ApCoCoA-1:BB.BBscheme: Difference between revisions
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<command> | <command> | ||
<title>BB.BBscheme</title> | |||
<short_description>Computes the defining equations of a border basis scheme.</short_description> | |||
<syntax> | <syntax> | ||
BB.BBscheme(OO:LIST):IDEAL | BB.BBscheme(OO:LIST):IDEAL | ||
</syntax> | </syntax> | ||
<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 < | Computes the defining equations of the border basis scheme using the commutators of the multiplication matrices. The input is a list <tt>OO</tt> of terms that specify an order ideal. The second element of <tt>OO</tt> must be a non-constant polynomial. The output is an ideal in the ring <tt>BBS = K[c_{ij}]</tt>. | ||
<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> | ||
<item>@return A list of polynomials representing the defining equations of the border basis scheme.</item> | <item>@return A list of polynomials representing the defining equations of the border basis scheme. The polynomials will belong to the ring <tt>BBS=K[c_{ij}]</tt>.</item> | ||
</itemize> | </itemize> | ||
<example> | <example> | ||
Use | Use QQ[x,y,z]; | ||
BB.BBscheme([1,x]); | 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], | ||
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------------------------------- | ------------------------------- | ||
</example> | </example> | ||
</description> | |||
<see>BB.HomBBscheme</see> | <types> | ||
<type>borderbasis</type> | |||
</types> | |||
<see>ApCoCoA-1:BB.HomBBscheme|BB.HomBBscheme</see> | |||
<key>BBscheme</key> | |||
<key>BB.BBscheme</key> | |||
<key>borderbasis.BBscheme</key> | |||
<wiki-category>ApCoCoA-1:Package_borderbasis</wiki-category> | |||
</command> | </command> | ||
Latest revision as of 09:39, 7 October 2020
| This article is about a function from ApCoCoA-1. |
BB.BBscheme
Computes 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]) -------------------------------
