ApCoCoA-1:BBSGen.TraceSyzLin: Difference between revisions

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{{Version|1}}
<command>
<command>
   <title>BBSGen.TraceSyzLin</title>
   <title>BBSGen.TraceSyzLin</title>
   <short_description>: This function computes the K[c]-linear summand of trace syzygy polynomials.
   <short_description>: This function computes the K[c]-linear summand of trace polynomials.(see <ref>ApCoCoA-1:BBSGen.TraceSyzFull|BBSGen.TraceSyzFull</ref>)</short_description>
              </short_description>
    
    
<syntax>
<syntax>


TraceSyzLin(OO,BO,N);
BBSGen.TraceSyzLin(OO,BO,N);
TraceSyzLin(OO:LIST,BO:LIST,N:INTEGER):LIST
BBSGen.TraceSyzLin(OO:LIST,BO:LIST,N:INTEGER):LIST
</syntax>
</syntax>
   <description>
   <description>


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>
   <item>@param  The order ideal OO, border BO, the number of Indeterminates of the polynomial.
   <item>@param  The order ideal OO, border BO, the number of Indeterminates of the polynomial ring K[x_1,...,x_N].
</item>
</item>
   <item>@return  List of Tau^kl_i s, which have constant coefficients in the trace syzygy polynomial.
   <item>@return  List of polynomials from K[t[1..N,1..N,1..Mu,1..Mu]] that is a sub-ring of  XX=K[c[1..Mu,1..Nu],t[1..N,1..N,1..Mu,1..Mu]].


  </item>
  </item>
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Use R::=QQ[x[1..2]];
Use R::=QQ[x[1..2]];


OO:=BB.Box([1,1]);
OO:=$apcocoa/borderbasis.Box([1,1]);
BO:=BB.Border(OO);
BO:=$apcocoa/borderbasis.Border(OO);
Mu:=Len(OO);
Mu:=Len(OO);
Nu:=Len(BO);
Nu:=Len(BO);
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   </description>
   </description>
   <types>
   <types>
     <type>borderbasis</type>
     <type>bbsmingensys</type>
     <type>ideal</type>
     <type>list</type>
     <type>apcocoaserver</type>
     <type>apcocoaserver</type>
   </types>
   </types>
<see>BB.Border</see>
  <see>BB.Box</see>
<see>BBSGen.Wmat</see>
<see>BBSGen.TraceSyzStep</see>
<see>BBSGen.TraceSyzFull</see>


   <key>Wmat</key>
<see>ApCoCoA-1:BBSGen.Wmat|BBSGen.Wmat</see>
   <key>BBSGen.Wmat</key>
<see>ApCoCoA-1:BBSGen.TraceSyzStep|BBSGen.TraceSyzStep</see>
   <key>bbsmingensys.Wmat</key>
<see>ApCoCoA-1:BBSGen.TraceSyzFull|BBSGen.TraceSyzFull</see>
   <wiki-category>Package_bbsmingensys</wiki-category>
 
   <key>TraceSyzLin</key>
   <key>BBSGen.TraceSyzLin</key>
   <key>bbsmingensys.TraceSyzLin</key>
   <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.TraceSyzLin

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

Syntax

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

Description




  • @param The order ideal OO, border BO, the number of Indeterminates of the polynomial ring K[x_1,...,x_N].

  • @return List of polynomials from K[t[1..N,1..N,1..Mu,1..Mu]] that is a sub-ring of XX=K[c[1..Mu,1..Nu],t[1..N,1..N,1..Mu,1..Mu]].



Example

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

OO:=$apcocoa/borderbasis.Box([1,1]);
BO:=$apcocoa/borderbasis.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