ApCoCoA-1:BBSGen.PurPow: Difference between revisions
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New page: <command> <title>BBSGen.PurPow</title> <short_description> </short_description> <syntax> BBSGen.PurPow(OO); BBSGen.PurPow(OO:LIST):LIST </syntax> <description> If b_j=x_i^d_i w... |
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<command> | <command> | ||
<title>BBSGen.PurPow</title> | <title>BBSGen.PurPow</title> | ||
<short_description> </short_description> | <short_description>This function finds the pure power indeterminates in the ring K[c]. </short_description> | ||
<syntax> | <syntax> | ||
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<description> | <description> | ||
If b_j=x_i^d_i where x_i is an indeterminate of the base ring K[x_1,..., | If b_j=x_i^d_i where x_i is an indeterminate of the base ring K[x_1,...,x_N] and d_i is some power, then c_ij is called a pure power indeterminate. | ||
This function computes the indices [i,j] of the pure power indterminates c_ij in the coordinate ring of the border basis scheme. | This function computes the indices [i,j] of the pure power indterminates c_ij in the coordinate ring of the border basis scheme. | ||
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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:= | BO:=$apcocoa/borderbasis.Border(OO); | ||
Mu:=Len(OO); | Mu:=Len(OO); | ||
Nu:=Len(BO); | Nu:=Len(BO); | ||
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[1, 3], [2, 3], [3, 3], [4, 3]] | [1, 3], [2, 3], [3, 3], [4, 3]] | ||
Class:=BBSGen.PurPow(OO); | |||
Use BBS::=CoeffRing[c[1..Mu,1..Nu]]; | Use BBS::=CoeffRing[c[1..Mu,1..Nu]]; | ||
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<see>ApCoCoA-1: BBSGen.LinIdepGen| BBSGen.LinIdepGen</see> | |||
<key>bbsmingensys. | |||
<wiki-category>Package_bbsmingensys</wiki-category> | <key>BBSGen.PurPow</key> | ||
<key>PurPow</key> | |||
<key>bbsmingensys.PurPow</key> | |||
<wiki-category>ApCoCoA-1:Package_bbsmingensys</wiki-category> | |||
</command> | </command> | ||
Latest revision as of 09:51, 7 October 2020
| This article is about a function from ApCoCoA-1. |
BBSGen.PurPow
This function finds the pure power indeterminates in the ring K[c].
Syntax
BBSGen.PurPow(OO); BBSGen.PurPow(OO:LIST):LIST
Description
If b_j=x_i^d_i where x_i is an indeterminate of the base ring K[x_1,...,x_N] and d_i is some power, then c_ij is called a pure power indeterminate.
This function computes the indices [i,j] of the pure power indterminates c_ij in the coordinate ring of the border basis scheme.
@param The order ideal OO.
@return List of the indices [i,j] of the pure powers c_ij.
Example
Use R::=QQ[x,y]; OO:=[1,x,y,xy]; BO:=$apcocoa/borderbasis.Border(OO); Mu:=Len(OO); Nu:=Len(BO); BBSGen.PurPow(OO); [[1, 2], [2, 2], [3, 2], [4, 2], [1, 3], [2, 3], [3, 3], [4, 3]] Class:=BBSGen.PurPow(OO); Use BBS::=CoeffRing[c[1..Mu,1..Nu]]; BBSGen.IndFinder(Class,Mu,Nu); [c[1,2], c[1,3], c[2,2], c[2,3], c[3,2], c[3,3], c[4,2], c[4,3]]
