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a package for computations with algebraic numbers



List of Algebraic Package Commands



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.

See Also