ApCoCoA-1:BB.BBasisForOI: Difference between revisions
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<command> | <command> | ||
<title>borderbasis.BorderBasis</title> | <title>borderbasis.BorderBasis</title> | ||
<short_description> | <short_description>border basis of an ideal</short_description> | ||
<syntax> | <syntax> | ||
$borderbasis.BorderBasis(F:LIST,OO:LIST):LIST | $borderbasis.BorderBasis(F:LIST,OO:LIST):LIST | ||
</syntax> | </syntax> | ||
<description> | <description> | ||
Computes the border basis of the ideal <formula>I=<F></formula> with respect to the order ideal OO. Gives an error messages if no border basis exists. Uses the <formula>O_{\sigma}(I)</formula> border basis and the | Computes the border basis of the ideal <formula>I=<F></formula> with respect to the order ideal OO. Gives an error messages if no border basis exists. Uses the <formula>O_{\sigma}(I)</formula> border basis and the border basis transformation algorithm. The input is a list of polynomials F and a list OO of terms that specify an order ideal. The output is a list of polynomials. | ||
<example> | |||
Use Q[x,y]; | |||
$borderbasis.BorderBasis([x^2, xy + y^2], [1,x,y,y^2]); | |||
[xy + y^2, x^2, y^3, xy^2] | |||
------------------------------- | |||
</example> | |||
</description> | </description> | ||
<see>BBasis</see> | |||
<key>Kreuzer</key> | <key>Kreuzer</key> | ||
<key>borderbasis.borderbasis</key> | <key>borderbasis.borderbasis</key> | ||
Revision as of 23:04, 7 November 2007
borderbasis.BorderBasis
border basis of an ideal
Syntax
$borderbasis.BorderBasis(F:LIST,OO:LIST):LIST
Description
Computes the border basis of the ideal <formula>I=<F></formula> with respect to the order ideal OO. Gives an error messages if no border basis exists. Uses the <formula>O_{\sigma}(I)</formula> border basis and the border basis transformation algorithm. The input is a list of polynomials F and a list OO of terms that specify an order ideal. The output is a list of polynomials.
Example
Use Q[x,y]; $borderbasis.BorderBasis([x^2, xy + y^2], [1,x,y,y^2]); [xy + y^2, x^2, y^3, xy^2] -------------------------------
