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

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(New page: <command> <title>BBSGen.NonStandPoly</title> <short_description> Finds the non-standard polynomials of the ring <tt>K[c_{ij}]</tt> with respect to the arrow grading. </short_descriptio...)
 
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<syntax>
 
<syntax>
BBSGen.NonStand(OO:LIST,BO:LIST,N:INT,W:MATRIX):LIST
+
BBSGen.NonStandPoly(OO:LIST,BO:LIST,N:INT,W:MATRIX):LIST
 
</syntax>
 
</syntax>
 
   <description>
 
   <description>
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   <item>@return A list of non-standard polynomials from <tt>BBS=K[c_{ij}]</tt> with their degree vectors from field <tt>K</tt>.</item>
+
   <item>@return A list of non-standard polynomials from <tt>K[c_{ij}]</tt> with their degree vectors from field <tt>K</tt>.</item>
 
</itemize>
 
</itemize>
 
<example>
 
<example>
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NonStandPoly(OO,BO,W,N);
 
  
 
   [  c[1,2]c[3,1] + c[1,4]c[4,1] - c[1,3],
 
   [  c[1,2]c[3,1] + c[1,4]c[4,1] - c[1,3],

Revision as of 19:00, 13 February 2012

BBSGen.NonStandPoly

Finds the non-standard polynomials of the ring K[c_{ij}] with respect to the arrow grading. 

Syntax

BBSGen.NonStandPoly(OO:LIST,BO:LIST,N:INT,W:MATRIX):LIST

Description


  • @param OO A list of terms representing an order ideal.

  • @param BO A list of terms representing the border.

  • @param N The number of elements of the Polynomial ring K[x_1,...x_n].

  • @param W The weight matrix.


  • @return A list of non-standard polynomials from K[c_{ij}] with their degree vectors from field K.

Example

Use R::=QQ[x[1..2]];

OO:=BB.Box([1,1]);
BO:=BB.Border(OO);
Mu:=Len(OO);
Nu:=Len(BO);
 W:=Wmat(OO,BO,N);
Use XX::=QQ[c[1..Mu,1..Nu],t[1..N,1..N,1..Mu,1..Mu]]; 


BBSGen.NonStandPoly(OO,BO,N,W);



  [  c[1,2]c[3,1] + c[1,4]c[4,1] - c[1,3],
    R :: Vector(1, 2)],
  [ c[1,1]c[2,2] + c[1,3]c[4,2] - c[1,4],
    R :: Vector(2, 1)],
  [ 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)],
  [c[2,2]c[3,1] + c[2,4]c[4,1] - c[2,3],
    R :: Vector(1, 1)],
  [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)],
  [c[2,2]c[3,1] + c[3,3]c[4,2] - c[3,4],
    R :: Vector(1, 1)],
  [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)],
  [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.NonStand

BB.Box

BB.Border