Algebraica package for computations with algebraic numbers DescriptionList of Algebraic Package Commands
<Text-field style="Heading 2" layout="Heading 2" bookmark="info">Description</Text-field> 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.
<Text-field style="Heading 2" layout="Heading 2" bookmark="bkmrk0">List of Algebraic Package Commands</Text-field> 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.