Difference between revisions of "ApCoCoA-1:DA.DiffTO"

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(Corrected example.)
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{{Version|1}}
 
<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):MATRIX
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DA.DiffTO(D:STRING):MAT
 
</syntax>
 
</syntax>
 
<description>
 
<description>
This function returns the matrix corresponding to the indicated term ordering D.
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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:
-- <quotes>Lex</quotes>:    Lexicographic ordering with 1&lt;x[1,0]&lt;x[1,1]&lt;x[1,2]&lt;...&lt;x[2,0]&lt;x[2,1]&lt;...  
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-- "Lex":    Lexicographic ordering with 1&lt;x[1,0]&lt;x[1,1]&lt;x[1,2]&lt;...&lt;x[2,0]&lt;x[2,1]&lt;...  
-- <quotes>DegLex</quotes>:  S > T iff Deg(S) > Deg(T) or Deg(S) = Deg(T) and S >_Lex T
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-- "DegLex":  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
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-- "WLex":    S > T iff Weight(S) > Weight(T) or Weight(S) = Weight(T) and S >_Lex T
-- <quotes>Ord</quotes>:    Lexicographic ordering with 1&lt;x[1,0]&lt;x[2,0]&lt;...&lt;x[1,1]&lt;x[2,1]&lt;...
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-- "Ord":    Lexicographic ordering with 1&lt;x[1,0]&lt;x[2,0]&lt;...&lt;x[1,1]&lt;x[2,1]&lt;...
-- <quotes>DegOrd</quotes>:  S > T iff Deg(S) > Deg(T) or Deg(S) = Deg(T) and S >_Ord T
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-- "DegOrd":  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
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-- "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(<quotes>Lex</quotes>));
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Use QQ[x[1..1,0..20]], Ord(DA.DiffTO("Lex"));
 
</example>
 
</example>
 
</description>
 
</description>
  
<see>DA.Weight</see>
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<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>
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<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&lt;x[1,0]&lt;x[1,1]&lt;x[1,2]&lt;...&lt;x[2,0]&lt;x[2,1]&lt;... 
-- "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&lt;x[1,0]&lt;x[2,0]&lt;...&lt;x[1,1]&lt;x[2,1]&lt;...
-- "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