Difference between revisions of "ApCoCoA-1:DA.DiffTO"
From ApCoCoAWiki
(Corrected example.) |
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<command> | <command> | ||
<title>DA.DiffTO</title> | <title>DA.DiffTO</title> | ||
<short_description>Matrix corresponding to predefined differential term orderings.</short_description> | <short_description>Matrix corresponding to predefined differential term orderings.</short_description> | ||
<syntax> | <syntax> | ||
| − | DA.DiffTO(D:STRING): | + | DA.DiffTO(D:STRING):MAT |
</syntax> | </syntax> | ||
<description> | <description> | ||
| − | This function returns the matrix corresponding to the indicated term ordering D. | + | This function returns the matrix corresponding to the indicated term ordering <tt>D</tt>. |
<itemize> | <itemize> | ||
<item>@param <em>D</em> Name of a predefined differential term ordering.</item> | <item>@param <em>D</em> Name of a predefined differential term ordering.</item> | ||
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-- Assume that the current ring is given by QQ[x[1..n,0..m]]. | -- Assume that the current ring is given by QQ[x[1..n,0..m]]. | ||
-- Then D can be one of the following values: | -- 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 as follows: | ||
Use QQ[x[1..1,0..20]]; | Use QQ[x[1..1,0..20]]; | ||
| − | Use QQ[x[1..1,0..20]], Ord(DiffTO( | + | Use QQ[x[1..1,0..20]], Ord(DA.DiffTO("Lex")); |
</example> | </example> | ||
</description> | </description> | ||
| − | <see>DA.Weight</see> | + | <see>ApCoCoA-1:DA.Weight|DA.Weight</see> |
<key>DiffTO</key> | <key>DiffTO</key> | ||
<key>DA.DiffTO</key> | <key>DA.DiffTO</key> | ||
<key>diffalg.DiffTO</key> | <key>diffalg.DiffTO</key> | ||
<key>differential.DiffTO</key> | <key>differential.DiffTO</key> | ||
| − | <wiki-category>Package_diffalg</wiki-category> | + | <wiki-category>ApCoCoA-1:Package_diffalg</wiki-category> |
</command> | </command> | ||
Latest revision as of 13:29, 29 October 2020
| 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"));
