DifferenceRoot[lde] represents a function that solves the linear difference equation specified by lde[a, n].

DifferentialRoot[lde] represents a function that solves the linear differential equation specified by lde[y, x].

Discriminant[poly, var] computes the discriminant of the polynomial poly with respect to the variable var.Discriminant[poly, var, Modulus -> p] computes the discriminant ...

Polynomial algorithms are at the core of classical "computer algebra". Incorporating methods that span from antiquity to the latest cutting-edge research at Wolfram Research, ...

Built into Mathematica is the world's largest collection of both numerical and symbolic equation solving capabilities—with many original algorithms, all automatically ...

CharacteristicPolynomial[m, x] gives the characteristic polynomial for the matrix m. CharacteristicPolynomial[{m, a}, x] gives the generalized characteristic polynomial with ...

Some integer functions. The remainder on dividing 17 by 3. The integer part of 17/3.

DifferenceRootReduce[expr, n] attempts to reduce expr to a single DifferenceRoot object as a function of n.

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

Packing a large number of sophisticated algorithms—many recent and original—into a powerful collection of functions, Mathematica draws on almost every major result in number ...