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

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(New page: <command> <title>BBSGen.PurPow</title> <short_description> </short_description> <syntax> BBSGen.PurPow(OO); BBSGen.PurPow(OO:LIST):LIST </syntax> <description> If b_j=x_i^d_i w...)
 
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{{Version|1}}
 
<command>
 
<command>
 
   <title>BBSGen.PurPow</title>
 
   <title>BBSGen.PurPow</title>
   <short_description> </short_description>
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   <short_description>This function finds the pure power indeterminates in the ring K[c]. </short_description>
 
    
 
    
 
<syntax>
 
<syntax>
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   <description>  
 
   <description>  
  
If  b_j=x_i^d_i where x_i is an indeterminate of the base ring K[x_1,...,x_n] and d_i is some power, then c_ij is called a pure power indeterminate.
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If  b_j=x_i^d_i where x_i is an indeterminate of the base ring K[x_1,...,x_N] and d_i is some power, then c_ij is called a pure power indeterminate.
  
 
This function computes the indices [i,j] of the pure power indterminates c_ij in the coordinate ring of the border basis scheme.
 
This function computes the indices [i,j] of the pure power indterminates c_ij in the coordinate ring of the border basis scheme.
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Use R::=QQ[x,y];
 
Use R::=QQ[x,y];
 
OO:=[1,x,y,xy];
 
OO:=[1,x,y,xy];
BO:=BB.Border(OO);
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BO:=$apcocoa/borderbasis.Border(OO);
 
Mu:=Len(OO);
 
Mu:=Len(OO);
 
Nu:=Len(BO);
 
Nu:=Len(BO);
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[1, 3], [2, 3], [3, 3], [4, 3]]
 
[1, 3], [2, 3], [3, 3], [4, 3]]
  
List:=BBSGen.PurPow(OO);
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Class:=BBSGen.PurPow(OO);
  
 
Use BBS::=CoeffRing[c[1..Mu,1..Nu]];  
 
Use BBS::=CoeffRing[c[1..Mu,1..Nu]];  
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<see> BBSGen.InFinder</see>
 
  
<see> BBSGen.LinIdepGen</see>
 
  
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<see>ApCoCoA-1: BBSGen.LinIdepGen| BBSGen.LinIdepGen</see>
   <key>bbsmingensys.Wmat</key>
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   <wiki-category>Package_bbsmingensys</wiki-category>
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  <key>BBSGen.PurPow</key>
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  <key>PurPow</key>
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   <key>bbsmingensys.PurPow</key>
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   <wiki-category>ApCoCoA-1:Package_bbsmingensys</wiki-category>
 
</command>
 
</command>

Latest revision as of 09:51, 7 October 2020

This article is about a function from ApCoCoA-1.

BBSGen.PurPow

This function finds the pure power indeterminates in the ring K[c].

Syntax

BBSGen.PurPow(OO);
BBSGen.PurPow(OO:LIST):LIST

Description


If b_j=x_i^d_i where x_i is an indeterminate of the base ring K[x_1,...,x_N] and d_i is some power, then c_ij is called a pure power indeterminate.

This function computes the indices [i,j] of the pure power indterminates c_ij in the coordinate ring of the border basis scheme.

  • @param The order ideal OO.

  • @return List of the indices [i,j] of the pure powers c_ij.


Example

Use R::=QQ[x,y];
OO:=[1,x,y,xy];
BO:=$apcocoa/borderbasis.Border(OO);
Mu:=Len(OO);
Nu:=Len(BO);

BBSGen.PurPow(OO);
[[1, 2], [2, 2], [3, 2], [4, 2], 
[1, 3], [2, 3], [3, 3], [4, 3]]

Class:=BBSGen.PurPow(OO);

Use BBS::=CoeffRing[c[1..Mu,1..Nu]]; 

BBSGen.IndFinder(Class,Mu,Nu);
[c[1,2],  c[1,3],  c[2,2], c[2,3], 
c[3,2], c[3,3], c[4,2],  c[4,3]]





BBSGen.LinIdepGen