Difference between revisions of "ApCoCoA-1:BBSGen.NonStand"

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m (insert version info)
 
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{{Version|1}}
 
<command>
 
<command>
   <title>BBSGen.Wmat</title>
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   <title>BBSGen.NonStand</title>
 
   <short_description>This function computes the non-standard indeterminates from K[c] with respect to the arrow grading. </short_description>
 
   <short_description>This function computes the non-standard indeterminates from K[c] with respect to the arrow grading. </short_description>
 
    
 
    
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</syntax>
 
</syntax>
 
   <description>
 
   <description>
Let W be the weight matrix with respect to the arrow grading.(see <ref>BBSGen.Wmat</ref>)  
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Let W be the weight matrix with respect to the arrow grading(see <ref>ApCoCoA-1:BBSGen.Wmat|BBSGen.Wmat</ref>).
An indeterminate c_ij\in K[c] is called standard, if deg_W(c_ij)=log(b_j)-log(t_i) has exactly one  strictly positive component. If c_ij is not standard then it is called non-standard. This function computes such non-standard indeterminates from ring K[c].
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An indeterminate c_ij in K[c] is called standard, if deg_W(c_ij)=log(b_j)-log(t_i) has exactly one  strictly positive component. If c_ij is not standard then it is called non-standard. This function computes such non-standard indeterminates from ring K[c].
  
 
<itemize>
 
<itemize>
   <item>@param The order ideal OO, the border BO the number of Indeterminates of the Polynomial Ring and the Weight Matrix. (see <commandref>BB.Border</commandref> from the package borderbasis)</item>
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   <item>@param The order ideal OO, the border BO the number of indeterminates of the polynomial ring K[x_1,...,x_N] and the weight matrix(<ref>ApCoCoA-1:BBSGen.Wmat|BBSGen.Wmat</ref>). </item>
 
   <item>@return List of Indeterminates and their degree with respect to  the arrow grading.  </item>
 
   <item>@return List of Indeterminates and their degree with respect to  the arrow grading.  </item>
 
</itemize>
 
</itemize>
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Use R::=QQ[x[1..2]];
 
Use R::=QQ[x[1..2]];
  
OO:=BB.Box([1,1]);
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OO:=$apcocoa/borderbasis.Box([1,1]);
BO:=BB.Border(OO);   
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BO:=$apcocoa/borderbasis.Border(OO);   
 
N:=Len(Indets());
 
N:=Len(Indets());
 
W:=BBSGen.Wmat(OO,BO,N);
 
W:=BBSGen.Wmat(OO,BO,N);
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   </types>
 
   </types>
  
<see> BBSGen.Wmat</see>
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<see>ApCoCoA-1: BBSGen.Wmat| BBSGen.Wmat</see>
   <key>Wmat</key>
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   <key>NonStand</key>
   <key>BBSGen.Wmat</key>
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   <key>BBSGen.NonStand</key>
   <key>bbsmingensys.Wmat</key>
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   <key>bbsmingensys.NonStand</key>
   <wiki-category>Package_bbsmingensys</wiki-category>
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   <wiki-category>ApCoCoA-1:Package_bbsmingensys</wiki-category>
 
</command>
 
</command>

Latest revision as of 09:50, 7 October 2020

This article is about a function from ApCoCoA-1.

BBSGen.NonStand

This function computes the non-standard indeterminates from K[c] with respect to the arrow grading.

Syntax

BBSGen.NonStand(OO,BO,N,W);
BBSGen.NonStand(OO:LIST,BO:LIST,N:INTEGER,W:MATRIX):LIST

Description

Let W be the weight matrix with respect to the arrow grading(see BBSGen.Wmat).

An indeterminate c_ij in K[c] is called standard, if deg_W(c_ij)=log(b_j)-log(t_i) has exactly one strictly positive component. If c_ij is not standard then it is called non-standard. This function computes such non-standard indeterminates from ring K[c].

  • @param The order ideal OO, the border BO the number of indeterminates of the polynomial ring K[x_1,...,x_N] and the weight matrix(BBSGen.Wmat).

  • @return List of Indeterminates and their degree with respect to the arrow grading.


Example

Use R::=QQ[x[1..2]];

OO:=$apcocoa/borderbasis.Box([1,1]);
BO:=$apcocoa/borderbasis.Border(OO);   
N:=Len(Indets());
W:=BBSGen.Wmat(OO,BO,N);

XX::=QQ[c[1..Mu,1..Nu],t[1..N,1..N,1..Mu,1..Mu]]; 
Use XX;


BBSGen.NonStand(OO,BO,N,W);

[[c[1,3], [R :: 1, R :: 2]], 
[c[1,4], [R :: 2, R :: 1]],
[c[2,3], [R :: 1, R :: 1]], 
[c[3,4], [R :: 1, R :: 1]]]
  




BBSGen.Wmat