Overview - Maple Help

Algebraic

a package for computations with algebraic numbers

Description

 • The Algebraic package is a package for computing with polynomials and rational functions whose coefficients are algebraic numbers, in arbitrary characteristic. The main functionality is computing normal forms and greatest common divisors.
 • Algebraic numbers and functions can be represented by radicals or by RootOfs, or a mixture of them. Nested radicals or RootOfs are supported as well.
 • Non-algebraic expressions, such as, e.g., powers with non-rational exponents or special functions, are not directly supported by the routines in this package. Such subexpressions will be frozen and, where appropriate, their arguments handled recursively and independently.
 • To avoid ambiguities, it is recommended that all RootOfs are indexed.

List of Algebraic Package Commands

 • The following is a list of available commands.
 Content - extract the greatest common divisor of the coefficients of a polynomial
 ConvertRootOf - convert algebraic objects to RootOf representation
 Degree - compute the formal algebraic degree of a tower of extensions
 Divide - test for divisibility of multivariate polynomials
 Expand - expand products and powers into a sum
 ExtendedEuclideanAlgorithm - perform the extended Euclidean algorithm on a pair of polynomials
 GetAlgebraics - extract all algebraic objects from a given object
 GreatestCommonDivisor - compute the greatest common divisor and cofactors of two polynomials
 MakeMonic - rewrite a RootOf as an equivalent monic RootOf
 Normal - determine the normal form of a rational function with algebraic coefficients
 PrimitivePart - remove all common factors from the coefficients of a polynomial
 PseudoDivision - perform fraction-free division on a pair of polynomials
 Quotient - compute the quotient when Euclidean division is performed on two polynomials
 Reduce - reduce powers of RootOfs modulo their defining polynomials
 Remainder - compute the remainder when Euclidean division is performed on two polynomials
 Resultant - determine the resultant of two polynomials with respect to a variable
 Squarefree - factor a polynomial into a product of powers of square-free polynomials.
 • To display the help page for a particular Algebraic command, see Getting Help with a Command in a Package.