Difference between revisions of "ApCoCoA-1:BBSGen.NonTriv"
From ApCoCoAWiki
| Line 14: | Line 14: | ||
<itemize> | <itemize> | ||
| − | <item>@para Order ideal OO, border BO, the number of indeterminates of the polynomial ring K[x_1,...,x_N] and the | + | <item>@para Order ideal OO, border BO, the number of indeterminates of the polynomial ring K[x_1,...,x_N] and the weight matrix(see <ref>BBSGen.Wmat</ref>). </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> | ||
</itemize> | </itemize> | ||
| Line 23: | Line 22: | ||
Use R::=QQ[x[1..2]]; | Use R::=QQ[x[1..2]]; | ||
| − | OO:= | + | OO:=$apcocoa/borderbasis.Box([1,1]); |
| − | BO:= | + | BO:=$apcocoa/borderbasis.Border(OO); |
Mu:=Len(OO); | Mu:=Len(OO); | ||
Nu:=Len(BO); | Nu:=Len(BO); | ||
| Line 93: | Line 92: | ||
<type>apcocoaserver</type> | <type>apcocoaserver</type> | ||
</types> | </types> | ||
| − | |||
| − | |||
<see>BBSGen.NonTriv</see> | <see>BBSGen.NonTriv</see> | ||
Revision as of 23:19, 14 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 K[x_1,...,x_N] and the weight matrix(see BBSGen.Wmat).
@return List of non-trivial generators of the vanishing ideal of the border basis scheme.
Example
Use R::=QQ[x[1..2]];
OO:=$apcocoa/borderbasis.Box([1,1]);
BO:=$apcocoa/borderbasis.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)]]
