Difference between revisions of "ApCoCoA-1:BBSGen.TraceSyzLinStep"
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| + | {{Version|1}} | ||
<command> | <command> | ||
| − | <title>BBSGen. | + | <title>BBSGen.TraceSyzLinStep</title> |
| − | <short_description> | + | <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>ApCoCoA-1:BBSGen.TraceSyzFull|BBSGen.TraceSyzFull</ref>) |
</short_description> | </short_description> | ||
<syntax> | <syntax> | ||
| − | BBSGen. | + | BBSGen.TraceSyzLinStep(Pi,X,OO,BO,N); |
| − | BBSGen. | + | BBSGen.TraceSyzLinStep(Pi:POLY,X:POLY,OO:LIST,BO:LIST,N:INTEGER):LIST |
</syntax> | </syntax> | ||
<description> | <description> | ||
Note the following: | Note the following: | ||
| − | The chosen variable must be a divisor of the term Pi | + | The chosen variable must be a divisor of the term Pi. |
| − | Pi must be a product of at least two different indeterminates. | + | Pi must be a product of at least two different indeterminates otherwise the result is 0. |
<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 | + | <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]. |
</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> | ||
| Line 26: | Line 27: | ||
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); | ||
| − | + | N:=Len(Indets()); | |
| − | Pi:=x[1]^2x[2]; | + | Pi:=x[1]^2x[2];----Term |
X:=x[1]; ------------Choice of the Variable | X:=x[1]; ------------Choice of the Variable | ||
| Line 40: | Line 41: | ||
| − | t[1,2,1,3] + t[1,2,2,4] | + | t[1,2,1,3] + t[1,2,2,4] |
------------------------------- | ------------------------------- | ||
| Line 46: | Line 47: | ||
</description> | </description> | ||
<types> | <types> | ||
| − | <type> | + | <type>bbsmingensys</type> |
| − | <type> | + | <type>poly</type> |
<type>apcocoaserver</type> | <type>apcocoaserver</type> | ||
</types> | </types> | ||
| − | <see>BBSGen.Wmat</see> | + | <see>ApCoCoA-1:BBSGen.Wmat|BBSGen.Wmat</see> |
| − | <see>BBSGen.TraceSyzLin</see> | + | <see>ApCoCoA-1:BBSGen.TraceSyzLin|BBSGen.TraceSyzLin</see> |
| − | <see>BBSGen.TraceSyzStep</see> | + | <see>ApCoCoA-1:BBSGen.TraceSyzStep|BBSGen.TraceSyzStep</see> |
| − | <see>BBSGen.TraceSyzFull</see> | + | <see>ApCoCoA-1:BBSGen.TraceSyzFull|BBSGen.TraceSyzFull</see> |
| − | <key> | + | <key>TraceSyzLinStep</key> |
| − | <key>BBSGen. | + | <key>BBSGen.TraceSyzLinStep</key> |
| − | <key>bbsmingensys. | + | <key>bbsmingensys.TraceSyzLinStep</key> |
| − | <wiki-category>Package_bbsmingensys</wiki-category> | + | <wiki-category>ApCoCoA-1:Package_bbsmingensys</wiki-category> |
</command> | </command> | ||
Latest revision as of 09:51, 7 October 2020
| This article is about a function from ApCoCoA-1. |
BBSGen.TraceSyzLinStep
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.TraceSyzLinStep(Pi,X,OO,BO,N); BBSGen.TraceSyzLinStep(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. Pi must be a product of at least two different indeterminates otherwise the result is 0.
@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].
@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:=$apcocoa/borderbasis.Box([1,1]); BO:=$apcocoa/borderbasis.Border(OO); Mu:=Len(OO); Nu:=Len(BO); N:=Len(Indets()); Pi:=x[1]^2x[2];----Term 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] -------------------------------
