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

From ApCoCoAWiki
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<itemize>
 
<itemize>
   <item>@param  The term Pi from K[x_1,...,x_N], the distinguished variable of choice from {x_1,...,x_N},  order ideal OO, border BO, the number of indeterminates of the polynomial ring K[x_1,...,x_N].(see <see>BB.Border</see> and  <see>BB.Box</see> from package borderbasis)
+
   <item>@param  The term Pi from K[x_1,...,x_N], the distinguished variable of choice from {x_1,...,x_N},  order ideal OO, border BO, the number of indeterminates of the polynomial ring K[x_1,...,x_N].
 
</item>
 
</item>
 
   <item>@return  Trace polynomial T_{Pi,X} with respect to a term Pi and a variable X.</item>
 
   <item>@return  Trace polynomial T_{Pi,X} with respect to a term Pi and a variable X.</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);

Revision as of 23:29, 14 June 2012

BBSGen.TraceSyzStep

This function computes the trace polynomial T_{Pi,X} with respect to a given term Pi and a variable from ring K[x_1,...,x_N].(see BBSGen.TraceSyzFull)

Syntax

BBSGen.TraceSyzStep(Pi,X,OO,BO,N);
BBSGen.TraceSyzStep(Pi:POLY,X:POLY,OO:LIST,BO:LIST,N:INTEGER):LIST

Description

 Note the following:
 The chosen variable must be a divisor of the term Pi other wise the result is 0.
 Pi must be a product of at least two different indeterminates. 
 
  • @param The term Pi from K[x_1,...,x_N], the distinguished variable of choice from {x_1,...,x_N}, order ideal OO, border BO, the number of indeterminates of the polynomial ring K[x_1,...,x_N].

  • @return Trace polynomial T_{Pi,X} with respect to a term Pi and a variable X.


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());
Pi:=x[1]^2x[2];

X:=x[1];   ------------Choice of the Indeterminate

Use XX::=QQ[c[1..Mu,1..Nu],t[1..N,1..N,1..Mu,1..Mu]]; 
 
 BBSGen.TraceSyzStep(Pi,X,OO,BO,N);
  
c[1,2]t[1,2,3,1] + c[2,2]t[1,2,3,2] + 
c[3,2]t[1,2,3,3] + c[4,2]t[1,2,3,4] + 
c[1,4]t[1,2,4,1] + c[2,4]t[1,2,4,2] +
 c[3,4]t[1,2,4,3] + c[4,4]t[1,2,4,4] +
 t[1,2,1,3] + t[1,2,2,4]

-------------------------------


BBSGen.Wmat

BBSGen.TraceSyzLin

BBSGen.TraceSyzLinStep

BBSGen.TraceSyzFull