FUNCTIONS OF TWO OR MORE REAL NUMBERS: functionname(a,b,c,d,e,...), up to 25 arguments

sum, product, powertower, average

FUNCTIONS OF A LIST OF REAL NUMBERS: functionname([a,b,c,...])

objsum, objproduct, objaverage, objgeometricmean, objstdeviation

delta(list): Returns the discrete derivative of a list.
accumulate(list,a): Returns the discrete integral of a list with offset a.
polyfit(y): Returns the polynomial through points [x0,y0], [x1,y1], [x2,y2],...

FUNCTIONS OF ONE REAL NUMBER: functionname(x)

identity, negate, absolute, sign, inverse, integer, part, double, half,
square, squareroot, cube, cuberoot, triangle, triangleroot, exp, ln,
hypersquare, hyperroot, lambert, unlambert, hypercube, hypercuberoot, lnstirling, gamma

FUNCTIONS OF TWO REAL NUMBERS: functionname(x,y)

minus, divide, power, log, zeta

OTHER FUNCTIONS OF REAL NUMBERS:

linear(a,b): Solves for x in a linear equation: ax+b=0.
quadratic(a,b,c): Solves for x in a quadratic equation: ax²+bx+c=0.
cubic(a,b,c,d): Solves for x in a cubic equation: ax³+bx²+cx+d=0.
rectify(x,LOWER,UPPER): Returns x if x is between LOWER and UPPER values.
normaldistribution(x,mean,spread): Value of the normal distribution with specified spread around the mean.

roundoff(x,n): Rounds off x to n significant figures.
normalize(x): Checks and corrects for floating-point errors.

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FUNCTIONS OF ONE NATURAL NUMBER: functionname(a)

succ, factorization, leastprimefactor, nextprime, previousprime, primecount
aliquots, factors, sumofproperfactors, totient
fibonacci, factorial, doublefactorial, odditorial
digitsum, dectohex, dectobin

isapowerof(n): Returns the list of all q such that n is a non-trivial power of q.

FUNCTIONS OF TWO NATURAL NUMBERS: functionname(a,b)

residue, gcf, lcm, choose, ackermann

FUNCTIONS OF THREE NATURAL NUMBERS: functionname(a,b,c)

hyper(a,n,b): n=1: addition, n=2: multiplication, n=3: exponentiation, n=4: tetration, etc.

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SCIENTIFIC NOTATION:

scientific(x): Returns object [a,b] = a*10^b.
scifix(X): Conforms object X to standard scientific notation.

scisum(X,Y): Sum of two numbers in scientific notation.
sciproduct(X,Y): Product of two numbers in scientific notation.
scidivide(X,Y): Division of two numbers in scientific notation.

sciraise(a,b): Returns a^b expressed in scientific notation.

unscientific(X): Evaluation of sci-notation object X.
stringunscientific(X): Evaluation of sci-notation object X as a real-number string.

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RANDOM FUNCTIONS:

randominteger(a,b): Generates a random integer from a to b inclusive.
randomreal(r1,r2): Generates a random real number between r1 and r2.
randomndigitprime(n): Generates a random n-digit prime number.

scramble(list): Randomly rearranges the contents of a list.

password(n,lc,UC): Generates a random password from n numerals, lc lowercase letters, and UC uppercase letters.
passwordu(n,lc,UC): Generates a random password from n numerals, lc lowercase letters, and UC uppercase letters, with no potentially ambiguous characters.

passwordformat(format): Generates a random password using a given formatted string.
passwordformatu(format): Generates a random password using a given formatted string, with no potentially ambiguous characters.

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GEOMETRIC AND TRIGONOMETRIC FUNCTIONS:

pythagorean(A,B): Distance between two points in n-space.

degrees, radians, squaredegrees, steradians

arc(deg,min,sec): Converts base-60 notation into decimal.

sin	cos	tan	csc	sec	cot
arcsin	arccos	arctan	arccsc	arcsec	arccot
sinh	cosh	tanh	csch	sech	coth
arcsinh	arccosh	arctanh	arccsch	arcsech	arccoth

sinc, gd, arcgd

arctan2(x,y): Arctangent adjusted for quadrant of xy plane; maps to (-pi --- pi).
arctan3(x,y): Arctangent adjusted for quadrant of xy plane; maps to (0 --- 2*pi).

polartoxy([r,theta]): Transforms polar coordinates to rectangular coordinates.
sphericaltoxyz([r,theta,phi]): Transforms spherical coordinates to rectangular coordinates.

greatcircledistance(r,[long,lat],[long,lat]): Distance between two points on a sphere.
areaoftriangle(a,b,c): Area of a triangle with sides of length a, b, c.
correspondingangles(a,b,c): Opposite angles of a triangle with sides of length a, b, c.
areaofpolygon(pointlist): Area of a polygon at coords [x1,y1], [x2,y2], ..., [xn,yn].
lineintersection(A,B, C,D): Intersection point of two lines AB, CD in the cartesian plane.
segmentintersection(A,B, C,D): Intersection point of two line segments AB, CD in the cartesian plane.

