FunctionSpacePrimitiveElement(R, F)

primelt.spad line 101 [edit on github]

• R: Join(IntegralDomain, Comparable, CharacteristicZero)

• F: FunctionSpace R

FunctionsSpacePrimitiveElement provides functions to compute primitive elements in functions spaces.

primitiveElement: (F, F) -> Record(primelt: F, pol1: SparseUnivariatePolynomial F, pol2: SparseUnivariatePolynomial F, prim: SparseUnivariatePolynomial F) if F has AlgebraicallyClosedField

primitiveElement(a1, a2) returns [a, q1, q2, q] such that k(a1, a2) = k(a), ai = qi(a), and q(a) = 0. The minimal polynomial for a2 may involve a1, but the minimal polynomial for a1 may not involve a2; This operations uses resultant.

primitiveElement: List F -> Record(primelt: F, poly: List SparseUnivariatePolynomial F, prim: SparseUnivariatePolynomial F)

primitiveElement([a1, ..., an]) returns [a, [q1, ..., qn], q] such that then k(a1, ..., an) = k(a), ai = qi(a), and q(a) = 0. This operation uses the technique of spadglossSee{groebner bases}{Groebner basis}.