Here is a list of everything it can do functions etc... It has a gargantuan function database for math.
help - Print help (or help on a function/command)
load - Load a file into the interpretor
cd - Change directory
pwd - Print current directory
ls - List files in the current directory
plugin - Load a plugin

Basic:
AskString - Ask a question and return a string. Optionally pass in a default.
Compose - Compose two functions
ComposePower - Compose a function with itself n times, passing x as argument, and returning x if n == 0
Evaluate - Parse and evaluate a string
GetCurrentModulo - Get current modulo from the context outside the function
Identity - Identity function, returns its argument
IntegerFromBoolean - Make integer (0 or 1) from a boolean value
IsBoolean - Check if argument is a boolean (and not a number)
IsDefined - Check if a variable or function is defined
IsFunction - Check if argument is a function
IsFunctionOrIdentifier - Check if argument is a function or an identifier
IsFunctionRef - Check if argument is a function reference
IsMatrix - Check if argument is a matrix
IsNull - Check if argument is a null
IsString - Check if argument is a text string
IsValue - Check if argument is a number
Parse - Parse a string (but do not execute)
ProtectAll - Mark all currently defined variables as protected. They will be treated as system defined variables from
now on.
SetFunctionFlags - Set flags for a function, currently "PropagateMod" and "NoModuloArguments"
SetHelp - Set the category and help description line for a function
SetHelpAlias - Sets up a help alias
UndefineAll - Undefine all unprotected (user defined) global variables and parameters. Does not reset or change
protected (system) parameters.
UserVariables - Return a vector of all global unprotected (user defined) variable names.
chdir - Changes current directory
display - Display a string and an expression
error - Prints a string to the error stream
exit,quit - Exits the program
false,False,FALSE - The false boolean value
manual - Displays the user manual
print - Prints an expression
printn - Prints an expression without a trailing newline
protect - Protect a variable from being modified. It will be treated as a system defined variable from now on.
Protected parameters can still be modified.
set - Set a global variable
string - Make a string
true,True,TRUE - The true boolean value
undefine,Undefine - Undefine a variable (including all locals and globals of the same name)
unprotect - Unprotect a variable from being modified. It will be treated as a user defined variable from now on.
version - Return version as a 3-vector
wait - Waits a specified number of seconds
warranty - Gives the warranty information

Parameters:
ChopTolerance - Tolerance of the Chop function
ContinuousNumberOfTries - How many iterations to try to find the limit for continuity and limits
ContinuousSFS - How many successive steps to be within tolerance for calculation of continuity
ContinuousTolerance - Tolerance for continuity of functions and for calculating the limit
DerivativeNumberOfTries - How many iterations to try to find the limit for derivative
DerivativeSFS - How many successive steps to be within tolerance for calculation of derivative
DerivativeTolerance - Tolerance for calculating the derivatives of functions
ErrorFunctionTolerance - Tolerance of the ErrorFunction
FloatPrecision - Floating point precision
FullExpressions - Print full expressions, even if more than a line
GaussDistributionTolerance - Tolerance of the GaussDistribution function
IntegerOutputBase - Integer output base
IsPrimeMillerRabinReps - Number of extra Miller-Rabin tests to run on a number before declaring it a prime in IsPrime
LinePlotDrawLegends - If to draw legends or not on line plots.
LinePlotWindow - Line plotting window (limits) as a 4-vector of the form [x1,x2,y1,y2]
MaxDigits - Maximum digits to display
MaxErrors - Maximum errors to display
MixedFractions - If true, mixed fractions are printed
NumericalIntegralFunction - The function used for numerical integration in NumericalIntegral
NumericalIntegralSteps - Steps to perform in NumericalIntegral
OutputChopExponent - Display 0.0 when floating point number is less than 10^-x (0=never chop)
OutputChopWhenExponent - Only chop numbers when another number is greater than 10^-x
OutputStyle - Output style: normal, latex, mathml or troff
ResultsAsFloats - Convert all results to floats before printing
ScientificNotation - Use scientific notation
SumProductNumberOfTries - How many iterations to try for InfiniteSum and InfiniteProduct
SumProductSFS - How many successive steps to be within tolerance for InfiniteSum and InfiniteProduct
SumProductTolerance - Tolerance for InfiniteSum and InfiniteProduct
SurfacePlotWindow - Surface plotting window (limits) as a 6-vector of the form [x1,x2,y1,y2,z1,z2]
VectorfieldNormalized - Normalize vectorfields if true. That is, only show direction and not magnitude.

