Difference between revisions of "ApCoCoA-1:BBSGen.TraceSyzLinStep"
From ApCoCoAWiki
(New page: <command> <title>BBSGen.TraceSyzStep</title> <short_description>: This function only computes the K[c_ij-]linear summand of trace syzygy polynomial for the degree of the given monomi...) |
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<command> | <command> | ||
<title>BBSGen.TraceSyzStep</title> | <title>BBSGen.TraceSyzStep</title> | ||
| − | <short_description>: This function | + | <short_description>: 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 <ref>BBSGen.TraceSyzFull</ref>) |
</short_description> | </short_description> | ||
<syntax> | <syntax> | ||
| − | TraceSyzLin(OO,BO,N); | + | BBSGen.TraceSyzLin(Pi,X,OO,BO,N); |
| − | TraceSyzLin(OO:LIST,BO:LIST,N:INTEGER): | + | BBSGen.TraceSyzLin(Pi:POLY,X:POLY,OO:LIST,BO:LIST,N:INTEGER):LIST |
</syntax> | </syntax> | ||
<description> | <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. | ||
| + | |||
<itemize> | <itemize> | ||
| − | <item>@param The | + | <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> | </item> | ||
| − | <item>@return K[ | + | <item>@return K[c]-linear summand of the trace polynomial with respect to Pi and the variable X.</item> |
</itemize> | </itemize> | ||
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Nu:=Len(BO); | Nu:=Len(BO); | ||
| − | + | Pi:=x[1]^2x[2]; | |
| − | X:=x[1]; ------------Choice of the | + | X:=x[1]; ------------Choice of the Variable |
Use XX::=QQ[c[1..Mu,1..Nu],t[1..N,1..N,1..Mu,1..Mu]]; | Use XX::=QQ[c[1..Mu,1..Nu],t[1..N,1..N,1..Mu,1..Mu]]; | ||
| − | BBSGen.TraceSyzLinStep( | + | BBSGen.TraceSyzLinStep(Pi,X,OO,BO,N); |
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<type>apcocoaserver</type> | <type>apcocoaserver</type> | ||
</types> | </types> | ||
| − | + | ||
| − | |||
<see>BBSGen.Wmat</see> | <see>BBSGen.Wmat</see> | ||
<see>BBSGen.TraceSyzLin</see> | <see>BBSGen.TraceSyzLin</see> | ||
Revision as of 19:46, 8 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. (see
and
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); 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] -------------------------------
