system aptbrks, aptbrkv
brick, find a point with given local coordinates in aptbrkp
brick, geometric data for a aptbrkv
brick, randomly sample points in a aptbrks
brick, see if a point is in, and find distances to surfaces aptbrkn
brick, see if a point is in, and find local coordinates aptbrkn
C
calculate (implied in any entry without a verb)
cartesian coordinates, transform to or from aptcsys, aptcsyv
cartesian coordinates, volume bounded by surfaces of aptbrkn, aptbrkp
cartesian coordinates, volume bounded by surfaces of aptbrks, aptbrkv
center and edges of a quadrangle, fit a quadric surface to aptqhyp
center and radius of circle through 3 points (major plane) aptcirc
center and radius of circumscribed circle of a triangle apttrig
center and radius of inscribed circle of a triangle apttrig
center and radius of sphere on an axis, and through 2 points aptspha
center and radius of sphere through four specified points aptsphp
center of circle tangent to two specified tangent circles aptcirl, aptcirk
center of sphere tangent to three specified tangent spheres aptsphl, aptsphk
center of symmetry, axes and type of a quadric surface aptaxis
center, radius and orientation of circle through 3 points aptcirp
centers and radii of circles tangent to 3 tangent circles aptcirk
centers and radii of spheres tangent to 4 tangent spheres aptsphk
centers of circles tangent to three specified tangent circles aptcirk
centers of curvature at a point on a quadric surface, extremes aptcris
centers of spheres tangent to four specified tangent spheres aptsphl, aptsphk
centroid of a brick (bounded by coordinate surfaces) aptbrkv
centroid of a brick, coordinates, lengths and areas through aptbrkv
centroid of a tetrahedron apttetd, aptrans
centroid of a triangle apttrid, apttrig
centroid of a triangle (major plane) apttric
centroid of a volume bounded by coordinate surfaces aptbrkp, aptbrkv
character data, sort, in either direction aptsorm
character data, sort, in either direction (one column) aptsort
character set, randomly sample characters from aptchrn
character string into integer words, copy digits from a aptatob
character string, convert from integer to (oct, dec, hex) aptchia
character string, convert to integer (oct, dec, hex) aptchai
character string, convert to integer and floating point aptchtp
character string, convert to integer and floating point aptffip, aptchap
character string, convert to integer and floating point aptsubs, aptsubm
character string, delimited, find in another character string aptchfs
character string, delimited, find in another character string aptquot, aptfbrk
character string, find in another character string aptchfp
character string, form from a stem and ASCII subscript aptsuba, aptsubb
character string, form from a stem and ASCII subscripts aptsubb
character string, form from a stem and integer subscripts aptsubi
character string, increment or decrement characters in aptchin
character string, longer than eight characters, parse aptchtp
character string, longer than eight characters, parse aptffip, aptchap
character string, longer than eight characters, parse aptsubs, aptsubm
character string, move from one location to another aptchmv
character string, put random characters in aptchrn
character string, reduce multiple blanks to a single blank in aptblsq
character string, remove leading and/or trailing blanks from a aptrmbl
character string, replace characters in aptchrp
character string, replace in a character string aptchmv
character string, squeeze out a character aptchsq
character string, store ASCII integer character into aptchia
character string, translate hexadeimal into a decimal number apthexd
character string, translate into a stem and subscript aptsubr
character string, translate into a stem and subscripts, more aptsubm
character string, translate into integer (oct, dec, hex) aptchai
character string, translate into integer and floating point aptchtp
character string, translate into integer and floating point aptffip, aptchap
character string, translate into integer and floating point aptsubs, aptsubm
character, delimiter, use to separate data fields aptffip, aptchap
character, delimiter, use to separate data fields aptquot, aptfbrk
character, squeeze out of a character string aptchsq
characteristics of quadric curves (conic sections) aptplqu
characters, duplicate, find in Sudoku puzzle row, column, box aptsudu
characters, increment or decrement in a character string aptchin
characters, move from one location to another aptchmv
characters, non-graphic, find in a character string and replace aptchip
characters, random, put into a character string aptchrn
characters, replace in a character string aptchrp
characters, translate ASCII (oct, dec, hex) into integer aptchai
characters, translate integer into ASCII (oct, dec, hex) aptchia
chemistry, 1999 fundamental constants, in cm-g-sh-keV units aptconl
chemistry, 1999 fundamental constants, in SI units aptconm
Chinese Remainder Theorem Problem inverse aptcrtr
Chinese Remainder Theorem Problem solution aptcrts
circle of intersection of a plane and a quadric surface aptplqu
circle of intersection of a plane and a sphere aptplqu
circle of intersection of a plane and a sphere aptplsp, aptplis
circle of intersection of two spheres aptplqu
circle of intersection of two spheres aptspsp
circle tangent to a circle? (major plane) aptcinc
circle tangent to three specified tangent circles, radius of aptcirt, aptcirk
circle tangent to two specified tangent circles, center of aptcirl, aptcirk
circle through 3 points, center and radius of (major plane) aptcirc
circle through 3 points, center, radius and orientation of aptcirp
circle, annulus of, randomly sample points inside aptlocd
circle, distance from a point to a aptwhis
circle, intersection with a line (major plane) aptlnic
circle, intersection with another circle (major plane) aptcinc
circle, line tangent to? (major plane) aptlnic
circle, project points onto (major plane) aptproc
circle, radially project points onto (major plane) aptproc
circle, randomly sample points inside aptlocd
circle, randomly sample points inside annulus of aptlocd
circle, randomly sample points on (any plane) aptlocd
circles coincident (major plane)? aptcinc
circles tangent to three specified tangent circles, radii of aptcirt, aptcirk
circles, intersection of two (major plane) aptcinc
circular annulus, randomly sample points in aptlocd
circular cylinder and a plane, distance between, intersection aptplcy, aptplis
circular cylinder and a plane, distance between, intersection aptplqu
circular cylinder and a sphere, distance between, intersection aptspcy
circular cylinder, distance from a plane to a, intersection aptplcy, aptplis
circular cylinder, distance from a plane to a, intersection aptplqu
circular cylinder, distance from a sphere to a aptspcy
circular cylinder, intersection with a plane, distance aptplcy, aptplis
circular cylinder, intersection with a sphere, distance aptspcy
circular cylinder, proximal line to a plane, distance aptplcy, aptplis
circular cylinder, proximal line to a plane, distance aptplqu
circular cylinder, proximal point to a sphere, distance aptspcy
circular cylinder, proximal point to another circular cylinder aptcycy
circular cylinders, distance between (apart or overlapping) aptcycy
circular cylinders, distance between axes aptcycy
circular cylinders, proximal points on axes, surfaces aptcycy
circumscribed circle of a regular polygon aptpoly
circumscribed circle of a regular polygon (major plane) aptpolc
circumscribed circle of a triangle, perpendicular bisectors apttrig
classify a quadrangle shape (major plane) aptqvac
classify a quadric surface, and center of symmetry and axes aptaxis
classify a quadric surface, and center of symmetry and extrema aptqext
coaxial, see if two circular cylinders are aptcycy
coefficients of continued fraction, find, given value aptcofr
coincident circles (major plane)? aptcinc
coincident circular cylinders? aptcycy
coincident lines (major plane)? aptlnlc
coincident lines? aptlnln
coincident planes? aptplpl, aptplis
coincident points (major axis)? aptvdil
coincident points (major plane)? aptvdic
coincident points? aptdist, aptvdis
coincident spheres? aptspsp
colinear points (major plane)? apttric
colinear points? aptpfit
colinear points? apttrid, aptvpln
colon, use as a field delimiter (:) aptfbrk
colon, use as a field delimiter (:) aptffip, aptchap
columnar data, delete rows containing duplicate values aptdeld
columnar data, sort, any direction or mode (one column) aptsort
columnar data, sort, any direction, mode or # of columns aptsorm
combinations and permutation of N things taken M at a time aptbpac
combinations and permutation of N things taken M at a time aptcomb, aptperm
combinations of N things taken M at a time aptcomb, aptcomf
combinations of N things taken M at a time, number of aptcomf
combine a stem and an ASCII subscript into a character string aptsuba, aptsubb
combine a stem and ASCII subscripts into a character string aptsubb
combine a stem and integer subscripts into a character string aptsubi
combined symmetry operations (see "matrix", "operator")
comma, use as a field delimiter (,) aptfbrk
comma, use as a field delimiter (,) aptffip, aptchap
common divisor of a set of integers, find the greatest aptcmad
common multiple of a set of integers, find the least aptcmad
comp, Boolean operation "complement" on a machine word aptbitb
complement of a machine word (Boolean operation "comp.") aptbitb
complex roots of a cubic equation, and real roots aptcubs
complex roots of a quadratic equation, and real roots aptqrts, aptqrtv
complex roots of a quartic polynomial equation, and real roots aptquar
components of vectors, limit range of values (major plane) aptvtoc
components of vectors, limit range of values of aptvtol
components of vectors, lower limits on values aptvlim
components of vectors, lower limits on values (major plane) aptvlic
components, vector, in a plane aptvplp
components, vector, parallel and perpendicular to a vector aptvpap
components, vector, parallel to another vector (major plane) aptvcvc
concatenate the digits of two nonzero big integers aptbcat
concentric, see if two circular cylinders are aptcycy
concentric, see if two spheres are aptspsp
cone (see also "quadric surface")
cone symmetric around a major axis, equation of aptcois, aptcnis
cone symmetric around the z axis, equation of aptcniz
cone, distance from a plane to, intersection aptplqu, aptplis
cone, distance from a point to a aptwhis
cone, elliptic, distance from a plane to an aptplqu
cone, equation of, on a major axis, given two points aptcnis
cone, equation of, on a major axis, given vertex and angle aptcois
cone, equation of, on the z axis, given two points aptcniz
cone, intersection with a linear track, normal, angle aptrkcy, aptrkis
cone, intersection with a major plane aptplis
cone, right circular, randomly sample points in aptscnv
cone, right circular, randomly sample points in annulus aptscnv
cone, right circular, randomly sample points in frustrum aptscnv
cone, right circular, randomly sample points on surface aptscns, aptscnv
conic sections (see "quadric surface")
conic sections, characteristics of quadric curves aptplqu
conjugate axis of a hyperbola or hyperbolic cylinder aptplqu
constants, 1999 values of the fundamental aptconl, aptconm
continued fraction, find coefficients of, given value aptcofr
continued fraction, find value of, given coefficients aptcofv
contract bits from a type integer*1 array into machine words aptbitp
control characters, find in a character string and replace aptchip
Control-V, use as an escape character (^V) aptfbrk
convergents of a continued fraction, partial sums aptcofr, aptcofv
conversion factors for energy units, 1999 values of aptconl, aptconm
convert a big integer (any base) into a decimal integer aptbtod
convert a big integer (any base) into a floating point aptbtod
convert a character string to integer (oct, dec, hex) aptchai
convert a character string to integer and floating point aptchtp
convert a character string to integer and floating point aptffip, aptchap
convert a character string to integer and floating point aptsubs, aptsubm
convert an angle to degrees, grads, radians, arc deg, min, sec aptcang
convert an integer into ASCII characters (oct, dec, hex) aptchia
convert an integer into ASCII characters (oct, dec, hex) aptchia
convert coordinate systems aptcsys, aptcsyv
convert from a decimal integer into a big integer (any base) aptdtob
convert from floating point into a big integer (any base) aptftob, aptltob
convex quadrangle, test for aptqvac
coordinate differences aptdist, aptvdis
coordinate differences (major plane) aptvdic
coordinate differences in groups of points aptdirt, aptprim
coordinate system, cartesian, volume bounded by surfaces of aptbrkn, aptbrkp
coordinate system, cartesian, volume bounded by surfaces of aptbrks, aptbrkv
coordinate system, cylindrical, volume bounded by surfaces of aptbrkn, aptbrkp
coordinate system, cylindrical, volume bounded by surfaces of aptbrks, aptbrkv
coordinate system, spherical, volume bounded by surfaces of aptbrkn, aptbrkp
coordinate system, spherical, volume bounded by surfaces of aptbrks, aptbrkv
coordinate system, transform aptcsys, aptcsyv
coordinates of a brick, minimum, centroid and maximum aptbrkv
coordinates, linearly combine aptvadd, aptvsum
coordinates, linearly combine (major plane) aptvadc, aptvsuc
coplanar vector triple? aptrips
copy digits from a character string into integer words aptatob
cosine and sine of an angle (major plane) aptvanc
cosine of an angle aptvang
cosine of angle between unit vectors aptvdos, aptvdot
cosine of angle between unit vectors (major plane) aptvdoc
cosine of vertex angle of a quadrangle aptvang
cosine of vertex angle of a quadrangle (major plane) aptvanc
cosine of vertex angle of a triangle aptvang
cosine of vertex angle of a triangle (major plane) aptvanc
cosine-power PDF, randomly sample direction vectors from aptscap, aptscar
cosine-power PDF, randomly sample direction vectors from aptscav
crack free-format input lines, read and aptffip, aptchap
crack free-format input lines, with ASCII words of any length aptffip, aptchap
cross product of two vectors aptvaxb, aptvxun
cross product of two vectors (major plane) aptvaxc, aptvxuc
crystal structures, unique directions and distances in aptdirt, aptprim
cube, generate aptcube
cubic equation, real and complex roots of aptcubs
cumulative PDF bins, randomly sample aptcums, aptcumt
cumulative PDF, generate aptcump
curly brackets, use as field delimiters {} aptfbrk
curvature at a point on a quadric surface, extreme values of aptcris
curve, parabolic, produced by uniform acceleration aptparb
curve, produced by time-dependent acceleration aptacct
curve, quadric, minimum and maximum points on (major plane) aptqexc, aptqext
curves of intersection between planes and quadric surfaces aptplqu
curves, quadric, characteristics of aptplqu
cut a triangle into two parts with equal areas, perimeters aptrabc, aptrcab
cut a triangle into two parts with equal areas, perimeters aptrcut, aptrext
cut through a quadric surface with a major plane aptplis
cylinder (see also "quadric surface")
cylinder symmetric around a major axis, equation of aptcyis
cylinder with a specified axis and radius, equation of aptclis, aptcyis
cylinder, circular, distance from a plane to a, intersection aptplcy, aptplis
cylinder, circular, distance from a plane to a, intersection aptplqu
cylinder, circular, distance from a sphere to a, intersection aptspcy
cylinder, circular, intersection with a plane, distance aptplcy, aptplis
cylinder, circular, intersection with a sphere, distance aptspcy
cylinder, circular, proximal line to a plane, distance aptplcy, aptplis
cylinder, circular, proximal line to a plane, distance aptplqu
cylinder, circular, proximal point to a sphere, distance aptspcy
cylinder, circular, proximal point to another circular cyl aptcycy
cylinder, distance from a point to a aptwhis
cylinder, elliptic, distance from a plane to aptplqu
cylinder, equation of, symmetric around a major axis aptcyis
cylinder, equation of, with a specified axis and radius aptclis, aptcyis
cylinder, hyperbolic, distance from a plane to aptplqu
cylinder, intersection with a linear track (1-D) aptrkcl
cylinder, intersection with a linear track, normal, angle aptrkcy, aptrkis
cylinder, intersection with a major plane aptplis
cylinder, project onto, options aptprcy
cylinder, project points onto, options aptprcy
cylinder, randomly sample points in aptlocy
cylinder, randomly sample points in annulus of aptlocy
cylinder, randomly sample points on aptlocy
cylinders, circular, distance between (apart or overlapping) aptcycy
cylinders, circular, distance between axes aptcycy
cylinders, circular, proximal points on axes, surfaces aptcycy
cylindrical annulus, randomly sample points in aptlocy
cylindrical coordinates, direction between two points in aptdist
cylindrical coordinates, distance between two points in aptdist
cylindrical coordinates, intersection of linear track in aptrkcy, aptrkis
cylindrical coordinates, intersection of linear track in (1-D) aptrkcl
cylindrical coordinates, move a point in aptmove, aptmvcy
cylindrical coordinates, transform to or from aptcsys, aptcsyv
cylindrical coordinates, volume bounded by surfaces of aptbrkn, aptbrkp
cylindrical coordinates, volume bounded by surfaces of aptbrks, aptbrkv
cylindrical quadric surface tangent to another quadric surface aptqupr
cylindrically project points onto a sphere aptprsp
cylindrically scale a set of points or vectors around an axis aptsclr
D
data fields, delimited, separate a character string into aptffip, aptchap
data fields, delimited, separate a character string into aptquot, aptfbrk
data look-up in a table (binary search) aptlook
data range, test for (any mode) aptword
data values between two specified limits (any mode)? aptword
data, floating point, round-off of aptrnds, aptnint
data, reorder in any direction or mode aptsorm
data, reorder in any direction or mode (one column) aptsort
data, reorder in random order aptrand
decimal characters, ASCII, translate an integer into aptchia
decimal characters, ASCII, translate into an integer aptchai
decimal characters, ASCII, translate into an integer aptchtp
decimal digits from a character string, copy into integer words aptatob
decimal fraction, reciprocal integer series for a aptiris
decimal integer, convert to big integer (any base) from a aptdtob
decimal integer, convert a big integer (any base) into aptbtod
decimal number in a specified number base, find the value of a aptbase
decimal number, integer plus reciprocal integer series for a aptiris
decimal number, translate hexadecimal string into apthexd
decimal number, translate into hexadecimal string apthexa
decrement or increment characters in a character string aptchin
degrees, convert an angle to aptcang
degrees, minutes, seconds, convert an angle to aptcang
delete duplicate values from a sorted or unsorted array aptdeld
delimited character string (see "symbol")
delimited character string, find in another string aptchfs
delimited character string, find in another string aptquot, aptfbrk
delimited character strings, convert mode of aptchap, aptchtp
delimited character strings, convert to integer (oct, dec, hex) aptchai
delimited character strings, read and convert mode of aptffip, aptchap
delimited fields, separate a character string into aptffip, aptchap
delimited fields, separate a character string into aptquot, aptfbrk
delimiter, use of escape character to ignore aptquot, aptfbrk
delimiter, use of to separate and translate data fields aptffip, aptchap
delimiter, use of to separate and translate data fields aptquot, aptfbrk
derivatives of a polynomial equation, evaluate at a set of args aptpole
derivatives of a polynomial equation, real roots of aptpolr
descending order, reorder data aptsorm
descending order, reorder data (one column) aptsort
determinant of 3 by 3 matrix aptrips, aptdet3
determinant of 4 by 4 matrix aptdet4
deviation from the mean, standard aptmean
difference between coordinates in groups of points aptdirt, aptprim
difference between vectors or coordinates aptdist, aptvdis
difference between vectors or coordinates (major plane) aptvdic
difference of two big integers (any base), find the aptbsub
diffraction pattern, crystal directions that determine it aptdirt, aptprim
digit in a big integer, find the number of occurrences of each aptbsum
digit, squeeze out of a character string aptchsq
digits of a big integer array, reverse the order of aptbrev
digits of two nonzero big integers, concatenate the aptbcat
digits, increment or decrement in a character string aptchin
digits, replace in a character string aptchrp
direction between two points aptdist, aptvdis
direction between two points (major plane) aptvdic
direction vector, randomly sample, uniform (scalar) aptsciz
direction vectors in a specified plane, randomly sample aptscad
direction vectors, randomly sample at a fixed scatter angle aptscan, aptscaz
direction vectors, randomly sample at a fixed scatter angle aptscma, aptscmz
direction vectors, randomly sample in a specified plane aptscad
direction vectors, randomly sample within an angle interval aptscar
direction vectors, randomly sample, cosine-power PDF aptscap, aptscar
direction vectors, randomly sample, cosine-power PDF aptscav
direction vectors, randomly sample, isotropic aptscap, aptscat
direction vectors, randomly sample, isotropic aptscav
direction vectors, randomly sample, isotropic, limits aptscar
direction vectors, randomly sample, uniform aptscap, aptscat
direction vectors, randomly sample, uniform aptscav
direction vectors, randomly sample, uniform, limits aptscar
direction, effect of linear motion on, any coordinate system aptmove
direction, effect of linear motion on, cylindrical coordinates aptmvcy
direction, effect of linear motion on, spherical coordinates aptmove, aptmovs
direction, extrema of a quadric curve in a specified aptqexv
direction, motion with distance and, any coordinates aptmove
direction, motion with distance and, cylindrical coordinates aptmove, aptmvcy
direction, motion with distance and, spherical coordinates aptmove, aptmovs