Constants:
CatalanConstant - Catalan's Constant (0.915...)
EulerConstant,gamma - Euler's Constant gamma
GoldenRatio - The Golden Ratio
Gravity - Free fall acceleration
e - The natural number e
pi - The number pi

Numeric:
AbsoluteValue,abs - Absolute value
Chop - Replace very small number with zero
ComplexConjugate,conj,Conj - Calculates the conjugate
Denominator - Get the denominator of a rational number
FractionalPart - Return the fractional part of a number
Im,ImaginaryPart - Get the imaginary part of a complex number
IntegerQuotient - Division w/o remainder
IsComplex - Check if argument is a complex (non-real) number
IsComplexRational - Check if argument is a possibly complex rational number
IsFloat - Check if argument is a floating point number (non-complex)
IsGaussInteger,IsComplexInteger - Check if argument is a possibly complex integer
IsInteger - Check if argument is an integer (non-complex)
IsNonNegativeInteger - Check if argument is a non-negative real integer
IsPositiveInteger,IsNaturalNumber - Check if argument is a positive real integer
IsRational - Check if argument is a rational number (non-complex)
IsReal - Check if argument is a real number
Numerator - Get the numerator of a rational number
Re,RealPart - Get the real part of a complex number
Sign,sign - Return the sign (-1,0,1)
ceil,Ceiling - Get the lowest integer more than or equal to n
exp - The exponential function
float - Make number a float
floor,Floor - Get the highest integer less than or equal to n
ln - The natural logarithm
log - Logarithm of any base (calls DiscreteLog if in modulo mode), if base is not given, e is used
log10 - Logarithm of x base 10
log2,lg - Logarithm of x base 2
max,Max,Maximum - Returns the maximum of arguments or matrix
min,Min,Minimum - Returns the minimum of arguments or matrix
rand - Generate random float
randint - Generate random integer
round,Round - Round a number
sqrt,SquareRoot - The square root
trunc,Truncate,IntegerPart - Truncate number to an integer (return the integer part)

Trigonometry:
acos,arccos - The arccos (inverse cos) function
acosh,arccosh - The arccosh (inverse cosh) function
acot,arccot - The arccot (inverse cot) function
acoth,arccoth - The arccoth (inverse coth) function
acsc,arccsc - The inverse cosecant function
acsch,arccsch - The inverse hyperbolic cosecant function
asec,arcsec - The inverse secant function
asech,arcsech - The inverse hyperbolic secant function
asin,arcsin - The arcsin (inverse sin) function
asinh,arcsinh - The arcsinh (inverse sinh) function
atan,arctan - Calculates the arctan function
atan2,arctan2 - Calculates the arctan2 function (arctan(y/x) if x>0)
atanh,arctanh - The arctanh (inverse tanh) function
cos - Calculates the cosine function
cosh - Calculates the hyperbolic cosine function
cot - The cotangent function
coth - The hyperbolic cotangent function
csc - The cosecant function
csch - The hyperbolic cosecant function
sec - The secant function
sech - The hyperbolic secant function
sin - Calculates the sine function
sinh - Calculates the hyperbolic sine function
tan - Calculates the tan function
tanh - The hyperbolic tangent function

