Examples

• ex-OrderingGrading1.C

PseudoConstructors

• MakeTermOrdMat(ConstMatrixView M) -- produce a matrix (with non-neg integer entries and having same number of columns as M) which defines a term ordering refining the partial ordering defined by the input matrix M; error if this cannot be done.

• MakeTermOrdMat(ConstMatrixView M, MachineInt GrDim) -- Same as MakeTermOrdMat(M) except that the first GrDim rows of the output matrix are equal to the first GrDim rows of M.

• LexMat(MachineInt n) returns a ConstMatrix for "lex" ordering
• StdDegLexMat(MachineInt n) returns a ConstMatrix for "DegLex" ordering
• StdDegRevLexMat(MachineInt n) returns a ConstMatrix for "DegRevLex" orderig
• XelMat(MachineInt n) returns a ConstMatrix for "Xel" ordering
• RevLexMat(MachineInt n) returns a ConstMatrix for "RevLex" ordering (not a term order!)

• ElimMat(IndetsToElim, NumIndets) -- returns a matrix defining an elimination ordering for IndetsToElim.

• ElimMat(IndetsToElim, GradingM) -- returns a matrix defining an elimination ordering for IndetsToElim compatible with the grading in GradingM.

• ElimHomogMat(IndetsToElim, GradingM) -- returns a matrix defining an elimination ordering for IndetsToElim with the added knowledge that it will be used with an ideal homogeneous wrt GradingM (non-trivial)

Queries

Let M be a matrix over RingZZ or RingQQ with integer entries.

• IsTermOrdering(M) -- true iff matrix M defines a term ordering

• IsPositiveGrading(M) -- true iff M defines a positive grading (i.e. no null columns and first non-zero entry in each column is positive)