Difference between revisions of "ApCoCoA-1:BB.BBasis"
(Documented additional method parameter and added an example.) |
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| Line 5: | Line 5: | ||
<syntax> | <syntax> | ||
BB.BBasis(I:IDEAL):LIST of POLY | BB.BBasis(I:IDEAL):LIST of POLY | ||
| + | BB.BBasis(I:IDEAL, Method:STRING):LIST of POLY | ||
</syntax> | </syntax> | ||
<description> | <description> | ||
| Line 10: | Line 11: | ||
<par/> | <par/> | ||
Let <tt>sigma</tt> be a degree compatible term ordering. The function <tt>BBasis</tt> calls the ApCoCoAServer to compute the O_sigma(I)-border basis of the zero-dimensional input ideal <tt>I</tt> and returns it as a list of polynomials. | Let <tt>sigma</tt> be a degree compatible term ordering. The function <tt>BBasis</tt> calls the ApCoCoAServer to compute the O_sigma(I)-border basis of the zero-dimensional input ideal <tt>I</tt> and returns it as a list of polynomials. | ||
| + | <par/> | ||
| + | You may specify a method parameter which indicates which variation of the Border Basis Algorithm should be used for the computation of the border basis. Possible method values are <tt>StandardBBA</tt>, <tt>MatrixBBA</tt> (polynomial reduction via transformation to matrices and row echelon form computation), and <tt>HeuristicBBA</tt> (uses a heuristic strategy for the computing universe enlargements). The default method is <tt>StandardBBA</tt>. | ||
<par/> | <par/> | ||
The return value will be the computed border basis. | The return value will be the computed border basis. | ||
| Line 15: | Line 18: | ||
<item>@param <em>I</em> A zero-dimensional ideal of which to compute a border basis.</item> | <item>@param <em>I</em> A zero-dimensional ideal of which to compute a border basis.</item> | ||
<item>@return A list of border basis polynomials.</item> | <item>@return A list of border basis polynomials.</item> | ||
| + | </itemize> | ||
| + | The following parameter is optional. | ||
| + | <itemize> | ||
| + | <item>@param <em>Method</em> A string that specifies which variation of the Border Basis Algorithm to use. Possible method values are <quotes>StandardBBA</quotes> (default), <quotes>MatrixBBA</quotes>, and <quotes>HeuristicBBA</quotes>.</item> | ||
</itemize> | </itemize> | ||
<example> | <example> | ||
Use QQ[x, y], DegLex; | Use QQ[x, y], DegLex; | ||
I := Ideal([x^2, xy + y^2]); | I := Ideal([x^2, xy + y^2]); | ||
| − | BB := BBasis(I); | + | BB := BB.BBasis(I); |
BB; | BB; | ||
------------------------------- | ------------------------------- | ||
[xy + y^2, x^2, y^3, xy^2] | [xy + y^2, x^2, y^3, xy^2] | ||
| + | ------------------------------- | ||
| + | </example> | ||
| + | <example> | ||
| + | Use QQ[x, y, z]; | ||
| + | I := Ideal([x^2, y^2, z^2]); | ||
| + | BB := BB.BBasis(I, "MatrixBBA"); | ||
| + | BB; | ||
| + | |||
| + | ------------------------------- | ||
| + | [z^2, y^2, x^2, yz^2, xz^2, y^2z, x^2z, xy^2, x^2y, xyz^2, xy^2z, x^2yz] | ||
------------------------------- | ------------------------------- | ||
</example> | </example> | ||
Revision as of 13:18, 26 June 2009
BB.BBasis
Computes the border basis of a zero-dimensional ideal.
Syntax
BB.BBasis(I:IDEAL):LIST of POLY BB.BBasis(I:IDEAL, Method:STRING):LIST of POLY
Description
Please note: The function(s) explained on this page is/are using the ApCoCoAServer. You will have to start the ApCoCoAServer in order to use it/them.
Let sigma be a degree compatible term ordering. The function BBasis calls the ApCoCoAServer to compute the O_sigma(I)-border basis of the zero-dimensional input ideal I and returns it as a list of polynomials.
You may specify a method parameter which indicates which variation of the Border Basis Algorithm should be used for the computation of the border basis. Possible method values are StandardBBA, MatrixBBA (polynomial reduction via transformation to matrices and row echelon form computation), and HeuristicBBA (uses a heuristic strategy for the computing universe enlargements). The default method is StandardBBA.
The return value will be the computed border basis.
@param I A zero-dimensional ideal of which to compute a border basis.
@return A list of border basis polynomials.
The following parameter is optional.
@param Method A string that specifies which variation of the Border Basis Algorithm to use. Possible method values are "StandardBBA" (default), "MatrixBBA", and "HeuristicBBA".
Example
Use QQ[x, y], DegLex; I := Ideal([x^2, xy + y^2]); BB := BB.BBasis(I); BB; ------------------------------- [xy + y^2, x^2, y^3, xy^2] -------------------------------
Example
Use QQ[x, y, z]; I := Ideal([x^2, y^2, z^2]); BB := BB.BBasis(I, "MatrixBBA"); BB; ------------------------------- [z^2, y^2, x^2, yz^2, xz^2, y^2z, x^2z, xy^2, x^2y, xyz^2, xy^2z, x^2yz] -------------------------------