Number Theory:
AreRelativelyPrime - Are a and b relatively prime?
BernoulliNumber - Return the nth Bernoulli number
ChineseRemainder,CRT - Find the x that solves the system given by the vector a and modulo the elements of m, using the Chinese
Remainder Theorem
CombineFactorizations - Given two factorizations, give the factorization of the product, see Factorize
ConvertFromBase - Convert a vector of values indicating powers of b to a number
ConvertToBase - Convert a number to a vector of powers for elements in base b
DiscreteLog - Find discrete log of n base b in F_q where q is a prime using the Silver-Pohlig-Hellman algoritm
Divides - Checks divisibility (if m divides n)
EulerPhi - Compute phi(n), the Euler phi function, that is the number of integers between 1 and n relatively prime
to n
ExactDivision - Return n/d but only if d divides n else returns garbage (this is faster than writing n/d)
Factorize - Return factorization of a number as a matrix
Factors - Return all factors of a number
FermatFactorization - Attempt fermat factorization of n into (t-s)*(t+s), returns t and s as a vector if possible, null
otherwise
FindPrimitiveElementMod - Find the first primitive element in F_q (q must be a prime)
FindRandomPrimitiveElementMod - Find a random primitive element in F_q (q must be a prime)
IndexCalculus - Compute discrete log base b of n in F_q (q a prime) using the factor base S. S should be a column of
primes possibly with second column precalculated by IndexCalculusPrecalculation.
IndexCalculusPrecalculation - Run the precalculation step of IndexCalculus for logarithms base b in F_q (q a prime) for the
factor base S (where S is a column vector of primes). The logs will be precalculated and returned
in the second column.
IsEven - Tests if an integer is even
IsMersennePrimeExponent - Test if Mp is a Mersenne prime using a table
IsNthPower - Tests if a rational number is a perfect power
IsOdd - Tests if an integer is odd
IsPerfectPower - Check a number for being any perfect power (a^b)
IsPerfectSquare - Check a number for being a perfect square
IsPrime - Tests primality of integers, for numbers greater than 25*10^9 false positive is with low probability
depending on IsPrimeMillerRabinReps
IsPrimitiveMod - Check if g is primitive in F_q, where q is a prime. If q is not prime results are bogus.
IsPrimitiveModWithPrimeFactors - Check if g is primitive in F_q, where q is a prime and f is a vector of prime factors of q-1.
If q is not prime results are bogus.
IsPseudoprime - If n is a pseudoprime base b but not a prime, that is if b^(n-1) == 1 mod n
IsStrongPseudoprime - Test if n is a strong pseudoprime to base b but not a prime
Jacobi,JacobiSymbol - Calculate the Jacobi symbol (a/b) (b should be odd)
JacobiKronecker,JacobiKroneckerSymbol - Calculate the Jacobi symbol (a/b) with the Kronecker extension (a/2)=(2/a) when a odd,
or (a/2)=0 when a even
LeastAbsoluteResidue - Return the residue of a mod n with the least absolute value (in the interval -n/2 to n/2)
Legendre,LegendreSymbol - Calculate the Legendre symbol (a/p)
LucasLehmer - Test if Mp is a Mersenne prime using the Lucas-Lehmer test
LucasNumber - Returns the n'th Lucas number
MaximalPrimePowerFactors - Return all maximal prime power factors of a number
MersennePrimeExponents - Vector with the known Mersenne prime exponents
MillerRabinTest - Use the Miller-Rabin primality test on n, reps number of times. The probability of false positive is
(1/4)^reps
MillerRabinTestSure - Use the Miller-Rabin primality test on n with enough bases that assuming the Generalized Reimann
Hypothesis the result is deterministic
ModInvert - Returns inverse of n mod m
MoebiusMu - Return the Moebius mu function evaluated in n
NextPrime - Returns the least prime greater than n (if n is positive)
PadicValuation - Returns the padic valuation (number of trailing zeros in base p).
PowerMod - Compute a^b mod m
Prime,prime - Return the n'th prime (up to a limit)
PrimeFactors - Return all prime factors of a number
PseudoprimeTest - Pseudoprime test, true iff b^(n-1) == 1 (mod n)
RemoveFactor - Removes all instances of the factor m from the number n
SilverPohligHellmanWithFactorization - Find discrete log of n base b in F_q where q is a prime using the Silver-Pohlig-Hellman
algoritm, given f being the factorization of q-1
SqrtModPrime - Find square root of n mod p (a prime). Null is returned if not a quadratic residue.
StrongPseudoprimeTest - Run the strong pseudoprime test base b on n
gcd,GCD - Greatest common divisor
lcm,LCM - Least common multiplier