directions between pairs of points, unique in groups of points aptdirt, aptprim
directions of extreme curvature at a point on a quadric surface aptcris
directions, unique, in regular arrays of points aptdirt, aptprim
distance along a parabolic trajectory vs time aptparb
distance along a uniformly accelerated trajectory vs time aptparb
distance between the axes of two circular cylinders aptcycy
distance between two circular cylinders, or overlap aptcycy
distance between two lines aptlnln
distance between two lines (major plane) aptlnlc
distance between two parallel planes aptplpl, aptplis
distance between two points on a major axis aptvdil
distance between two points, and direction aptdist, aptvdis
distance between two points, and direction (major plane) aptvdic
distance between two points, and direction in groups of points aptdirt
distance from a circular cylinder to a plane, intersection aptplcy, aptplis
distance from a circular cylinder to a sphere, intersection aptspcy
distance from a circular cylinder to another circular cylinder aptcycy
distance from a line to a line (major plane) aptlnlc
distance from a line to a line, direction, proximal points aptlnln
distance from a line to a plane aptlnpl, aptlntr
distance from a line to a point aptptln
distance from a line to a point (major plane) aptptlc
distance from a nonplanar quadrangle to a point aptquad
distance from a parabolic trajectory to a line aptparl
distance from a parabolic trajectory to a plane aptparp
distance from a parabolic trajectory to a point aptpars
distance from a plane to a circular cylinder, intersection aptplcy, aptplis
distance from a plane to a circular cylinder, intersection aptplqu
distance from a plane to a cone, intersection aptplqu
distance from a plane to a line aptlnpl, aptlntr
distance from a plane to a quadric surface, intersection aptplqu
distance from a plane to a sphere, intersection aptplsp, aptplis
distance from a plane to an axisymmetric quadric surface aptplqu
distance from a plane to an ellipsoid, intersection aptplqu
distance from a point to a circle aptwhis
distance from a point to a circular hyperboloid aptwhis
distance from a point to a cone aptwhis
distance from a point to a cylinder aptwhis
distance from a point to a hyperbolic paraboloid aptwhis
distance from a point to a hyperbolic paraboloid (approx) (OBS) aptqprr, aptqprt
distance from a point to a hyperbolic paraboloid (approx) (OBS) aptquad
distance from a point to a line aptptln
distance from a point to a line (major plane) aptptlc
distance from a point to a nonplanar quadrangle aptquad
distance from a point to a pair of intersecting planes aptwhis
distance from a point to a pair of parallel planes aptwhis
distance from a point to a paraboloid aptwhis
distance from a point to a plane aptptpl, aptwhis
distance from a point to a quadric surface aptwhis
distance from a point to a quadric surface (approx) (OBS) aptqprr, aptqprt
distance from a point to a quadric surface, exact or approx aptquad
distance from a point to a sphere aptwhis
distance from a point to a triangular face aptript, apttrip
distance from a point to an ellipsoid aptwhis
distance from a point to an elliptic hyperboloid aptwhis
distance from a point to an elliptic paraboloid aptwhis
distance from a point to plane of a triangle aptript, apttrip
distance from a quadrangle surface to a point aptquad
distance from a sphere to a circular cylinder, intersection aptspcy
distance from a sphere to another sphere, intersection aptspsp
distance from a uniformly accelerated trajectory to a line aptparl
distance from a uniformly accelerated trajectory to a plane aptparp
distance from a uniformly accelerated trajectory to a point aptpars
distance from plane of a triangle to the origin aptpfit
distance, fractional, limit range of value of aptfdad, aptfdav
distance, motion with direction and, any coordinates aptmove
distance, motion with direction and, cylindrical coordinates aptmove, aptmvcy
distance, motion with direction and, spherical coordinates aptmove, aptmovs
distances between points, and directions in groups of points aptdirt
distances from a point to edges of a quadrangle (major plane) aptqdic, aptqinc
distances from a point to edges of a tetrahedron aptetrn
distances from a point to edges of a triangle aptripl, apttrip
distances from a point to edges of a triangle (major plane) apttinc
distances from a point to faces of a tetrahedron aptetrn
distances from a point to surfaces of a brick aptbrkn
distances from Steiner vertex of a triangle to its vertices aptsver
divide a spherical pentagon into 5 spherical triangles aptpent
divide big integers (arrays of digits in specified number base) aptbdiv
divisor of a set of integers, find the greatest common aptcmad
divisors, remainders for several, find integer when given aptcrts
divisors, remainders for several, find when given integer aptcrtr
dodecahedron, generate a regular aptdode
dot product of vectors aptvdos, aptvdot
dot product of vectors (major plane) aptvdoc
double area of a triangle by extending two sides aptrext
double quotes, use as a field delimiter ("), with an escape aptquot
drop file, destroy or save on termination after an error aptnerr
duplicate characters, find in row, column, box of Sudoku puzzle aptsudu
duplicate values, delete from a sorted or unsorted array aptdeld
E
eccentricity of a hyperbola or hyperbolic cylinder aptplqu
eccentricity of an ellipse or elliptic cylinder aptplqu
edge lengths of a brick (bounded by coordinate surfaces) aptbrkv
edge lengths of a regular polygon aptpoly
edge lengths of a regular polygon (major plane) aptpolc
edge lengths of a triangle apttrid, apttrig
edge lengths of a triangle (major plane) apttric, aptpolc
edge lengths, three, find if form a real triangle aptrich
edge of a quadrangle, perpendicular bisector of aptpbln
edge of a quadrangle, perpendicular bisector of (major plane) aptpblc
edge of a tetrahedron at specified angles from two other edges aptetrv
edge of a triangle, perpendicular bisector (major plane) aptpblc
edge of a triangle, perpendicular bisector of aptpbln, apttrig
edge vectors of a triangle, lengths apttrig
edge weights (see "local coordinates")
edges of a cube, coordinates of ends of aptcube
edges of a quadrangle, distances from a point (major plane) aptqdic, aptqinc
edges of a regular dodecahedron, coordinates of ends of aptdode
edges of a regular icosahedron, coordinates of ends of apticos
edges of a regular octahedron, coordinates of ends of aptocta
edges of a regular polygon, lengths of aptpoly
edges of a regular polygon, lengths of (major plane) aptpolc
edges of a regular tetrahedron, coordinates of ends of apttetr
edges of a tetrahedron, distances from a point to aptetrn
edges of a triangle, distances from a point to (major plane) apttinc
edges of a triangle, distances from a point to the aptripl, apttrip
edges of a triangle, extend two to double area aptrext
edges of a triangle, midpoints apttrig
edges, center of a quadrangle, fit a quadric surface to aptqhyp
edges, project equilateral triangle onto triangle with given aptripr
effect of linear motion on position and direction, any coords aptmove
effect of linear motion on position and direction, cylindrical aptmove, aptmvcy
effect of linear motion on position and direction, spherical aptmove, aptmovs
eliminate duplicate values or rows from a table aptdeld
ellipse (see "circle", "quadric curve")
ellipse of intersection between a plane and a quadric surface aptplqu
ellipse, eccentricity, major and minor axis aptplqu
ellipsoid (see also "quadric surface")
ellipsoid at the origin, aligned with the axes, equation of aptesis
ellipsoid symmetric around major axis, equation of aptelis
ellipsoid, distance from a plane to, intersection aptplqu, aptplis
ellipsoid, distance from a point to an aptwhis
ellipsoid, equation of, given three semiaxes aptesis
ellipsoid, equation of, on major axis, given center, 2 points aptelis
ellipsoid, intersection with a linear track, normal, angle aptrkis
ellipsoid, intersection with a major plane aptplis
elliptic cylinder, eccentricity, major and minor axis aptplqu
elliptic paraboloid, distance from a point to aptwhis
energy unit conversion factors, 1999 values of aptconl, aptconm
energy, randomly sample, from a relativistic Maxwellian PDF aptmaxw
equal areas and perimeters, cut a triangle into two parts with aptrabc, aptrcab
equal areas and perimeters, cut a triangle into two parts with aptrcut, aptrext
equal-probability PDF bin values, randomly sample apteqxs, aptrans
equal-probability PDF bins, randomly sample apteqsb
equal-probability PDF, generate apteqin, apteqxn
equation of a cone on a major axis, given two points aptcnis
equation of a cone on a major axis, given vertex and angle aptcois
equation of a cone on the z axis, given two points aptcniz
equation of a cylinder on a major axis, given the radius aptcyis
equation of a cylinder with a specified axis and radius aptclis, aptcyis
equation of a hyperboloid of two sheets on a major axis aptelis
equation of a plane through three points aptpfit
equation of a quadric surface after a matrix operation aptrois
equation of a quadric surface after a specified translation apttris
equation of a quadric surface, extrema on parabolic trajectory aptparx
equation of a sphere at the origin, given radius aptesis
equation of an ellipsoid aligned with the major axes aptesis
equation of an ellipsoid at the origin, given three semiaxes aptesis
equation of an ellipsoid on a major axis aptelis, aptesis
equation, cubic, real and complex roots of a aptcubs
equation, polynomial, evaluate at a set of arguments aptpole
equation, polynomial, real roots using Newtonian iteration aptnewt
equation, polynomial, real roots, extrema, inflection points aptpolr
equation, polynomial, reduce order by factoring out root aptpolf
equation, quadratic, real or complex roots of a aptqrts, aptqrtv
equation, quartic polynomial, real and complex roots of a aptquar
equations, solve a set of linear aptsolv
equilateral projection of triangle with specified edges aptripr
equilateral projection of triangle with specified vertices aptripp
equilateral triangle, projection onto specified triangle aptripp, aptripr
equipartition of a triangle by a straight line cut aptrabc, aptrcab
equipartition of a triangle by a straight line cut aptrcut, aptrext
equivalence of two machine words, Boolean "xnor" or "eqv" aptbitb
eqv, Boolean operation "equivalence" on two machine words aptbitb
error messages, write to specified IOCs, and return or exit aptnerr
escape character, use to ignore a delimiter character aptquot, aptfbrk
estimated distance from a point to a quadric surface aptquad
estimated distance from a point to a quadric surface (OBS) aptqprr, aptqprt
Euler's totient function for arithmetic modulo an integer aptpfac
evaluate a polynomial equation at a set of arguments aptpole
exclusive or of two machine words (Boolean operation .xor.) aptbitb
expand bits from machine words into a type integer*1 array aptbite
exponential of a big integer (any base), find the aptbexp
exponential PDF, randomly sample values from aptexpl, aptexps
extend two edges of a triangle to double area aptrext
extrapolate from two points, any combo of linear/log axes aptintp
extrema of a polynomial equation, and roots, inflection points aptpolr
extrema of a polynomial equation, using evaluation aptpole
extrema of a quadric curve (major plane) aptqexc, aptqext
extrema of a quadric surface equation on a parabolic trajectory aptparx
extrema of a quadric surface in a specified direction aptqexv
extrema of a quadric surface, and axis intercept points aptqupt
extrema of a quadric surface, and type and symmetry center aptqext
extreme curvatures at a point on a quadric surface aptcris
F
face, triangular of tetrahedron, distances from a point aptetrn
face, triangular, distance from a point to a apttrip
face, triangular, point on which side? apttrip
face, triangular, proximal point apttrip
faces of a cube, generate aptcube
faces of a regular dodecahedron, generate aptdode
faces of a regular icosahedron, generate apticos
faces of a regular octagon, generate aptocta
faces of a regular tetrahedron, generate apttetr
faces of a tetrahedron, distances of a point from aptetrn
factor a root out of a polynomial equation, reduce its order aptpolf
factorial function, find all prime factors of a aptpfft
factorial function, in integer and real form aptfact
factorial of a big integer (any base), find the aptbfac
factors of a factorial function, find all prime aptpfft
factors of a big integer (any base), find all prime aptpfab
factors of an integer, find all prime, and totient function aptpfac
factors of an integer, find all unexponentiated aptafac
factors, irreducible proportion geometric, and prime numbers aptprim
factors, prime, for irreducible proportions in geometric arrays aptprim
factors, prime, of a big integer (any base) aptpfab
factors, prime, of an integer, and Euler's totient function aptpfac
factors, unexponentiated, of an integer aptafac
families of quadric surfaces, quadric surface where two ortho aptqper
family of quadric surfaces, extreme curvatures at a point aptcris
family of quadric surfaces, plane tangent to at a point aptqnor
family of quadric surfaces, vector normal to at a point aptqnor
fields, delimited, separate a character string into aptffip, aptchap
fields, delimited, separate a character string into aptquot, aptfbrk
fields, delimited, translate into integer (oct, dec, hex) aptchai
fields, delimited, translate into integer and floating point aptchtp
fields, delimited, translate into integer and floating point aptffip, aptchap
fields, delimited, translate into integer and floating point aptsubs, aptsubm
figure, geometric (see "circle", triangle", quadrangle")
figure, geometric (see also "polygon")
file names longer than eight characters, parse from input aptchtp
file names longer than eight characters, parse from input aptffip, aptchap
fill a bit string with random bits aptbitr
fill a character string with random characters aptchrn
fill a type integer*1 array with bits from machine words aptbite
fill machine words with bits from a type integer*1 array aptbitp
find (implied in any entry without a verb)
find a big integer (any base) in any other number base aptbasb
find a bit string in a machine word aptbitf
find a character string in another character string aptchfp
find a character string in another character string aptquot, aptfbrk
find a delimited character string in another character string aptchfs
find a delimited character string in another character string aptquot, aptfbrk
find a power of a big integer (any base) aptbpow
find a root of a big integer (any base) aptbrtn
find all prime factors of a factorial function aptpfft
find all prime factors of a big integer (any base) aptpfab
find all prime factors of an integer aptpfac, aptpfab
find all unexponentiated factors of an integer aptafac
find an integer given remainders for several divisors aptcrts
find duplicate characters in Sudoku puzzle row, column, box aptsudu
find Euler's totient function for arithmetic modulo an integer aptpfac
find non-graphic characters in a character string and replace aptchip
find remainders for several divisors when given integer aptcrtr
find the difference of two big integers (any base) aptbsub
find the exponential of a big integer (any base) aptbexp
find the factorial of a big integer (any base) aptbfac
find the greatest common divisor and least common multiple aptcmad
find the greatest common divisor of a set of integers aptcmad
find the least common multiple of a set of integers aptcmad
find the log (base 10) of a big integer (any base) aptbtod
find the modulus of a a big integer (any base) aptbmod
find the number of occurrences of each digit in a big integer aptbsum
find the prime factors of a big integer (any base) aptpfab
find the product of two big integers (any base) aptbmul
find the quotient of two big integers (any base) aptbdiv
find the remainder of division of two big integers (any base) aptbdiv
find the sum of two big integers (any base) aptbadd
find the value of a big integer in a specified number base aptbasb
find the value of a decimal number in a specified number base aptbase
first derivative of a polynomial equation, evaluate at args aptpole
first derivative of a polynomial equation, real roots of aptpolr
fit a plane to three points aptpfit
fit a quadric surface to edges, center of a quadrangle aptqhyp
fit a quadric surface to nine points aptqfit
fit a sphere to an axis and two specifed points on its surface aptspha
fit a sphere to four specifed points on its surface aptsphp
fixed scattering angle, randomly sample azimuth angle for aptscan, aptscaz
fixed scattering angle, randomly sample azimuth angle for aptscma, aptscmz
floating point data, round-off aptrnds, aptnint
floating point data, sort (one column) aptsort
floating point data, sort, in either direction aptsorm
floating point values, randomly sample from an interval aptrfps, aptrfpt
floating point, convert to a big integer (any base) from a aptftob, aptltob
floating point, convert from a big integer (any base) into a aptbtod, aptltob
form a real triangle, find if three edge lengths can aptrich
four points, sphere through aptsphp
fourth-order polonomial, real and complex roots of aptquar
fraction, continued, find coefficients of, give value aptcofr
fraction, continued, find value of, give coefficients aptcofv
fraction, decimal, reciprocal integer series for a aptiris
fraction, rational, find for a continued fraction, given coeff aptcofv
fractional distance, limit range of value of aptfdad, aptfdav
fractional distances of triangle equipartition cut line aptrabc, aptrcab
fractional distances of triangle equipartition cut line aptrcut, aptrext
free-format input lines, read and parse using field delimiters aptffip, aptchap
free-format input lines, read and parse using field delimiters aptquot, aptfbrk
frequencies, randomly sample from a Planck or Wien spectrum aptxnup
frustrum of a cone, randomly sample points on aptscns, aptscnv
frustrum of an annulus of a cone, randomly sample points in aptscnv
function for arithmetic modulo an integer, find Euler's totient aptpfac
function, find all prime factors of a factorial aptpfft
function, quadric surface, value at a specified point aptqval
function, value of a quadric surface, at a point aptwhis
fundamental constants, 1999 values of aptconl, aptconm
fuzzy geometry (see "adjust", "limit", "range", "round-off")
G
generate a cube aptcube
generate a cumulative PDF from tabulated data aptcump
generate a PDF to randomly sample from, aliased aptalin
generate a PDF to randomly sample from, cumulative aptcump
generate a PDF to randomly sample from, equal-probability apteqin, apteqxn
generate a regular dodecahedron aptdode
generate a regular hexahedron (cube) aptcube
generate a regular icosahedron apticos
generate a regular octahedron aptocta
generate a regular polygon aptpoly
generate a regular polygon (major plane) aptpolc
generate a regular tetrahedron apttetr
generate an aliased PDF from tabulated data aptalin
generate an equal-probability PDF from tabulated data apteqin, apteqxn
generate bins to randomly sample from, aliased bins aptalin
generate bins to randomly sample from, cumulative aptcump
generate bins to randomly sample from, equal-probabilitility apteqin, apteqxn
generate combinations and permutations of M out of N things aptbpac
generate combinations and permutations of M out of N things aptcomb, aptperm
geometric factors, irreducible proportion, and prime numbers aptprim
geometric optics (see "ray tracing")
geometric series, find ratio given first term, sum, length aptgrat
geometry, fuzzy (see "adjust", "limit", "range", "round-off")
grads, convert an angle to aptcang
grapestakes, distance between stakes in unique directions aptdirt
grapestakes, unique directions of rows in a regular array of aptdirt, aptprim
greatest common divisor of a set of integers, find the aptcmad
group separated into smaller groups, number of ways aptcomg
groups of points, unique directions and their minimum distances aptdirt, aptprim
H
hexadecimal characters, ASCII, translate an integer into aptchia
hexadecimal characters, ASCII, translate into an integer aptchai
hexadecimal string, translate a decimal number into apthexa
hexadecimal string, translate into a decimal number apthexd
histogram PDF, generate bins to randomly sample, aliased aptalin
histogram PDF, generate bins to randomly sample, cumulative aptcump
histogram PDF, generate bins to randomly sample, equal-prob apteqin, apteqxn
histogram PDF, randomly sample bins, aliased aptalsb, aptalst
histogram PDF, randomly sample bins, cumulative aptcums, aptcumt
histogram PDF, randomly sample from aliased bins aptalsh, aptalsl
histogram PDF, randomly sample from cumulative PDF bins aptalsh, aptalsl
histogram PDF, randomly sample from equal-probability bins apteqsb, apteqxs
horizon, perspective projection with a specified aptpers
hyperbola (see also "quadric curve")
hyperbola of intersection between a plane and a quadric surface aptplqu
hyperbola, eccentricity, transverse and conjugate axes aptplqu
hyperbola, intersection with a line (major plane) aptrkcy
hyperbolic cylinder, distance from a point to a aptwhis
hyperbolic cylinder, eccentricity, transverse, conjugate axes aptplqu
hyperbolic paraboloid, distance from a plane to a aptplqu
hyperbolic paraboloid, distance from a point to a aptwhis
hyperbolic paraboloid, distance from a point to a (approx) aptquad
hyperbolic paraboloid, distance from a point to a (approx)(OBS) aptqprr, aptqprt
hyperbolic paraboloid, fit to edges, center of a quadrangle aptqhyp
hyperboloid (see also "quadric surface")
hyperboloid of one sheet, distance from a point to a aptwhis
hyperboloid of one sheet, distance from a point to a (approx) aptqprr, aptqprt
hyperboloid of two sheets symmetric around major axis aptelis
hyperboloid of two sheets, distance from a point to a aptwhis
hyperboloid of two sheets, distance from a point to a (approx) aptqprr, aptqprt
hyperboloid, circular, distance from a point to aptwhis
hyperboloid, elliptical, distance from a point to aptwhis
hyperboloid, elliptical, distance from a point to (approx)(OBS) aptqprr, aptqprt
