Difference between revisions of "ApCoCoA-1:BB.BBscheme"
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KHiddemann (talk | contribs) (adding formula tags) |
(Reviewed text and added example) |
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<command> | <command> | ||
<title>borderbasis.BBscheme</title> | <title>borderbasis.BBscheme</title> | ||
| − | <short_description> | + | <short_description>defining equations of border basis scheme</short_description> |
<syntax> | <syntax> | ||
$borderbasis.BBscheme(OO:LIST):IDEAL | $borderbasis.BBscheme(OO:LIST):IDEAL | ||
</syntax> | </syntax> | ||
<description> | <description> | ||
| − | Computes the defining equations of the border basis scheme using the commutators of the multiplication matrices. The input is an order ideal | + | 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 output is an ideal in the ring <formula>BBS = K[c_{ij}]</formula>. |
| + | <example> | ||
| + | Use Q[x,y,z]; | ||
| + | $borderbasis.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]) | ||
| + | ------------------------------- | ||
| + | </example> | ||
</description> | </description> | ||
| + | <see>borderbasis.HomBBscheme</see> | ||
<key>Kreuzer</key> | <key>Kreuzer</key> | ||
<key>borderbasis.bbscheme</key> | <key>borderbasis.bbscheme</key> | ||
Revision as of 22:40, 7 November 2007
borderbasis.BBscheme
defining equations of border basis scheme
Syntax
$borderbasis.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 output is an ideal in the ring <formula>BBS = K[c_{ij}]</formula>.
Example
Use Q[x,y,z]; $borderbasis.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]) -------------------------------
