Difference between revisions of "ApCoCoA-1:DA.DiffTO"
From ApCoCoAWiki
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-- Assume that the current ring is given by Q[x[1..n,0..m]]. | -- Assume that the current ring is given by Q[x[1..n,0..m]]. | ||
-- Then D can be one of the following values: | -- Then D can be one of the following values: | ||
| − | -- | + | -- <quotes>Lex</quotes>: Lexicographic ordering with 1<x[1,0]<x[1,1]<x[1,2]<...<x[2,0]<x[2,1]<... |
| − | -- | + | -- <quotes>DegLex</quotes>: S > T iff Deg(S) > Deg(T) or Deg(S) = Deg(T) and S >_Lex T |
| − | -- | + | -- <quotes>WLex</quotes>: S > T iff Weight(S) > Weight(T) or Weight(S) = Weight(T) and S >_Lex T |
| − | -- | + | -- <quotes>Ord</quotes>: Lexicographic ordering with 1<x[1,0]<x[2,0]<...<x[1,1]<x[2,1]<... |
| − | -- | + | -- <quotes>DegOrd</quotes>: S > T iff Deg(S) > Deg(T) or Deg(S) = Deg(T) and S >_Ord T |
| − | -- | + | -- <quotes>WOrd</quotes>: S > T iff Weight(S) > Weight(T) or Weight(S) = Weight(T) and S >_Ord T |
-- | -- | ||
-- Use as follows: | -- Use as follows: | ||
Use Q[x[1..1,0..20]]; | Use Q[x[1..1,0..20]]; | ||
| − | Use Q[x[1..1,0..20]], Ord(DiffTO( | + | Use Q[x[1..1,0..20]], Ord(DiffTO(<quotes>Lex</quotes>)); |
</example> | </example> | ||
</description> | </description> | ||
Revision as of 13:14, 27 April 2009
DA.DiffTO
Matrix corresponding to predefined differential term orderings.
Syntax
DA.DiffTO(D:STRING):MATRIX
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 Q[x[1..n,0..m]]. -- Then D can be one of the following values: -- <quotes>Lex</quotes>: Lexicographic ordering with 1<x[1,0]<x[1,1]<x[1,2]<...<x[2,0]<x[2,1]<... -- <quotes>DegLex</quotes>: S > T iff Deg(S) > Deg(T) or Deg(S) = Deg(T) and S >_Lex T -- <quotes>WLex</quotes>: S > T iff Weight(S) > Weight(T) or Weight(S) = Weight(T) and S >_Lex T -- <quotes>Ord</quotes>: Lexicographic ordering with 1<x[1,0]<x[2,0]<...<x[1,1]<x[2,1]<... -- <quotes>DegOrd</quotes>: S > T iff Deg(S) > Deg(T) or Deg(S) = Deg(T) and S >_Ord T -- <quotes>WOrd</quotes>: S > T iff Weight(S) > Weight(T) or Weight(S) = Weight(T) and S >_Ord T -- -- Use as follows: Use Q[x[1..1,0..20]]; Use Q[x[1..1,0..20]], Ord(DiffTO(<quotes>Lex</quotes>));
