Difference between revisions of "ApCoCoA-1:BBSGen.TraceSyzStep"
From ApCoCoAWiki
Line 16: | Line 16: | ||
<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]. | + | <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> | ||
Line 25: | Line 25: | ||
Use R::=QQ[x[1..2]]; | Use R::=QQ[x[1..2]]; | ||
− | OO:= | + | OO:=$apcocoa/borderbasis.Box([1,1]); |
− | BO:= | + | BO:=$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] -------------------------------