I
icosahedron, generate a regular apticos
ignore delimiter by use of an escape character aptquot, aptfbrk
imaginary roots of a cubic polynomial aptcubs
imaginary roots of a quadratic polynomial aptqrts, aptqrtv
imaginary roots of a quartic polynomial equation aptquar
imbedded blanks, squeeze out of a character string aptchsq
imbedded blanks, translate data fields with aptchtp
imbedded blanks, translate data fields with aptsubs, aptsubm
increment or decrement characters in a character string aptchin
indices and values of minimum and maximum of an array aptmnlg, aptmnmx
indices and values of positive minimum and maximum of an array aptmnlg
inflection points of a polynomial equation, and roots, extrema aptpolr
inflection points of a polynomial equation, using evaluation aptpole
initial position and velocity of a parabolic trajectory aptpart
initialize data to randomly sample aliased bins aptalin
initialize data to randomly sample cumulative aptcump
initialize data to randomly sample equal-probability apteqin, apteqxn
input lines, read and parse using field delimiters aptffip, aptchap
input lines, read and parse using field delimiters aptquot, aptfbrk
inscribed circle of a regular polygon aptpoly
inscribed circle of a regular polygon (major plane) aptpolc
inscribed circle of a triangle, angle bisectors apttrig
inside or outside a brick, a point, and distances? aptbrkn
inside or outside a quadrangle, a point (major plane)? aptqinc
inside or outside a quadric surface? aptqval, aptwhis
inside or outside a tetrahedron, a point? aptetrn
inside or outside a triangle, a point (major plane)? apttinc
inside or outside a triangle, a point? apttrip
int, Boolean operation "intersection" on two machine words aptbitb
integer array, reverse the order of an aptbrev
integer data, sort, in either direction aptsorm
integer data, sort, in either direction (one column) aptsort
integer for which remainders for several divisors given, find aptcrts
integer multiple of a factor, round off number to, if close aptnint
integer plus reciprocal integer series for a decimal number aptiris
integer subscripts, form subscripted variable from a stem and aptsubi
integer words, copy digits from a character string into aptatob
integer*1 array, expand bits from machine words into a type aptbite
integer, big (any base), convert from decimal integer into a aptdtob
integer, big (any base), convert from floating point into a aptftob, aptltob
integer, big (any base), convert into decimal integer aptbtod
integer, big (any base), convert into floating point aptbtod
integer, big (any base), count the occurrences of each digit in aptbsum
integer, big (any base), find a power of a aptbpow
integer, big (any base), find a root of a aptbrtn
integer, big (any base), find in any other number base aptbasb
integer, big (any base), find the exponential of a aptbexp
integer, big (any base), find the factorial of a aptbfac
integer, big (any base), find the log (base 10) of a aptbtod
integer, big (any base), find the prime factors of a aptpfab
integer, big (any base), reverse the order of the digits of a aptbrev
integer, find all prime factors and Euler's totient function of aptpfac
integer, find all unexponentiated factors aptafac
integer, find Euler's totient function for arithmetic modulo an aptpfac
integer, find remainders, given several divisors aptcrtr
integer, find the number of occurrences of each digit in a big aptbsum
integer, multiplicative inverse of, in modular arithmetic aptmord
integer, order of an, in modular arithmetic aptmord
integer, randomly sample from a sequence of integers aptrins
integer, round off floating point number to nearest, if close aptnint
integer, squeeze out of a character string aptchsq
integer, translate from ASCII octal, decimal or hexadecimal aptchai
integer, translate into ASCII octal, decimal or hexadecimal aptchia
integers, big (any base), find the difference of two aptbsub
integers, big (any base), find the modulus of two aptbmod
integers, big (any base), find the product of two aptbmul
integers, big (any base), find the quotient of two aptbdiv
integers, big (any base), find the remainder of division of two aptbdiv
integers, big (any base), find the sum of two aptbadd
integers, concatenate the digits of two nonzero big aptbcat
integers, find the greatest common divisor of a set of aptcmad
integers, find the least common multiple of a set of aptcmad
integers, increment or decrement in a character string aptchin
integers, randomly sample with any degree of striation aptrint
integers, replace in a character string aptchrp
intercepts on major and symmetry axes of a quadric surface aptqupt
interpolate between two points, any combo of linear/log axes aptintp
intersecting planes, distance from a point to a pair of aptwhis
intersection of a circle with a line (major plane) aptlnic
intersection of a cone with a linear track, normal, angle aptrkis
intersection of a cone with a major plane aptplis
intersection of a cylinder with a linear track (1-D) aptrkcl
intersection of a cylinder with a linear track, normal, angle aptrkcy, aptrkis
intersection of a cylinder with a major plane aptplis
intersection of a cylinder with a plane, distance aptplcy
intersection of a hyperbola with a line (major plane) aptrkcy
intersection of a line with a circle (major plane) aptlnic
intersection of a line with a hyperbola (major plane) aptrkcy
intersection of a line with a line (major plane) aptlnlc
intersection of a line with a plane aptlnpl
intersection of a line with a plane through a triangle aptlntr
intersection of a linear track with a cone, normal, angle aptrkcy, aptrkis
intersection of a linear track with a cylinder (1-D) aptrkcl
intersection of a linear track with a cylinder, normal, angle aptrkcy, aptrkis
intersection of a linear track with a line (major plane) aptrklc
intersection of a linear track with a major plane aptrksl
intersection of a linear track with a plane aptrkpl
intersection of a linear track with a quadric surface, normal aptrkis
intersection of a linear track with a sphere (1-D) aptrkrl
intersection of a linear track with a sphere, normal, angle aptrkis
intersection of a linear track with a triangle aptrkpl
intersection of a linear track with an ellipsoid, normal, angle aptrkis
intersection of a major plane with a cone aptplis
intersection of a major plane with a cylinder aptplis
intersection of a major plane with a quadric surface aptplis
intersection of a major plane with an ellipsoid aptplis
intersection of a parabolic trajectory with a line aptparl
intersection of a parabolic trajectory with a plane aptparp, aptparq
intersection of a parabolic trajectory with a point aptparh, aptpars
intersection of a parabolic trajectory with a quadric surface aptparq
intersection of a plane with a circular cylinder, distance aptplcy, aptplis
intersection of a plane with a circular cylinder, distance aptplqu
intersection of a plane with a cone, distance aptplqu
intersection of a plane with a line aptlnpl, aptlntr
intersection of a plane with a quadric surface, distance aptplqu
intersection of a plane with a sphere (none, point or circle?) aptplqu
intersection of a plane with a sphere (none, point or circle?) aptplsp, aptplis
intersection of a plane with an axisymmetric surface, distance aptplqu
intersection of a plane with an ellipsoid, distance aptplqu
intersection of a quadric surface with a major plane aptplis
intersection of a quadric surface with a plane, distance aptplqu
intersection of a quadric surface with another quadric surface aptintq
intersection of a sphere with a linear track (1-D) aptrkrl
intersection of a sphere with a linear track, normal, angle aptrkis
intersection of a sphere with a major plane aptplis
intersection of a sphere with a plane (none, point or circle?) aptplsp, aptplis
intersection of a triangle with a line aptlntr
intersection of a uniformly accelerated track with a line aptparl
intersection of a uniformly accelerated track with a plane aptparp, aptparq
intersection of a uniformly accelerated track with a point aptparh, aptpars
intersection of a uniformly accelerated track with a quadric aptparq
intersection of an ellipsoid with a linear track, normal, angle aptrkis
intersection of an ellipsoid with a major plane aptplis
intersection of three quadric surfaces, triple point of aptripq
intersection of triangle altitudes, medians, angle bisectors apttrig
intersection of triangle perpendicular bisectors of edges apttrig
intersection of two circles (major plane) aptcinc
intersection of two lines aptlnln
intersection of two machine words (Boolean operation .and.) aptbitb
intersection of two machine words (Boolean operation .int.) aptbitb
intersection of two planes, line of aptplpl, aptplis
intersection of two quadric surfaces, points on the curve of aptintq
intersection of two spheres (none, point or circle?) aptspsp
interval, uniformly randomly sample in (floating point) aptrfps, aptrfpt
interval, uniformly randomly sample in (integer) aptrins, aptrint
invariant point (see "inversion", "reflection", "rotation")
invariant point (see also "scale", "scaling")
inverse of aptrabc, aptrcab, aptrcut aptrext
inverse, multiplicative, of an integer in modular arithmetic aptmord
inversion operator, to invert a set of points or vectors aptinvp, aptsclu
invert a point or vector (major plane) aptinvc
invert a point or vector, and operator to aptinvp, aptsclu
invert a quadric surface aptrois
invert a square matrix, any size aptsolv
irrational number, find rational approximations for aptcofr
irreducible proportion geometric factors, prime numbers and aptprim
isotropic (see also "uniform")
isotropically randomly sample a direction vector (scalar) aptsciz, aptscmz
isotropically randomly sample direction vectors aptscan, aptscma
isotropically randomly sample direction vectors aptscap, aptscat
isotropically randomly sample direction vectors aptscav
isotropically randomly sample direction vectors in a plane aptscad
isotropically scale a set of points or vectors aptsclu
iteration, Newtonian, to find real roots of polynomial equation aptnewt
J
K
kissing circle, center of one tangent to two others aptcirl, aptcirk
kissing circles, radii of two, each tangent to three others aptcirt, aptcirk
kissing sphere, center of one tangent to three others aptsphl, aptsphk
kissing spheres, radii of two, each tangent to four others aptspht, aptsphk
L
latus rectum of a hyperbola or hyperbolic cylinder aptplqu
latus rectum of a parabola or parabolic cylinder aptplqu
leading and/or trailing blanks, remove from a character string aptrmbl
least common multiple of a set of integers, find the aptcmad
left-shift bits in a machine word, wrap-around or pull aptbits
left-shift characters in a character string aptchmv
length of a triangle equipartion cut line aptrabc, aptrcab
length of a triangle equipartion cut line aptrcut, aptrext
length of a vector aptvunb, aptvusz
lengths of regular polygon edges aptpoly
lengths of regular polygon edges (major plane) aptpolc
lengths of triangle edges aptpoly
lengths of triangle edges apttrid, apttrig
lengths of triangle edges (major plane) apttric, aptpolc
lengths of triangle edges, find if three can form real triangle aptrich
letter, squeeze out of a character string aptchsq
letters, increment or decrement in a character string aptchin
letters, replace in a character string aptchrp
limit range of values aptfdad, aptfdav
limit range of values of vector components aptvtol
limit range of values of vector components (major plane) aptvtoc
limits, data values between two specified (any mode)? aptword
limits, lower, on values of vector components aptvlim
limits, lower, on values of vector components (major plane) aptvlic
line (see also "track", "vector")
line at specified angles from two other lines aptetrv
line between two points, length of (major plane) aptvdic
line between two points, length of and vector along aptdirt
line between two points, length of and vector along aptdist, aptvdis
line between two points, vector along (major plane) aptvdic
line if intersection of a plane and a quadric surface aptplqu
line in a plane? aptlnpl, aptlntr
line of intersection of two planes aptplpl, aptplis
line of tangency of a plane and a quadric surface aptplqu
line perpendicular to another line (major plane) aptvplc
line tangent to a circle (major plane)? aptlnic
line, distance form a parabolic trajectory, and proximal point aptparl
line, distance from a parabolic trajectory to aptparl
line, distance from a plane to a aptlnpl, aptlntr
line, distance from a point to a aptptln
line, distance from a point to a (major plane) aptptlc
line, distance from a uniformly accelerated trajectory to aptparl
line, intersection with a circle (major plane) aptlnic
line, intersection with a hyperbola (major plane) aptrkcy
line, intersection with a line (major plane) aptlnlc
line, intersection with a linear track (major plane) aptrklc
line, intersection with a parabolic trajectory aptparl
line, intersection with a plane aptlnpl, aptlntr
line, intersection with a uniformly accelerated trajectory aptparl
line, perpendicular bisector of aptpbln
line, perpendicular bisector of (major plane) aptpblc
line, perspective projection of points onto (major plane) aptperc
line, point on (major plane)? aptptlc
line, point on? aptptln
line, project points onto (major plane) aptperc
line, proximal point to a parabolic trajectory aptparl
line, proximal point to a uniformly accelerated trajectory aptparl
line, randomly sample points on aptspar, aptbrks
line, reflect from (major plane) aptrefc
line, straight, that cuts triangle into equal areas, perimeters aptrabc, aptrcab
line, straight, that cuts triangle into equal areas, perimeters aptrcut, aptrext
line, vector parallel to aptvdis
line, vector parallel to (major plane) aptvdic
linear equations, solve a set of aptsolv
linear motion effect on position and direction, any coords aptmove
linear motion effect on position and direction, cylindrical aptmove, aptmvcy
linear motion effect on position and direction, spherical aptmove, aptmovs
linear PDF, randomly sample values from aptslid, aptsliv
linear PDFs, randomly sample in specified bins aptalsl
linear projection of a quadric surface aptqupr
linear projection of points aptprop
linear projection of points (major plane) aptperc
linear track, intersection with a cylinder (1-D) aptrkcl
linear track, intersection with a line (major plane) aptrklc
linear track, intersection with a major plane aptrksl
linear track, intersection with a plane aptrkpl
linear track, intersection with a quadric surface, normal aptrkis
linear track, intersection with a sphere (1-D) aptrkrl
linear track, intersection with a triangle aptrkpl
linear track, intersection with an axisymmetric surface aptrkcy, aptrkis
linear-linear two-point interpolation or extrapolation aptintp
linear-log two-point interpolation or extrapolation aptintp
linearly combine vectors or coordinates aptvadd, aptvsum
linearly combine vectors or coordinates (major plane) aptvadc, aptvsuc
linearly scale a set of points or vectors aptscll
linearly scale a set of points or vectors (major plane) aptsclc
lines between points, lengths of and vectors along aptdirt
lines coincident or parallel (major plane)? aptlnlc
lines coincident or parallel? aptlnln
lines of intersection of a plane and a quadric surface aptplqu
lines parallel or coincident (major plane)? aptlnlc
lines parallel or coincident? aptlnln
lines, distance between aptlnln
lines, distance between (major plane) aptlnlc
local coordinates in a brick, point with aptbrkp
local coordinates in a quadrangle, point with aptquwt, aptetrw
local coordinates in a tetrahedron, point with aptetrw
local coordinates in a triangle, point with aptrlop
local coordinates in a triangle, point with (major plane) aptrloc
local coordinates of a point in a quadrangle (major plane) aptfdqc, aptqfdc
local coordinates of a point in a tetrahedron aptetrl, aptetrn
local coordinates of a point in a triangle aptripl, apttrip
local coordinates of a point in a triangle (major plane) aptripc
log (base 10) of real number into big integer, translate from aptltob
log (base 10) of a big integer (any base), find the aptbtod
log-linear two-point interpolation or extrapolation aptintp
log-log two-point interpolation or extrapolation aptintp
log-scale minimum and maximum of an array, values and indices aptmnlg
long ASCII strings, parse from free-format input lines aptchtp
long ASCII strings, parse from free-format input lines aptffip, aptchap
look-up value in a table, binary search aptlook
Lorentz transformation aptscll
Lorentz transformation (major plane) aptsclc
lower case characters, randomly sample from aptchrn
lower limits on values of vector components aptvlim
lower limits on values of vector components (major plane) aptvlic
M
machine word, Boolean "and", "int", "nand", "or", "un" aptbitb
machine word, Boolean "nor", "xor", "xnor", "eqv" aptbitb
machine word, complement of aptbitb
machine word, find bit string in aptbitf
machine word, find character string in aptchfp
machine word, find delimited character string in aptchfs
machine word, find delimited character string in aptquot, aptfbrk
machine word, put random bits into aptbitr
machine word, shift right or left, with wrap-around or pull aptbits
machine words, equivalence, complement, nor, not of two aptbitb
machine words, intersection, union, exclusive or, of two aptbitb
magnitude of a vector aptvunb, aptvusz
major axes (x, y, z, u, v, w, r) aptvdil
major axes, intercepts of a quadric surface on aptqupt
major axes, rotation operator to rotate by 3 angles around aptrots
major axis, distance between two points on aptvdil
major axis, equation of a cone on aptcois, aptcnis
major axis, equation of a cylinder on aptcyis
major axis, equation of a hyperboloid of two sheets on aptelis
major axis, equation of an ellipsoid on aptelis, aptesis
major axis, points coincident? aptvdil
major axis, randomly sample directions at fixed angle from aptscma, aptscmz
major axis, test for points being coincident aptvdil
major plane (see apt subroutines ending with "c")
major plane, add vectors aptvadc
major plane, adjust values of vector components aptvlic, aptvtoc
major plane, angle between two unit vectors, cosine of aptvdoc
major plane, angle between two unit vectors, sine of aptvaxc, aptvxuc
major plane, angle between two vectors, sine and cosine of aptvanc
major plane, angle bisector aptbanc
major plane, angle, cosine and sine of aptvanc
major plane, angle, cosine of, between unit vectors aptvdoc
major plane, angle, rotate a vector by a specified aptrotc
major plane, angle, sine of, between two unit vectors aptvaxc, aptvxuc
major plane, angle, vector bisecting aptbanc
major plane, area between two lines aptvaxc, aptvxuc
major plane, area of a regular polygon aptpolc
major plane, area, edge lengths, centroid of a triangle apttric
major plane, areas of vertices of a quadrangle aptqvac
major plane, bisector of a line aptpblc
major plane, bisector of a vertex angle of a quadrangle aptbanc
major plane, bisector of a vertex angle of a triangle, vector aptbanc
major plane, bisector of an angle in aptbanc
major plane, bisector of edge of a quadrangle, perpendicular aptpblc
major plane, bisector of edge of a triangle, perpendicular aptpblc
major plane, boomerang quadrangle, test for aptqvac
major plane, bowtied quadrangle, test for aptqvac
major plane, centroid of a triangle apttric
major plane, centroid, area, edge lengths of a triangle apttric
major plane, circle tangent to a circle? aptcinc
major plane, circle through 3 specified points in aptcirc
major plane, circle, intersection with a line aptlnic
major plane, circle, intersection with another circle aptcinc
major plane, circle, line tangent to? aptlnic
major plane, circle, radially project points onto aptproc
major plane, circles coincident? aptcinc
major plane, circles tangent to each other, radii, centers aptcirk
major plane, circles tangent to each other, radii, centers aptcirl, aptcirt
major plane, circles, intersection of two aptcinc
major plane, circumscribed circle of a regular polygon aptpolc
major plane, classify a quadrangle shape aptqvac
major plane, coincident circles? aptcinc
major plane, coincident lines? aptlnlc
major plane, coincident points? aptvdic
major plane, components of vector parallel to another vector aptvcvc
major plane, components of vectors, limit range of values aptvtoc
major plane, components of vectors, lower limits on values aptvlic
major plane, components, vector, parallel to another vector aptvcvc
major plane, coordinate differences aptvdic
major plane, coordinates, linearly combine aptvadc, aptvsuc
major plane, cosine and sine of an angle between two vectors aptvanc
major plane, cosine of angle between unit vectors aptvdoc
major plane, cosine of vertex angle of a quadrangle aptvanc
major plane, cosine of vertex angle of a triangle aptvanc
major plane, cross product of two vectors aptvaxc, aptvxuc
major plane, direction vector and distance between two points aptvdic
major plane, distance between two lines aptlnlc
major plane, distance between two points aptvdic
major plane, distance from a line to a line aptlnlc
major plane, distance from a line to a point aptptlc
major plane, distance from a point to a line aptptlc
major plane, distances from a point to edges of a quadrangle aptqdic, aptqinc
major plane, distances from a point to edges of a triangle apttinc
major plane, distances from a point to quadrangle edges in aptqdic, aptqinc
major plane, distances from a point to triangle edges in aptqdic, apttinc
major plane, dot product of two vectors aptvdoc
major plane, edge lengths of a regular polygon aptpolc
major plane, edge lengths of a triangle apttric, aptpolc
major plane, edge lengths, area, centroid of a triangle apttric
major plane, edge of a quadrangle, perpendicular bisector of aptpblc
major plane, edge of a triangle, perpendicular bisector aptpblc
major plane, edges of a quadrangle, distances from a point aptqdic, aptqinc
major plane, edges of a regular polygon, lengths of aptpolc
major plane, edges of a triangle, distances from a point apttinc
major plane, generate a regular polygon, properties aptpolc