Matrix Manipulation:
ApplyOverMatrix - Apply a function over all entries of a matrix and return a matrix of the results
ApplyOverMatrix2 - Apply a function over all entries of 2 matrices (or 1 value and 1 matrix) and return a matrix of the
results
ColumnsOf - Gets the columns of a matrix as a horizontal vector
ComplementSubmatrix - Remove column(s) and row(s) from a matrix
CompoundMatrix - Calculate the kth compund matrix of A
CountZeroColumns - Count the number of zero columns in a matrix
DeleteColumn - Delete a column of a matrix
DeleteRow - Delete a row of a matrix
DiagonalOf - Gets the diagonal entries of a matrix as a column vector
DotProduct - Get the dot product of two vectors (no conjugates)
ExpandMatrix - Expands a matrix just like we do on unquoted matrix input
HermitianProduct,InnerProduct - Get the hermitian product of two vectors
I,eye - Make an identity matrix of a given size
IndexComplement - Return the index complement of a vector of indexes
IsDiagonal - Is a matrix diagonal
IsIdentity - Check if a number or a matrix is 1 or identity respectively
IsLowerTriangular - Is a matrix lower triangular
IsMatrixInteger - Check if a matrix is an integer (non-complex) matrix
IsMatrixNonnegative - Check if a matrix is nonnegative, that is if each element is nonnegative
IsMatrixPositive - Check if a matrix is positive, that is if each element is positive
IsMatrixRational - Check if a matrix is a rational (non-complex) matrix
IsMatrixReal - Check if a matrix is a real (non-complex) matrix
IsMatrixSquare - Is a matrix square
IsUpperTriangular - Is a matrix upper triangular
IsValueOnly - Check if a matrix is a matrix of numbers
IsVector - Is argument a horizontal or a vertical vector
IsZero - Check if a number or a matrix is all zeros
LowerTriangular - Zero out entries above the diagonal
MakeDiagonal,diag - Make diagonal matrix from a vector
MakeVector - Make column vector out of matrix by putting columns above each other
MatrixProduct - Calculate the product of all elements in a matrix
MatrixSum - Calculate the sum of all elements in a matrix
MatrixSumSquares - Calculate the sum of squares of all elements in a matrix
OuterProduct - Get the outer product of two vectors
ReverseVector - Reverse elements in a vector
RowSum - Calculate sum of each row in a matrix
RowSumSquares - Calculate sum of squares of each row in a matrix
RowsOf - Gets the rows of a matrix as a vertical vector
SetMatrixSize - Make new matrix of given size from old one
SortVector - Sort vector elements
StripZeroColumns - Removes any all-zero columns of M
StripZeroRows - Removes any all-zero rows of M
Submatrix - Return column(s) and row(s) from a matrix
SwapRows - Swap two rows in a matrix
UpperTriangular - Zero out entries below the diagonal
columns - Get the number of columns of a matrix
elements - Get the number of elements of a matrix
ones - Make an matrix of all ones (or a row vector)
rows - Get the number of rows of a matrix
zeros - Make an matrix of all zeros (or a row vector)

