ApCoCoA-1:BBSGen.TraceSyzLinStep: Difference between revisions
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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] -------------------------------
