Mathematica includes functions for performing a variety of specific algebraic transformations. Some are algorithmically straightforward; others include highly sophisticated ...

Although Diophantine equations provide classic examples of undecidability, Mathematica in practice succeeds in solving a remarkably wide range of such equations—automatically ...

Decompose[poly, x] decomposes a polynomial, if possible, into a composition of simpler polynomials.

To get a square root sign, press the Control key and the 2 key at the same time. Press Ctrl+2 or Ctrl+@. Type inside the placeholder (which is already selected).

JacobiP[n, a, b, x] gives the Jacobi polynomial P_n^(a, b)(x).

 

FactorSquareFreeList[poly] gives a list of square-free factors of a polynomial, together with their exponents.

FromCoefficientRules[list, {x_1, x_2, ...}] constructs a polynomial from a list of rules for exponent vectors and coefficients.

Exponent[expr, form] gives the maximum power with which form appears in the expanded form of expr. Exponent[expr, form, h] applies h to the set of exponents with which form ...

FactorTermsList[poly] gives a list in which the first element is the overall numerical factor in poly, and the second element is the polynomial with the overall factor ...