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Algebraic

a package for computations with algebraic numbers

 

Description

List of Algebraic Package Commands

Description

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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.

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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.

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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.

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To avoid ambiguities, it is recommended that all RootOfs are indexed.

List of Algebraic Package Commands

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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.

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To display the help page for a particular Algebraic command, see Getting Help with a Command in a Package.

See Also

evala