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

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<itemize>
 
<itemize>
   <item>@param  The term Pi, the distinguished variable of choice that divides Pi,  order ideal OO, border BO, the number of Indeterminates of the Polynomial. (see <see>BB.Border</see> and  <see>BB.Box</see> from package borderbasis)
+
   <item>@param  The term Pi, the distinguished variable of choice that divides Pi,  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>
 
</item>
 
   <item>@return  K[c]-linear summand of the  trace  polynomial with respect to Pi and the variable  X.</item>
 
   <item>@return  K[c]-linear summand of the  trace  polynomial with respect to Pi and the variable  X.</item>
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Mu:=Len(OO);
 
Mu:=Len(OO);
 
Nu:=Len(BO);
 
Nu:=Len(BO);
 
+
N:=Len(Indets());
 
Pi:=x[1]^2x[2];
 
Pi:=x[1]^2x[2];
  

Revision as of 22:18, 14 June 2012

BBSGen.TraceSyzStep

This function computes the K[c]-linear summand of 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.TraceSyzLin(Pi,X,OO,BO,N);
BBSGen.TraceSyzLin(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, the distinguished variable of choice that divides Pi, order ideal OO, border BO, the number of Indeterminates of the polynomial ring K[x_1,...,x_N]. (see

    BB.Border

    and

    BB.Box

    from package borderbasis)

  • @return K[c]-linear summand of the trace polynomial with respect to Pi and the variable X.


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

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

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

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


BBSGen.Wmat

BBSGen.TraceSyzLin

BBSGen.TraceSyzStep

BBSGen.TraceSyzFull