Difference between revisions of "ApCoCoA-1:BBSGen.NonTriv"
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Revision as of 18:03, 7 June 2012
BBSGen.NonTriv
- This function computes the non-trivial polynomials of the generating set \tau of the vanishing ideal of a border basis scheme.
The functions from the package borderbasis BB.Box, BBSGen.Wmat must be used as input.
Syntax
BBSGen.NonTriv(OO,BO,W,N); BBSGen.NonTriv(OO:LIST,BO:LIST,W:MATRIX,N:INT):LIST;
Description
@para Order ideal OO, border BO, the number of Indeterminates of the Polynomial Ring and the Weight Matrix.
@return List of non-trivial generators of the vanishing ideal of the border basis scheme.
Example
Use R::=QQ[x[1..2]];
OO:=BB.Box([1,1]);
BO:=BB.Border(OO);
W:=BBSGen.Wmat(OO,BO,N);
Mu:=Len(OO);
Nu:=Len(BO);
N:=Len(Indets());
Use XX::=QQ[c[1..Mu,1..Nu],t[1..N,1..N,1..Mu,1..Mu]];
Set Indentation;
BBSGen.NonTriv(OO,BO,W,N);
[
[
t[1,2,1,2],
c[1,2]c[3,1] + c[1,4]c[4,1] - c[1,3],
R :: Vector(1, 2)],
[
t[1,2,1,3],
-c[1,1]c[2,2] - c[1,3]c[4,2] + c[1,4],
R :: Vector(2, 1)],
[
t[1,2,1,4],
-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)],
[
t[1,2,2,2],
c[2,2]c[3,1] + c[2,4]c[4,1] - c[2,3],
R :: Vector(1, 1)],
[
t[1,2,2,3],
-c[2,1]c[2,2] - c[2,3]c[4,2] - c[1,2] + c[2,4],
R :: Vector(2, 0)],
[
t[1,2,2,4],
-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)],
[
t[1,2,3,2],
c[3,1]c[3,2] + c[3,4]c[4,1] + c[1,1] - c[3,3],
R :: Vector(0, 2)],
[
t[1,2,3,3],
-c[2,2]c[3,1] - c[3,3]c[4,2] + c[3,4],
R :: Vector(1, 1)],
[
t[1,2,3,4],
-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)],
[
t[1,2,4,2],
c[3,1]c[4,2] + c[4,1]c[4,4] + c[2,1] - c[4,3],
R :: Vector(0, 1)],
[
t[1,2,4,3],
-c[2,2]c[4,1] - c[4,2]c[4,3] - c[3,2] + c[4,4],
R :: Vector(1, 0)],
[
t[1,2,4,4],
-c[2,4]c[4,1] + c[3,3]c[4,2] + c[2,3] - c[3,4],
R :: Vector(1, 1)]]
