Download Eigenmath.pdf Example scripts quantum harmonic oscillator hydrogen wavefunctions gamma matrix algebra free particle dirac equation maxwell in tensor form static spherical metric bondi metric circular polarization elliptical polarization vector calculus demo rotation matrix demo abs adj and arccos arccosh arcsin arcsinh arctan arctanh arg ceiling check choose circexp coeff cofactor conj contract cos cosh cross curl d defint deg denominator det dim do dot draw erf erfc eval exp expand expcos expsin factor factorial filter float floor for gcd hermite hilbert imag inner integral inv isprime laguerre lcm leading legendre log mag mod not nroots numerator or outer polar prime print product quote quotient rank rationalize real rect roots simplify sin sinh sqrt stop subst sum tan tanh taylor test transpose unit zero abs(x) Returns the absolute value or vector length of x. src adj(m) Returns the adjunct of matrix m. The inverse of m is equal to adj(m) divided by det(m). src and(a,b,...) Logical-and of predicate expressions. src arccos(x) Returns the inverse cosine of x. src arccosh(x) Returns the inverse hyperbolic cosine of x. src arcsin(x) Returns the inverse sine of x. src arcsinh(x) Returns the inverse hyperbolic sine of x. src arctan(x) Returns the inverse tangent of x. src arctanh(x) Returns the inverse hyperbolic tangent of x. src arg(z) Returns the angle of complex z. src ceiling(x) Returns the smallest integer not less than x. src check(x) If x is true then continue, else stop. src choose(n,k) Returns the number of combinations of n items taken k at a time. src circexp(x) Returns expression x with circular and hyperbolic functions converted to exponential forms. Sometimes this will simplify an expression. src 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. src cofactor(m,i,j) Returns the cofactor of m for row i and column j. src conj(z) Returns the complex conjugate of z. src 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. src cos(x) Returns the cosine of x. src cosh(x) Returns the hyperbolic cosine of x. src 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. src 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). src deg(p,x) Returns the degree of polynomial p(x). src denominator(x) Returns the denominator of expression x. src det(m) Returns the determinant of matrix m. src dim(a,n) Returns the cardinality of the nth index of tensor "a". src do(a,b,...) Evaluates each argument from left to right. Returns the result of the last argument. src dot(a,b,...) Returns the dot or inner product of tensors. src draw(f,x) Draws a graph of f(x). Drawing ranges can be set with xrange and yrange. src erf(x) Error function of x. src erfc(x) Complementary error function of x. src eval(f,x,a) Returns f evaluated at x=a. src exp(x) Returns the exponential of x. src expand(r,x) Returns the partial fraction expansion of the ratio of polynomials r in x. src expcos(x) Returns the exponential cosine of x. src expsin(x) Returns the exponential sine of x. src factor(n) Factors integer n. src 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. src factorial(x) Can be entered as x! src filter(f,a,b,...) Returns f excluding any terms containing a, b, etc. src float(x) Converts rational numbers and integers to floating point values. The symbol pi is also converted. src floor(x) Returns the largest integer not greater than x. src for(i,j,k,a,b,...) For i equals j through k evaluate a, b, etc. src gcd(a,b,...) Returns the greatest common divisor. src hermite(x,n) Returns the nth Hermite polynomial in x. src hilbert(n) Returns an n by n Hilbert matrix. src imag(z) Returns the imaginary part of complex z. src inner(a,b,...) Returns the inner product of tensors. Same as the dot product. src integral(f,x) Returns the integral of f with respect to x. src inv(m) Returns the inverse of matrix m. src isprime(n) Returns 1 if n is a prime number, returns zero otherwise. src laguerre(x,n,a) Returns the nth Laguerre polynomial in x. If "a" is omitted then a=0 is used. src lcm(a,b,...) Returns the least common multiple. src leading(p,x) Returns the leading coefficient of polynomial p in x. src legendre(x,n,m) Returns the nth Legendre polynomial in x. If m is omitted then m=0 is used. src log(x) Returns the natural logarithm of x. src mag(z) Returns the magnitude of complex z. src mod(a,b) Returns the remainder of the result of "a" divided by b. src not(x) Returns the logical negation of x. src 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. src numerator(x) Returns the numerator of expression x. src or(a,b,...) Logical-or of predicate expressions. src outer(a,b,...) Returns the outer product of tensors. Also known as the tensor product. src polar(z) Returns complex z in polar form. src prime(n) Returns the nth prime number. The domain of n is 1 to 10000. src print(a,b,...) Evaluate expressions and print the results. Useful for printing from inside a "for" loop. src product(i,j,k,f) For i equals j through k evaluate f. Returns the product of all f. src quote(x) Returns expression x without evaluating it first. src 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). src rank(a) Returns the number of indices that tensor "a" has. src rationalize(x) Returns x with everything over a common denominator. src real(z) Returns the real part of complex z. src rect(z) Returns complex z in rectangular form. src 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. src simplify(x) Returns x in a simpler form. src sin(x) Returns the sine of x. src sinh(x) Returns the hyperbolic sine of x. src sqrt(x) Returns the square root of x. src stop() In a script, it does what it says. src subst(a,b,c) Substitutes "a" for b in c and returns the result. src sum(i,j,k,f) For i equals j through k evaluate f. Returns the sum of all f. src tan(x) Returns the tangent of x. src tanh(x) Returns the hyperbolic tangent of x. src 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. src 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. src 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. src unit(n) Returns an n by n identity matrix. src zero(i,j,...) Returns a null tensor with dimensions i, j, etc. Useful for creating a tensor and then setting the component values. src