major plane, hyperbola, intersection with a line aptrkcy
major plane, inscribed circle of a regular polygon aptpolc
major plane, inside or outside a quadrangle, a point? aptqinc
major plane, inside or outside a triangle, a point? apttinc
major plane, intersection of a circle with a line in aptlnic
major plane, intersection of a hyperbola with a line aptrkcy
major plane, intersection of a line with a circle in aptlnic
major plane, intersection of a line with a hyperbola aptrkcy
major plane, intersection of a line with a line aptlnlc
major plane, intersection of a linear track with a line in aptrklc
major plane, intersection of two circles in aptcinc
major plane, intersection of two lines in aptlnlc
major plane, intersection with a cone aptplis
major plane, intersection with a cylinder aptplis, aptplcy
major plane, intersection with a linear track aptrksl
major plane, intersection with a quadric surface aptplis
major plane, intersection with a sphere aptplis, aptplsp
major plane, intersection with an ellipsoid aptplis
major plane, invert a point or vector in aptinvc
major plane, lengths of regular polygon edges aptpolc
major plane, lengths of triangle edges apttric, aptpolc
major plane, limit range of values of vector components aptvtoc
major plane, limits, lower, on values of vector components aptvlic
major plane, line between two points, vector and length aptvdic
major plane, line perpendicular to another line aptvplc
major plane, line tangent to a circle? aptlnic
major plane, line, distance from a point to a aptptlc
major plane, line, intersection with a circle aptlnic
major plane, line, intersection with a hyperbola aptrkcy
major plane, line, intersection with a line aptlnlc
major plane, line, intersection with a linear track aptrklc
major plane, line, perpendicular bisector of aptpblc
major plane, line, perspective projection of points onto aptperc
major plane, line, point on? aptptlc
major plane, line, reflect from aptrefc
major plane, line, vector parallel to aptvdic
major plane, linear track, intersection with a line aptrklc
major plane, linearly combine vectors or coordinates aptvadc, aptvsuc
major plane, linearly scale a set of points or vectors aptsclc
major plane, lines coincident or parallel? aptlnlc
major plane, lines, distance between aptlnlc
major plane, local coordinates in a triangle, point with aptrloc
major plane, local coordinates of a point in a quadrangle in aptfdqc, aptqfdc
major plane, local coordinates of a point in a triangle in aptripc
major plane, Lorentz transformation aptsclc
major plane, lower limits on values of vector components aptvlic
major plane, minimum and maximum points of a quadric curve aptqexc, aptqext
major plane, nearest point on a line, to a point aptptlc
major plane, normalize a vector product to a unit vector aptvxuc
major plane, normalize a vector to a unit vector aptvuac, aptvubc
major plane, on a line, a point? aptptlc
major plane, origin, translate to a specified point apttrac
major plane, orthogonal vectors? aptvdoc
major plane, parallel lines? aptlnlc
major plane, parallel vectors? aptvaxc, aptvxuc
major plane, parallelogram area at a vertex aptvaxc, aptvxuc
major plane, perpendicular bisector of a line in aptpblc
major plane, perpendicular bisector of edge of a quadrangle aptpblc
major plane, perpendicular bisector of edge of a triangle aptpblc
major plane, perpendicular to a line, the line aptvplc
major plane, perpendicular vectors? aptvdoc
major plane, perspective projection of points onto a line aptperc
major plane, point in a triangle with given local coordinates aptrloc
major plane, point in a triangle, local coordinates of aptripc
major plane, point inside or outside a quadrangle? aptqinc
major plane, point inside or outside a triangle? apttinc
major plane, point on a line? aptptlc
major plane, point with given distance, direction from a point aptvadc, aptvsuc
major plane, point with given local coordinates in a triangle aptrloc
major plane, point, distance from a line to a aptptlc
major plane, point, distances from edges of a quadrangle to a aptqdic, aptqinc
major plane, point, distances from edges of a triangle to a apttinc
major plane, point, invert a aptinvc
major plane, point, linearly scale aptsclc
major plane, point, local coordinates in a triangle aptripc
major plane, point, proximal on a line, to a point aptptlc
major plane, point, reflect from a line aptrefc
major plane, point, translate through space apttrac
major plane, points coincident? aptvdic
major plane, points in a quadrangle, randomly sample aptqloc
major plane, points in a triangle, randomly sample aptqloc, apttloc
major plane, points, direction and distance between two aptvdic
major plane, points, linearly scale aptsclc
major plane, points, perspective projection onto a line aptperc
major plane, points, radially project onto a circle aptproc
major plane, points, randomly sample, in a quadrangle aptqloc
major plane, points, randomly sample, in a triangle aptqloc, apttloc
major plane, points, vector between two aptvdic
major plane, polygon, regular, generation and properties of aptpolc
major plane, product of two vectors, cross or vector aptvaxc, aptvxuc
major plane, product of two vectors, dot or scalar aptvdoc
major plane, project onto a line, perspective aptperc
major plane, project points onto a circle, radially aptproc
major plane, project points onto a perspective view line aptperc
major plane, properties of regular polygons aptpolc
major plane, proximal point on a line, to a point aptptlc
major plane, quadrangle edges, distances from a point to aptqdic, aptqinc
major plane, quadrangle vertex angle, sine and cosine of aptvanc
major plane, quadrangle vertex areas and shape type aptqvac
major plane, quadrangle, cosine and sine of a vertex angle aptvanc
major plane, quadrangle, distances from a point to edges of aptqdic, aptqinc
major plane, quadrangle, local coordinates of a point in aptfdqc, aptqfdc
major plane, quadrangle, perpendicular bisector of an edge aptpblc
major plane, quadrangle, point in, local coordinates of aptfdqc, aptqfdc
major plane, quadrangle, point inside or outside? aptqinc
major plane, quadrangle, randomly sample points in aptqloc
major plane, quadrangle, sine and cosine of a vertex angle aptvanc
major plane, quadrangle, vector bisecting a vertex angle aptbanc
major plane, radially project points onto a circle aptproc
major plane, radius of circumscribed circle of regular polygon aptpolc
major plane, radius of inscribed circle of a regular polygon aptpolc
major plane, randomly sample points in a quadrangle in aptqloc
major plane, randomly sample points in a triangle in apttloc, aptqloc
major plane, range of values of vector components, limit aptvtoc
major plane, reflect a point or vector from a line aptrefc
major plane, reflect from a plane perpendicular to a aptrefl
major plane, regular polygon generation and properties aptpolc
major plane, rotate a vector by a specified angle aptrotc
major plane, scalar product of two vectors aptvdoc
major plane, scale linearly, points or vectors aptsclc
major plane, shape type of a quadrangle (bowtie or boomerang?) aptqvac
major plane, sine and cosine of an angle between two vectors aptvanc
major plane, sine of angle between two unit vectors aptvaxc, aptvxuc
major plane, sine of vertex angle of a quadrangle aptvanc
major plane, sine of vertex angle of a triangle aptvanc
major plane, sum of vectors, with specified coefficients aptvadc, aptvsuc
major plane, tangent circles? aptcinc
major plane, tangent, between line and circle aptlnic
major plane, test for circle being tangent to a line aptlnic
major plane, test for circles being coincident aptcinc
major plane, test for circles being tangent aptcinc
major plane, test for line being tangent to a circle aptlnic
major plane, test for lines being coincident or parallel aptlnlc
major plane, test for parallel vectors aptvaxc, aptvxuc
major plane, test for point being inside a quadrangle aptqinc
major plane, test for point being inside a triangle apttinc
major plane, test for point being on a line aptptlc
major plane, test for points being coincident aptvdic
major plane, test for quadrangle convex, boomerang or bowtie aptqvac
major plane, test for vectors being parallel aptvaxc, aptvxuc
major plane, test for vectors being perpendicular aptvdoc
major plane, track, linear, intersection with a line aptrklc
major plane, translate points in a apttrac
major plane, triangle area, centroid, edge lengths apttric
major plane, triangle edges, distances from a point to aptqdic, aptqinc
major plane, triangle edges, distances from a point to apttinc
major plane, triangle vertex angle, sine and cosine of aptvanc
major plane, triangle, bisector of a vertex angle aptbanc
major plane, triangle, cosine of a vertex angle aptvanc
major plane, triangle, distances from a point to edges of aptqdic, aptqinc
major plane, triangle, distances from a point to edges of apttinc
major plane, triangle, local coordinates of a point in aptripc
major plane, triangle, perpendicular bisector of an edge aptpblc
major plane, triangle, point in, local coordinates of aptripc
major plane, triangle, point inside or outside? apttinc
major plane, triangle, point with given local coordinates aptrloc
major plane, triangle, randomly sample points in aptqloc, apttloc
major plane, triangle, sine of a vertex angle aptvanc
major plane, triangle, vector bisecting a vertex angle aptbanc
major plane, two lines coincident or parallel? aptlnlc
major plane, two lines, distance or intersection between aptlnlc
major plane, two points coincident? aptvdic
major plane, two points, distance and vector between aptvdic
major plane, two vectors parallel? aptvaxc, aptvxuc
major plane, two vectors perpendicular? aptvdoc
major plane, uniformly randomly sample points in a quadrangle aptqloc
major plane, uniformly randomly sample points in a triangle apttloc
major plane, unit vector perpendicular to two other vectors aptvxuc
major plane, unit vector, normalize aptvuac, aptvubc
major plane, unit vectors, cosine of angle between aptvdoc
major plane, unit vectors, sine of angle between two aptvaxc, aptvxuc
major plane, values, limit range of, vector components aptvtoc
major plane, values, lower limits on vector components aptvlic
major plane, vector between two points aptvdic
major plane, vector bisecting a vertex angle of a quadrangle aptbanc
major plane, vector bisecting a vertex angle of a triangle aptbanc
major plane, vector components parallel to another vector aptvcvc
major plane, vector components, limit range of values of aptvtoc
major plane, vector components, lower limits on values of aptvlic
major plane, vector components, parallel to another vector aptvcvc
major plane, vector cross product aptvaxc, aptvxuc
major plane, vector differences aptvdic
major plane, vector direction and distance between two points aptvdic
major plane, vector dot product aptvdoc
major plane, vector parallel to a line in aptvdic
major plane, vector perpendicular to a line aptvplc
major plane, vector product of two vectors aptvaxc, aptvxuc
major plane, vector scalar product aptvdoc
major plane, vector sum with specified coefficients aptvadc, aptvsuc
major plane, vector, invert a aptinvc
major plane, vector, linearly scale aptsclc
major plane, vector, normalize to a unit vector aptvuac, aptvubc
major plane, vector, reflect a aptrefc
major plane, vector, rotate by a specified angle aptrotc
major plane, vectors parallel? aptvaxc, aptvxuc
major plane, vectors perpendicular? aptvdoc
major plane, vectors, linearly combine aptvadc, aptvsuc
major plane, vertex angle of a quadrangle, bisecting vector aptbanc
major plane, vertex angle of a quadrangle, sine and cosine of aptvanc
major plane, vertex angle of a triangle, bisecting vector aptbanc
major plane, vertex angle of a triangle, sine and cosine of aptvanc
major plane, vertex areas and shape type of a quadrangle aptqvac
major plane, vertices of a regular polygon aptpolc
major plane, view point, perspective projection with specified aptperc
major plane, weighted sum of two vectors aptvadc, aptvsuc
major planes (x-y, y-z, z-x, u-v, v-w, w-x, z-r)
manipulate bits aptbitb, aptbite
manipulate bits (more) aptbitf, aptbitm
manipulate bits (more) aptbitp, aptbitr
manipulate bits (more) aptbits
manipulate characters and character strings aptchai
manipulate characters and character strings (more) aptchfp
manipulate characters and character strings (more) aptchfs, aptchia
manipulate characters and character strings (more) aptchin, aptchmv
manipulate characters and character strings (more) aptchrn, aptchrp
manipulate characters and character strings (more) aptchsq
manipulate characters and character strings (more) aptchtp
manipulate characters and character strings (more) aptffip, aptchap
manipulate characters and character strings (more) aptffip, aptchap
manipulate characters and character strings (more) aptsubr
manipulate characters and character strings (more) aptsubs, aptsubm
masking operations "and", "int", "nand", "or", "un" aptbitb
masking operations "nor", "xor", "xnor", "eqv" aptbitb
masking operations ("comp", "not" aptbitb
masking operations ("shl". "shr") aptbits
matching bit string, find in a machine word aptbitf
matching character string, find (delimited) in another string aptchfs
matching character string, find in a character string aptchfp
mathematics (see "equation")
matrices, product of two square aptmprd
matrix multiply square matrices aptmprd
matrix operation on a point or vector aptmopv
matrix operation on a quadric surface aptrois
matrix operator (see "operator")
matrix product of two square matrices aptmprd
matrix, 3 by 3, determinant of aptdet3
matrix, 4 by 4, determinant of aptdet4
matrix, invert square aptsolv
maximum and minimum coordinates of a brick, and centroid aptbrkv
maximum and minimum of an array, positive values and indices aptmnlg
maximum and minimum of an array, values and indices aptmnlg, aptmnmx
maximum and minimum points of a polynomial equation aptpole, aptpolr
maximum and minimum points of a quadric curve (major plane) aptqexc, aptqext
maximum and minimum points of a quadric surface aptqupt
maximum and minimum points of a quadric surface, and type aptqext, aptqexv
Maxwellian PDF, relativistic, randomly sample values from aptmaxw
mean value of an array aptmean
medians of a triangle, centroid apttrig
mensuration (see "angle", "area", "length", "volume")
message, error, write to specified IOCs, and return or exit aptnerr
midpoints of edges of a triangle apttrig
minimum and maximum coordinates of a brick, and centroid aptbrkv
minimum and maximum of an array, positive values and indices aptmnlg
minimum and maximum of an array, values and indices aptmnlg, aptmnmx
minimum and maximum points of a polynomial equation aptpole, aptpolr
minimum and maximum points of a quadric curve (major plane) aptqexc, aptqext
minimum and maximum points of a quadric surface aptqupt
minimum and maximum points of a quadric surface, and type aptqext, aptqexv
minimum distance between a point and a nonplanar quadrangle aptquad
minimum distance between a point and a plane aptptpl
minimum distance between points for each unique direction aptdirt
minimum distance between two lines aptlnln
minutes, seconds, degrees, convert an angle to aptcang
mix data randomly aptrand
mode, convert a character string to floating point aptchtp
mode, convert a character string to floating point aptffip, aptchap
mode, convert a character string to floating point aptsubs, aptsubm
mode, convert a character string to integer (decimal) aptchtp
mode, convert a character string to integer (decimal) aptffip, aptchap
mode, convert a character string to integer (decimal) aptsubs, aptsubm
mode, convert a character string to integer (oct, dec, hex) aptchai
mode, convert from integer to character (oct, dec, hex) aptchia
mode, sort data in any (character, integer, fl pt) aptsorm
mode, sort data in any (one column) aptsort
modular arithmetic, multiplicative inverse of an integer in aptmord
modular arithmetic, order of an integer in aptmord
modulus of a big integer (any base), find the aptbmod
modulo an integer, find Euler's totient function for arithmetic aptpfac
Monte Carlo (see "randomly sample", "PDF", "probability")
move a bit string from one machine word to another aptbitm
move a character string from one location to another aptchmv
move a point any distance in any direction, any coordinates aptmove
move a point any distance in any direction, cylindrical aptmove, aptmvcy
move a point any distance in any direction, spherical aptmove, aptmovs
mult big integers (arrays of digits in specified number base) aptbmul
multiple blanks, reduce to a single blank in character string aptblsq
multiple of a set of integers, find the least common aptcmad
multiple quotes, treatment when used as a delimiter aptquot
multiple-column sort of data arrays, any direction or mode aptsorm
multiple-subscripted variables, separate stem and subscripts aptsubm
multiplicative inverse of an integer in modular arithmetic aptmord
N
n-dimensional square matrices, product of two aptmprd
n-dimensional square matrix, inverse of aptsolv
name, longer than eight characters, parse from input lines aptffip, aptchap
nearest integer multiple of a factor, round off number to aptnint
nearest point on a line, to a point aptptln
nearest point on a line, to a point (major plane) aptptlc
nearest point on a nonplanar quadrangle, to a point aptquad
nearest point on a parabolic trajectory, to a line aptparl
nearest point on a parabolic trajectory, to a plane aptparp
nearest point on a parabolic trajectory, to a point aptpars
nearest point on a plane, to a point aptptpl
nearest point on a quadric surface, to a point aptwhis
nearest point on a quadric surface, to a point (approx) aptquad
nearest point on a quadric surface, to a point (approx) (OBS) aptqprr, aptqprt
nearest point on a triangular face, to a point apttrip
nearest point on a uniformly accelerated trajectory, to a line aptparl
nearest point on a uniformly accelerated trajectory, to a plane aptparp
nearest point on a uniformly accelerated trajectory, to a point aptpars
nearest triple point of three quadric surfaces to a given point aptripq
Newtonian iteration, to find real root of a polynomial equation aptnewt
non-ASCII characters, find in a character string and replace aptchip
non-graphic characters, find in a character string and replace aptchip
non-printing characters, find in a character string and replace aptchip
nor of two machine words (Boolean operation .nor.) aptbitb
nor, Boolean operation "nor" on two machine words aptbitb
normal (see also "orthogonal", "perpendicular")
Normal PDF, randomly sample values from aptnorm
normal vector at intersection of a line with a quadric surface aptrkis
normal vector of a quadric surface function at a point aptcris
normal vector of a quadric surface function at a point aptwhis, aptqnor
normal vector to plane of a triangle aptpfit
normal vector to plane of a triangle aptvpln, apttrig
normalize a vector product to a unit vector aptvxun
normalize a vector product to unit vector (major plane) aptvxuc
normalize to a unit vector aptvuna, aptvunb
normalize to a unit vector (major plane) aptvuac, aptvubc
normalize to a unit vector (scalar) aptvunz, aptvusz
not of two machine words (Boolean operation .not.) aptbitb
not, Boolean operation "not" on two machine words aptbitb
null characters, find in a character string and replace aptchip
number (see "data")
number base, find the value of a big integer in a specified aptbasb
number base, find the value of a decimal number in a specified aptbase
number in a specified number base, find the value of a decimal aptbase
number of combinations of N things taken M at a time aptcomf, aptcomb
number of permutations of N things taken M at a time aptbpac
number of permutations of N things taken M at a time aptperf, aptperm
number of ways to separate a group into smaller groups aptcomg
number, squeeze out of a character string aptchsq
numbers, increment or decrement in a character string aptchin
numbers, prime, and irreducible proportion geometric factors aptprim
numbers, replace in a character string aptchrp
numeric character, squeeze out of a character string aptchsq
numeric characters, random, put into a character string aptchrn
O
occurrences of each digit in a big integer, find the number of aptbsum
octahedron, generate a regular aptocta
octal characters, ASCII, translate an integer into aptchia
octal characters, ASCII, translate into an integer aptchai
on a line, a point (major plane)? aptptlc
on a line, a point? aptptln
one-dimensional axis, distance between two points on aptvdil
one-dimensional cylinder, intersection with a linear track aptrkcl
one-dimensional major plane, intersection with a linear track aptrksl
one-dimensional sphere, intersection with a linear track aptrkrl
operations "and", "int", "nand", "or", "un", do on words aptbitb
operations "comp", "not", do on words aptbitb
operations "nor", "xor", "xnor", "eqv", do on words aptbitb
operator, product of, with a vector aptmopv
operator, product of, with another operator aptmprd
operator, reflection aptrefs
operator, reflection, analyze, to find axis aptrefq
operator, rotation (see apt subroutines beginning with aptrot)
operator, rotation, analyze, to find axis, angle aptrotq
operator, rotation, for 3 angles around 3 major axes aptrots
operator, rotation, for a specified angle and axis aptrota
operator, rotation, to make a plane parallel to another plane aptrotp, aptrott
operator, rotation, to make one vector parallel to another aptrott, aptrotv
operator, to cylindrically scale a set of points or vectors aptsclr
operator, to invert a set of points or vectors aptinvp, aptsclu
operator, to isotropically scale a set of points or vectors aptsclu
operator, to linearly scale a set of points or vectors aptscll
operator, to scale cylindrically around a specified axis aptsclr
operator, to scale isotropically, a set of points or vectors aptsclu
operator, to scale linearly aptscll
operator, to scale uniformly, a set of points or vectors aptsclu
operator, to uniformly scale a set of points or vectors aptsclu
operators, multiply two matrix aptmprd
or, Boolean operation "or" = "union" on two machine words aptbitb
