Difference between revisions of "ApCoCoA-1:BB.BBscheme"
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<command> | <command> | ||
| − | <title> | + | <title>BB.BBscheme</title> |
<short_description>defining equations of border basis scheme</short_description> | <short_description>defining equations of border basis scheme</short_description> | ||
<syntax> | <syntax> | ||
| − | + | BB.BBscheme(OO:LIST):IDEAL | |
</syntax> | </syntax> | ||
<description> | <description> | ||
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<example> | <example> | ||
Use Q[x,y,z]; | 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], | 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[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], | ||
| Line 19: | Line 19: | ||
</example> | </example> | ||
</description> | </description> | ||
| − | <see> | + | <see>BB.HomBBscheme</see> |
<key>kreuzer</key> | <key>kreuzer</key> | ||
| + | <key>bb.bbscheme</key> | ||
<key>borderbasis.bbscheme</key> | <key>borderbasis.bbscheme</key> | ||
<wiki-category>Package_borderbasis</wiki-category> | <wiki-category>Package_borderbasis</wiki-category> | ||
</command> | </command> | ||
Revision as of 19:43, 8 November 2007
BB.BBscheme
defining equations of 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]) -------------------------------
