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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− | BBSGen. | + | 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> | + | <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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[ 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)]] -------------------------------