Difference between revisions of "ApCoCoA-1:BBSGen.NonStand"
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| − | Let W be the weight matrix with respect to the arrow grading(see <ref>BBSGen.Wmat</ref>). | + | 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]. | 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>BBSGen.Wmat</ref>). </item> | + | <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> | ||
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</types> | </types> | ||
| − | <see> BBSGen.Wmat</see> | + | <see>ApCoCoA-1: BBSGen.Wmat| BBSGen.Wmat</see> |
<key>NonStand</key> | <key>NonStand</key> | ||
<key>BBSGen.NonStand</key> | <key>BBSGen.NonStand</key> | ||
Revision as of 08:03, 7 October 2020
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]]]
