GroebnerSolve(lv, F, R)

groebsol.spad line 1 [edit on github]

• lv : List(Symbol)
• F : GcdDomain
• R : GcdDomain

Solve systems of polynomial equations using Groebner bases Total order Groebner bases are computed and then converted to lex ones This package is mostly intended for internal use.

genericPosition : (List(DistributedMultivariatePolynomial(lv, F)), List(OrderedVariableList(lv))) -> Record(dpolys : List(DistributedMultivariatePolynomial(lv, F)), coords : List(Integer))

genericPosition(lp, lv) puts a radical zero dimensional ideal in general position, for system lp in variables lv.

groebSolve : (List(DistributedMultivariatePolynomial(lv, F)), List(OrderedVariableList(lv))) -> List(List(DistributedMultivariatePolynomial(lv, F)))

groebSolve(lp, lv) reduces the polynomial system lp in variables lv to triangular form. Algorithm based on groebner bases algorithm with linear algebra for change of ordering. Preprocessing for the general solver. The polynomials in input are of type DMP.

testDim : (List(HomogeneousDistributedMultivariatePolynomial(lv, F)), List(OrderedVariableList(lv))) -> Union(List(HomogeneousDistributedMultivariatePolynomial(lv, F)), "failed")

testDim(lp, lv) tests if the polynomial system lp in variables lv is zero dimensional.