ApCoCoA-1:BBSGen.NonStand: Difference between revisions
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<command> | <command> | ||
<title>BBSGen.NonStand</title> | <title>BBSGen.NonStand</title> | ||
<short_description> | <short_description>This function computes the non-standard indeterminates from K[c] with respect to the arrow grading. </short_description> | ||
<syntax> | <syntax> | ||
BBSGen.NonStand(OO:LIST,BO:LIST,N: | BBSGen.NonStand(OO,BO,N,W); | ||
BBSGen.NonStand(OO:LIST,BO:LIST,N:INTEGER,W:MATRIX):LIST | |||
</syntax> | </syntax> | ||
<description> | <description> | ||
Let W be the weight matrix with respect to the arrow grading(see <ref>ApCoCoA-1:BBSGen.Wmat|BBSGen.Wmat</ref>). | |||
An indeterminate c_ij in K[c] is called standard, if deg_W(c_ij)=log(b_j)-log(t_i) has exactly one strictly positive component. If c_ij is not standard then it is called non-standard. This function computes such non-standard indeterminates from ring K[c]. | |||
<itemize> | <itemize> | ||
<item>@param The order ideal OO, the border BO the number of indeterminates of the polynomial ring K[x_1,...,x_N] and the weight matrix(<ref>ApCoCoA-1:BBSGen.Wmat|BBSGen.Wmat</ref>). </item> | |||
<item>@return List of Indeterminates and their degree with respect to the arrow grading. </item> | |||
</itemize> | |||
<item>@ | |||
<example> | <example> | ||
Use R::=QQ[x[1..2]]; | |||
OO:=$apcocoa/borderbasis.Box([1,1]); | |||
BO:=$apcocoa/borderbasis.Border(OO); | |||
N:=Len(Indets()); | |||
W:=BBSGen.Wmat(OO,BO,N); | |||
XX::=QQ[c[1..Mu,1..Nu],t[1..N,1..N,1..Mu,1..Mu]]; | |||
Use XX; | |||
BBSGen.NonStand(OO,BO,N,W); | BBSGen.NonStand(OO,BO,N,W); | ||
[[c[1,3], [R :: 1, R :: 2]], | [[c[1,3], [R :: 1, R :: 2]], | ||
[c[1,4], [R :: 2, R :: 1]], | |||
[c[2,3], [R :: 1, R :: 1]], | |||
[c[3,4], [R :: 1, R :: 1]]] | |||
</example> | </example> | ||
</description> | </description> | ||
<types> | <types> | ||
<type> | <type>borderbasis</type> | ||
<type>list</type> | |||
</types> | </types> | ||
<see>ApCoCoA-1: BBSGen.Wmat| BBSGen.Wmat</see> | |||
<key>NonStand</key> | |||
<key>BBSGen.NonStand</key> | <key>BBSGen.NonStand</key> | ||
<key>bbsmingensys.NonStand</key> | <key>bbsmingensys.NonStand</key> | ||
<wiki-category>Package_bbsmingensys</wiki-category> | <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.NonStand
This function computes the non-standard indeterminates from K[c] with respect to the arrow grading.
Syntax
BBSGen.NonStand(OO,BO,N,W); BBSGen.NonStand(OO:LIST,BO:LIST,N:INTEGER,W:MATRIX):LIST
Description
Let W be the weight matrix with respect to the arrow grading(see BBSGen.Wmat).
An indeterminate c_ij in K[c] is called standard, if deg_W(c_ij)=log(b_j)-log(t_i) has exactly one strictly positive component. If c_ij is not standard then it is called non-standard. This function computes such non-standard indeterminates from ring K[c].
@param The order ideal OO, the border BO the number of indeterminates of the polynomial ring K[x_1,...,x_N] and the weight matrix(BBSGen.Wmat).
@return List of Indeterminates and their degree with respect to the arrow grading.
Example
Use R::=QQ[x[1..2]]; OO:=$apcocoa/borderbasis.Box([1,1]); BO:=$apcocoa/borderbasis.Border(OO); N:=Len(Indets()); W:=BBSGen.Wmat(OO,BO,N); XX::=QQ[c[1..Mu,1..Nu],t[1..N,1..N,1..Mu,1..Mu]]; Use XX; BBSGen.NonStand(OO,BO,N,W); [[c[1,3], [R :: 1, R :: 2]], [c[1,4], [R :: 2, R :: 1]], [c[2,3], [R :: 1, R :: 1]], [c[3,4], [R :: 1, R :: 1]]]
