Difference between revisions of "ApCoCoA-1:BBSGen.NonStandPoly"
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| + | <command> | ||
| + | <title>BBSGen.Wmat</title> | ||
| + | <short_description>This function computes the non-standard polynomials among the generators of the vanishing ideal of border basis | ||
| + | scheme. | ||
| + | |||
| + | </short_description> | ||
| + | |||
| + | <syntax> | ||
| + | NonStandPoly(OO,BO,W,N); | ||
| + | NonStandPoly(OO:LIST,BO:LIST,W:MATRIX,N:INTEGER):LIST | ||
| + | </syntax> | ||
| + | <description> | ||
| + | |||
| + | <itemize> | ||
| + | <item>@param The order ideal OO, BO border of OO , the number of indeterminates of the polynomial ring N and the Weight Matrix. | ||
| + | </item> | ||
| + | <item>@return List of polynomials and their degree wrt. the arrow grading. .</item> | ||
| + | </itemize> | ||
| + | |||
| + | |||
| + | <example> | ||
| + | Use R::=QQ[x[1..2]]; | ||
| + | |||
| + | OO:=BB.Box([1,1]); | ||
| + | BO:=BB.Border(OO); | ||
| + | W:=Wmat(OO,BO,N); | ||
| + | XX::=QQ[c[1..Mu,1..Nu],t[1..N,1..N,1..Mu,1..Mu]]; | ||
| + | Use XX; | ||
| + | |||
| + | NonStandPoly(OO,BO,W,N); | ||
| + | |||
| + | [ c[1,2]c[3,1] + c[1,4]c[4,1] - c[1,3], | ||
| + | R :: Vector(1, 2)], | ||
| + | [ c[1,1]c[2,2] + c[1,3]c[4,2] - c[1,4], | ||
| + | R :: Vector(2, 1)], | ||
| + | [ c[1,1]c[2,4] - c[1,2]c[3,3] - c[1,4]c[4,3] + c[1,3]c[4,4], | ||
| + | R :: Vector(2, 2)], | ||
| + | [c[2,2]c[3,1] + c[2,4]c[4,1] - c[2,3], | ||
| + | R :: Vector(1, 1)], | ||
| + | [c[2,1]c[2,4] - c[2,2]c[3,3] - c[2,4]c[4,3] + c[2,3]c[4,4] + c[1,4], | ||
| + | R :: Vector(2, 1)], | ||
| + | [c[2,2]c[3,1] + c[3,3]c[4,2] - c[3,4], | ||
| + | R :: Vector(1, 1)], | ||
| + | [c[2,4]c[3,1] - c[3,2]c[3,3] - c[3,4]c[4,3] + c[3,3]c[4,4] - c[1,3], | ||
| + | R :: Vector(1, 2)], | ||
| + | [c[2,4]c[4,1] - c[3,3]c[4,2] - c[2,3] + c[3,4], | ||
| + | R :: Vector(1, 1)]] | ||
| + | |||
| + | |||
| + | |||
| + | </example> | ||
| + | |||
| + | </description> | ||
| + | <types> | ||
| + | <type>borderbasis</type> | ||
| + | <type>ideal</type> | ||
| + | <type>apcocoaserver</type> | ||
| + | </types> | ||
| + | <see>BB.Border</see> | ||
| + | <see>BB.Box</see> | ||
| + | <key>Wmat</key> | ||
| + | <key>BBSGen.Wmat</key> | ||
| + | <key>bbsmingensys.Wmat</key> | ||
| + | <wiki-category>Package_bbsmingensys</wiki-category> | ||
| + | </command> | ||
Revision as of 16:12, 31 May 2012
BBSGen.Wmat
This function computes the non-standard polynomials among the generators of the vanishing ideal of border basis
scheme.
Syntax
NonStandPoly(OO,BO,W,N); NonStandPoly(OO:LIST,BO:LIST,W:MATRIX,N:INTEGER):LIST
Description
@param The order ideal OO, BO border of OO , the number of indeterminates of the polynomial ring N and the Weight Matrix.
@return List of polynomials and their degree wrt. the arrow grading. .
Example
Use R::=QQ[x[1..2]];
OO:=BB.Box([1,1]);
BO:=BB.Border(OO);
W:=Wmat(OO,BO,N);
XX::=QQ[c[1..Mu,1..Nu],t[1..N,1..N,1..Mu,1..Mu]];
Use XX;
NonStandPoly(OO,BO,W,N);
[ c[1,2]c[3,1] + c[1,4]c[4,1] - c[1,3],
R :: Vector(1, 2)],
[ c[1,1]c[2,2] + c[1,3]c[4,2] - c[1,4],
R :: Vector(2, 1)],
[ c[1,1]c[2,4] - c[1,2]c[3,3] - c[1,4]c[4,3] + c[1,3]c[4,4],
R :: Vector(2, 2)],
[c[2,2]c[3,1] + c[2,4]c[4,1] - c[2,3],
R :: Vector(1, 1)],
[c[2,1]c[2,4] - c[2,2]c[3,3] - c[2,4]c[4,3] + c[2,3]c[4,4] + c[1,4],
R :: Vector(2, 1)],
[c[2,2]c[3,1] + c[3,3]c[4,2] - c[3,4],
R :: Vector(1, 1)],
[c[2,4]c[3,1] - c[3,2]c[3,3] - c[3,4]c[4,3] + c[3,3]c[4,4] - c[1,3],
R :: Vector(1, 2)],
[c[2,4]c[4,1] - c[3,3]c[4,2] - c[2,3] + c[3,4],
R :: Vector(1, 1)]]