interiorpoint(vertexlist,point): Tests if a point lies inside a polygon.
windingnumber(vertexlist,point): Count of the number of times a polygon wraps around a point (positive for counterclockwise).

incenter(A,B,C): Incenter point of a triangle with vertices A B C.

tetrahedrondihedralangle(A,B,C,D): Dihedral angle at edge AB of a tetrahedron with vertices A B C D.
tetrahedronsolidangle(A,B,C,D): Solid angle at vertex A of a tetrahedron with vertices A B C D.
tetrahedronvolume(A,B,C,D): Volume of a tetrahedron with vertices A B C D.

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FUNCTIONS OF POLYNOMIALS:

polyvalue(P,x): Evaluates object P as a polynomial in x for a specific value of x.

polysum(P1,P2): Adds two polynomials.
objpolysum([P1,P2,P3,...]): Adds a list of polynomials.
polyproduct(P1,P2): Multiplies two polynomials.
objpolyproduct([P1,P2,P3,...]): Multiplies a list of polynomials.

polypower(P,n): Returns the nth power of a polynomial.
polydivide(P1,P2): Polynomial division (use polyresidue for remainder).
polyresidue(P1,P2): Remainder after polynomial division.
polydelta(P): Delta analysis of polynomial P.
polyderivative(P): Discrete derivative of polynomial P.

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FUNCTIONS OF RATIONAL* NUMBERS:

fvalue: Converts a fraction to a real number.
freduce: Reduces a fraction to lowest terms.
finverse: Reciprocal, ie., inverts a fraction (result is reduced).
fsum: Adds two fractions (result is reduced).
fminus: Subtracts two fractions (result is reduced).
fproduct: Multiplies two fractions (result is reduced).
fdivide: Divides two fractions (result is reduced).

fareysequence(a,b,n): Sorted list of fractions between a and b with denominator not exceeding n.

(* Note: Enclose all rational values in brackets: eg. enter a/b as [a,b].)

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FUNCTIONS OF CONTINUED FRACTIONS:

collapsevalue(c): Converts a continued fraction to a real number.
collapsefrac(c): Converts a continued fraction to a simple reduced fraction.

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FUNCTIONS OF ONE COMPLEX* NUMBER: functionname(x)

conjugate, cinverse, csquareroot, cln, eulerize
czeta

ctetration(c,n): Returns the n'th powertower of c.
mandelbrotiterate(c,n): Returns the n'th iterate of z²+c.
mandelescape(x,y,n): Escape time for Mandelbrot iteration (up to maximum of n).

FUNCTIONS OF ONE EULER* NUMBER: functionname(x)

uneulerize: Converts polar form r e^{i angle} to complex number a+bi.

FUNCTIONS OF TWO COMPLEX* NUMBERS: functionname(x,y)

csum, cminus, cproduct, cdivide, cpower

FUNCTIONS OF TWO EULER* NUMBERS: functionname(x,y)

eulersum, eulerproduct

(*Note: Enclose all complex values in brackets: eg. enter a+bi as [a,b], or r e^{i angle} as [r,angle].)

quaternionproduct(q1,q2)

nthrootsofunity(n): List of the n complex nth roots of 1.

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FUNCTIONS OF ONE BOOLEAN VALUE: functionname(p)

not

FUNCTIONS OF TWO BOOLEAN VALUES: functionname(p,q)

and, or, nand, nor, implies, xor, equivalence

FUNCTIONS OF A LIST OF BOOLEAN VALUES: functionname([p,q,r,...])

objand, objor, objxor

PREDICATES:

truthtable(varlist,predicate): Generates a truth table for a logical predicate.

forall(variable,predicate,list)
exists(variable,predicate,list)
forallmulti(varlist,predicate,list)
existsmulti(varlist,predicate,list)

quantification(boundvariables,predicate,list)

findleast(var,pred(var),n): Returns the least value (up to n) which satisfies pred(var).
findall(var,pred(var),n): Returns a list of all values (up to n) which satisfies pred(var).

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TESTS OF ONE NATURAL NUMBER: functionname(n)

prime, issquare, iscube, squarefree

TESTS OF TWO REAL NUMBERS: functionname(x,y)

greaterthan, lessthan, equals

approximatelyequal(x,y,epsilon): Tests if two numbers are approximately equal.
relativelyclose(x,y,epsilon): Tests if two numbers are relatively close to each other.

TESTS OF THREE NATURAL NUMBERS: functionname(a,b,c)

congruent

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CONSTANTS: functionname()

e, pi, phi, gammaconstant

numbermax: Floating-point double precision maximum non-infinite value.
numbermin: Floating-point double precision minimum non-zero value.
integermax: Maximum safe integer value.
integermin: Minimum safe integer value.