order data, any direction or mode (multiple columns) aptsorm
order data, any direction or mode (one column) aptsort
order data, in random order aptrand
order of a polynomial equation, reduce be factoring out root aptpolf
order of an integer array, reverse the aptbrev
order of an integer in modular arithmetic aptmord
order of the digits of a big integer (any base), reverse the aptbrev
origin, translate to a specified point apttran
origin, translate to a specified point (major plane) apttrac
orthocenter of a triangle (intersection of altitudes) apttrig
orthogonal (see also "normal", "perpendicular")
orthogonal quadric surface families, quadric surface where aptqper
orthogonal vector triple? aptripv
orthogonal vectors (major plane)? aptvdoc
orthogonal vectors? aptvdos, aptvdot
outline of a quadric surface, project in a specified direction aptqupr
overlap between a circular cylinder and a plane aptplcy, aptplis
overlap between a circular cylinder and a sphere aptspcy
overlap between a plane and a circular cylinder aptplcy, aptplis
overlap between a plane and a sphere aptplsp, aptplis
overlap between a sphere and a circular cylinder aptspcy
overlap between a sphere and a plane aptplsp, aptplis
overlap between two circular cylinders, or distance apart aptcycy
overlap between two spheres, or distance apart aptspsp
P
pack bits from a type integer*1 array into machine words aptbitp
pair of points, vector and distance between aptdist
pairs of points, unique directions and minimum distances beween aptdirt
parabola (see "quadric surface")
parabola of intersection of a plane and a quadric surface aptplqu
parabolic cylinder, distance from a plane to a aptplqu
parabolic cylinder, distance from a point to a aptwhis
parabolic trajectory, given points on vs time aptpart
parabolic trajectory, intersection with a line aptparl
parabolic trajectory, intersection with a plane aptparp, aptparq
parabolic trajectory, intersection with a point aptparh, aptpars
parabolic trajectory, intersection with a quadric surface aptparq
parabolic trajectory, path length vs time aptparb
parabolic trajectory, points on vs time aptparb, aptpart
parabolic trajectory, proximal point to line aptparl
parabolic trajectory, proximal point to plane aptparp
parabolic trajectory, proximal point to point aptpars
parabolic trajectory, proximal point to quadric surface aptparx
parabolic trajectory, velocities on vs time aptparb
paraboloid, circular, distance from a plane to a aptplqu
paraboloid, distance from a point to a aptwhis
paraboloid, elliptic, distance from a plane to aptplqu
paraboloid, elliptic, distance from a point to aptwhis
paraboloid, hyperbolic, distance from a plane to a aptplqu
paraboloid, hyperbolic, distance from a point to a aptwhis
paraboloid, hyperbolic, distance from a point to a (approx) aptqprr, aptqprt
paraboloid, hyperbolic, fit to edges, center of a quadrangle aptqhyp
parallel axes of two circular cylinders? aptcycy
parallel lines (major plane)? aptlnlc
parallel lines? aptlnln
parallel planes, distance from a point to a pair of aptwhis
parallel planes? aptplpl, aptplis
parallel projection of points onto a plane aptprop
parallel projection of points onto a sphere aptprsp
parallel to another vector, component of a vector aptvpap
parallel vectors (major plane)? aptvaxc, aptvxuc
parallel vectors? aptvaxb, aptvxun
parallel, rotation operator to make two planes aptrotp, aptrott
parallel, rotation operator to make two vectors aptrott, aptrotv
parallelogram area at a vertex aptvaxb, aptvxun
parallelogram area at a vertex (major plane) aptvaxc, aptvxuc
parallelogram, randomly sample points in (any plane) aptspar, aptbrks
parallelopiped, randomly sample points in aptspar, aptbrks
parentheses, use as field delimiters () aptfbrk
parse free-format input lines into ASCII strings, any length aptffip, aptchap
parse free-format input lines into ASCII, integer, flt-point aptchtp
parse free-format input lines into ASCII, integer, flt-point aptffip, aptchap
partial sums, convergents of a continued fraction aptcofr, aptcofv
particle trajectory with a time-dependent acceleration aptacct
particle, parabolic trajectory of uniformly accelerated aptparb, aptpart
path length on a parabolic trajectory to a proximal point aptparl, aptparp
path length on a parabolic trajectory to a proximal point aptpars, aptparx
path length on a parabolic trajectory to an intersection aptparh, aptparl
path length on a parabolic trajectory to an intersection aptparq
path length on a parabolic trajectory vs time aptparb
path length on a uniformly accelerated trajectory vs time aptparb
path of particle with a time-dependent acceleration aptacct
path, parabolic, intersection or proximal point with line aptparl
path, parabolic, intersection or proximal point with plane aptparp, aptparq
path, parabolic, intersection or proximal point with point aptparh, aptpars
path, parabolic, intersection with quadric surface aptparq
path, parabolic, position and velocity vs time aptparb, aptpart
path, parabolic, proximal point on line aptparl
path, parabolic, proximal point on plane aptparp
path, parabolic, proximal point to a quadric surface aptparx
path, parabolic, proximal point to point aptpars
pattern matching (see "character string", "bit string")
PDF bins, randomly sample, aliased aptalsb, aptalst
PDF bins, randomly sample, cumulative aptcums, aptcumt
PDF bins, randomly sample, equal-probability apteqsb
PDF, aliased bins, generate aptalin
PDF, aliased bins, randomly sample aptalsb, aptalst
PDF, aliased bins, randomly sample values from specified aptalsh, aptalsl
PDF, cosine-power (cos**p) aptscap, aptscar
PDF, cosine-power (cos**p) aptscav
PDF, cumulative bins, generate aptcump
PDF, cumulative bins, randomly sample aptcums, aptcumt
PDF, equal-probablity bins, generate apteqin, apteqxn
PDF, equal-probablity bins, randomly sample apteqsb
PDF, equal-probablity bins, randomly sample values from apteqxs
PDF, exponential aptexpl, aptexps
PDF, generate, from tabulated data, aliased aptalin
PDF, generate, from tabulated data, cumulative aptcump
PDF, generate, from tabulated data, equal-probability apteqin, apteqxn
PDF, histogram, aliased, generate bins aptalin
PDF, histogram, aliased, randomly sample bins aptalsb, aptalst
PDF, histogram, aliased, randomly sample values from bins aptalsh, aptalsl
PDF, histogram, cumulative, generate bins aptcump
PDF, histogram, cumulative, randomly sample bins aptcums, aptcumt
PDF, histogram, equal-probability, generate bins apteqin, apteqxn
PDF, histogram, equal-probability, randomly sample bins apteqsb
PDF, histogram, equal-probability, randomly sample values apteqxs
PDF, linear, randomly sample from aptslid, aptsliv
PDF, linear, randomly sample in specified bins aptalsl
PDF, Normal, randomly sample from aptnorm
PDF, Planck or Wien spectrum, randomly sample from aptxnup
PDF, power-law, randomly sample from aptspod
PDF, relativistic Maxwellian, randomly sample from aptmaxw
PDF, tabulated, aliased, generate bins aptalin
PDF, tabulated, aliased, randomly sample bins aptalsb, aptalst
PDF, tabulated, aliased, randomly sample values from bins aptalsh, aptalsl
PDF, tabulated, cumulative, generate bins aptcump
PDF, tabulated, cumulative, randomly sample bins aptcums, aptcumt
PDF, tabulated, equal-probability, generate bins apteqin, apteqxn
PDF, tabulated, equal-probability, randomly sample bins apteqsb
PDF, tabulated, equal-probability, randomly sample values apteqxs
PDF, uniform, randomly sample a direction vector (scalar) aptsciz, aptscma
PDF, uniform, randomly sample bins apteqsb, aptrans
PDF, uniform, randomly sample direction vectors aptscan, aptscar
PDF, uniform, randomly sample direction vectors aptscat, aptscma
pentagon, spherical, divide into 5 spherical triangles aptpent
perimeters, equal, straight line that cuts a triangle to get aptrabc, aptrcab
perimeters, equal, straight line that cuts a triangle to get aptrcut, aptrext
permutations and combinations of M things taken N at a time aptbpac
permutations and combinations of M things taken N at a time aptperf, aptcomf
permutations and combinations of M things taken N at a time aptperm, aptcomb
permutations of N things taken M at a time aptbpac
permutations of N things taken M at a time aptperm, aptperf
permutations of N things taken M at a time, number of aptbpac
permutations of N things taken M at a time, number of aptperf
perpendicular (see also "normal", "orthogonal")
perpendicular bisector of a line (major plane) aptpblc
perpendicular bisector of edge of a quadrangle aptpbln
perpendicular bisector of edge of a quadrangle (major plane) aptpblc
perpendicular bisector of edge of a triangle aptpbln, apttrig
perpendicular bisector of edge of a triangle (major plane) aptpblc
perpendicular bisectors of triangle edges, circumscribed circle apttrig
perpendicular to a line, the bisecting plane aptpbln
perpendicular to a line, the line (major plane) aptvplc
perpendicular to a plane, the vector aptvpln, aptpfit
perpendicular to another vector, component of a vector aptvpap
perpendicular vectors (major plane)? aptvdoc
perpendicular vectors? aptvdos, aptvdot
perpendiculars from triangle vertices to opposite sides apttrig
perspective projection of points onto a line (major plane) aptperc
perspective projection of points onto a plane aptpers
perspective view plane, project points onto aptpers
physics, 1999 fundamental constants, in cm-g-sh-keV units aptconl
physics, 1999 fundamental constants, in SI units aptconm
piecewise linear tabulated PDF, aliased bins for aptalin
piecewise linear tabulated PDF, cumulative bins for aptcump
piecewise linear tabulated PDF, equal-probability bins for apteqin, apteqxn
Planck or Wien spectrum, randomly sample values from aptxnup
plane (see also "major plane")
plane (see also "quadrangle", "surface", "triangle"))
plane and vector, rotate onto another plane and vector aptrott
plane of a triangle, distance of point from aptript, apttrip
plane of a triangle, vector normal to aptvpln, aptpfit
plane perpendicular to a major plane, reflect from aptrefl
plane perpendicularly bisecting a line aptpbln
plane perpendicularly bisecting a quadrangle edge aptpbln
plane perpendicularly bisecting a triangle edge aptpbln
plane tangent to a family of quadric surfaces at a point aptqnor
plane tangent to a sphere aptsphl, aptsphk
plane tangent to a sphere? aptplsp, aptplis
plane through three points, vector normal to aptvpln, aptpfit
plane, components of a vector on aptvplp
plane, direction vectors in, randomly sample aptscad
plane, distance from a circular cylinder to, intersection aptplqu
plane, distance from a circular cylinder to, intersection aptplsp, aptplis
plane, distance from a cone to, intersection aptplqu
plane, distance from a line to a aptlnpl, aptlntr
plane, distance from a parabolic trajectory to aptparp
plane, distance from a point to a aptptpl, aptwhis
plane, distance from a quadric surface to, intersection aptplqu
plane, distance from a sphere to, intersection aptplqu
plane, distance from a sphere to, intersection aptplsp, aptplis
plane, distance from a uniformly accelerated trajectory to aptparp
plane, distance from an axisymmetric quadric surface to aptplqu
plane, distance from an ellipsoid to, intersection aptplqu
plane, distance from another plane to, intersection aptplpl, aptplis
plane, distance from another plane to, intersection aptplqu
plane, fit to three points aptpfit, aptqhyp
plane, intersection with a circular cylinder, distance aptplcy, aptplis
plane, intersection with a line aptlnpl, aptlntr
plane, intersection with a linear track aptrkpl
plane, intersection with a parabolic trajectory aptparp, aptparq
plane, intersection with a sphere (none, point or circle?) aptplsp, aptplis
plane, intersection with a uniformly accelerated trajectory aptparp, aptparq
plane, line in? aptlnpl, aptlntr
plane, major (see also "major plane")
plane, major, intersection with a linear track aptrksl
plane, parallel projection of points onto aptprop
plane, perspective projection of points onto aptpers
plane, point on which side? aptptpl
plane, proximal line to a circular cylinder, distance aptplcy, aptplis
plane, proximal point to a parabolic trajectory aptparp
plane, proximal point to a sphere, distance aptplsp, aptplis
plane, proximal point to a uniformly accelerated trajectory aptparp
plane, proximal point to another plane, distance aptplpl, aptplis
plane, proximal point to another plane, distance aptplqu
plane, r-z, equation of a cone through two points in aptcnis
plane, r-z, equation of an ellipsoid through two points in aptelis
plane, r-z, intersection of a 3-D linear track with a line in aptrkcy
plane, r-z, move a point in, with a specified direction aptmove, aptmvcy
plane, randomly sample direction vectors in a specified aptscad
plane, reflect a point or vector from aptrefl, aptrefs
plane, reflect a point or vector from (major plane) aptrefc
plane, reflection, vector normal to aptrefq
plane, rotation operator to make parallel to another plane aptrotp, aptrott
plane, vector perpendicular to aptvpln, aptpfit
plane, view factor projection of points onto aptradv
plane, z-r, equation of a cone through two points in aptcnis, aptcniz
plane, z-r, equation of an ellipsoid through two points in aptelis
plane, z-r, intersection of a 3-D linear track with a line in aptrkcy
plane, z-r, move a point in, with a specified direction aptmove, aptmvcy
planes coincident or parallel? aptplpl, aptplis
planes parallel or coincident? aptplpl, aptplis
planes, intersection of two, line of aptplpl, aptplis
planes, major (x-y, y-z, z-x, u-v, v-w, w-u, z-r) apt***c
planes, volume bounded by, in cartesian coordinate system aptbrkn, aptbrkp
planes, volume bounded by, in cartesian coordinate system aptbrks, aptbrkv
point in a brick with given local coordinates aptbrkp
point in a brick, local coordinates of, distances from surfaces aptbrkn
point in a quadrangle nearest another point aptquad
point in a quadrangle with given local coordinates aptquwt, aptetrw
point in a quadrangle, local coordinates of aptfdqc, aptqfdc
point in a tetrahedron with given local coordinates aptetrw
point in a tetrahedron, local coordinates of aptetrl
point in a triangle nearest nonplanar point apttrip
point in a triangle with given local coordinates aptrlop
point in a triangle with given local coordinates (major plane) aptrloc
point in a triangle, local coordinates of aptripl, apttrip
point in a triangle, local coordinates of (major plane) aptripc
point inside or outside a brick, distances from surfaces aptbrkn
point inside or outside a quadrangle (major plane)? aptqinc
point inside or outside a quadric surface? aptwhis
point inside or outside a tetrahedron? aptetrn
point inside or outside a triangle (major plane)? apttinc
point inside or outside a triangle? apttrip
point of intersection of three quadric surfaces aptripq
point of tangency of a plane and a quadric surface aptplqu
point of tangency of a plane and a sphere aptplqu
point of tangency of a plane and a sphere aptplsp, aptplis
point of tangency of a plane and an ellipsoid aptplqu
point of tangency of two spheres aptspsp
point on a line (major plane)? aptptlc
point on a line? aptptln, aptspcy
point on a parabolic trajectory vs time aptparb
point on a quadric surface nearest another point aptwhis
point on a quadric surface nearest another point (approx) aptquad
point on a quadric surface nearest another point (approx) (OBS) aptqprr, aptpqrt
point on a quadric surface, extreme curvatures at a aptcris
point on a trajection of a particle with time-dependent accel aptacct
point on a uniformly accelerated trajectory vs time aptparb
point with given distance and direction from a point aptvadd, aptvsum
point with given distance, direction from point (major plane) aptvadc, aptvsuc
point with given local coordinates in a brick aptbrkp
point with given local coordinates in a quadrangle aptquwt, aptetrw
point with given local coordinates in a tetrahedron aptetrw
point with given local coordinates in a triangle aptrlop
point with given local coordinates in a triangle (major plane) aptrloc
point, cylindrically scale, relative to a specified axis aptsclr
point, distance from a line to a aptptln
point, distance from a line to a (major plane) aptptlc
point, distance from a nonplanar quadrangle to a aptquad
point, distance from a nonplanar quadrangle to a aptquad
point, distance from a parabolic trajectory to aptpars
point, distance from a plane of a triangle to a aptript, apttrip
point, distance from a plane to a aptptpl
point, distance from a quadric surface, and proximal point aptwhis, aptquad
point, distance from a quadric surface, and proximal point(OBS) aptqprr, aptqprt
point, distance from a triangular face to a aptript, apttrip
point, distances from edges of a quadrangle to a (major plane) aptqdic, aptqinc
point, distances from edges of a triangle to a aptripl, apttrip
point, distances from edges of a triangle to a (major plane) apttinc
point, distances from the faces of a tetrahedron to a aptetrn
point, intersection with a parabolic trajectory aptparh, aptpars
point, invariant (see "inversion", "reflection", "rotation")
point, invariant (see also "scale", "scaling")
point, invert (major plane) aptinvc
point, invert, and operator to aptinvp, aptsclu
point, isotropically scale, and operator to aptsclu
point, linearly scale (major plane) aptsclc
point, linearly scale, relative to a specified plane aptscll
point, local coordinates in a brick, distances from surfaces aptbrkn
point, local coordinates in a tetrahedron aptetrl
point, local coordinates in a triangle aptripl, apttrip
point, local coordinates in a triangle (major plane) aptripc
point, matrix operation on a aptmopv
point, proximal on a line aptptln
point, proximal on a line (major plane) aptptlc
point, proximal on a nonplanar quadrangle aptquad
point, proximal on a parabolic trajectory, to a point aptpars
point, proximal on a plane aptptpl
point, proximal on a triangular face apttrip
point, reflect a, analyze the operator to aptrefq
point, reflect from a line (major plane) aptrefc
point, reflect from a plane of aptrefl, aptrefs
point, rotate (see also "operator", "rotate")
point, rotate around an axis by a specified angle aptrota, aptmopv
point, rotate around major axes by specified angles aptrots, aptmopv
point, translate through space apttran
point, translate through space (major plane) apttrac
point, uniformly scale, and operator to aptsclu
point, value of a quadric surface function at a specified aptqval
points coincident (major axis)? aptvdil
points coincident (major plane)? aptvdic
points coincident? aptdist, aptvdis
points colinear (major plane)? apttric
points colinear? aptpfit
points colinear? apttrid, aptvpln
points in a brick, randomly sample aptbrks
points in a circle, randomly sample (any plane) aptlocd, aptbrks
points in a circular annulus, randomly sample aptlocd, aptbrks
points in a cone, randomly sample aptscnv, aptbrks
points in a conical annulus, randomly sample aptscnv, aptbrks
points in a conical frustrum, randomly sample aptscnv, aptbrks
points in a cylinder, randomly sample aptlocy, aptbrks
points in a cylindrical annulus, randomly sample aptlocy, aptbrks
points in a parallelopiped, randomly sample aptspar, aptbrks
points in a quadrangle, randomly sample (major plane) aptqloc
points in a sphere, randomly sample aptlocs, aptbrks
points in a spherical annulus, randomly sample aptlocs, aptbrks
points in a tetrahedron, randomly sample aptetrp
points in a triangle, randomly sample apttlod
points in a triangle, randomly sample (major plane) aptqloc, apttloc
points of intersection of two quadric surfaces aptintq
points on a circle, randomly sample (any plane) aptlocd, aptbrks
points on a cone, randomly sample aptscns, aptscnv
points on a cylinder, randomly sample aptlocy, aptscns
points on a cylinder, randomly sample aptscnv, aptbrks
points on a disk, randomly sample (any plane) aptlocd, aptbrks
points on a linear or parabolic trajectory vs time aptparb
points on a parabolic trajectory vs time aptparb, aptpart
points on a quadric surface, extrema and axis intercepts aptqupt
points on a sphere, randomly sample aptlocs, aptbrks
points on a time-dependent accelerated trajectory aptacct
points on a uniformly accelerated trajectory vs time aptparb
points on an annular disk, randomly sample (any plane) aptlocd, aptbrks
points, 2, center and radius of sphere through, on an axis aptspha
points, 3, center and radius of circle through (major plane) aptcirc
points, 3, center, orientation and radius of circle through aptcirp
points, 3, plane through, equation of aptpfit
points, 4, center and radius of sphere through aptsphp
points, 4, quadric surface through quadrangle edges and vertex aptqhyp
points, 9, quadric surface through aptqfit
points, cylindrically scale, relative to a specified axis aptsclr
points, direction and distance between two aptdist, aptvdis
points, direction and distance between two (major plane) aptvdic
points, distance between two (major axis) aptvdil
points, invert (see "operator", "inversion")
points, linearly scale (major plane) aptsclc
points, linearly scale, relative to a specified plane aptscll
points, parallel projection onto a plane aptprop
points, perspective projection onto a line (major plane) aptperc
points, perspective projection onto a plane aptpers
points, project onto a cylinder, options aptprcy
points, project onto a line (major plane) aptperc
points, project onto a plane, parallel aptprop
points, project onto a plane, perspective aptpers
points, project onto a plane, view factor aptradv
points, project onto a sphere, options aptprsp
points, project onto a sphere, radial aptpros
points, proximal, of a plane and a quadric surface aptplqu
points, proximal, of a sphere and a cylinder aptspcy
points, proximal, of two cylinders aptcycy
points, proximal, of two lines aptlnln
points, proximal, of two quadric surfaces aptintq
points, proximal, of two spheres aptspsp
points, radially project onto a circle (major plane) aptproc
points, radially project onto a sphere aptpros, aptprsp
points, randomly sample, in a circle aptlocd, aptbrks
points, randomly sample, in a circular annulus aptlocd, aptbrks
points, randomly sample, in a cylinder aptlocy, aptbrks
points, randomly sample, in a cylindrical annulus aptlocy, aptbrks
