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abs(x)

Returns the absolute value or vector length of x. source code

adj(m)

Returns the adjunct of matrix m. The inverse of m is equal to adj(m) divided by det(m). source code

and(a,b,...)

Logical-and of predicate expressions. source code

arccos(x)

Returns the inverse cosine of x. source code

arccosh(x)

Returns the inverse hyperbolic cosine of x. source code

arcsin(x)

Returns the inverse sine of x. source code

arcsinh(x)

Returns the inverse hyperbolic sine of x. source code

arctan(x)

Returns the inverse tangent of x. source code

arctanh(x)

Returns the inverse hyperbolic tangent of x. source code

arg(z)

Returns the angle of complex z. source code

ceiling(x)

Returns the smallest integer not less than x. source code

check(x)

If x is true then continue, else stop. source code

choose(n,k)

Returns the number of combinations of n items taken k at a time. source code

circexp(x)

Returns expression x with circular and hyperbolic functions converted to exponential forms. Sometimes this will simplify an expression. source code

coeff(p,x,n)

Returns the coefficient of x to the n in polynomial p. The x argument can be omitted for polynomials in x. source code

cofactor(m,i,j)

Returns the cofactor of m for row i and column j. source code

conj(z)

Returns the complex conjugate of z. source code

contract(a,i,j)

Returns "a" summed over indices i and j. If i and j are omitted then 1 and 2 are used. contract(m) is equivalent to the trace of matrix m. source code

cos(x)

Returns the cosine of x. source code

cosh(x)

Returns the hyperbolic cosine of x. source code

cross(u,v)

Returns the cross product of vectors u and v.

curl(u)

Returns the curl of vector u.

d(f,x)

Returns the partial derivative of f with respect to x. source code

defint(f,x,a,b)

Returns the definite integral of f with respect to x evaluated from "a" to b. The argument list can be extended for multiple integrals. For example, defint(f,x,a,b,y,c,d). source code

deg(p,x)

Returns the degree of polynomial p(x). source code

denominator(x)

Returns the denominator of expression x. source code

det(m)

Returns the determinant of matrix m. source code

dim(a,n)

Returns the cardinality of the nth index of tensor "a". source code

do(a,b,...)

Evaluates each argument from left to right. Returns the result of the last argument. source code

dot(a,b,...)

Returns the dot or inner product of tensors. source code

draw(f,x)

Draws a graph of f(x). Drawing ranges can be set with xrange and yrange. source code

erf(x)

Error function of x. source code

erfc(x)

Complementary error function of x. source code

eval(f,x,a)

Returns f evaluated at x=a. source code

exp(x)

Returns the exponential of x. source code

expcos(x)

Returns the exponential cosine of x. source code

expsin(x)

Returns the exponential sine of x. source code

factor(n)

Factors integer n. source code

factor(p,x)

Factors polynomial p of x. The x can be omitted for polynomials in x. The polynomial should be factorable over integers. The argument list can be extended for multivariate polynomials. For example, factor(p,x,y) factors p over x and then over y. source code

factorial(x)

Can be entered as x! source code

filter(f,a,b,...)

Returns f excluding any terms containing a, b, etc. source code

float(x)

Converts rational numbers and integers to floating point values. The symbol pi is also converted. source code

floor(x)

Returns the largest integer not greater than x. source code

for(i,j,k,a,b,...)

For i equals j through k evaluate a, b, etc. source code

gcd(a,b,...)

Returns the greatest common divisor. source code

hermite(x,n)

Returns the nth Hermite polynomial in x. source code

hilbert(n)

Returns an n by n Hilbert matrix. source code

imag(z)

Returns the imaginary part of complex z. source code

inner(a,b,...)

Returns the inner product of tensors. Same as the dot product. source code

integral(f,x)

Returns the integral of f with respect to x. source code

inv(m)

Returns the inverse of matrix m. source code

isprime(n)

Returns 1 if n is a prime number, returns zero otherwise. source code

laguerre(x,n,a)

Returns the nth Laguerre polynomial in x. If "a" is omitted then a=0 is used. source code

lcm(a,b,...)

Returns the least common multiple. source code

legendre(x,n,m)

Returns the nth Legendre polynomial in x. If m is omitted then m=0 is used. source code

log(x)

Returns the natural logarithm of x. source code

mag(z)

Returns the magnitude of complex z. source code

mod(a,b)

Returns the remainder of the result of "a" divided by b. source code

not(x)

Returns the logical negation of x. source code

nroots(p,x)

Returns all of the roots, both real and complex, of polynomial p in x. The roots are computed numerically. The coefficients of p can be real or complex. source code

numerator(x)

Returns the numerator of expression x. source code

or(a,b,...)

Logical-or of predicate expressions. source code

outer(a,b,...)

Returns the outer product of tensors. Also known as the tensor product. source code

polar(z)

Returns complex z in polar form. source code

prime(n)

Returns the nth prime number. The domain of n is 1 to 10000. source code

print(a,b,...)

Evaluate expressions and print the results. Useful for printing from inside a "for" loop. source code

product(i,j,k,f)

For i equals j through k evaluate f. Returns the product of all f. source code

quote(x)

Returns expression x without evaluating it first. source code

quotient(p,q,x)

Returns the quotient of polynomial p(x) over q(x). The last argument can be omitted for polynomials in x. The remainder can be calculated by p-q*quotient(p,q). source code

rank(a)

Returns the number of indices that tensor "a" has. source code

rationalize(x)

Returns x with everything over a common denominator. source code

real(z)

Returns the real part of complex z. source code

rect(z)

Returns complex z in rectangular form. source code

roots(p,x)

Returns the values of x such that p(x)=0. The polynomial p should be factorable over integers. Returns a vector for multiple roots. source code

simplify(x)

Returns x in a simpler form. source code

sin(x)

Returns the sine of x. source code

sinh(x)

Returns the hyperbolic sine of x. source code

sqrt(x)

Returns the square root of x. source code

stop()

In a script, it does what it says. source code

subst(a,b,c)

Substitutes "a" for b in c and returns the result. source code

sum(i,j,k,f)

For i equals j through k evaluate f. Returns the sum of all f. source code

tan(x)

Returns the tangent of x. source code

tanh(x)

Returns the hyperbolic tangent of x. source code

taylor(f,x,n,a)

Returns the Taylor expansion of f(x) around x=a. If "a" is omitted then a=0 is used. The argument n is the degree of the expansion. source code

test(a,b,c,d,...)

If "a" is true then b is returned else if c is true then d is returned, etc. If the number of arguments is odd then the last argument is returned when all else fails. source code

transpose(a,i,j)

Returns the transpose of "a" with respect to indices i and j. If i and j are omitted then 1 and 2 are used. Hence a matrix can be transposed with a single argument. source code

unit(n)

Returns an n by n identity matrix. source code

zero(i,j,...)

Returns a null tensor with dimensions i, j, etc. Useful for creating a tensor and then setting the component values. source code

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