subst
Replaces a variable with an expression, everywhere it occurs free.
expr(symbolic) -- e.g. x^2 + xvar(string) -- the variable to replacereplacement(symbolic) -- e.g. a + 1
Polynomials
freeVars
The free variables of an expression, sorted.
expr(symbolic) -- e.g. a*x + b*y
polyDivide
Polynomial long division: the quotient and remainder.
dividend(symbolic) -- e.g. x^3 - 1divisor(symbolic) -- e.g. x - 1
polyGcd
The monic greatest common divisor of two polynomials.
a(symbolic) -- a polynomialb(symbolic) -- a polynomial
resultant
The resultant of two polynomials: zero exactly when they share a root.
a(symbolic) -- a polynomialb(symbolic) -- a polynomial
polyDegree
The degree of a polynomial.
poly(symbolic) -- e.g. 3*x^4 + x
polyCoeff
The coefficient of x^k in a polynomial.
poly(symbolic) -- e.g. 3*x^4 + 5*xk(number) -- the power
symSum
The exact sum of an expression over an integer range of an index (at most 10,000 terms).
body(symbolic) -- e.g. k^2index(string) -- e.g. kfrom(number) -- first indexto(number) -- last index
symProduct
The exact product of an expression over an integer range of an index.
body(symbolic) -- e.g. kindex(string) -- e.g. kfrom(number) -- first indexto(number) -- last index
geometricSum
The sum of an infinite geometric series a + a*r + a*r^2 + ..., only when |r| < 1.
first(symbolic) -- the first term aratio(number) -- the common ratio r
exactSin
The exact value of sin at a whole number of degrees, when one exists; none otherwise.
degrees(number) -- e.g. 30
exactCos
The exact value of cos at a whole number of degrees, when one exists; none otherwise.
degrees(number) -- e.g. 45
exactTan
The exact value of tan at a whole number of degrees; none where it is undefined or not exact.
degrees(number) -- e.g. 60
polyDerivative
The derivative of a polynomial in one variable.
poly(symbolic) --