ApCoCoA-1:BB.BBscheme: Difference between revisions
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<command> | <command> | ||
<title>BB.BBscheme</title> | |||
<short_description>Compute the defining equations of a border basis scheme.</short_description> | |||
<syntax> | <syntax>BB.BBscheme(OO:LIST):IDEAL</syntax> | ||
BB.BBscheme(OO:LIST):IDEAL | <description> | ||
</syntax> | 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 BBS = K[c_{ij}]. | ||
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 | |||
<itemize> | <itemize> | ||
<item>@param <em>OO</em> A list of terms representing an order ideal.</item> | <item>@param <em>OO</em> A list of terms representing an order ideal.</item> | ||
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------------------------------- | ------------------------------- | ||
</example> | </example> | ||
</description> | |||
<types> | <types> | ||
<type>list</type> | <type>list</type> | ||
</types> | </types> | ||
<see>BB.HomBBscheme</see> | |||
<key>BBscheme</key> | |||
<key>BB.BBscheme</key> | |||
<key>borderbasis.BBscheme</key> | |||
<wiki-category>Package_borderbasis</wiki-category> | |||
</command> | </command> | ||
Revision as of 10:53, 24 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 BBS = K[c_{ij}].
@param OO A list of terms representing an order ideal.
@return A list of polynomials representing the defining equations of the border basis scheme. The polynomials will belong to the ring BBS=K[c_{ij}].
Example
Use QQ[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]) -------------------------------
