Difference between revisions of "ApCoCoA-1:BBSGen.NonStand"
From ApCoCoAWiki
m (insert version info) |
|||
| (11 intermediate revisions by 3 users not shown) | |||
| Line 1: | Line 1: | ||
| + | {{Version|1}} | ||
<command> | <command> | ||
| − | <title>BBSGen. | + | <title>BBSGen.NonStand</title> |
| − | <short_description>This function computes the non-standard | + | <short_description>This function computes the non-standard indeterminates from K[c] with respect to the arrow grading. </short_description> |
<syntax> | <syntax> | ||
| − | NonStand(OO,BO,N,W); | + | BBSGen.NonStand(OO,BO,N,W); |
| − | NonStand(OO:LIST,BO:LIST,N:INTEGER,W:MATRIX):LIST | + | 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 | + | 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 | + | <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> | <item>@return List of Indeterminates and their degree with respect to the arrow grading. </item> | ||
</itemize> | </itemize> | ||
| Line 23: | Line 24: | ||
BO:=$apcocoa/borderbasis.Border(OO); | BO:=$apcocoa/borderbasis.Border(OO); | ||
N:=Len(Indets()); | 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]]; | XX::=QQ[c[1..Mu,1..Nu],t[1..N,1..N,1..Mu,1..Mu]]; | ||
| Line 33: | Line 34: | ||
[[c[1,3], [R :: 1, R :: 2]], | [[c[1,3], [R :: 1, R :: 2]], | ||
[c[1,4], [R :: 2, R :: 1]], | [c[1,4], [R :: 2, R :: 1]], | ||
| − | + | [c[2,3], [R :: 1, R :: 1]], | |
[c[3,4], [R :: 1, R :: 1]]] | [c[3,4], [R :: 1, R :: 1]]] | ||
| Line 46: | Line 47: | ||
</types> | </types> | ||
| − | <see> BBSGen.Wmat</see> | + | <see>ApCoCoA-1: BBSGen.Wmat| BBSGen.Wmat</see> |
| − | <key> | + | <key>NonStand</key> |
| − | <key>BBSGen. | + | <key>BBSGen.NonStand</key> |
| − | <key>bbsmingensys. | + | <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]]]
