Difference between revisions of "ApCoCoA-1:BB.TransformBBIntoGB"
From ApCoCoAWiki
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Let <tt>BB</tt> be a list of polynomials that form a <formula>\mathcal{O}_\sigma(I)</formula>-border basis of a zero-dimensional ideal <formula>I</formula>. This function extracts the reduced <formula>\sigma</formula>-Groebner basis contained in the <formula>\mathcal{O}_\sigma(I)</formula>-border basis <tt>BB</tt> and returns it as a list of polynomials. | Let <tt>BB</tt> be a list of polynomials that form a <formula>\mathcal{O}_\sigma(I)</formula>-border basis of a zero-dimensional ideal <formula>I</formula>. This function extracts the reduced <formula>\sigma</formula>-Groebner basis contained in the <formula>\mathcal{O}_\sigma(I)</formula>-border basis <tt>BB</tt> and returns it as a list of polynomials. | ||
| − | + | <itemize> | |
| + | <item>@param <em>BB</em> A border basis of an ideal.</item> | ||
| + | <item>@return A list of polynomials that represents the reduced Groebner basis of the ideal generated by the input polynomials in BB.</item> | ||
| + | </itemize> | ||
<example> | <example> | ||
Use Z/(32003)[x,y,z],DegLex; | Use Z/(32003)[x,y,z],DegLex; | ||
Revision as of 16:44, 22 April 2009
BB.TransformBBIntoGB
Transform a border basis into a Groebner basis.
Syntax
BB.TransformBBIntoGB(BB:LIST of POLY):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 BB be a list of polynomials that form a <formula>\mathcal{O}_\sigma(I)</formula>-border basis of a zero-dimensional ideal <formula>I</formula>. This function extracts the reduced <formula>\sigma</formula>-Groebner basis contained in the <formula>\mathcal{O}_\sigma(I)</formula>-border basis BB and returns it as a list of polynomials.
@param BB A border basis of an ideal.
@return A list of polynomials that represents the reduced Groebner basis of the ideal generated by the input polynomials in BB.
Example
Use Z/(32003)[x,y,z],DegLex; I := Ideal( 4*x+5*y+6, 2*x^2*z+4*y^2*z+4*y*z^2+3*x*y+25*y^2+7*x*z+2*y-3*z, x^2*y+3*x*y*z+x*z^2+15*x^2+x*y+9*y*z+7 ); BB := BBasis(I); -- compute a border basis of I GB := BB.TransformBBIntoGB(BB); GB; ------------------------------- [x + 8002y - 16000, y^2z - 5614yz^2 + 6179y^2 - 2246yz - 4492y - 3370z, y^3 + 12128yz^2 + 2045y^2 - 10508yz + 10240z^2 + 3337y - 8088z - 11495, z^4 - 928yz^2 + 15802z^3 - 8546y^2 - 13286yz - 15491z^2 - 13314y + 5553z - 11227, yz^3 - 9667yz^2 + 11342z^3 + 6752y^2 + 8104yz - 15091z^2 - 950y - 15081z + 885] -------------------------------
