Difference between revisions of "ApCoCoA-1:BBSGen.NonTriv"
From ApCoCoAWiki
| Line 1: | Line 1: | ||
<command> | <command> | ||
<title>BBSGen.NonTriv</title> | <title>BBSGen.NonTriv</title> | ||
| − | <short_description>: This function computes the non-trivial polynomials of the generating set | + | <short_description>: This function computes the non-trivial polynomials of the generating set of the vanishing ideal of a border basis scheme. |
</short_description> | </short_description> | ||
| Line 13: | Line 13: | ||
<description> | <description> | ||
| − | |||
<itemize> | <itemize> | ||
| − | <item>@para Order ideal OO, border BO, the number of Indeterminates of the Polynomial Ring and the Weight Matrix. | + | <item>@para Order ideal OO, border BO, the number of Indeterminates of the Polynomial Ring and the Weight Matrix. (see package borderbasis <commandref>BB.Box</commandref>, <commandref>BB.Border</commandref>) |
</item> | </item> | ||
<item>@return List of non-trivial generators of the vanishing ideal of the border basis scheme. </item> | <item>@return List of non-trivial generators of the vanishing ideal of the border basis scheme. </item> | ||
| Line 26: | Line 25: | ||
OO:=BB.Box([1,1]); | OO:=BB.Box([1,1]); | ||
BO:=BB.Border(OO); | BO:=BB.Border(OO); | ||
| − | |||
Mu:=Len(OO); | Mu:=Len(OO); | ||
Nu:=Len(BO); | Nu:=Len(BO); | ||
N:=Len(Indets()); | N:=Len(Indets()); | ||
| + | W:=BBSGen.Wmat(OO,BO,N); | ||
Use XX::=QQ[c[1..Mu,1..Nu],t[1..N,1..N,1..Mu,1..Mu]]; | Use XX::=QQ[c[1..Mu,1..Nu],t[1..N,1..N,1..Mu,1..Mu]]; | ||
Revision as of 09:57, 8 June 2012
BBSGen.NonTriv
- This function computes the non-trivial polynomials of the generating set of the vanishing ideal of a border basis scheme.
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. (see package borderbasis <commandref>BB.Box</commandref>, <commandref>BB.Border</commandref>)
@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);
Mu:=Len(OO);
Nu:=Len(BO);
N:=Len(Indets());
W:=BBSGen.Wmat(OO,BO,N);
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)]]
