Difference between revisions of "ApCoCoA-1:BB.BBscheme"
From ApCoCoAWiki
m (ApCoCoA:Borderbasis.BBscheme moved to ApCoCoA:BB.BBscheme: new alias) |
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<command> | <command> | ||
<title>BB.BBscheme</title> | <title>BB.BBscheme</title> | ||
| − | <short_description>defining equations of border basis scheme</short_description> | + | <short_description>Compute the defining equations of a border basis scheme.</short_description> |
<syntax> | <syntax> | ||
BB.BBscheme(OO:LIST):IDEAL | BB.BBscheme(OO:LIST):IDEAL | ||
Revision as of 16:20, 21 April 2009
BB.BBscheme
Compute the defining equations of a border basis scheme.
Syntax
BB.BBscheme(OO:LIST):IDEAL
Description
Computes the defining equations of the border basis scheme using the commutators of the multiplication matrices. The input is a list OO of terms that specify an order ideal. The second element of OO must be a non-constant polynomial. The output is an ideal in the ring <formula>BBS = K[c_{ij}]</formula>.
Example
Use Q[x,y,z]; BB.BBscheme([1,x]); BBS :: Ideal(c[1,5]c[2,2] - c[1,4], c[1,2]c[1,5] - c[1,5]c[2,4] + c[1,4]c[2,5], c[2,2]c[2,5] + c[1,2] - c[2,4], c[1,5]c[2,2] - c[1,4], c[1,5]c[2,1] - c[1,3], c[1,1]c[1,5] - c[1,5]c[2,3] + c[1,3]c[2,5], c[2,1]c[2,5] + c[1,1] - c[2,3], c[1,5]c[2,1] - c[1,3], c[1,4]c[2,1] - c[1,3]c[2,2], c[1,2]c[1,3] - c[1,1]c[1,4] + c[1,4]c[2,3] - c[1,3]c[2,4], c[1,2]c[2,1] - c[1,1]c[2,2] + c[2,2]c[2,3] - c[2,1]c[2,4], c[1,4]c[2,1] - c[1,3]c[2,2]) -------------------------------
