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

From ApCoCoAWiki
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<command>
 
<command>
 
   <title>BBSGen.TraceSyzLin</title>
 
   <title>BBSGen.TraceSyzLin</title>
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   <short_description>: This function computes the K[c]-linear summand of trace syzygy polynomials.
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   <short_description>: This function computes the K[c]-linear summand of trace polynomials.(see <ref>BBSGen.TraceSyzFull</ref>)
 
               </short_description>
 
               </short_description>
 
    
 
    
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   <description>
 
   <description>
  
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−
Description: Let  Tau^kl_ij :=t[k,l,i,j] be the (i,j) ^th entry of matrix the operation  [A_k,A_l].  The result of the Trace Syzygy computation is K[c]-linear combination of  Tau^kl_ij    that is equal to 0. This function only computes the  summands of trace syzygy, which has constant and non-zero coefficient.
 
  
  
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<itemize>
 
<itemize>
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   <item>@param  The order ideal OO, border BO, the number of Indeterminates of the polynomial.
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   <item>@param  The order ideal OO, border BO, the number of Indeterminates of the polynomial.(see <commandref>BB.Border</commandref>
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  <commandref>BB.Box</commandref> from package borderbasis)
 
</item>
 
</item>
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   <item>@return  List of Tau^kl_i s, which have constant coefficients in the trace syzygy polynomial.
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   <item>@return  List of polynomials from K[t[1..N,1..N,1..Mu,1..Mu]] \subset XX.
  
 
  </item>
 
  </item>
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     <type>apcocoaserver</type>
 
     <type>apcocoaserver</type>
 
   </types>
 
   </types>
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<see>BB.Border</see>
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−
  <see>BB.Box</see>
 
 
  <see>BBSGen.Wmat</see>
 
  <see>BBSGen.Wmat</see>
 
<see>BBSGen.TraceSyzStep</see>
 
<see>BBSGen.TraceSyzStep</see>

Revision as of 18:24, 8 June 2012

BBSGen.TraceSyzLin

This function computes the K[c]-linear summand of trace polynomials.(see BBSGen.TraceSyzFull)

Syntax

TraceSyzLin(OO,BO,N);
TraceSyzLin(OO:LIST,BO:LIST,N:INTEGER):LIST

Description




  • @param The order ideal OO, border BO, the number of Indeterminates of the polynomial.(see <commandref>BB.Border</commandref> 

     <commandref>BB.Box</commandref> from package borderbasis)

  • @return List of polynomials from K[t[1..N,1..N,1..Mu,1..Mu]] \subset XX.



Example

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

OO:=BB.Box([1,1]);
BO:=BB.Border(OO);
Mu:=Len(OO);
Nu:=Len(BO);
N:=Len(Indets());
 W:=BBSGen.Wmat(OO,BO,N);

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

BBSGen.TraceSyzLin(OO,BO,N); 

[
  t[1,2,1,3] + t[1,2,2,4],
  2t[1,2,1,2] + 2t[1,2,3,4],
  t[1,2,1,3] + t[1,2,2,4],
  2t[1,2,1,4]]
-------------------------------


BBSGen.Wmat

BBSGen.TraceSyzStep

BBSGen.TraceSyzFull




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