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STRING CONSTANTS:

emptystring, numerals, alphabet, qwerty, quickbrownfox, p45, googol, monsterorder, greek, russian, symbols, arecibo

alphabetbbb(): Capital letters of alphabet rendered in BlackBoardBold.
greekletternames(): Returns the names of the letters of the Greek alphabet as a list.
greekletter(lettername): Returns the named Greek-alphabet character.

FUNCTIONS OF ONE STRING*: functionname(a)

stringlength, stringhead, stringtail, stringend, stringchop, stringreverse, stringscramble, hextodec, bintodec

quote(x): Embeds a string in quotemarks; turns anything else into a string.
unquote(s): Removes outer quotemarks from a string; otherwise interprets string.

wordlist(s): Returns a list of words from one string (delimiter=space).
stringpermute(s): Returns the list of distinct permutations of a string.
allwordsoflengthn(s,n): Sorted list of all n-length words formed from characters of s.
extractnumbers(s): List of natural numbers embedded in s.
stringrandom(s,n): Generates a random string of length n.

stringrepeat(s,n): Returns n copies of string s as one string.
stringsplit(s,n): Chops up a string into n-character pieces.
rot(s,n): Rotates alphabet characters in string by n places.
rot13(s): Classic ROT13 encryption/decryption.

pangramtest(s): Tests a string for the occurence of all 26 letters (case insensitive).

caseforce(s,latincase,greekcase): Forces uppercase or lowercase on either Latin or Greek letters in a string.

textalignleft(s,length): Formats a string to a specified length, aligned to the left.
textalignright(s,length): Formats a string to a specified length, aligned to the right.
textaligncenter(s,length): Formats a string to a specified length, aligned to the center.

FUNCTIONS OF TWO STRINGS:

stringmatches(u,v): Returns true iff string u is a permutation of string v.
stringsearch(u,v): Returns the list of indexes where string v occurs in string u.
stringmismatch(u,v): Returns the first index where string u differs from string v.
stringfilter(u,v): Strips characters out of string u not found in string v.
stringcomparison(u,v,‑): Compares strings u and v and shows where they differ.

FUNCTIONS OF THREE STRINGS:

replaceall(u,v,s): Replaces all occurences of string u with string v in string s.
encodetext(source,destination,originaltext): Encrypts a string via simple substitution cipher.

FUNCTIONS OF AN ARBITRARY NUMBER OF STRINGS*:

stringmerge(a,b,c,...): Merges up to 25 strings.
objstringmerge(list): Merges all strings in a list.

(*Note: Enclose all string values in 'single-quote marks'.)

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FUNCTIONS OF NUMERICAL STRINGS:

numstring(r): Converts any number to a long (zero-padded) numeric string.

stringparse(x): Formats a number or a real-number string into spaced triplets.
stringparsecomma(x): Formats into triplets using commas.
stringunparse(x): Removes all spaces or commas from a real-number string.

decimalalign(number,leading,trailing): Aligns the decimal point of a number or a real-number string.

stringsum(a,b): Adds two natural-number strings.
stringminus(a,b): Subtracts two natural-number strings.
stringsumsigned(a,b): Adds two signed natural-number strings.
stringsumreal(x,y): Adds two real-number strings.
stringsumrealsigned(x,y): Adds two signed real-number strings.

stringproduct(a,b): Multiplies two natural-number strings.
stringproductsigned(a,b): Multiplies two signed natural-number strings.
stringproductreal(x,y): Multiplies two real-number strings.
stringproductrealsigned(x,y): Multiplies two signed real-number strings.

stringdivide(a,b): Divides two natural-number strings (ignores remainder).
stringresidue(a,b): Remainder after division of two natural-number strings.
stringdividereal(x,y,prec): Divides two real-number strings to given precision.
stringdividerealsigned(x,y,prec): Divides two signed real-number strings to given precision.

repeatingdecimal(start,block): Converts a repeating decimal to a reduced fraction.

continuedfractionreal(x): Continued fraction of a real-number string.
continuedfractionratio(a,b): Continued fraction of the ratio of two natural-number strings.

stringsquareroot(x,prec): Squareroot of a real-number string to given precision.
stringcuberoot(x,prec): Cuberoot of a real-number string to given precision.
stringfifthroot(x,prec): Fifth-root of a real-number string to given precision.

stringsin(x,prec): Sine of a real-number string to given precision.
stringcos(x,prec): Cosine of a real-number string to given precision.
stringtan(x,prec): Tangent of a real-number string to given precision.

stringarcsin(x,prec): Arcsine of a real-number string to given precision.
stringarccos(x,prec): Arccosine of a real-number string to given precision.
stringarctan(x,prec): Arctangent of a real-number string to given precision.

