Difference between revisions of "ApCoCoA-1:BBSGen.NonTriv"
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| + | {{Version|1}} | ||
<command> | <command> | ||
<title>BBSGen.NonTriv</title> | <title>BBSGen.NonTriv</title> | ||
| − | <short_description> | + | <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> | ||
| + | |||
<syntax> | <syntax> | ||
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<description> | <description> | ||
| − | |||
| − | |||
<itemize> | <itemize> | ||
| − | <item>@para Order ideal OO, border BO, the number of | + | <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>ApCoCoA-1:BBSGen.Wmat|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> | ||
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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); | ||
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]]; | ||
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<types> | <types> | ||
<type>borderbasis</type> | <type>borderbasis</type> | ||
| − | <type> | + | <type>bbsmingensys</type> |
| + | <type>list</type> | ||
<type>apcocoaserver</type> | <type>apcocoaserver</type> | ||
</types> | </types> | ||
| − | |||
| − | |||
| − | <see>BBSGen. | + | <see>ApCoCoA-1:BBSGen.Wmat|BBSGen.Wmat</see> |
| − | <see>BBSGen.Poldeg</see> | + | <see>ApCoCoA-1:BBSGen.Poldeg|BBSGen.Poldeg</see> |
| − | <key>BBSGen. | + | <key>BBSGen.NonTriv</key> |
| − | + | <key>NonTriv</key> | |
| − | <wiki-category>Package_bbsmingensys</wiki-category> | + | |
| + | <wiki-category>ApCoCoA-1:Package_bbsmingensys</wiki-category> | ||
</command> | </command> | ||
Latest revision as of 09:51, 7 October 2020
| This article is about a function from ApCoCoA-1. |
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)]]
