ApCoCoA-1:DA.DiffTO

From ApCoCoAWiki
This article is about a function from ApCoCoA-1.

DA.DiffTO

Matrix corresponding to predefined differential term orderings.

Syntax

DA.DiffTO(D:STRING):MAT

Description

This function returns the matrix corresponding to the indicated term ordering D.

  • @param D Name of a predefined differential term ordering.

  • @return The matrix corresponding to the predefined term ordering.

Example

-- Assume that the current ring is given by QQ[x[1..n,0..m]]. 
-- Then D can be one of the following values:
-- "Lex":     Lexicographic ordering with 1<x[1,0]<x[1,1]<x[1,2]<...<x[2,0]<x[2,1]<... 
-- "DegLex":  S > T iff Deg(S) > Deg(T) or Deg(S) = Deg(T) and S >_Lex T
-- "WLex":    S > T iff Weight(S) > Weight(T) or Weight(S) = Weight(T) and S >_Lex T
-- "Ord":     Lexicographic ordering with 1<x[1,0]<x[2,0]<...<x[1,1]<x[2,1]<...
-- "DegOrd":  S > T iff Deg(S) > Deg(T) or Deg(S) = Deg(T) and S >_Ord T
-- "WOrd":    S > T iff Weight(S) > Weight(T) or Weight(S) = Weight(T) and S >_Ord T
--
-- Use as follows:
Use QQ[x[1..1,0..20]];
Use QQ[x[1..1,0..20]], Ord(DA.DiffTO("Lex"));

DA.Weight