stringexp(x,prec): Exponential (e^x) of a real-number string to given precision.
stringln(x,prec): Natural logarithm of a real-number string to given precision.

stringpower(a,n): Nth power of a natural-number string.
stringpowerreal(x,n): Nth power of a real-number string.
stringpowerrealreal(x,y,prec): Real-power of a real-number string to given precision.

objstringsum(list): Sum of a list of number-strings.
objstringproduct(list): Product of a list of number-strings.
stringproductofpowers(obj,prec): See help(stringproductofpowers).
stringsumofproductsofpowers(obj,prec): See help(stringsumofproductsofpowers).

stringfibonacci(n): Returns the nth fibonacci number as a natural-number string.
stringfactorial(n): Returns n! as a natural-number string.
stringdoublefactorial(n): Returns n!! as a natural-number string.
stringodditorial(n): Returns 1*3*5*7*...*2n+1 as a natural-number string.
stringchoose(a,b): Returns choose(a,b) as a natural-number string.

stringgcf(a,b): Returns the greatest common factor of two natural-number strings.
stringfreduce([a,b]): Converts the ratio of two natural-number strings to lowest terms.

stringtau(x,prec): SQRT(1-x²) of a real-number string to given precision.

stringpi(n): Pi (3.14159...) to n decimal places as a string.
stringe(n): E (2.71828...) to n decimal places as a string.
stringphi(n): Phi (1.61803...) to n decimal places as a string.

stringroundoff(x,n): Rounds-off a number-string to n significant digits.

signed32bit(x): Signed 32-bit-string of x.

stringbaseconvert(a,b1,b2): Converts a natural-number string from base b1 to b2 (2-60).
stringbaseconvertreal(a,b1,b2): Converts a real-number string from base b1 to b2 (2-60).
decodenumberstring(a): Ordered list of digit values for a base-specific number string (up to base 60).

stringpad(n,s): Pads string s with leading zeroes (up to total length n).
stringunpad(s): Removes leading zeroes from string s.
stringfactorization(s,lim): Factorization of numberstring s (up to prime limit lim).

romannumeral(n): Lower-case Roman numeral for n (for n=1 to 3999).
romannumeralvalue(s): Numerical value of a Roman numeral (for s='i' to 'mmmcmxcix').

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FUNCTIONS OF SETS:

strip(obj): Strips out duplicate elements of a list (non-recursive).

emptyset(): Constant; returns the empty set only.
successor(set): Returns the set-successor of a set*.
ordinal(n): Returns an object isomorphic to the nth Von Neumann ordinal.
powerset(set): Returns the powerset of a set*.
cardinality(set): Returns the cardinality of a set*.
union(set1,set2): Returns the union of two sets*.
intersection(set1,set2): Returns the intersection of two sets*.
sans(set1,set2): Returns the set of all elements in set1* that are NOT in set2*.
singletonset(set): Returns the set of all singletons of a given set*.
setpair(set1,set2): Returns the set which contains both (and only) set1* and set2*.
setunion(set): Returns the set of the elements of the elements of the given set*.
setintersection(set): Returns the intersection of the elements of the given set*.
separation(var,pred,set): Filters set* by predicate (enter var & pred as 'strings').
orderedpair(set1,set2): Kuratowski ordered pair of two sets* (or urelements).
listpair(orderedpair): Returns the length-2 list of an ordered pair.
cartesianproduct(set1,set2): Returns the set of all ordered pairs of two sets*.
setfunction(list1,list2): Returns the one-to-one relation of two ordered lists.
setchoice(setlist): Returns a random choice-set from a list of sets*.

TESTS OF SETS:

setequals(set1,set2): Returns true iff set1* equals set2*.
subset(set1,set2): Returns true iff set1* is a subset of set2*.
iselement(x,set): Returns true iff x is an element of the given set*.
partition(set1,set2): Returns true iff set1* is a set of sets which partitions set2*.

(*Note: The input values are automatically pre-stripped for these functions.)

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MATRIX FUNCTIONS:

identitymatrix(n): Returns an identity matrix of order n.
matrixsum(A,B): Returns the sum of two matrixes.
matrixproduct(A,B): Returns the product of two matrixes.
minor(A,u,v): Returns a minor of matrix A (u'th row, v'th column (offset=0)).
determinant(A): Returns the determinant of a square matrix.
transpose(A): Returns the transpose of a matrix.
matrixinverse(A): Returns the inverse of a square matrix.
matrixinversefrac(A): Returns the inverse of a square matrix (fraction notation).
matrixpower(A,n): Returns the nth power of a square matrix.

matrixgeneralsum(sumxy,A,B): Sum of two matrixes using a customized summation operation.
matrixgeneralproduct(mulxy,sumxy,A,B): Product of two matrixes using customized operations.

conversiontable(L): Generates a matrix of conversion factors from a given list.

matrixorient(A,r): Returns a reflected/rotated matrix (see: help(matrixorient)).

matrixformat(A): Displays a matrix in conventional table format.

