Difference between revisions of "ApCoCoA-1:BBSGen.NonStand"
From ApCoCoAWiki
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<command> | <command> | ||
<title>BBSGen.Wmat</title> | <title>BBSGen.Wmat</title> | ||
| − | <short_description>This function computes the non-standard Indeterminates with respect to the arrow grading | + | <short_description>This function computes the non-standard Indeterminates from K[c] with respect to the arrow grading. </short_description> |
<syntax> | <syntax> | ||
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</syntax> | </syntax> | ||
<description> | <description> | ||
| + | Let W be the weight matrix with respect to the arrow grading.(see <ref>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 and the Weight Matrix.</item> | + | <item>@param The order ideal OO, the border BO the number of Indeterminates of the Polynomial Ring and the Weight Matrix. (see <commandref>BB.Border</commandref> from the package borderbasis)</item> |
| − | <item>@return List of Indeterminates and their degree | + | <item>@return List of Indeterminates and their degree with respect to the arrow grading. </item> |
</itemize> | </itemize> | ||
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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); |
| + | N:=Len(Indets()); | ||
W:=BBSGen.Wmat(OO,BO,N); | W:=BBSGen.Wmat(OO,BO,N); | ||
| + | XX::=QQ[c[1..Mu,1..Nu],t[1..N,1..N,1..Mu,1..Mu]]; | ||
| + | Use XX; | ||
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[c[2,3], [R :: 1, R :: 1]], | [c[2,3], [R :: 1, R :: 1]], | ||
[c[3,4], [R :: 1, R :: 1]]] | [c[3,4], [R :: 1, R :: 1]]] | ||
| + | |||
| + | |||
</example> | </example> | ||
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<type>list</type> | <type>list</type> | ||
</types> | </types> | ||
| − | + | ||
| − | |||
<see> BBSGen.Wmat</see> | <see> BBSGen.Wmat</see> | ||
<key>Wmat</key> | <key>Wmat</key> | ||
Revision as of 09:42, 8 June 2012
BBSGen.Wmat
This function computes the non-standard Indeterminates from K[c] with respect to the arrow grading.
Syntax
NonStand(OO,BO,N,W); 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 and the Weight Matrix. (see <commandref>BB.Border</commandref> from the package borderbasis)
@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]]]
