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 Groebner basis.