ApCoCoA-1:BBSGen.LinIndepGen: Difference between revisions
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New page: <command> <title>BBSGen.LinIndepGen</title> <short_description>This function computes the equivalent indeterminates modulo m^2 of BBS where m is the maximal ideal generated by the inde... |
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<command> | <command> | ||
<title>BBSGen.LinIndepGen</title> | <title>BBSGen.LinIndepGen</title> | ||
<short_description>This function computes the equivalent indeterminates modulo m^2 | <short_description>Let OO be an order ideal and BO be its border. Let Mu:=Len(OO) and Nu:=Len(BO). This function computes the equivalent indeterminates from K[c_11,...,c_Mu Nu] modulo m^2, where m is the maximal ideal generated by the indeterminates {c_11,...,c_Mu Nu} from the coordinate ring of the border basis scheme. As out-put, it gives every equivalence class as a list.</short_description> | ||
<syntax> | <syntax> | ||
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</syntax> | </syntax> | ||
<description> | <description> | ||
<itemize> | <itemize> | ||
<item>@param The order ideal OO.</item> | <item>@param The order ideal OO.</item> | ||
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Use R::=QQ[x,y]; | Use R::=QQ[x,y]; | ||
OO:=[1,x,y,xy]; | OO:=[1,x,y,xy]; | ||
BO:=BB.Border(OO); | |||
Mu:=Len(OO); | |||
Nu:=Len(BO); | |||
BBSGen.LinIndepGen(OO); | BBSGen.LinIndepGen(OO); | ||
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<see>ApCoCoA-1: BBSGen.PurPow| BBSGen.PurPow</see> | |||
<key>bbsmingensys. | |||
<wiki-category>Package_bbsmingensys</wiki-category> | <key>LinIndepGen</key> | ||
<key>BBSGen.LinIndepGen</key> | |||
<key>bbsmingensys.LinIndepGen</key> | |||
<wiki-category>ApCoCoA-1:Package_bbsmingensys</wiki-category> | |||
</command> | </command> | ||
Latest revision as of 09:50, 7 October 2020
| This article is about a function from ApCoCoA-1. |
BBSGen.LinIndepGen
Let OO be an order ideal and BO be its border. Let Mu:=Len(OO) and Nu:=Len(BO). This function computes the equivalent indeterminates from K[c_11,...,c_Mu Nu] modulo m^2, where m is the maximal ideal generated by the indeterminates {c_11,...,c_Mu Nu} from the coordinate ring of the border basis scheme. As out-put, it gives every equivalence class as a list.
Syntax
BBSGen.LinIndepGen(OO): BBSGen.LinIndepGen(OO:LIST):LIST
Description
@param The order ideal OO.
@return The list of classes of indeterminates modulo m^2.
Example
Use R::=QQ[x,y]; OO:=[1,x,y,xy]; BO:=BB.Border(OO); Mu:=Len(OO); Nu:=Len(BO); BBSGen.LinIndepGen(OO); [[[3, 3], [1, 1]], [[1, 2], [2, 4]], [[4, 3], [2, 1]], [[2, 2]], [[3, 1]], [[4, 4], [3, 2]], [4, 2], [4, 1]] Class:=BBSGen.LinIndepGen(OO); Use BBS::=CoeffRing[c[1..Mu,1..Nu]]; BBSGen.IndFinder(Class,Mu,Nu); [[c[3,3], c[1,1]], [c[1,2], c[2,4]], [c[4,3], c[2,1]], c[2,2], c[3,1], [c[4,4], c[3,2]], c[4,1], c[4,2]] ------------------------------- -------------------------------
