abs adj and arccos arccosh arcsin arcsinh arctan arctanh arg ceiling check choose coeff cofactor conj contract cos cosh d deg denominator det dim display do dot draw erf erfc eval exp expcos expsin factor factorial filter float floor for gcd hermite hilbert imag inner integral inv isprime laguerre lcm legendre log mag mod not numerator or outer polar prime product quote quotient rank rationalize real rect roots simplify sin sinh sqrt stop subst sum tan tanh taylor test trace transpose unit zero abs(x) Returns the absolute value or vector length of x. adj(m) Returns the adjunct of matrix m. The inverse of m is equal to adj(m) divided by det(m). and(a,b,...) Logical-and of predicate expressions. Example and(A=B,B=C) arccos(x) Returns the inverse cosine of x. arccosh(x) Returns the inverse hyperbolic cosine of x. arcsin(x) Returns the inverse sine of x. arcsinh(x) Returns the inverse hyperbolic sine of x. arctan(x) Returns the inverse tangent of x. arctanh(x) Returns the inverse hyperbolic tangent of x. arg(z) Returns the angle of complex z. ceiling(x) Returns the smallest integer not less than x. check(x) If x is true then continue, else stop. Example check(A=B) choose(n,k) Returns the number of combinations of n items taken k at a time, choose(n,k)=n!/(k!*(n-k)!) 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. cofactor(m,i,j) Returns the cofactor of m for row i and column j. conj(z) Returns the complex conjugate of z. Example conj(3+4*i) contract(a,i,j) Returns "a" summed over indices i and j. If i and j are omitted then 1 and 2 are used. cos(x) Returns the cosine of x. cosh(x) Returns the hyperbolic cosine of x. d(f,x) Returns the partial derivative of f with respect to x. deg(p,x) Returns the degree of polynomial p(x). denominator(x) Returns the denominator of expression x. det(m) Returns the determinant of matrix m. dim(a,n) Returns the cardinality of the nth index of tensor "a". display(x) Evaluates expression x and displays the result. Useful for printing from inside a "for" loop. do(a,b,...) Evaluates each argument from left to right. Returns the result of the last argument. dot(a,b,...) Returns the dot or inner product of tensors. draw(f,x) Draws a graph of f(x). Drawing ranges can be set with xrange and yrange. erf(x) Error function of x. erfc(x) Complementary error function of x. eval(f,x,a) Returns f evaluated at x=a. exp(x) Returns the exponential of x. expcos(x) Returns the exponential cosine of x. expsin(x) Returns the exponential sine of x. factor(n) Factors integer n. factor(p,x) Factors polynomial p(x). The x can be omitted for polynomials in x. Polynomial p should be factorable over integers. factorial(x) For example, Enter 100! Result 93326215443944152681699238856266700490715968264381621468592963895217599993229915 608941463976156518286253697920827223758251185210916864000000000000000000000000 filter(f,a,b,...) Returns f excluding any terms containing a, b, etc. float(x) Converts rational numbers and integers to floating point values. The symbol pi is also converted. Enter float(100!) Result 9.33262e+157 floor(x) Returns the largest integer not greater than x. for(i,j,k,a,b,...) For i equals j through k evaluate a, b, etc. Enter x=0 y=2 for(k,1,9,x=sqrt(2+x),y=2*y/x) float(y) Result 3.14159 gcd(a,b,...) Returns the greatest common divisor. hermite(x,n) Returns the nth Hermite polynomial in x. hilbert(n) Returns an n by n Hilbert matrix. imag(z) Returns the imaginary part of complex z. inner(a,b,...) Returns the inner product of tensors. Same as the dot product. integral(f,x) Returns the integral of f with respect to x. inv(m) Returns the inverse of matrix m. isprime(n) Returns 1 if n is a prime number, returns zero otherwise. laguerre(x,n,a) Returns the nth Laguerre polynomial in x. If "a" is omitted then a=0 is used. lcm(a,b,...) Returns the least common multiple. legendre(x,n,m) Returns the nth Legendre polynomial in x. If m is omitted then m=0 is used. log(x) Returns the natural logarithm of x. mag(z) Returns the magnitude of complex z. mod(a,b) Returns the remainder of the result of "a" divided by b. not(x) Returns the logical inverse of x. Example not(A=B) numerator(x) Returns the numerator of expression x. or(a,b,...) Logical-or of predicate expressions. Example or(A=B,A=C) outer(a,b,...) Returns the outer product of tensors. Also known as the tensor product. polar(z) Returns complex z in polar form. prime(n) Returns the nth prime number, 1≤n≤10000. print(x) Print x in tty mode. product(i,j,k,f) For i equals j through k evaluate f. Returns the product of all f. quote(x) Returns expression x without evaluating it first. 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). rank(a) Returns the number of indices that tensor "a" has. rationalize(x) Returns x with everything over a common denominator. real(z) Returns the real part of complex z. rect(z) Returns complex z in rectangular form. 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. simplify(x) Returns x in a simpler form. sin(x) Returns the sine of x. sinh(x) Returns the hyperbolic sine of x. sqrt(x) Returns the square root of x. stop() In a script, it does what it says. subst(a,b,c) Substitutes "a" for b in c and returns the result. sum(i,j,k,f) For i equals j through k evaluate f. Returns the sum of all f. tan(x) Returns the tangent of x. tanh(x) Returns the hyperbolic tangent of x. 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. Enter taylor(1/cos(x),x,6) Result 1 2 5 4 61 6 1 + --- x + ---- x + ----- x 2 24 720 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. trace(m) Returns the trace of matrix m. The function trace(m) is equivalent to contract(m). 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. unit(n) Returns an n by n identity matrix. zero(i,j,...) Returns a zero tensor with dimensions i, j, etc. Useful for creating a tensor and then setting the component values. Enter A=zero(2,2) A[1,2]=a A Result 0 a 0 0