# LinGroebnerPackage(lv, F)ΒΆ

Given a Groebner basis `B` with respect to the total degree ordering for a zero-dimensional ideal `I`, compute a Groebner basis with respect to the lexicographical ordering by using linear algebra. This is an internal package, operations in this package may crash the system on invalid input.

anticoord: (List F, DistributedMultivariatePolynomial(lv, F), List DistributedMultivariatePolynomial(lv, F)) -> DistributedMultivariatePolynomial(lv, F)

``anticoord ``undocumented

choosemon: (DistributedMultivariatePolynomial(lv, F), List DistributedMultivariatePolynomial(lv, F)) -> DistributedMultivariatePolynomial(lv, F)

``choosemon ``undocumented

computeBasis: List HomogeneousDistributedMultivariatePolynomial(lv, F) -> List HomogeneousDistributedMultivariatePolynomial(lv, F)

computeBasis is a helper function which computes a basis of a linear space which contains a lexicographic Groebner basis. It expects a basis (ordered by total degree, reverse lexicographic) of a zero dimensional ideal.

coord: (HomogeneousDistributedMultivariatePolynomial(lv, F), List HomogeneousDistributedMultivariatePolynomial(lv, F)) -> Vector F

``coord ``undocumented

groebgen: List DistributedMultivariatePolynomial(lv, F) -> Record(glbase: List DistributedMultivariatePolynomial(lv, F), glval: List Integer)

``groebgen ``undocumented

intcompBasis: (OrderedVariableList lv, List HomogeneousDistributedMultivariatePolynomial(lv, F), List HomogeneousDistributedMultivariatePolynomial(lv, F)) -> List HomogeneousDistributedMultivariatePolynomial(lv, F)

``intcompBasis ``undocumented

linGenPos: List HomogeneousDistributedMultivariatePolynomial(lv, F) -> Record(gblist: List DistributedMultivariatePolynomial(lv, F), gvlist: List Integer)

``linGenPos ``undocumented

minPol: (List HomogeneousDistributedMultivariatePolynomial(lv, F), List HomogeneousDistributedMultivariatePolynomial(lv, F), OrderedVariableList lv) -> HomogeneousDistributedMultivariatePolynomial(lv, F)

``minPol ``undocumented

minPol: (List HomogeneousDistributedMultivariatePolynomial(lv, F), OrderedVariableList lv) -> HomogeneousDistributedMultivariatePolynomial(lv, F)

``minPol ``undocumented

totolex: List HomogeneousDistributedMultivariatePolynomial(lv, F) -> List DistributedMultivariatePolynomial(lv, F)

``totolex ``undocumented

transform: DistributedMultivariatePolynomial(lv, F) -> HomogeneousDistributedMultivariatePolynomial(lv, F)

``transform ``undocumented