Linear Algebra:
AuxilliaryUnitMatrix - Get the auxilliary unit matrix of size n
BilinearForm - Evaluate (v,w) with respect to the bilinear form given by the matrix A
BilinearFormFunction - Return a function that evaluates two vectors with respect to the bilinear form given by A
CharacteristicPolynomial,CharPoly - Get the characteristic polynomial as a vector
CharacteristicPolynomialFunction - Get the characteristic polynomial as a function
ColumnSpace - Get a basis matrix for the columnspace of a matrix
CommutationMatrix - Return the commutation matrix K(m,n) which is the unique m*n by m*n matrix such that K(m,n) *
MakeVector(A) = MakeVector(A.') for all m by n matrices A.
CompanionMatrix - Companion matrix of a polynomial (as vector)
ConjugateTranspose - Conjugate transpose of a matrix (adjoint)
Convolution,convol - Calculate convolution of two horizontal vectors
ConvolutionVector - Calculate convolution of two horizontal vectors
CrossProduct - CrossProduct of two vectors in R^3
DeterminantalDivisorsInteger - Get the determinantal divisors of an integer matrix (not its characteristic)
DirectSum - Direct sum of matrices
DirectSumMatrixVector - Direct sum of a vector of matrices
Eigenvalues,eig - Get the eigenvalues of a matrix (Currently only for up to 4x4 or triangular matrices)
Eigenvectors - Get the eigenvalues and eigenvectors of a matrix (Currently only for up to 2x2 matrices)
GramSchmidt - Apply the Gram-Schmidt process (to the columns) with respect to inner product given by B (if not given
use hermitian product)
HankelMatrix - Hankel matrix
HilbertMatrix - Hilbert matrix of order n
Image - Get the image (columnspace) of a linear transform
InfNorm - Get the Inf Norm of a vector
InvariantFactorsInteger - Get the invariant factors of a square integer matrix (not its characteristic)
InverseHilbertMatrix - Inverse Hilbert matrix of order n
IsHermitian - Is a matrix hermitian
IsInSubspace - Test if a vector is in a subspace
IsInvertible - Is a matrix (or number) invertible (Integer matrix is invertible iff it's invertible over the integers)
IsInvertibleField - Is a matrix (or number) invertible over a field
IsNormal - Is a matrix normal
IsPositiveDefinite - Is a matrix positive definite
IsPositiveSemidefinite - Is a matrix positive semidefinite
IsSkewHermitian - Is a matrix skew-hermitian
IsUnitary - Is a matrix unitary
JordanBlock,J - Get the jordan block corresponding to lambda and n
Kernel - Get the kernel (nullspace) of a linear transform
LUDecomposition - Get the LU decomposition of A and store the result in the L and U which should be references. If not
possible returns false.
Minor - Get the i-j minor of a matrix
NonPivotColumns - Return the columns that are not the pivot columns of a matrix
Norm,norm - Get the p Norm (or 2 Norm if no p is supplied) of a vector
NullSpace - Get the nullspace of a matrix
Nullity,nullity - Get the nullity of a matrix
OrthogonalComplement - Get the orthogonal complement of the columnspace
PivotColumns - Return pivot columns of a matrix, that is columns which have a leading 1 in rref form, also returns the
row where they occur
Projection - Projection of vector v onto subspace W given a sesquilinear form B (if not given use hermitian product)
QRDecomposition - Get the QR decomposition of A, returns R and Q can be a reference
Rank,rank - Get the rank of a matrix
RayleighQuotient - Return the Rayleigh quotient of a matrix and a vector
RayleighQuotientIteration - Compute an eigenvalue using the Rayleigh Quotient Iteration method until we are epsilon from
eigenvalue or for maxiter iterations
RosserMatrix - Rosser matrix, a classic symmetric eigenvalue test problem
Rotation2D,RotationMatrix - Rotation around origin in R^2
Rotation3DX - Rotation around origin in R^3 about the x-axis
Rotation3DY - Rotation around origin in R^3 about the y-axis
Rotation3DZ - Rotation around origin in R^3 about the z-axis
RowSpace - Get a basis matrix for the rowspace of a matrix
SesquilinearForm - Evaluate (v,w) with respect to the sesquilinear form given by the matrix A
SesquilinearFormFunction - Return a function that evaluates two vectors with respect to the sesquilinear form given by A
SmithNormalFormField - Smith Normal Form for fields (will end up with 1's on the diagonal)
SmithNormalFormInteger - Smith Normal Form for square integer matrices (not its characteristic)
SolveLinearSystem - Solve linear system Mx=V, return solution V if there is a unique solution, null otherwise. Extra two
reference parameters can optionally be used to get the reduced M and V.
ToeplitzMatrix - Return the Toeplitz matrix constructed given the first column c and (optionally) the first row r.
Trace,trace - Calculate the trace of a matrix
Transpose - Transpose of a matrix
VandermondeMatrix,vander - Return the Vandermonde matrix
VectorAngle - The angle of two vectors, given an inner product
VectorSpaceDirectSum - The direct sum of the vector spaces M and N
VectorSubspaceIntersection - Intersection of the subspaces given by M and N
VectorSubspaceSum - The sum of the vector spaces M and N, that is {w | w=m+n, m in M, n in N}
adj,Adjugate - Get the classical adjoint (adjugate) of a matrix
cref,CREF,ColumnReducedEchelonForm - Compute the Column Reduced Echelon Form
det,Determinant - Get the determinant of a matrix
ref,REF,RowEchelonForm - Get the row echelon form of a matrix
rref,RREF,ReducedRowEchelonForm - Get the reduced row echelon form of a matrix

