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

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(New page: <command> <title>DiffTO</title> <short_description>Returns the matrix corresponding to predefined differential term orderings.</short_description> <syntax> DA.DiffTO(D:STRING):MATRIX </syn...)
 
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<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 D.
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Assume that the current ring is given by Q[x[1..n,0..m]]. Then D can be one of the following values:
 
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{| class="wikitable" style="text-align:left"
 
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|-
 
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! <tt>S</tt> (as <tt>STRING</tt>) !! Corresponding term ordering
 
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|-
 
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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;...
 
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|-
 
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| "DegLex" || S > T iff Deg(S) > Deg(T) or Deg(S) = Deg(T) and S >_Lex T
 
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|-
 
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| "WLex" ||  S > T iff Weight(S) > Weight(T) or Weight(S) = Weight(T) and S >_Lex T
 
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|-
 
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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;...
 
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|-
 
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| "DegOrd" ||  S > T iff Deg(S) > Deg(T) or Deg(S) = Deg(T) and S >_Ord T
 
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|-
 
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| "WOrd" ||  S > T iff Weight(S) > Weight(T) or Weight(S) = Weight(T) and S >_Ord T
 
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|}
 
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<example>
 
<example>
 +
-- Assume that the current ring is given by Q[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 Q[x[1..1,0..20]];
 
Use Q[x[1..1,0..20]], Ord(DiffTO("Lex"));
 
Use Q[x[1..1,0..20]], Ord(DiffTO("Lex"));
 
</example>
 
</example>

Revision as of 09:02, 22 December 2008

DiffTO

Returns the 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.

Example

-- Assume that the current ring is given by Q[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 Q[x[1..1,0..20]];
Use Q[x[1..1,0..20]], Ord(DiffTO("Lex"));

Diffalg.Weight




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