points, randomly sample, in a parallelogram (any plane) aptspar, aptbrks
points, randomly sample, in a parallelopiped aptspar, aptbrks
points, randomly sample, in a quadrangle (major plane) aptqloc
points, randomly sample, in a sphere aptlocs, aptbrks
points, randomly sample, in a spherical annulus aptlocs, aptbrks
points, randomly sample, in a tetrahedron aptetrp
points, randomly sample, in a triangle apttlod
points, randomly sample, in a triangle (major plane) aptqloc, apttloc
points, randomly sample, on a circle (any plane) aptlocd, aptbrks
points, randomly sample, on a line aptspar, aptbrks
points, randomly sample, on an annular disk (any plane) aptlocd, aptbrks
points, reflect (see "operator", "reflection")
points, rotate (see "operator", "rotation")
points, rotate around an axis depending on axial position aptwist
points, rotate around an axis depending on radial position aptwirl
points, scale (see "operator", "scaling")
points, transform the coordinate system of aptcsys, aptcsyv
points, translate through space apttran
points, translate through space (major plane) apttrac
points, unique directions and their minimum distances between aptdirt
points, vector between two aptdist, aptvdis
points, vector between two (major plane) aptvdic
points, vector normal to plane through three aptvpln, aptpfit
points, vectors between, unique, and their minimum lengths aptdirt
points, view factor projection onto a plane aptradv
polygon (see also "triangle", "quadrangle")
polygon, regular, generate aptpoly
polygon, regular, generate (major plane) aptpolc
polygon, regular, properties of aptpoly
polygon, regular, properties of (major plane) aptpolc
polyhedron (see also "cube", "dodecahedron", "icosahedron")
polyhedron (see also "octahedron", "tetrahedron")
polyhedron, regular, generate, cube aptcube
polyhedron, regular, generate, dodecahedron aptdode
polyhedron, regular, generate, icosahedron apticos
polyhedron, regular, generate, octahedron aptocta
polyhedron, regular, generate, tetrahedron apttetr
polynomial equation, evaluate at a set of arguments aptpole
polynomial equation, reduce order by factoring out root aptpolf
polynomial roots, fourth order, real and complex (quartic) aptquar
polynomial roots, real, and extrema, inflection points aptpolr
polynomial roots, real, using Newtonian iteration aptnewt
polynomial roots, second order, real or complex (quadratic) aptqrts, aptqrtv
polynomial roots, third order, real and complex (cubic) aptcubs
position, effect of linear motion on, any coordinate system aptmove
position, effect of linear motion on, cylindrical coordinates aptmove, aptmvcy
position, effect of linear motion on, spherical coordinates aptmove, aptmovs
positions and times on a parabolic trajectory aptparb, aptpart
positions and times on a time-dependent accelerated trajectory aptacct
power of a big integer (any base), find a aptbpow
power-law PDF, randomly sample values from aptspod
precision, round-off floating point data to specified aptrnds, aptnint
prime factors of a factorial function, find all aptpfft
prime factors of a big integer (any base), find the aptpfab
prime factors of an integer, find all aptpfac, aptpfab
principal axis transformation of a quadric surface aptaxis
probability distribution function (see "PDF")
product of a matrix and a vector aptmopv
product of three vectors, scalar aptrips
product of three vectors, vector aptripv
product of two big integers (any base), find the aptbmul
product of two matrices aptmprd
product of two vectors, cross or vector aptvaxb, aptvxun
product of two vectors, cross or vector (major plane) aptvaxc, aptvxuc
product of two vectors, dot or scalar aptvdos, aptvdot
product of two vectors, dot or scalar (major plane) aptvdoc
project a quadric surface in a specified direction aptqupr
project a vector onto a plane aptvplp
project an equilateral triangle onto a specified triangle aptripp, aptripr
project onto a circle (major plane) aptproc
project onto a cylinder, options aptprcy
project onto a line, perspective (major plane) aptperc
project onto a plane, parallel aptprop
project onto a plane, perspective aptpers
project onto a plane, view factor aptradv
project onto a sphere, options aptprsp
project onto a sphere, radial aptpros, aptprsp
project points onto a circle, radial (major plane) aptproc
project points onto a cylinder, options aptprcy
project points onto a line, perspective (major plane) aptperc
project points onto a plane, parallel aptprop
project points onto a plane, perspective aptpers
project points onto a plane, view factor aptradv
project points onto a sphere, options aptprsp
project points onto a sphere, radial aptpros, aptprsp
properties of regular polygons aptpoly
properties of regular polygons (major plane) aptpolc
proportion, irreducible, geometric factors, and prime numbers aptprim
proximal line on a circular cylinder, to a plane aptplcy, aptplis
proximal line on a circular cylinder, to a plane aptplqu
proximal line on a cone, to a plane, distance aptplqu
proximal line on a plane, to a circular cylinder aptplcy, aptplis
proximal line on a plane, to a circular cylinder aptplqu
proximal line on a plane, to a cone aptplqu
proximal line on a plane, to a hyperbolic paraboloid aptplqu
proximal lines on a circular cylinder and a plane aptplcy, aptplis
proximal lines on a plane and a circular cylinder aptplcy, aptplis
proximal lines on a plane and a circular cylinder aptplqu
proximal lines on a plane and a cone aptplqu
proximal point in a quadrangle, to another point aptquad
proximal point in a triangle, to non-planar point apttrip
proximal point on a circular cylinder, to a plane aptplqu
proximal point on a circular cylinder, to a sphere aptspcy
proximal point on a cone, to a point aptwhis
proximal point on a cylinder, to a point aptwhis
proximal point on a line, to a point aptptln
proximal point on a line, to a point (major plane) aptptlc
proximal point on a nonplanar quadrangle, to a point aptquad
proximal point on a parabolic trajectory, to line aptparl
proximal point on a parabolic trajectory, to plane aptparp
proximal point on a parabolic trajectory, to point aptpars
proximal point on a paraboloid, to a point aptwhis
proximal point on a plane, to a point aptptpl
proximal point on a plane, to a sphere aptplsp, aptplis
proximal point on a quadric surface, to a plane aptplqu
proximal point on a quadric surface, to a point aptwhis, aptquad
proximal point on a quadric surface, to a point (approx) (OBS) aptqprr, aptqprt
proximal point on a sphere, to a circular cylinder aptspcy
proximal point on a sphere, to a plane aptplqu
proximal point on a sphere, to a plane aptplsp, aptplis
proximal point on a sphere, to a point aptwhis
proximal point on a sphere, to another sphere aptspsp
proximal point on a triangular face, to a point apttrip
proximal point on a uniformly accelerated trajectory, to line aptparl
proximal point on a uniformly accelerated trajectory, to plane aptparp
proximal point on a uniformly accelerated trajectory, to point aptpars
proximal point on an axisymmetric surface, to a plane aptplqu
proximal point on an ellipsoid, to a plane, distance aptplqu
proximal point on the axis of a circular cylinder, to a sphere aptspcy
proximal points on a circular cylinder and a sphere aptspcy
proximal points on a parabolic trajectory, to a quadric surface aptparx
proximal points on a plane and a quadric surface aptplqu
proximal points on a plane and a sphere aptplqu
proximal points on a plane and a sphere aptplsp, aptplis
proximal points on a plane and an axisymmetric surface aptplqu
proximal points on a plane and an ellipsoid aptplqu
proximal points on a sphere and a circular cylinder aptspcy
proximal points on a sphere and a plane aptspcy
proximal points on the axes of two circular cylinders aptcycy
proximal points on two circular cylinders aptcycy
proximal points on two quadric surfaces aptintq
pull bits right or left from one machine word into another aptbits
puzzle, solve a sudoku aptsudo, aptsudx
Q
quadrangle (see also "surface", "triangle")
quadrangle edges, distances from a point to (major plane) aptqdic, aptqinc
quadrangle vertex angle, cosine of aptvang
quadrangle vertex angle, sine and cosine of (major plane) aptvanc
quadrangle vertex areas and shape type (major plane) aptqvac
quadrangle, cosine and sine of a vertex angle (major plane) aptvanc
quadrangle, cosine of a vertex angle aptvang
quadrangle, distance from a point to a aptquad
quadrangle, distances from a point to edges of (major plane) aptqdic, aptqinc
quadrangle, local coordinates of a point in (major plane) aptfdqc, aptqfdc
quadrangle, nonplanar, distance from a point to a aptquad
quadrangle, perpendicular bisector of an edge aptpbln
quadrangle, perpendicular bisector of an edge (major plane) aptpblc
quadrangle, point in nearest another point aptquad
quadrangle, point in, local coordinates of (major plane) aptfdqc, aptqfdc
quadrangle, point inside or outside (major plane)? aptqinc
quadrangle, point with given local coordinates aptquwt, aptetrw
quadrangle, proximal point to a point aptquad
quadrangle, quadric surface fit to edges and ceneter of a aptqhyp
quadrangle, randomly sample points in (major plane) aptqloc
quadrangle, sine and cosine of a vertex angle (major plane) aptvanc
quadrangle, vector bisecting a vertex angle aptbang
quadrangle, vector bisecting a vertex angle (major plane) aptbanc
quadratic equation, real or complex roots of a aptqrts, aptqrtv
quadric curve (see "circle", "ellipse", "hyperbola")
quadric curve (see also "parabola")
quadric curve, minimum and maximum points on (major plane) aptqexc, aptqext
quadric surface (see also "cone", "cylinder", "ellipsoid")
quadric surface (see also "sphere", "hyperboloid")
quadric surface equation, extrema on a parabolic trajectory aptparx
quadric surface function, value at a specified point aptqval
quadric surface where two quadric surfaces families are ortho aptqper
quadric surface, center of symmetry of aptaxis
quadric surface, classify a aptaxis
quadric surface, distance from a plane to, intersection aptplqu, aptplis
quadric surface, distance from a point to a aptwhis, aptquad
quadric surface, distance from a point to a (approx) (OBS) aptqprr, aptqprt
quadric surface, extrema and axis intercept points aptqupt
quadric surface, extrema and type and symmetry center aptqext
quadric surface, extrema in a specified direction aptqexv
quadric surface, extreme curvatures at a point, centers aptcris
quadric surface, fit to edges and center of a quadrangle aptqhyp
quadric surface, fit to nine points aptqfit
quadric surface, intersection with a linear track aptrkis
quadric surface, intersection with a major plane aptplis
quadric surface, intersection with a parabolic trajectory aptparq
quadric surface, invert a aptrois
quadric surface, minimum, maximum and saddle points on aptqext, aptqexv
quadric surface, normal vector and tangent plane at a point aptqnor
quadric surface, principal axis transformation of aptaxis
quadric surface, project in a specified direction aptqupr
quadric surface, reflect a aptrois
quadric surface, rotate a aptaxis, aptrois
quadric surface, scale a aptrois
quadric surface, side on which a point is on, distance aptwhis, aptquad
quadric surface, side on which a point is on, distance (approx) aptqprt, aptqprr
quadric surface, standard form of aptaxis
quadric surface, symmetry operations on aptrois
quadric surface, translate through space aptaxis, apttris
quadric surfaces, intersections or proximal points of aptintq
quadric surfaces, triple point of intersection of aptripq
quartic polynomial equation, real and complex roots of aptquar
quotes, use as field delimiters, single and double aptquot
quotient of two big integers (any base), find the aptbdiv
R
r-z plane, equation of a cone through two points in aptcnis
r-z plane, equation of an ellipsoid through two points in aptelis
r-z plane, intersection of a 3-D linear track with a line in aptrkcy
r-z plane, move a point in, with a specified direction aptmove, aptmvcy
radial position, rotate points around axis depending on aptwirl
radially project points onto a circle (major plane) aptproc
radially project points onto a cylinder aptprcy
radially project points onto a sphere aptpros, aptprsp
radians, convert an angle to aptcang
radii and centers of circles tangent to 3 tangent circles aptcirk
radii and centers of spheres tangent to 4 tangent spheres aptsphk
radii of circles tangent to three specified tangent circles aptcirt, aptcirk
radii of spheres tangent to four specified tangent spheres aptspht, aptsphk
radius of circle tangent to three specified tangent circles aptcirt, aptcirk
radius of circumscribed circle of a regular polygon aptpoly
radius of circumscribed circle of a triangle apttrig
radius of circumscribed circle of regular polygon (major plane) aptpolc
radius of curvature at a point on a quadric surface, extreme aptcris
radius of inscribed circle of a regular polygon aptpoly
radius of inscribed circle of a regular polygon (major plane) aptpolc
radius of inscribed circle of a triangle apttrig
radius of sphere tangent to four specified tangent spheres aptspht, aptsphk
radius, center of circle through 3 points (major plane) aptcirc
radius, center of sphere on an axis, and through 2 points aptspha
radius, center of sphere through 4 specified points aptsphp
radius, center, orientation of circle through 3 points aptcirp
random characters, put into a character string aptchrn
random characters, put into a character string aptchrn
randomly reorder data aptrand
randomly sample a direction vector, uniform aptsciz
randomly sample a floating point value from a range of values aptrfps
randomly sample aliased PDF bins aptalsb, aptalst
randomly sample an integer from a sequence of integers aptrins
randomly sample azimuth angle for a fixed scatter angle aptscan, aptscaz
randomly sample azimuth angle for a fixed scatter angle aptscma, aptscmz
randomly sample bins, aliased PDF aptalsb, aptalst
randomly sample bins, cumulative PDF aptcums, aptcumt
randomly sample bins, equal-probability PDF apteqsb
randomly sample bits, and put into a machine word aptbitr
randomly sample characters from a character set aptchrn
randomly sample characters, and put into a character string aptchrn
randomly sample cumulative PDF bins aptcums, aptcumt
randomly sample direction vectors in a specified plane aptscad
randomly sample direction vectors within an angle interval aptscar
randomly sample direction vectors, cosine-power PDF aptscap, aptscar
randomly sample direction vectors, cosine-power PDF aptscav
randomly sample direction vectors, fixed angle from axis aptscan, aptscaz
randomly sample direction vectors, fixed angle from axis aptscma, aptscmz
randomly sample direction vectors, uniform aptscat
randomly sample equal-probability PDF bin values apteqxs, aptrans
randomly sample equal-probability PDF bins apteqsb
randomly sample floating point values from an interval aptrfpt
randomly sample frequencies from a Planck or Wien spectrum aptxnup
randomly sample from a cumulative PDF, bins aptcums, aptcumt
randomly sample from a cumulative PDF, generate bins for aptcump
randomly sample from a histogram PDF, aliased bin generation aptalin
randomly sample from a histogram PDF, aliased bin values aptalsh, aptalsl
randomly sample from a histogram PDF, aliased bins aptalsb, aptalst
randomly sample from a histogram PDF, cumulative bin generation aptcump
randomly sample from a histogram PDF, cumulative bins aptcums, aptcumt
randomly sample from a histogram PDF, equal-probability bins apteqsb, apteqxs
randomly sample from a histogram PDF, equal-probability init apteqin, apteqxn
randomly sample from a Planck or Wien PDF or spectrum aptxnup
randomly sample from a relativistic Maxwellian PDF aptmaxw
randomly sample from a tabulated PDF, aliased bin generation aptalin
randomly sample from a tabulated PDF, aliased bin values aptalsh, aptalsl
randomly sample from a tabulated PDF, aliased bins aptalsb, aptalst
randomly sample from a tabulated PDF, cumulative bin generation aptcump
randomly sample from a tabulated PDF, cumulative bins aptcums, aptcumt
randomly sample from a tabulated PDF, equal-probability bins apteqsb, apteqxs
randomly sample from a tabulated PDF, equal-probability init apteqin, apteqxn
randomly sample from an aliased PDF, bins aptalsb, aptalst
randomly sample from an aliased PDF, generate bins aptalin
randomly sample from an aliased PDF, values from specified bins aptalsh, aptalsl
randomly sample from an equal-probability PDF, bins apteqsb
randomly sample from an equal-probability PDF, initialize apteqin, apteqxn
randomly sample from an equal-probability PDF, values apteqxs, aptrans
randomly sample from an exponential PDF aptexpl, aptexps
randomly sample from linear PDFs in specified bins aptalsl
randomly sample from uniform PDFs in specified bins aptalsh
randomly sample integers, with any degree of striation aptrint
randomly sample points in a circle aptlocd, aptbrks
randomly sample points in a circular annulus aptlocd, aptbrks
randomly sample points in a cone aptscnv, aptbrks
randomly sample points in a conical annulus aptscnv, aptbrks
randomly sample points in a conical frustrum aptscnv, aptbrks
randomly sample points in a cylinder aptlocy, aptbrks
randomly sample points in a cylindrical annulus aptlocy, aptbrks
randomly sample points in a parallelogram (any plane) aptspar, aptbrks
randomly sample points in a parallelopiped aptspar, aptbrks
randomly sample points in a quadrangle (major plane) aptqloc
randomly sample points in a sphere aptlocs, aptbrks
randomly sample points in a spherical annulus aptlocs, aptbrks
randomly sample points in a tetrahedron aptetrp
randomly sample points in a triangle apttlod
randomly sample points in a triangle (major plane) aptqloc, apttloc
randomly sample points on a circle (any plane) aptlocd, aptbrks
randomly sample points on a cone aptscns, aptscnv
randomly sample points on a cylinder aptlocy, aptbrks
randomly sample points on a sphere aptlocs, aptbrks
randomly sample points on an annular disk (any plane) aptlocd, aptbrks
randomly sample values from a linear PDF aptslid, aptsliv
randomly sample values from a Normal PDF aptnorm
randomly sample values from a Planck or Wien PDF aptxnup
randomly sample values from a power-law PDF aptspod
randomly sample values from a relativistic Maxwellian PDF aptmaxw
randomly sample values from a set of equal-probability bins apteqxs
randomly sample values from an exponential PDF aptexpl, aptexps
randomly sample values from specified bins, linear PDF aptalsl
randomly sample values from specified bins, uniform PDF aptalsh
randomly sample, generate PDF to, aliased bins aptalin
randomly sample, generate PDF to, cumulative bins aptcump
randomly sample, generate PDF to, equal-probability bins apteqin, apteqxn
range of values of vector components, limit aptvtol
range of values of vector components, limit (major plane) aptvtoc
range, data values in a specified (any mode)? aptword
ratio, find for geom series, given first term, sum, length aptgrat
rational approximations of an irrational number aptcofr, aptcofv
rational fraction approximation of an irrational number aptcofr
rational fractions, value, find for a continued fraction aptcofv
ray tracing (see "distance", "intersection", "side", "track")
read and parse free-format input lines aptffip, aptchap
real roots of a cubic equation, and complex roots aptcubs
real roots of a polynomial equation using Newtonian iteration aptnewt
real roots of a polynomial equation, and extrema, infl pts aptpolr
real roots of a quadratic equation, and complex roots aptqrts, aptqrtv
real roots of a quartic polynomial equation, and complex roots aptquar
real triangle, find if three edge lengths can form aptrich
reciprocal integer series for a decimal fraction aptiris
rectangular coordinates, volume bounded by surfaces of aptbrkn, aptbrkp
rectangular coordinates, volume bounded by surfaces of aptbrks, aptbrkv
reduce an array or table to unique values or lines aptdeld
reduce multiple blanks to a single blank in character string aptblsq
reduce order of a polynomial equation by factoring out a root aptpolf
reflect a point or vector from a line (major plane) aptrefc
reflect a point or vector from a plane aptrefl, aptrefs
reflect a point or vector, analyze the operator to aptrefq
reflect a quadric surface aptrois
reflect from a plane normal to a major plane aptrefl
reflect from a plane, of points or vectors aptrefs
reflection operator, analyze, to find axis aptrefq
reflection operator, to reflect from a plane aptrefs
reflection plane, vector normal to aptrefq
regular arrays, distinct directions in aptdirt, aptprim
regular dodecahedron, generate aptdode
regular hexahedron, generate (a cube) aptcube
regular icosahedron, generate apticos
regular octahedron, generate aptocta
regular polygon, generation and properties of aptpoly
regular polygon, generation and properties of (major plane) aptpolc
regular polyhedron, generate, cube aptcube
regular polyhedron, generate, dodecahedron aptdode
regular polyhedron, generate, icosahedron apticos
regular polyhedron, generate, octahedron aptocta
regular polyhedron, generate, tetrahedron apttetr
regular tetrahedron, generate apttetr
relative precision, round-off floating point data to aptrnds
relativistic Maxwellian PDF, randomly sample values from aptmaxw
remainder of division of two big integers (any base), find the aptbdiv
remainders for several divisors, find integer when given aptcrts
remainders for several divisors, find when given integer aptcrts
remove leading and/or trailing blanks from a character string aptrmbl
reorder data, any direction or mode (multiple columns) aptsorm
reorder data, any direction or mode (one column) aptsort
reorder data, in random order aptrand
replace a bit string with random bits aptbitr
replace a character string with random characters aptchrn
replace characters in a character string aptchrp, aptchip
replace non-graphic characters in a character string aptchip
replace part of a character string with another string aptchmv
replacement, randomly sample without aptrans
reverse the order of an integer array aptbrev
right-fill a character string with blanks aptchsq