Combinatorics:
Catalan - Get n'th catalan number
Combinations - Get all combinations of k numbers from 1 to n as a vector of vectors
DoubleFactorial - Double factorial: n(n-2)(n-4)...
Factorial - Factorial: n(n-1)(n-2)...
FallingFactorial - Falling factorial: (n)_k = n(n-1)...(n-(k-1))
Fibonacci,fib - Calculate n'th Fibonacci number
FrobeniusNumber - Calculate the Frobenius number for a coin problem
GaloisMatrix - Galois matrix given a linear combining rule (a_1*x_+...+a_n*x_n=x_(n+1))
GreedyAlgorithm - Use greedy algorithm to find c, for c . v = n. (v must be sorted)
HarmonicNumber,HarmonicH - Harmonic Number, the nth harmonic number of order r
Hofstadter - Hofstadter's function q(n) defined by q(1)=1, q(2)=1, q(n)=q(n-q(n-1))+q(n-q(n-2))
LinearRecursiveSequence - Compute linear recursive sequence using galois stepping
Multinomial - Calculate multinomial coefficients
NextCombination - Get combination that would come after v in call to combinations, first combination should be [1:k].
Pascal - Get the pascal's triangle as a matrix
Permutations - Get all permutations of k numbers from 1 to n as a vector of vectors
RisingFactorial,Pochhammer - (Pochhammer) Rising factorial: (n)_k = n(n+1)...(n+(k-1))
StirlingNumberFirst,StirlingS1 - Stirling number of the first kind
StirlingNumberSecond,StirlingS2 - Stirling number of the second kind
Subfactorial - Subfactorial: n! times sum_{k=1}^n (-1)^k/k!
Triangular - Calculate the nth triangular number
nCr,Binomial - Calculate combinations (binomial coefficient)
nPr - Calculate permutations

Calculus:
CompositeSimpsonsRule - Integration of f by Composite Simpson's Rule on the interval [a,b] with n subintervals with error of
max(f'''')*h^4*(b-a)/180, note that n should be even
CompositeSimpsonsRuleTolerance - Integration of f by Composite Simpson's Rule on the interval [a,b] with the number of steps
calculated by the fourth derivative bound and the desired tolerance
Derivative - Attempt to calculate derivative by trying first symbolically and then numerically
EvenPeriodicExtension - Return a function which is the even periodic extension of f defined on the interval [0,L]
FourierSeriesFunction - Return a function which is a Fourier series with the coefficients given by the vectors a (sines) and b
(cosines). Note that a@(1) is the constant coefficient!
InfiniteProduct - Try to calculate an infinite product for a single parameter function
InfiniteProduct2 - Try to calculate an infinite product for a double parameter function with func(arg,n)
InfiniteSum - Try to calculate an infinite sum for a single parameter function
InfiniteSum2 - Try to calculate an infinite sum for a double parameter function with func(arg,n)
IsContinuous - Try and see if a real-valued function is continuous at x0 by calculating the limit there
IsDifferentiable - Test for differentiability by approximating the left and right limits and comparing
LeftLimit - Calculate the left limit of a real-valued function at x0
Limit - Calculate the limit of a real-valued function at x0. Tries to calculate both left and right limits.
MidpointRule - Integration by midpoint rule
NumericalDerivative,NDerivative - Attempt to calculate numerical derivative
NumericalFourierCosineSeriesCoefficients - Numerically compute the coefficients for a cosine Fourier series for a function on
[0,L] up to the Nth coefficient.
NumericalFourierCosineSeriesFunction - Return a function which is the Fourier cosine series of f on [0,L] with coefficients up
to N computed numerically
NumericalFourierSeriesCoefficients - Numerically compute the coefficients for a Fourier series with half-period L up to the Nth
coefficient.
NumericalFourierSeriesFunction - Return a function which is the Fourier series of f with half-period L with coefficients up to N
computed numerically
NumericalFourierSineSeriesCoefficients - Numerically compute the coefficients for a sine Fourier series for a function on [0,L]
up to the Nth coefficient.
NumericalFourierSineSeriesFunction - Return a function which is the Fourier sine series of f on [0,L] with coefficients up to N
computed numerically
NumericalIntegral - Integration by rule set in NumericalIntegralFunction of f from a to b using NumericalIntegralSteps steps
NumericalLeftDerivative - Attempt to calculate numerical left derivative
NumericalLimitAtInfinity - Attempt to calculate the limit of f(step_fun(i)) as i goes from 1 to N
NumericalRightDerivative - Attempt to calculate numerical right derivative
OddPeriodicExtension - Return a function which is the odd periodic extension of f defined on the interval [0,L]
OneSidedFivePointFormula - Compute one-sided derivative using five point formula
OneSidedThreePointFormula - Compute one-sided derivative using three-point formula
PeriodicExtension - Return a function which is the periodic extension of f defined on the interval [a,b]
RightLimit - Calculate the right limit of a real-valued function at x0
TwoSidedFivePointFormula - Compute two-sided derivative using five-point formula
TwoSidedThreePointFormula - Compute two-sided derivative using three-point formula