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ALGEBRAIC STRUCTURES:

cayleytable(S,operation): Creates a two-dimensional matrix M of an operation acting on a set: M(a,b) = a@b.

(1) closuretest(S,operation): Tests an operation on a set for closure: a@b is an element of S.
(2) associativitytest(S,operation): Tests an operation on a set for associativity: (a@b)@c = a@(b@c).
(3) idelementtest(S,operation): Tests an operation on a set for the existence of an identity element: e@a = a@e = a.
(4) inversestest(S,operation): Tests an operation on a set for the existence of inverse elements: a@i = i@a = e.

commutivitytest(S,operation): Tests an operation on a set for commutivity: a@b = b@a.

grouptest(S,operation): Tests if a set under a given operation is a group.

algebraicstructure(S,operation): Summary of all tests for an algebraic structure.

* Note: The two arguments for the above functions may optionally be passed as an object (i.e., a length-2 list): functionname([S,operation]).

cayleytablestructure(ct): Summary of all algebraic tests for a general Cayley table.
relabel(ct): Re-label entries in a cayley table.
setoperation(ct): Interprets a cayley table as a set under an operation.

rearrange(L,x): Re-arrangement of x based on sequence given in L.
generateset(s,cyclelist): Returns the list of strings composed of the characters of s.
reduction(s,rulelist): Returns the reduced string on application of the rulelist.

cyclicgroup(n): Natural-number representation of the order n cyclic group.
dihedralgroup(2n): Natural-number representation of the order 2n dihedral group.
dicyclicgroup(n): Natural-number representation of the order 4n dicyclic group.
symmetricgroup(n): Permutation representation of the order n! symmetric group.
alternatinggroup(n): Permutation representation of the order n!/2 alternating group.

directproduct(g1,g2): Direct-product of two group-representations.

cyclicgrouptest(S,operation): Tests if an operation on a set is a cyclic group.

ordersofelements(S,operation): Returns the list of orders of each element.
nontrivialorders(S,operation): Returns the multiplicity of element-orders.

subgrouptest(sb,S,operation): Tests if a subset of a group is also a group.
normalsubgrouptest(sb,S,operation): Tests if a subgroup of a group is a normal subgroup.

groupcenter(S,operation): Returns the center of a group.
commutatorsubset(S,operation): Returns the derived subgroup of a group.
cosets(N,S,operation): Returns the cosets of a normal subgroup of a group.

quotientgroup(N,S,operation): Returns the quotient-group of a group by one of its specified normal subgroups.

Special groups: trivialgroup, kleinfourgroup, quaterniongroup

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FUNCTIONS OF GENERAL OBJECTS:

listlength(A): Returns the length of list A.
isomorphic(A,B): Returns true if & only if A and B have the same structure.
identical(A,B): Returns true if & only if object A equals object B.

converttolist(A): Returns the one-dimensional list of all primitive items in A.

rotate(A,n): Rotates a list by n units to the right.
shiftout(A,n,NULL): Shifts a list by n units to the right without changing length.

directsum(A,B): Adds two isomorphic objects componentwise.
scalarmultiple(c,A): Multiplies every entry in object A by a constant number c.
dotproduct(A,B): Inner product of two lists of numbers; returns a scalar.
crossproduct(A,B): Vector product of two 3-vectors; returns a 3-vector.

isascalarmultipleof(A,B): Tests two objects for the existence of a number c such that A=cB.

peek(A,I): Returns the object from inside object A at coordinate-list I.
poke(A,I,x): Replaces an item in object A with x at coordinate-list I.
build(I,x): Returns a multidimensional x-filled array with dimensions I.
count(n): Returns the ordered list of natural numbers from 1 to n.
natural(n): Returns the ordered list of natural numbers less than n.

cartesianlist(A,B): Returns the cartesian product of two lists, parsed as a list.
cartesianmatrix(A,B): Returns the cartesian product of two lists, parsed as a matrix.
objcartesianlist([A,B,C,...]): Returns the cartesian product of a list of lists, parsed as a list.
objcartesianmatrix([A,B,C,...]): Returns the cartesian product of a list of lists, parsed as a multidimensional matrix.
cartesianpower(A,n): Cartesian product of n copies of list A, parsed as a list.
cartesianpowermatrix(A,n): Cartesian product of n copies of list A, parsed as a multidimensional matrix.
triangularlist(A,B): Returns the upper triangle of the cartesian product of two lists, parsed as a list.

pair(A,B): Pairs up elements of two equal-length lists.
skew(A,B,n): Pairs up elements of two equal-length lists, offset by n places.

