Difference between revisions of "ApCoCoA-1:BB.BBscheme"
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| + | {{Version|1}} | ||
<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 | |
</syntax> | </syntax> | ||
| − | + | <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 <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> | |
| − | <key> | + | <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. The polynomials will belong to the ring <tt>BBS=K[c_{ij}]</tt>.</item> | |
| − | + | </itemize> | |
| − | + | <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]) | ||
| + | ------------------------------- | ||
| + | </example> | ||
| + | </description> | ||
| + | <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]) -------------------------------