Functions:
Argument,Arg,arg - argument (angle) of complex number
DirichletKernel - Dirichlet kernel of order n
DiscreteDelta - Returns 1 iff all elements are zero
ErrorFunction,erf - The error function, 2/sqrt(pi) * int_0^x e^(-t^2) dt
FejerKernel - Fejer kernel of order n
GammaFunction,Gamma - The Gamma function (only real values implemented)
KroneckerDelta - Returns 1 iff all elements are equal
MinimizeFunction - Find the first value where f(x)=0
MoebiusDiskMapping - Moebius mapping of the disk to itself mapping a to 0
MoebiusMapping - Moebius mapping using the cross ratio taking z2,z3,z4 to 1,0, and infinity respectively
MoebiusMappingInftyToInfty - Moebius mapping using the cross ratio taking infinity to infinity and z2,z3 to 1 and 0 respectively
MoebiusMappingInftyToOne - Moebius mapping using the cross ratio taking infinity to 1 and z3,z4 to 0 and infinity respectively
MoebiusMappingInftyToZero - Moebius mapping using the cross ratio taking infinity to 0 and z2,z4 to 1 and infinity respectively
PoissonKernel - Poisson kernel on D(0,1) (not normalized to 1, that is integral of this is 2pi)
PoissonKernelRadius - Poisson kernel on D(0,R) (not normalized to 1)
RiemannZeta,zeta - The Riemann zeta function (only real values implemented)
UnitStep - The unit step function = 0 for x<0, 1 otherwise. This is the integral of the Dirac Delta function.
cis - The cis function, that is cos(x)+i*sin(x)
deg2rad - Convert degrees to radians
rad2deg - Convert radians to degrees

Equation Solving:
CubicFormula - Find roots of a cubic polynomial (given as vector of coefficients)
EulersMethod - Use classical Euler's method to numerically solve y'=f(x,y) for initial x0,y0 going to x1 with n
increments, returns y at x1
FindRootBisection - Find root of a function using the bisection method
FindRootFalsePosition - Find root of a function using the method of false position
FindRootMullersMethod - Find root of a function using the Muller's method
FindRootSecant - Find root of a function using the secant method
PolynomialRoots - Find roots of a polynomial (given as vector of coefficients)
QuadraticFormula - Find roots of a quadratic polynomial (given as vector of coefficients)
QuarticFormula - Find roots of a quartic polynomial (given as vector of coefficients)
RungeKutta - Use classical non-adaptive Runge-Kutta of fourth order method to numerically solve y'=f(x,y) for initial
x0,y0 going to x1 with n increments, returns y at x1

Statistics:
Average,average,Mean,mean - Calculate average of an entire matrix
GaussDistribution - Integral of the GaussFunction from 0 to x (area under the normal curve)
GaussFunction - The normalized Gauss distribution function (the normal curve)
Median,median - Calculate median of an entire matrix
PopulationStandardDeviation,stdevp - Calculate the population standard deviation of a whole matrix
RowAverage,RowMean - Calculate average of each row in a matrix
RowMedian - Calculate median of each row in a matrix
RowPopulationStandardDeviation,rowstdevp - Calculate the population standard deviations of rows of a matrix and return a
vertical vector
RowStandardDeviation,rowstdev - Calculate the standard deviations of rows of a matrix and return a vertical vector
StandardDeviation,stdev - Calculate the standard deviation of a whole matrix