concatenate(A,B): Concatenation of two lists.
objconcatenate([A,B,C,...]): Concatenation of a list of lists.
split(A,n): Chops up a list into n-length pieces.
append(X,A): Concatenates a copy of list X with each list in A.
permute(A): List of all permutations of list A.
matches(A,B): Returns true iff B is a permutation of A.
signature(A,B): Returns 1/-1 iff B is an even/odd permutation of A.
powerlist(A): Returns the list of all sublists of list A.
chooselist(A,n): Returns the list of all length-n sublists of list A.

multiplicity(A): Paired list of item-counts in object (or string) A.
sort(A): Sorts elements of a 1-d array.
sortbyindex(A,n): Sorts a 2-d array by its nth index (offset 0).
selectbyindex(A,s,n,t): Selects items at index s from a list of lists where-ever A[n]=t.

highwater(seq): Returns the list of indexes where a sequence reaches a record high.
highwatermarks(seq): Returns the list of values where a sequence reaches a record high.

life(matrix): Calculates one Conway's Game of Life generation of a binary matrix.
knightlife(matrix): One Game-of-Life generation of a binary matrix (knight-move neighborhood).

groupbytype(list): Groups items in a list by type (non-recursive).
groupbytypedeep(list): Recursively groups items in a list and all of its sublists by type.

format(A,n): Displays an object line-by-line (to n levels of depth).

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HTML FUNCTIONS:

rgb(r,g,b): Converts decimal (0-255) to an RGB hex triplet string.
rgbdec(string): Converts a RGB hex triplet string to decimal (0-255).
unicode(string): Converts a string to a list of unicode values.
unicodehtml(string): Converts a string to an HTML-unicoded string.
ustring(list): Converts a list of unicode values to a string.

html(tag,string): Embeds a string inside a pair of HTML tags.
htmlnest(taglist,string): Embeds a string inside a nested set of HTML tags.
htmltable(array): Generates an HTML table with data from a two-dimensional array.
htmltablei(array): Generates an HTML table (indented for clarity).

wikilink(text): Finds [[wikilinks]] in a text string & replaces them with urls.

bakecookie(c_name,data,expires): Creates a cookie. DEPRECATED
retrievecookie(c_name): Reads a cookie and returns it's value (if found). DEPRECATED
cookielist(): Returns all cookie-names and encoded cookie values as an object. DEPRECATED
tosscookie(c_name): Deletes one cookie by name. DEPRECATED
tossthecookies(): Deletes all active cookies on confirmation. DEPRECATED

bakelocalcookie(c_name,value): Creates a permanent locally-stored item.
retrievelocalcookie(c_name): Returns a locally-stored item.
tosslocalcookie(c_name): Deletes a locally-stored item.
localcookielist(): Returns the names of all active locally-stored items.

fetch(): Retrieves the query string passed by the URL.

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TIME AND DATE FUNCTIONS:

clock(): Time in milliseconds from 1970-01-01 00:00:00.000 (GMT).
today(): Today's date formatted as YYYY-MM-DD.
todayfull(): Today's local date and time formatted as YYYY-MM-DD XM hh:mm:ss.
utc(): Today's UTC date and time formatted as YYYY-MM-DD--hh:mm:ss (GMT).

calendarmonth(yyyy,m): Calendar print-out for the specified month.
calendaryear(yyyy): Calendar print-out for the specified year.
stardate('yyyy-mm-dd'): Calendar-date converted to stardate format.
juliandaynumber('yyyy-mm-dd'): Calendar-date converted to Julian Day Number.
easterday(yyyy): Calendar-date of Easter Sunday for a given year.

timefor(procedure): Elapsed time for evaluating a JavaScript procedure (milliseconds).

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PHYSICS FUNCTIONS:

dimensions(measure): Returns the physical dimensions (MKSA) of a measure or a unit of measure.
dimensionsproductofpowers(list): Returns the physical dimensions of the product of a list of powers of measures (default power is 1).

physicssum(A,B,C,...): Sum of up to 20 physics quantities.
physicsscalar(s,A): Scalar product of a physics quantity.
physicsproduct(A,B): Product of two physics quantities.
physicsdivide(A,B): Division of two physics quantities.
physicspower(A,n): Power of a physics quantity.
physicsproductofpowers(list): Returns the product of a list of powers of physics quantities (default power is 1).

physicsexpression(string): Evaluates a string as a physics expression. α π ħ ε₀ μ₀ σ Ω Å ° ′ ″ Δν_Cs
physicsparse(o): Converts a physics object to a physics quantity parsed as a string.
physicsconvert(Q,unit): Converts a physics quantity to different units.
physicstranslate(o,BaseUnits): Translates a physics object to an alternative unit system.
unitofmeasure(T,BaseSymbols): Translates a type of physics quantity to the corresponding unit in an alternative unit system in string form.
physicstranslatetostring(Q,BaseSymbols): Translates a physics quantity to an alternative unit system in string form.