right-shift bits in a machine word, wrap-around or pull aptbits
right-shift characters in a character string aptchmv
root of a big integer (any base), find a aptbrtn
root of a polynomial equation, factor out, reduce order aptpolf
roots of a cubic equation, real and complex aptcubs
roots of a polynomial equation, real, and extrema, infl pts aptpolr
roots of a polynomial equation, real, using evaluation aptpole
roots of a polynomial equation, real, using Newtonian iteration aptnewt
roots of a quadratic equation, real or complex aptqrts, aptqrtv
roots of a quartic polynomial equation, real and complex aptquar
rotate (see also "operator")
rotate a point or vector aptmopv, aptrot*
rotate a quadric surface aptrois
rotate a vector by a specified angle (major plane) aptrotc
rotate points around an axis depending on axial position aptwist
rotate points around an axis depending on radial position aptwirl
rotation (see also "operator")
rotation angle and axis of a specified rotation operator aptrotq
rotation angle, operator for a specified axis and aptrota
rotation angle, vary with position along rotation axis aptwist
rotation angle, vary with radius from rotation axis aptwirl
rotation axis and angle of a specified rotation operator aptrotq
rotation axis, operator for a specified angle and aptrota
rotation operator for 3 angles around 3 major axes aptrots
rotation operator for a specified axis and angle aptrota
rotation operator to make a plane parallel to another plane aptrotp, aptrott
rotation operator to make a vector parallel to another vector aptrott, aptrotv
rotation operator, analyze, to find axis, angle aptrotq
round-off floating point data aptrnds, aptnint
rows containing duplicate values, delete from a 2-D array aptdeld
rows formed by a reqular array of points, like a vineyard aptdirt, aptprim
rows in unique directions, minimum spacing in a regular array aptdirt, aptprim
S
saddle points, minima and maxima on a quadric surface aptqext, aptqexv
sample (see "randomly sample")
scalar product of three vectors aptrips
scalar product of two vectors aptvdos, aptvdot
scalar product of two vectors (major plane) aptvdoc
scale a quadric surface aptrois
scale cylindrically, points or vectors, relative to an axis aptsclr
scale isotropically, points or vectors, and operator to aptsclu
scale linearly, points or vectors (major plane) aptsclc
scale linearly, points or vectors, relative to a plane aptscll
scale uniformly, points or vectors, and operator to aptsclu
scaling operator, to cylindrically scale points or vectors aptsclr
scaling operator, to isotropically scale points or vectors aptsclu
scaling operator, to linearly scale points or vectors aptscll
scaling operator, to uniformly scale points or vectors aptsclu
scattering angle, randomly sample azimuth angle for fixed aptscan, aptscaz
scattering angle, randomly sample azimuth angle for fixed aptscma, aptscmz
search for a bit string in a machine word aptbitf
search for a character string in another character string aptchfp
search for a delimited character string in another string aptchfs
search for a delimited character string in another string aptquot, aptfbrk
second derivative of a polynomial equation, evaluate at args aptpole
second derivative of a polynomial equation, real roots of aptpolr
second-order polonomial, real or complex roots of a aptqrts, aptqrtv
second-order surface (see quadric surface)
seconds, degrees, minutes, convert an angle to aptcang
semiaxes, three, equation of an ellipsoid with aptesis
separate a character string into a stem and subscript, more aptsubr
separate a character string into a stem and subscripts, more aptsubm
separate a character string into delimited fields aptffip, aptchap
separate a character string into delimited fields aptquot, aptfbrk
separate a group into smaller groups, number of ways aptcomg
series, geometric, find ratio given first term, sum, length aptgrat
series, integer plus reciprocal integer, for a decimal number aptiris
series, reciprocal integer, for a decimal fraction aptiris
set of integers, find the greatest common divisor of a aptcmad
set of integers, find the least common multiple of a aptcmad
shape of a quadric surface at a point, curvatures aptcris
shape type of a quadrangle (bowtie or boomerang?) (major plane) aptqvac
sheets, one or two (see "hyperboloid")
shift bits right or left in a machine word, wrap-around or pull aptbits
shift characters left or right in a character string aptchmv
SI units, 1999 values of the fundamental constants in aptconm
side of a quadric surface a point is on aptwhis
sine and cosine of an angle (major plane) aptvanc
sine of angle between two unit vectors aptvaxb, aptvxun
sine of angle between two unit vectors (major plane) aptvaxc, aptvxuc
sine of vertex angle of a quadrangle (major plane) aptvanc
sine of vertex angle of a triangle (major plane) aptvanc
single quotes, use as a field delimiter ('), with an escape aptquot
single blank, reduce multiple blanks in a character string to aptblsq
slash, use as a field delimiter (/) aptfbrk
slash, use as a field delimiter (/) aptffip, aptchap
slice through a quadric surface with a major plane aptplis
solve a set of linear equations aptsolv
solve a sudoku puzzle aptsudo, aptsudx
sort arrays, any dimension, direction or mode aptsorm
sort arrays, any dimension, direction or mode (one column) aptsort
sort data, any direction or mode (multiple columns) aptsorm
sort data, any direction or mode (one column) aptsort
sorted or unsorted tables, eliminate duplicate rows aptdeld
sorted or unsorted tables, reduce to unique rows aptdeld
special characters (see "delimiter")
special relationships (also see "concentric", "in", "parallel")
special relationships (also see "orthogonal", "overlap")
special relationships (also see "perpendicular", "tangent")
special relationships (also see "test")
special relationships (see "coaxial", "coincident", "colinear")
spectrum, Planck or Wien, randomly sample from aptxnup
sphere (see also "quadric surface")
sphere and a circular cylinder, distance between, proximal pts aptspcy
sphere and a plane, distance between, proximal pts aptplsp, aptplis
sphere at the origin, equation of aptesis
sphere tangent to a plane? aptplsp, aptplis
sphere tangent to four specified tangent spheres, radius of aptspht, aptsphk
sphere tangent to three specified tangent spheres, center of aptsphl, aptsphk
sphere through 2 points, and on a axis, center and radius of aptspha
sphere through 4 specified points, center and radius of aptsphp
sphere, distance from a plane to a, intersection aptplqu
sphere, distance from a plane to a, intersection aptplsp, aptplis
sphere, distance from a point to a aptwhis
sphere, distance from a, to a circular cylinder aptspcy
sphere, intersection with a linear track aptrkis
sphere, intersection with a linear track (1-D) aptrkrl
sphere, intersection with a major plane (none, pt or circle?) aptplis
sphere, intersection with a plane (none, point or circle?) aptplsp, aptplis
sphere, intersection with another sphere (none, pt or circle?) aptspsp
sphere, project points onto aptpros, aptprsp
sphere, proximal point to a circular cylinder, distance aptspcy
sphere, proximal point to a plane, distance aptplsp, aptplis
sphere, radially project points onto aptpros, aptprsp
sphere, randomly sample points in aptlocs, aptbrks
sphere, randomly sample points in an annulus of aptlocs, aptbrks
sphere, randomly sample points on aptlocs, aptbrks
sphere, tile the surface with planar triangles aptil08
sphere, tile the surface with planar triangles aptil12, aptil20
spheres coincident? aptspsp
spheres tangent to four specified tangent spheres, radii of aptspht, aptsphk
spheres tangent? aptspsp
spherical annulus, randomly sample points in aptlocs, aptbrks
spherical coordinates, direction between two points in aptdist
spherical coordinates, distance between two points in aptdist
spherical coordinates, intersection of a linear track in (1-D) aptrkrl
spherical coordinates, move a point in aptmove, aptmovs
spherical coordinates, transform to or from aptcsys, aptcsyv
spherical coordinates, volume bounded by surfaces of aptbrkn, aptbrkp
spherical coordinates, volume bounded by surfaces of aptbrks, aptbrkv
spherical sector, randomly sample direction vectors in a aptscar
spherically project points onto a cylinder aptprcy
square brackets, use as field delimiters [] aptfbrk
square matrices, product of two aptmprd
squeeze a character out of a character string aptchsq
stakes (see "grapestakes")
standard deviation of an array aptmean
standard form of the equation of a quadric surface aptaxis
statistics, mean value and standard deviation aptmean
Steiner vertex of a triangle, distances, vertex weights aptsver
stem and ASCII subscript, combine into a character string aptsuba, aptsubb
stem and ASCII subscripts, combine into a character string aptsubb
stem and integer subscripts, combine into a character string aptsubi
store integer ASCII characters into a character string aptchia
store one character string into another aptchmv
straight line that cuts a triangle into equal areas, perimeters aptrabc, aptrcab
straight line that cuts a triangle into equal areas, perimeters aptrcut, aptrext
strange characters, find in a character string and replace aptchip
striation, randomly sample with, aliased bins aptalsb
striation, randomly sample with, cumulative PDF bins aptcums
striation, randomly sample with, equal-probability bins apteqsb, apteqxs
striation, randomly sample with, uniform PDF's aptrfpt, aptrint
string (see "bit string", "character string")
string, character, copy digits from, into individual words aptatob
string, character, form from a stem and ASCII subscript aptsuba, aptsubb
string, character, form from a stem and ASCII subscripts aptsubb
string, character, form from a stem and integer subscripts aptsubi
string, character, reduce multiple blanks to a single blank in aptblsq
string, longer than eight characters, parse from input line aptffip, aptchap
string, remove leading and/or trailing blanks from a character aptrmbl
subdivide spherical pentagon into 5 spherical triangles aptpent
subscript, append to a stem in a single character string aptsuba, aptsubb
subscript, translate a character string into stem and aptsubr, aptsubs
subscripted variable, form from a stem and an ASCII subscript aptsuba, aptsubb
subscripted variable, form from a stem and ASCII subscripts aptsubb
subscripted variable, form from a stem and integer subscripts aptsubi
subscripted variable, translate into variable and subscript aptsubr, aptsubs
subscripts, append to a stem in a single character string aptsubi
subscripts, ASCII, append to a stem in a character string aptsubb
subscripts, integer, append to a stem in a character string aptsubi
subscripts, translate a character string into stem and multiple aptsubm
substitute (see "replace")
subtract big integers (arrays of digits in spec number base) aptbsub
sudoku puzzle, find duplicate characters in row, column, box aptsudu
sudoku puzzle, solve a aptsudo, aptsudx
Sudoku puzzle, solve a aptsudo, aptsudx
sum of two big integers (any base), find the aptbadd
sum of vectors, with specified coefficients aptvadd, aptvsum
sum of vectors, with specified coefficients (major plane) aptvadc, aptvsuc
surface (see also "plane", "quadrangle", "quadric", "triangle")
surface function, quadric, value at a specifed point aptqval
surface of cone, randomly sample points on aptscns, aptscnv
surface of cylinder, randomly sample points on aptlocy
surface of disk, randomly sample points on aptlocd
surface of parallelogram, randomly sample points on aptspar, aptbrks
surface of sphere, randomly sample points on aptlocs
surface of sphere, tile with planar triangles aptil08
surface of sphere, tile with planar triangles aptil12, aptil20
surface of triangle, randomly sample points on apttlod
surface of triangle, randomly sample points on (major plane) aptqloc, apttloc
surface, quadric, extreme curvatures at a point on aptcris
surface, quadric, fit to edges and center of a quadrangle aptqhyp
surface, quadric, fit to nine points aptqfit
surface, quadric, intersection with a linear track, normal aptrkis, aptwhis
surface, quadric, minimum and maximum points on aptqext, aptqexv
surface, quadric, side of, distance of a point aptwhis, aptquad
surface, quadric, side of, distance of a point (approx) (OBS) aptqprr, aptqprt
surfaces of a brick, areas of aptbrkv
surfaces of a brick, distance from a point to aptbrkn
surfaces of a tetrahedron, distance from a point to aptetrn
surfaces of the coordinate system, volume bounded by (brick) aptbrkn, aptbrkp
surfaces of the coordinate system, volume bounded by (brick) aptbrks, aptbrkv
surfaces, quadric, intersections or proximal points of aptintq
surfaces, quadric, plane tangent to family of, at a point aptqnor
surfaces, quadric, triple point of intersection of three aptripq
surfaces, quadric, vector normal to family of, at a point aptqnor
symbol (delimited character string), convert mode of aptchai
symbol (delimited character string), convert mode of aptchtp
symbol (delimited character string), convert mode of aptsubs, aptsubm
symbol (delimited character string), find in another string aptchfs
symbol (delimited character string), find in another string aptquot, aptfbrk
symbols, parse a character string into aptffip, aptchap
symbols, read and parse an input line into aptffip, aptchap
symbols, translate into integer and floating point aptchtp
symbols, translate into integer and floating point aptffip, aptchap
symbols, translate into integer and floating point aptsubs, aptsubm
symmetric around a specified axis, cylinder aptclis, aptcyis
symmetric around major axis, cone aptcois, aptcnis
symmetric around major axis, cylinder aptcyis
symmetric around major axis, ellipsoid aptelis
symmetric around major axis, hyperboloid of two sheets aptelis
symmetric around the z axis, cone Through two specified points aptcniz
symmetry axes of a quadric surface, and center, type aptaxis
symmetry axes, intercepts of a quadric surface on aptqupt
symmetry center of a quadric surface, and type, axes aptaxis
symmetry center of a quadric surface, and type, extrema aptqext
symmetry operations (see "reflection", "rotation", "inversion")
symmetry operations on a quadric surface aptrois
syzygy (see "intersection", "tangent")
T
table look-up, by binary search, ascending or descending order aptlook
table, eliminate lines containing duplicate values aptdeld
table, randomize order of aptrand
table, reduce to lines containing unique values aptdeld
tabulated PDF, generate bins to randomly sample, aliased aptalin
tabulated PDF, generate bins to randomly sample, cumulative aptcump
tabulated PDF, generate bins to randomly sample, equal-prob apteqin, apteqxn
tabulated PDF, randomly sample bins, aliased aptalsb, aptalst
tabulated PDF, randomly sample bins, cumulative aptcums, aptcumt
tabulated PDF, randomly sample from aliased bins aptalsh, aptalsl
tabulated PDF, randomly sample from cumulative PDF bins aptalsh, aptalsl
tabulated PDF, randomly sample from equal-probability bins apteqsb, apteqxs
tangent circle, to two specified tangent circles, center of aptcirl, aptcirk
tangent circles (major plane)? aptcinc
tangent circles, to three specified tangent circles, radii of aptcirt, aptcirk
tangent circular cylinders? aptcycy
tangent plane, to a family of quadric surfaces, at a point aptqnor
tangent sphere, to three specified tangent spheres, center of aptsphl, aptsphk
tangent spheres, to four specified tangent spheres, radii of aptspht, aptsphk
tangent spheres? aptspsp
tangent to a quadric surface, a cylindrical quadric surface aptqupr
tangent to four specified tangent spheres, radii of spheres aptspht, aptsphk
tangent to three specified tangent circles, radii of circles aptcirt, aptcirk
tangent vectors, at extreme curvatures on a quadric surface aptcris
tangent, line and circle (major plane)? aptlnic
tangent, plane and circular cylinder? aptplcy, aptplis
tangent, plane and sphere? aptplsp, aptplis
tangent, sphere and circular cylinder? aptspcy
tangent, two quadric surfaces? aptintq
terminate after error detection, and write messages before aptnerr
terms of geometric series, find ratio given first, sum, number aptgrat
test for a bit string in a machine word aptbitf
test for a character string in another character string aptchfp
test for a delimited character string in another string aptchfs
test for a delimited character string in another string aptquot, aptfbrk
test for circle being tangent to a line (major plane) aptlnic
test for circles being coincident (major plane) aptcinc
test for circles being tangent (major plane) aptcinc
test for data values between two specified limits (any mode) aptword
test for line being in a plane aptlnpl, aptlntr
test for line being tangent to a circle (major plane) aptlnic
test for lines being coincident or parallel aptlnln
test for lines being coincident or parallel (major plane) aptlnlc
test for parabolic trajectory tangent to a line aptparl
test for parabolic trajectory tangent to a plane aptparp, aptparq
test for parabolic trajectory tangent to a quadric surface aptparq
test for plane being tangent to a sphere aptplsp, aptplis
test for planes being coincident or parallel aptplpl, aptplis
test for point being inside a brick, distances from surfaces aptbrkn
test for point being inside a quadrangle (major plane) aptqinc
test for point being inside a tetrahedron aptetrn
test for point being inside a triangle (major plane) apttinc
test for point being on a line aptptln
test for point being on a line (major plane) aptptlc
test for points being coincident aptdist, aptvdis
test for points being coincident (major axis) aptvdil
test for points being coincident (major plane) aptvdic
test for points being colinear aptpfit
test for points being colinear apttrid, aptvpln
test for points being colinear (major plane) apttric
test for quadrangle convex, boomerang or bowtie (major plane) aptqvac
test for sphere being tangent to a plane aptplsp, aptplis
test for spheres being coincident aptspsp
test for spheres being tangent aptspsp
test for uniformly accelerated trajectory tangent to a line aptparl
test for uniformly accelerated trajectory tangent to a plane aptparp, aptparq
test for uniformly accelerated trajectory tangent to a quadric aptparq
test for vectors being parallel aptvaxb, aptvxun
test for vectors being parallel (major plane) aptvaxc, aptvxuc
test for vectors being perpendicular (major plane) aptvdoc
test for vectors being perpendicular or orthogonal aptvdos, aptvdot
tetrahedron centroid and volume apttetd
tetrahedron edge at specified angles from two other edges aptetrv
tetrahedron volume and centroid apttetd
tetrahedron, distances of a point from faces of aptetrn
tetrahedron, distances of faces from a point aptetrn
tetrahedron, generate a regular apttetr
tetrahedron, local coordinates of a point in aptetrl
tetrahedron, point in, local coordinates of aptetrl
tetrahedron, point inside or outside? aptetrn
tetrahedron, point with given local coordinates aptetrw
tetrahedron, randomly sample points in aptetrp
third-order polonomial, real and complex roots of aptcubs
three points in major plane, circle through aptcirc
three points, circle through, center and orientation of aptcirp
three points, equation of plane through aptpfit
three points, plane through, vector normal to aptvpln, aptpfit
three points, vector normal to plane through aptvpln, aptpfit
three quadric surfaces, triple point of intersection of aptripq
tile the surface of a sphere with planar triangles aptil08
tile the surface of a sphere with planar triangles aptil12, aptil20
time-dependent accelerated trajectory, position and velocity on aptacct
times and positions on a parabolic trajectory aptparb, aptpart
times and positions on a time-dependent accelerated trajectory aptacct
totient function for arithmetic modulo an integer, find Euler's aptpfac
track (see also "line", "direction vector")
track, linear, intersection with a cylinder (1-D) aptrkcl
track, linear, intersection with a line (major plane) aptrklc
track, linear, intersection with a major plane aptrksl
track, linear, intersection with a plane aptrkpl
track, linear, intersection with a quadric surface, normal aptrkis
track, linear, intersection with a sphere (1-D) aptrkrl
track, linear, intersection with an axisymmetric surface aptrkcy, aptrkis
track, parabolic, intersection with a line aptparl
track, parabolic, intersection with a plane aptparp, aptparq
track, parabolic, intersection with a point aptparh, aptpars
track, parabolic, intersection with a quadric surface aptparq
track, parabolic, proximal point to a line aptparl
track, parabolic, proximal point to a plane aptparp
track, parabolic, proximal point to a point aptpars
track, parabolic, proximal point to a quadric surface aptparx
trailing blanks, remove leading and/or from a character string aptrmbl
trajectory of parabolic motion vs time aptparb, aptpart
trajectory of time-dependent accelerated motion vs time aptacct
trajectory, parabolic, intersection with a line aptparl
trajectory, parabolic, intersection with a plane aptparp, aptparq
trajectory, parabolic, intersection with a point aptparh, aptpars
trajectory, parabolic, intersection with a quadric surface aptparq
trajectory, parabolic, points proximal to a quadric surface aptparq
trajectory, parabolic, position and velocity on, vs time aptparb
trajectory, parabolic, proximal point to a line aptparl
trajectory, parabolic, proximal point to a plane aptparp
trajectory, parabolic, proximal point to a point aptpars
transform coordinate systems aptcsys, aptcsyv
translate a character string into a stem and subscript aptsubr, aptsubs
translate a character string into a stem and subscripts, more aptsubm
translate a character string into floating point mode aptchtp
translate a character string into floating point mode aptffip, aptchap
translate a character string into floating point mode aptsubs, aptsubm
translate a character string into integer mode aptchtp
translate a character string into integer mode aptffip, aptchap
translate a character string into integer mode aptsubs, aptsubm
translate a character string into integer mode (oct, dec, hex) aptchai
translate a decimal number into a hexadecimal string apthexa