Polynomials:
AddPoly - Add two polynomials (vectors)
DividePoly - Divide polynomial p by q, return the remainder in r
IsPoly - Check if a vector is usable as a polynomial
MultiplyPoly - Multiply two polynomials (as vectors)
NewtonsMethodPoly - Run newton's method on a polynomial to attempt to find a root, returns after two successive values are
within epsilon or after maxn tries (then returns null)
Poly2ndDerivative - Take second polynomial (as vector) derivative
PolyDerivative - Take polynomial (as vector) derivative
PolyToFunction - Make function out of a polynomial (as vector)
PolyToString - Make string out of a polynomial (as vector)
SubtractPoly - Subtract two polynomials (as vectors)
TrimPoly - Trim zeros from a polynomial (as vector)

Set Theory:
Intersection - Returns a set theoretic intersection of X and Y (X and Y are vectors pretending to be sets)
IsIn - Returns true if the element x is in the set X (where X is a vector pretending to be a set)
IsSubset - Returns true if X is a subset of Y
MakeSet - Returns a set where every element of X appears only once
SetMinus - Returns a set theoretic difference X-Y (X and Y are vectors pretending to be sets)
Union - Returns a set theoretic union of X and Y (X and Y are vectors pretending to be sets)

Miscellaneous:
ASCIIToString - Convert a vector of ASCII values to a string
AlphabetToString - Convert a vector of 0-based alphabet values (positions in the alphabet string) to a string
StringToASCII - Convert a string to a vector of ASCII values
StringToAlphabet - Convert a string to a vector of 0-based alphabet values (positions in the alphabet string), -1's for
unknown letters

Symbolic Operations:
SymbolicDerivative - Attempt to symbolically differentiate the function f, where f is a function of one variable.
SymbolicDerivativeTry - Attempt to symbolically differentiate the function f, where f is a function of one variable, returns
null if unsuccessful but is silent.
SymbolicNthDerivative - Attempt to symbolically differentiate a function n times
SymbolicNthDerivativeTry - Attempt to symbolically differentiate a function n times quietly and return null on failure
SymbolicTaylorApproximationFunction - Attempt to construct the taylor approximation function around x0 to the nth degree.

Plotting:
LinePlot - Plot a function with a line. First come the functions (up to 10) then optionally limits as x1,x2,y1,y2
LinePlotCParametric - Plot a parametric complex valued function with a line. First comes the function that returns x+iy then
optionally the t limits as t1,t2,tinc, then optionally the limits as x1,x2,y1,y2
LinePlotClear - Show the line plot window and clear out functions
LinePlotDrawLine - Draw a line from x1,y1 to x2,y2. x1,y1,x2,y2 can be replaced by a n by 2 matrix for a longer line
LinePlotParametric - Plot a parametric function with a line. First come the functions for x and y then optionally the t
limits as t1,t2,tinc, then optionally the limits as x1,x2,y1,y2
SlopefieldClearSolutions - Clear all the slopefield solutions
SlopefieldDrawSolution - Draw a solution for a slope field starting at x,y and using dx as increment
SlopefieldPlot - Draw a slope field. First comes the function dy/dx in terms of x and y (or a complex z) then optionally
the limits as x1,x2,y1,y2
SurfacePlot - Plot a surface function which takes either two arguments or a complex number. First comes the function
then optionally limits as x1,x2,y1,y2,z1,z2
VectorfieldClearSolutions - Clear all the vectorfield solutions
VectorfieldDrawSolution - Draw a solution for a vector field starting at x,y, using dt as increment for tlen units
VectorfieldPlot - Draw a vector field. First come the functions dx/dt and dy/dt in terms of x and y then optionally the
limits as x1,x2,y1,y2

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sudo apt-get install genius to install from terminal on debian base linux box or search for genius in synaptics on Ubuntu. It has a langauge called GEL where you can make programs using genius for doing math. It is very easy to use.

You know what came to mind as soon as i was done scrolling through this list?
Fuck you windows calc

lol yea I will use genius in some bash scripting for complex math problems. Makes my extended math class look minute lol. It does all those matrix functions people been coding on here also.

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Here is a online manual for genius http://www.jirka.org/genius-documentation/index.html

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A example of piping to genius
This echo to genius to use teh gcd function which is the greatest common denominator. Here the result is 6

That is huge list of commands. Very good.

OFFTOPIC :
I just fixed codecaine's "code" tags in post !