SI BASE UNITS:

meter, kilogram, second, ampere, kelvin, mole, candela

SI DERIVED UNITS:

hertz, newton, pascal, joule, watt, coulomb, volt, farad, ohm, tesla, weber, henry,
siemens, becquerel, lumen, lux, degreecelsius, gray, sievert, katal, radian, steradian

unit(x): A dimensionless physics quantity.

PHYSICAL CONSTANTS:

frequencystandard133cs, speedoflight, planckconstant, elementarycharge, boltzmannconstant, avogadroconstant, luminousefficacyconstant

gravitationalconstant, hbar, electricconstant, magneticconstant, coulombconstant, finestructureconstant,
electronmass, protonmass, neutronmass, bohrradius, classicalelectronradius, rydbergconstant, stefanboltzmannconstant,
universalgasconstant, molarmassconstant, vacuumimpedance, bohrmagneton, nuclearmagneton, protonchargeradius,
josephsonconstant, vonklitzingconstant, faradayconstant, wiendisplacementconstant, muonmass, taumass,
plancklength, planckmass, plancktime, planckenergy, planckcharge, plancktemperature

OTHER UNITS (non-SI):

standardgravity, standardatmosphere, atomicmassunit, faraday,
astronomicalunit, lightyear, parsec,
solarmass, jupitermass, earthmass, lunarmass,
solarluminosity, solarradius, earthradius

ADDITIONAL PHYSICS FUNCTIONS:

planckunit(measure): Planck unit for a given type of physics quantity.
planckstring(measure): Planck unit expressed as a string in terms of physical constants (c, G, ℏ, k_e, k).

fchekstring(Q): A physical quantity expressed as a string in terms of the seven SI fixed constants (Δν_Cs, c, h, e, k, N_A, K_cd).

comptonwavelength(mass): Compton wavelength of a particle.
blackholeradius(mass): Schwarzschild radius of a black hole.
blackholetemperature(mass): Hawking temperature of a black hole.

luminosity(abs-magnitude): Converts absolute magnitude to luminosity (in watts).
irradiance(app-magnitude): Converts apparent magnitude to irradiance (in watts per square meter).
absolutemagnitude(power): Absolute magnitude of a luminous source (equals apparent magnitude at 10 parsecs).
apparentmagnitude(power,distance): Apparent magnitude of a luminous source at a given distance.
luminositydistance(abs-magnitude,app-magnitude): Distance of a luminous source (in meters).

spectralradiance(wavelength,temperature): Spectral-wavelength radiance of a blackbody (in watts per steradian per square meter per meter).
spectralradiance2(frequency,temperature): Spectral-frequency radiance of a blackbody (in watts per steradian per square meter per hertz).
blackbodyluminousintensity(temperature,area): Luminous intensity of a blackbody (in candelas).
blackbodyluminousefficacy(temperature): Luminous efficacy of a blackbody (in lumens per watt).

hydrogenline(a,b): Wavelength of the hydrogen spectral line between quantum energy levels a and b (in meters).

RELATIVISTIC FUNCTIONS:

lorentzfactor(velocity): Relativistic dimensionless dilation factor (γ) for an object in motion.
kineticenergy(mass,speed): Relativistic kinetic energy of a moving object.
momentum(mass,speed): Relativistic momentum of a moving object.
velocityaddition(v1,v2): Relativistic velocity between two moving objects.
redshift(velocity): Relativistic redshift parameter (z) for a receding object.
ztovelocity(z): Speed of a receding object for a relativistic redshift of z.
gravitationaltimedilation(mass,radius): Time dilation factor at the surface of a spherical mass.

TEMPERATURE SCALE CONVERSION FUNCTIONS:

fahrenheittocelsius(°F): Converts Fahrenheit temperature to Celsius.
celsiustofahrenheit(°C): Converts Celsius temperature to Fahrenheit.
celsiustokelvin(°C): Converts Celsius temperature to Kelvin.
kelvintocelsius(K): Converts Kelvin temperature to Celsius.
fahrenheittokelvin(°F): Converts Fahrenheit temperature to Kelvin.
kelvintofahrenheit(K): Converts Kelvin temperature to Fahrenheit.