translate a hexadecimal string into a decimal number apthexd
translate a point any distance in any direction, any coords aptmove
translate a point any distance in any direction, cylindrical aptmove, aptmvcy
translate a point any distance in any direction, spherical aptmove, aptmovs
translate a point through space apttran
translate a point through space (major plane) apttrac
translate a quadric surface through space apttris
translate an integer into ASCII characters (oct, dec, hex) aptchia
transverse axis of a hyperbola or hyperbolic cylinder aptplqu
triangle (see also "plane", "quadrangle", "surface")
triangle altitude vectors, lengths, intersections apttrig
triangle area (major plane) apttric
triangle area and normal vector aptvpln, apttrig
triangle area, centroid and edge lengths apttrid, apttrig
triangle center of circumscribed circle, perp bisectors apttrig
triangle center of inscribed circle, angle bisectors apttrig
triangle centroid (major plane) apttric
triangle centroid, area and edge lengths apttrid, apttrig
triangle edge lengths (major plane) apttric
triangle edge lengths, area and centroid apttrid, apttrig
triangle edges, distances from a point to (major plane) aptqdic, aptqinc
triangle edges, distances from a point to (major plane) apttinc
triangle medians, intersections, centroid of triangle apttrig
triangle othocenter (intersection of altitudes) apttrig
triangle vertex angle, cosine of aptvang
triangle vertex angle, sine and cosine of (major plane) aptvanc
triangle, bisector of a vertex angle aptbang, apttrig
triangle, bisector of a vertex angle (major plane) aptbanc
triangle, cosine and sine of a vertex angle (major plane) aptvanc
triangle, cosine of a vertex angle aptvang
triangle, distance of point from plane of aptript, apttrip
triangle, distances from a point to edges of aptripl, apttrip
triangle, distances from a point to edges of (major plane) aptqdic, aptqinc
triangle, distances from a point to edges of (major plane) apttinc
triangle, equilateral, projection onto specified triangle aptripp, aptripr
triangle, extend two edges of to double area aptrext
triangle, intersection with a linear track aptrkpl
triangle, local coordinates of a point in aptripl, apttrip
triangle, local coordinates of a point in (major plane) aptripc
triangle, normal vector and area aptvpln, apttrig
triangle, perpendicular bisector of an edge of aptpbln, apttrig
triangle, perpendicular bisector of an edge of (major plane) aptpblc
triangle, planar point nearest nonplanar point apttrip
triangle, plane bisecting an edge of aptpbln
triangle, point in, local coordinates of aptripl, apttrip
triangle, point in, local coordinates of (major plane) aptripc
triangle, point inside or outside (major plane)? apttinc
triangle, point inside or outside? apttrip
triangle, point with given local coordinates (major plane) aptrloc
triangle, point with given local coordinates (vertex weights) aptrlop
triangle, project an equilateral triangle onto a specified aptripp, aptripr
triangle, randomly sample points in apttlod
triangle, randomly sample points in (major plane) aptqloc, apttloc
triangle, real, find if three edge lengths can form aptrich
triangle, sine and cosine of a vertex angle (major plane) aptvanc
triangle, spherical, 5 subdivided from spherical pentagon aptpent
triangle, Steiner vertex of a, distances, vertex weights aptsver
triangle, straight line that cuts into equal areas, perimeters aptrabc, aptrcab
triangle, straight line that cuts into equal areas, perimeters aptrcut, aptrext
triangle, vector bisecting a vertex angle aptbang, apttrig
triangle, vector bisecting a vertex angle (major plane) aptbanc
triangle, vector normal to plane of aptvpln, aptpfit
triangles, planar, tile the surface of a sphere with aptil08
triangles, planar, tile the surface of a sphere with aptil12, aptil20
triangles, tile the surface of a sphere with aptil08
triangles, tile the surface of a sphere with aptil12, aptil20
triangular face, distance from a point to a aptript, apttrip
triangular face, point nearest external point apttrip
triangular face, point on which side? aptript, apttrip
triangular faces of tetrahedron, distances from a point to the aptetrn
triple point of intersection of three quadric surfaces aptripq
triple product of three vectors, scalar aptrips
triple product of three vectors, vector aptripv
twist points around an axis depending on axial position aptwist
twist points around an axis depending on radial position aptwirl
two lines coincident or parallel (major plane) aptlnlc
two lines coincident or parallel? aptlnln
two lines, distance between aptlnln
two lines, distance between (major plane) aptlnlc
two lines, intersection between (major plane) aptlnlc
two planes coincident or parallel? aptplpl, aptplis
two planes, rotation operator to make parallel aptrotp, aptrott
two points coincident (major plane)? aptvdic
two points coincident? aptdist, aptvdis
two points, cone on a major axis through aptcnis
two points, cone on the z axis through aptcniz
two points, distance and vector between aptdist, aptvdis
two points, distance and vector between (major plane) aptvdic
two points, sphere through, on a specified axis aptspha
two spheres, intersection between (none, point or circle?) aptspsp
two vectors parallel (major plane)? aptvaxc, aptvxuc
two vectors parallel? aptvaxb, aptvxun
two vectors perpendicular (major plane)? aptvdoc
two vectors perpendicular? aptvdos, aptvdot
two vectors, rotation operator to make parallel aptrott, aptrotv
two-dimensional subroutines (see "major plane")
two-point interpolation or extrapolation, any linear/log axes aptintp
type character (oct, dec, hex), convert integer into aptchia
type character, convert to integer (oct, dec, hex) aptchai
type character, convert to integer and floating point aptchtp
type character, convert to integer and floating point aptffip, aptchap
type character, convert to integer and floating point aptsubs, aptsubm
type convert delimited character strings aptchai
type convert delimited character strings aptchtp
type convert delimited character strings aptsubs, aptsubm
type convert delimited character strings, read and aptffip, aptchap
type convert integers into ASCII characters (oct, dec, hex) aptchia
type integer, convert delimited character strings to aptchai
type integer, convert delimited character strings to aptchtp
type integer, convert delimited character strings to aptffip, aptchap
type integer, convert delimited character strings to aptsubs, aptsubm
type integer, convert into ASCII characters (oct, dec, hex) aptchia
type of quadric surface, symmetry center and axes aptaxis
type of quadric surface, symmetry center and extrema aptqext
type real, convert delimited character strings to aptchtp
type real, convert delimited character strings to aptffip, aptchap
type real, convert delimited character strings to aptsubs, aptsubm
U
u-v plane (see "major plane")
un, Boolean operation "union" on two machine words aptbitb
unary Boolean operation "comp", do on a machine word aptbitb
unexponentiated factors of an integer, find aptafac
uniform acceleration, parabolic trajectory produced by aptparb
uniform PDF of a direction vector in space (scalar) aptsciz
uniform PDF of direction vectors in space aptscap, aptscat
uniform PDF of direction vectors in space aptscav
uniform PDF of direction vectors in space, in spherical segment aptscar
uniform PDFs, randomly sample in specified bins aptalsh
uniformly accelerated motion, parabolic trajectory of aptparb, aptparh
uniformly accelerated motion, parabolic trajectory of aptparl, aptparp
uniformly accelerated motion, parabolic trajectory of aptparq, aptpars
uniformly accelerated motion, parabolic trajectory of aptparx
uniformly accelerated trajectory, given points on vs time aptpart
uniformly accelerated trajectory, intersection with line aptparl
uniformly accelerated trajectory, intersection with plane aptparp, aptparq
uniformly accelerated trajectory, intersection with point aptparh, aptpars
uniformly accelerated trajectory, intersection with quadric aptparq
uniformly accelerated trajectory, path length vs time aptparb
uniformly accelerated trajectory, points on vs time aptparb
uniformly accelerated trajectory, proximal point to line aptparl
uniformly accelerated trajectory, proximal point to plane aptparp
uniformly accelerated trajectory, proximal point to point aptpars
uniformly accelerated trajectory, proximal point to surface aptparx
uniformly accelerated trajectory, velocities on vs time aptparb
uniformly randomly sample a direction vector (scalar) aptsciz, aptscmz
uniformly randomly sample direction vectors aptscan, aptscap
uniformly randomly sample direction vectors aptscat, aptscav
uniformly randomly sample direction vectors aptscma
uniformly randomly sample direction vectors in a plane aptscad
uniformly randomly sample in specified bins aptalsh
uniformly randomly sample integers from a sequence aptrins, aptrint
uniformly randomly sample points in a circle aptlocd, aptbrks
uniformly randomly sample points in a circular annulus aptlocd, aptbrks
uniformly randomly sample points in a cone aptscnv, aptbrks
uniformly randomly sample points in a conical annulus aptscnv, aptbrks
uniformly randomly sample points in a conical frustrum aptscnv, aptbrks
uniformly randomly sample points in a cylinder aptlocy, aptbrks
uniformly randomly sample points in a cylindrical annulus aptlocy, aptbrks
uniformly randomly sample points in a parallelogram aptspar, aptbrks
uniformly randomly sample points in a parallelopiped aptspar, aptbrks
uniformly randomly sample points in a quadrangle (major plane) aptqloc
uniformly randomly sample points in a sphere aptlocs, aptbrks
uniformly randomly sample points in a spherical annulus aptlocs, aptbrks
uniformly randomly sample points in a tetrahedron aptetrp
uniformly randomly sample points in a triangle apttlod
uniformly randomly sample points in a triangle (major plane) apttloc
uniformly randomly sample points on a circle aptlocd, aptbrks
uniformly randomly sample points on a cone aptscns, aptscnv
uniformly randomly sample points on a cylinder aptlocy, aptbrks
uniformly randomly sample points on a sphere aptlocs, aptbrks
uniformly randomly sample values from an interval aptrfps, aptrfpt
uniformly randomly sample without replacement aptrans
uniformly scale points or vectors, and operator to aptsclu
union of two machine words (Boolean operation .or. or .un.) aptbitb
unique directions between pairs of points in one or two groups aptdirt, aptprim
unique values or lines, reduce an array or table to aptdeld
unit direction vector (see "direction vector")
unit vector perpendicular to two other vectors aptvxun
unit vector perpendicular to two other vectors (major plane) aptvxuc
unit vector, normalize aptvuna, aptvunb
unit vector, normalize (major plane) aptvuac, aptvubc
unit vector, normalize (scalar) aptvunz, aptvusz
unit vectors, cosine of angle between aptvdos, aptvdot
unit vectors, cosine of angle between (major plane) aptvdoc
unit vectors, sine of angle between two aptvaxb, aptvxun
unit vectors, sine of angle between two (major plane) aptvaxc, aptvxuc
units cm-g-sh-keV, 1999 values of the fundamental constants in aptconl
units, SI, 1999 values of the fundamental constants in aptconm
unpack bits from machine words into a type integer*1 array aptbite
unsorted or sorted tables, eliminate duplicate rows aptdeld
unsorted or sorted tables, reduce to unique rows aptdeld
upper case characters, randomly sample from aptchrn
V
v-w plane (see "major plane")
value of a big integer in a specified number base, find the aptbasb
value of a decimal number in a specified number base, find the aptbase
value of continued fraction, find, given coefficients aptcofv
values (positive) and indices of the min and max of an array aptmnlg
values and indices of the minimum and maximum of an array aptmnlg, aptmnmx
values between two specified limits (any mode)? aptword
values of the fundamental constants, 1999 aptconl, aptconm
values, limit range of aptfdad, aptfdav
values, limit range of, vector components aptvtol
values, limit range of, vector components (major plane) aptvtoc
values, lower limits on vector components aptvlim
values, lower limits on vector components (major plane) aptvlic
values, randomly sample (see also "bins")
values, randomly sample, from a linear PDF aptslid, aptsliv
values, randomly sample, from a list of bins aptalsh, aptalsl
values, randomly sample, from a Normal PDF aptnorm
values, randomly sample, from a Planck or Wien spectrum aptxnup
values, randomly sample, from a power-law PDF aptspod
values, randomly sample, from a range of values (floating-pt) aptrfps, aptrfpt
values, randomly sample, from a range of values (integer) aptrins, aptrint
values, randomly sample, from a relativistic Maxwellian PDF aptmaxw
values, randomly sample, from an equal-probability PDF apteqxs
values, randomly sample, from an exponential PDF aptexpl, aptexps
variable, subscripted, form from a stem and ASCII subscript aptsuba, aptsubb
variable, subscripted, form from a stem and ASCII subscripts aptsubb
variable, subscripted, form from a stem and integer subscripts aptsubi
variable, subscripted, translate into variable and subscript aptsubr, aptsubs
variable, subscripted, translate into variable and subscripts aptsubm
vary angle of rotation with position along rotation axis aptwist
vary angle of rotation with radius from rotation axis aptwirl
vector (see also "direction vector", "line", "track")
vector and plane, rotate onto another vector and plane aptrott
vector at specified angles from two other vectors aptetru, aptetrv
vector between two points aptdist, aptvdis
vector between two points (major plane) aptvdic
vector bisecting a vertex angle of a quadrangle aptbang
vector bisecting a vertex angle of a quadrangle (major plane) aptbanc
vector bisecting a vertex angle of a triangle aptbang, apttrig
vector bisecting a vertex angle of a triangle (major plane) aptbanc
vector components in a plane aptvplp
vector components parallel and perpendicular to another vector aptvpap
vector components parallel to another vector (major plane) aptvcvc
vector components, limit range of values of aptvtol
vector components, limit range of values of (major plane) aptvtoc
vector components, lower limits on values of aptvlim
vector components, lower limits on values of (major plane) aptvlic
vector cross product aptvaxb, aptvxun
vector cross product (major plane) aptvaxc, aptvxuc
vector differences aptvdis
vector differences (major plane) aptvdic
vector direction and distance between two points aptdist, aptvdis
vector direction and distance between two points (major plane) aptvdic
vector dot product aptvdos, aptvdot
vector dot product (major plane) aptvdoc
vector length aptvunb, aptvusz
vector magnitude aptvunb, aptvusz
vector normal to a family of quadric surfaces, at a point aptqnor
vector parallel to a line between two points aptvdis
vector perpendicular to a line (major plane) aptvplc
vector perpendicular to a plane aptvpln, aptpfit
vector perpendicular to a triangle edge, through a vertex apttrig
vector product of three vectors aptripv
vector product of two vectors aptvaxb, aptvxun
vector product of two vectors (major plane) aptvaxc, aptvxuc
vector scalar product aptvdos, aptvdot
vector scalar product (major plane) aptvdoc
vector sum of two vectors aptvadd, aptvsum
vector sum of two vectors (major plane) aptvadc, aptvsuc
vector triple product aptripv
vector, cylindrically scale, relative to a specified axis aptsclr
vector, direction (see "direction vector")
vector, invert (major plane) aptinvc
vector, invert, and operator to aptinvp, aptsclu
vector, isotropically scale, and operator to aptsclu
vector, linearly scale (major plane) aptsclc
vector, linearly scale, relative to a specified plane aptscll
vector, matrix operation on aptmopv
vector, normal, of a quadric surface function at a point aptwhis
vector, normalize aptvuna, aptvunb
vector, normalize (major plane) aptvuac, aptvubc
vector, normalize (scalar) aptvunz, aptvusz
vector, reflect (major plane) aptrefc
vector, reflect a aptrefl, aptrefs
vector, reflect a, analyze the operator to aptrefq
vector, rotate a aptmopv, aptrot*
vector, rotate by a specified angle (major plane) aptrotc
vector, rotation operator to make parallel to another vector aptrott, aptrotv
vector, uniformly scale, and operator to aptsclu
vectors between pairs of points in a group, unique unit aptdirt
vectors of edges of a triangle apttrig
vectors parallel (major plane)? aptvaxc, aptvxuc
vectors parallel? aptvaxb, aptvxun
vectors perpendicular (major plane)? aptvdoc
vectors perpendicular? aptvdos, aptvdot
vectors, cross product of two aptvaxb, aptvxun
vectors, cross product of two (major plane) aptvaxc, aptvxuc
vectors, cylindrically scale, relative to a specified axis aptsclr
vectors, dot product of two aptvdos, aptvdot
vectors, linearly combine aptvadd, aptvsum
vectors, linearly combine (major plane) aptvadc, aptvsuc
vectors, linearly scale (major plane) aptsclc
vectors, linearly scale, relative to a specified plane aptscll
vectors, randomly sample at a fixed scatter angle aptscan, aptscaz
vectors, randomly sample at a fixed scatter angle aptscma, aptscmz
vectors, randomly sample in a specified plane aptscad
vectors, randomly sample, cosine-power PDF aptscap, aptscar
vectors, randomly sample, cosine-power PDF aptscav
vectors, randomly sample, isotropic aptscap, aptscat
vectors, randomly sample, isotropic aptscav
vectors, randomly sample, isotropic, limits aptscar
vectors, randomly sample, uniform aptscap, aptscat
vectors, randomly sample, uniform aptscav
vectors, randomly sample, uniform, limits aptscar
vectors, rotate (see "operator", "rotate", "rotation")
vectors, scalar product of three aptrips
vectors, transform the coordinate system of aptcsyv
vectors, vector product of three aptripv
velocity on a parabolic trajectory vs time aptparb, aptpart
velocity on a parabolic trajectory, initial aptparh, aptpart
velocity on a parabolic trajectory, initial, to intersect point aptparh
velocity on a time-dependent accelerated trajectory vs time aptacct
velocity on a uniformly accelerated trajectory vs time aptparb
velocity, randomly sample from a relativistic Maxwellian PDF aptmaxw
vertex angle and coordinate, equation of cone with given aptcois
vertex angle of a quadrangle, bisecting vector aptbang
vertex angle of a quadrangle, bisecting vector (major plane) aptbanc
vertex angle of a quadrangle, cosine of aptvang
vertex angle of a quadrangle, sine and cosine of (major plane) aptvanc
vertex angle of a triangle, bisecting vector aptbang, apttrig
vertex angle of a triangle, bisecting vector (major plane) aptbanc
vertex angle of a triangle, cosine of aptvang
vertex angle of a triangle, sine and cosine of (major plane) aptvanc
vertex angles of a triangle apttrig
vertex areas and shape type of a quadrangle (major plane) aptqvac
vertex coordinate and angle, equation of cone with given aptcois
vertex of a tetrahedron, given two edges, angles of third edge aptetrv
vertex weights (see "local coordinates")
vertex weights of Steiner vertex of a triangle aptsver
vertices of a cube aptcube
vertices of a regular dodecahedron aptdode
vertices of a regular icosahedron apticos
vertices of a regular octahedron aptocta
vertices of a regular polygon aptpoly
vertices of a regular polygon (major plane) aptpolc
vertices of a regular tetrahedron apttetr
vertices, edges of a quadrangle, quadric surface fit to aptqhyp
vertices, project equilateral triangle onto triangle with given aptripp
view factor projection of points onto a plane aptradv
view plane, perspective, project points onto aptpers
view point, perspective projection with a specified aptpers
view point, perspective projection with specified (major plane) aptperc
volume bounded by coordinate surfaces, randomly sample pts in aptbrks
volume of a brick (bounded by coordinate surfaces) aptbrkv
volume of a conical annulus, randomly sample points in aptscnv
volume of a conical frustrum, randomly sample points in aptscnv
volume of a cylindrical annulus, randomly sample points in aptlocy
volume of a parallelopiped, given three edge vectors aptrips
volume of a parallelopiped, randomly sample points in aptspar, aptbrks
volume of a spherical annulus, randomly sample points in aptlocs
volume of a tetrahedron apttetd
volume of a tetrahedron, randomly sample points in aptetrp
W
w-x plane (see "major plane")
wall, Steiner, of a triangle aptsver
weighted sum of two vectors aptvadd, aptvsum
weighted sum of two vectors (major plane) aptvadc, aptvsuc
weights (see "local coordinates")
Wien or Planck spectrum, randomly sample values from aptxnup
word, machine, contract bits from a type integer*1 array into aptbitp
word, machine, expand bits from into a type integer*1 array aptbite
word, machine, find bit string in a aptbitf
word, machine, find character string in a aptchfp
word, machine, find complement of a aptbitb
word, machine, find delimited character string in aptchfs
word, machine, find delimited character string in aptquot, aptfbrk
word, machine, move a bit string from one to another aptbitm
word, machine, put random bits into a bit string in a aptbitr
word, machine, shift right or left, with wrap-around or pull aptbits
words, machine, find Boolean "nor" and "not" of aptbitb
words, machine, find equivalence, complement of aptbitb
words, machine, find exclusive or, intersection, union of aptbitb
wrap-around shift right or left of a machine word aptbits
write error message to specified IOCs after error detection aptnerr
X
x-ray diffraction pattern, crystal directions that determine it aptdirt, aptprim
x-y plane (see "major plane")
xnor, Boolean operation "equivalence" on two machine words aptbitb
xor, Boolean operation "exclusive or" on two machine words aptbitb
xyz coordinates (see "rectangular", "cartesian")
Y
y-z plane (see "major plane")
Z
z axis, equation of a cone on, through two specified points aptcniz
z-r plane (see "major plane")
z-r plane, equation of a cone through two points in aptcnis
z-r plane, intersection of a 3-D linear track with a line in aptrkcy
z-r plane, move a point in, with a specified direction aptmove, aptmvcy
z-x plane (see "major plane")
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