Difference between revisions of "ApCoCoA-1:BBSGen.NonTriv"

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   <title>BBSGen.NonTriv</title>
 
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   <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>
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   <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>@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>
 
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<see>BBSGen.Wmat</see>
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<see>ApCoCoA-1:BBSGen.Wmat|BBSGen.Wmat</see>
<see>BBSGen.Poldeg</see>
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<see>ApCoCoA-1:BBSGen.Poldeg|BBSGen.Poldeg</see>
 
   <key>BBSGen.NonTriv</key>
 
   <key>BBSGen.NonTriv</key>
 
<key>NonTriv</key>
 
<key>NonTriv</key>

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)]]




BBSGen.Wmat

BBSGen.Poldeg