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SPECIAL FUNCTIONS:

help(function): Additional information for a function (if available).

last(): Returns the previous calculated result.
eval(string): Returns the implicit interpretation of a string.

define(newfunctionname,variablelist,expression): Defines a function for temporary use.
procedure(name,varlist,scriptcode): Defines a Javascript procedure for temporary use.

objectify(function,fname): Defines a one-argument function from an n-arity function.

insert(function,a): Substitutes a specific value for x in f(x) and returns the result.
insert2(function,a,b): Substitutes two specific values for x,y in f(x,y).
insert3(function,a,b,c): Substitutes three specific values for x,y,z in f(x,y,z).

apply(function,A): Applies a one-argument function to each item in list A.
apply2(function,A,B): Applies a two-argument function to two lists.
apply3(function,A,B,C): Applies a three-argument function to three lists.
applybottom(function,A): Applies a one-argument function to all bottommost entries in object A.
directcombine(function,A,B): Applies a two-argument function to all bottommost entries in isomorphic objects A and B.
applydepth(function,A,n): Applies a one-argument function to n-deep entries in object A.
applyleft(function,c,A): Applies a two-argument function to constant c and list A.
applyright(function,B,c): Applies a two-argument function to list B and constant c.
objapply([f,g,h,...],A): Applies a composition of functions to each item in list A.

chainleft(function,A): Chains a two-argument function to list A, evaluating to the left.
chainright(function,A): Chains a two-argument function to list A, evaluating to the right.

repeat(n,function,x): Repeats any single-input function n times on input x.
repeatsequence(n,function,x): Returns the list x, f(x), f(f(x)), f(f(f(x))), ...
sequence(function,a,b): Sequential list of a function from f(a) to f(b) inclusive.

sigma(function,a,b): Sum of terms of a function from f(a) to f(b) inclusive.
fsigma(function,a,b): Sum of fractions of f(a) to f(b) inclusive.
stringsigma(function,a,b): Sum of real-number strings of f(a) to f(b) inclusive.

zerobetween(function,a,b): Finds a zero for the specified function between a and b.
newtonsmethod(function,b,seed): Implements Newton's method for finding a value of x satisfying x=f^-1(b).

derivative(function,t,dx): Approximate value of df(x)/dx at x=t.
secondderivative(function,t,dx): Approximate value of d²f(x)/dx² at x=t.
partialderivative(function,vlist,vname,T,dv): Approximate value of δf(x,y,z,...)/δv with respect to variable v at coordinates T.

integrate(function,t1,t2,dx): Approximate value of definite integral from t1 to t2.
arclength(function,t1,t2,dx): Approximate value of the length of a curve from t1 to t2.

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MISCELLANEOUS FUNCTIONS:

chess(): Unicode characters for chess pieces.

expressdna(string): Amino-acid translation of a DNA/RNA strand.

moneychange(M,list): List of ways to make change for a given amount of money.
moneychangecount(M,list): Number of ways to make change for a given amount of money.

apportionment(rep,list): US House of Representatives apportionment by state populations.
blueness(S,atn,blue,red): Blueness of a series of elections (most-recent first), weighted by attenuation.

wavelengthnmtorgb(nm): Convert a visible-light wavelength (in nanometers) to three-channel RGB (0-255).

source(filename): Access raw data from an external file.

cladogram(object): Displays any object as a cladogram.
buildphylogeny(list): Constructs a tree-like object from a list of parent-child relations (use cladogram() to view).
ancestry(taxon,tree): Displays the ordered list of ancestors of a taxon in a phylogeny.

textblock(text,width,inset): Formats a selection of text as a block with fixed width and indentation.
boxcrate(X,Y,w,h): Creates a text-table with X*Y empty cells, with cell-size w*h.

atomicnumber(name-or-symbol): Atomic number of a chemical element.
elementname(number-or-symbol): Name of a chemical element.
elementsymbol(number-or-name): Symbol for a chemical element.

hyperspherehypervolume(n,radius): Hypervolume of an n-dimensional hypersphere.
hyperspherehypervolumeformula(n): Algebraic expression for the hypervolume of an n-dimensional hypersphere.

hyperspherehypersurface(n,radius): Hypersurface "area" of an n-dimensional hypersphere.
hyperspherehypersurfaceformula(n): Algebraic expression for the "hypersurface-area" of an n-dimensional hypersphere.

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SILLY FUNCTIONS:

tasteslikechicken(string): Returns true iff the input string tastes like chicken.
theanswertothequestionoflifetheuniverseandeverything()
thequestiontotheansweroflifetheuniverseandeverything()

rockpaperscissors(): Plays a round of Rock-Paper-Scissors.

cheeseshop(string): May I take your order, sir?

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KEYBOARDS:

GREEK

Α Β Γ Δ Ε Ζ Η Θ Ι Κ Λ Μ Ν Ξ Ο Π Ρ Σ Τ Υ Φ Χ Ψ Ω
α β γ δ ε ζ η θ ι κ λ μ ν ξ ο π ρ σ τ υ φ χ ψ ω

SYMBOLS

¬ ° ± × ÷ ħ • ⋅ ℵ ↑ → ↔ ⇒ ⇔ ∀ ∂ ∃ ∅ ∇ ∈ ∉ ∏ ∑
∓ √ ∞ ∧ ∨ ∩ ∪ ∫ ∮ ≅ ≈ ≠ ≡ ≤ ≥ ⊂ ⊃ ⊆ ⊇ ⊕ ⊗ ⊢ ⋊

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