Difference between revisions of "ApCoCoA-1:BBSGen.TraceSyzLin"
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(New page: <command> <title>BBSGen.TraceSyzLin</title> <short_description>: This function computes the K[c]-linear summand of trace syzygy polynomials. </short_description> <synt...) |
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<command> | <command> | ||
<title>BBSGen.TraceSyzLin</title> | <title>BBSGen.TraceSyzLin</title> | ||
| − | <short_description>: This function computes the K[c]-linear summand of trace | + | <short_description>: This function computes the K[c]-linear summand of trace polynomials.(see <ref>ApCoCoA-1:BBSGen.TraceSyzFull|BBSGen.TraceSyzFull</ref>)</short_description> |
| − | |||
<syntax> | <syntax> | ||
| − | TraceSyzLin(OO,BO,N); | + | BBSGen.TraceSyzLin(OO,BO,N); |
| − | TraceSyzLin(OO:LIST,BO:LIST,N:INTEGER):LIST | + | BBSGen.TraceSyzLin(OO:LIST,BO:LIST,N:INTEGER):LIST |
</syntax> | </syntax> | ||
<description> | <description> | ||
| − | |||
| − | |||
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<itemize> | <itemize> | ||
| − | <item>@param The order ideal OO, border BO, the number of Indeterminates of the polynomial. | + | <item>@param The order ideal OO, border BO, the number of Indeterminates of the polynomial ring K[x_1,...,x_N]. |
</item> | </item> | ||
| − | <item>@return List of | + | <item>@return List of polynomials from K[t[1..N,1..N,1..Mu,1..Mu]] that is a sub-ring of XX=K[c[1..Mu,1..Nu],t[1..N,1..N,1..Mu,1..Mu]]. |
</item> | </item> | ||
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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); | ||
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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.TraceSyzLin(OO,BO,N); | BBSGen.TraceSyzLin(OO,BO,N); | ||
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</description> | </description> | ||
<types> | <types> | ||
| − | <type> | + | <type>bbsmingensys</type> |
| − | <type> | + | <type>list</type> |
<type>apcocoaserver</type> | <type>apcocoaserver</type> | ||
</types> | </types> | ||
| − | |||
| − | |||
| − | |||
| − | |||
| − | |||
| − | <key> | + | <see>ApCoCoA-1:BBSGen.Wmat|BBSGen.Wmat</see> |
| − | <key>BBSGen. | + | <see>ApCoCoA-1:BBSGen.TraceSyzStep|BBSGen.TraceSyzStep</see> |
| − | <key>bbsmingensys. | + | <see>ApCoCoA-1:BBSGen.TraceSyzFull|BBSGen.TraceSyzFull</see> |
| − | <wiki-category>Package_bbsmingensys</wiki-category> | + | |
| + | <key>TraceSyzLin</key> | ||
| + | <key>BBSGen.TraceSyzLin</key> | ||
| + | <key>bbsmingensys.TraceSyzLin</key> | ||
| + | <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.TraceSyzLin
- This function computes the K[c]-linear summand of trace polynomials.(see BBSGen.TraceSyzFull)
Syntax
BBSGen.TraceSyzLin(OO,BO,N); BBSGen.TraceSyzLin(OO:LIST,BO:LIST,N:INTEGER):LIST
Description
@param The order ideal OO, border BO, the number of Indeterminates of the polynomial ring K[x_1,...,x_N].
@return List of polynomials from K[t[1..N,1..N,1..Mu,1..Mu]] that is a sub-ring of XX=K[c[1..Mu,1..Nu],t[1..N,1..N,1..Mu,1..Mu]].
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()); W:=BBSGen.Wmat(OO,BO,N); Use XX::=QQ[c[1..Mu,1..Nu],t[1..N,1..N,1..Mu,1..Mu]]; BBSGen.TraceSyzLin(OO,BO,N); [ t[1,2,1,3] + t[1,2,2,4], 2t[1,2,1,2] + 2t[1,2,3,4], t[1,2,1,3] + t[1,2,2,4], 2t[1,2,1,4]] -------------------------------
