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

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<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_description>
 
 
 
<syntax>
 
BBSGen.NonStandPoly(OO:LIST,BO:LIST,N:INT,W:MATRIX):LIST
 
</syntax>
 
  <description>
 
  
<itemize>
 
<item>@param <em>OO</em> A list of terms representing an order ideal.</item>
 
  <item>@param <em>BO</em> A list of terms representing the border.</item>
 
<item>@param <em>N</em> The number of elements of the Polynomial ring <tt>K[x_1,...x_n]</tt>.</item>
 
<item>@param <em>W</em> The weight matrix.</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>
 
<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)]]
 
 
 
 
-------------------------------
 
 
</example>
 
  </description>
 
  <types>
 
    <type>bbsmingensys</type>
 
  </types>
 
  <see>BBSGen.Wmat</see>
 
<see>BBSGen.NonStand</see>
 
  <see>BB.Box</see>
 
  <see>BB.Border</see>
 
<key>Wmat</key>
 
  <key>BBSGen.NonStandPoly</key>
 
  <key>bbsmingensys.NonStandPoly</key>
 
  <wiki-category>Package_bbsmingensys</wiki-category>
 
</command>
 

Revision as of 19:06, 13 February 2012