ApCoCoA-1:BB.TransformBBIntoGB: Difference between revisions
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{{Version|1}} | |||
<command> | <command> | ||
<title>BB.TransformBBIntoGB</title> | |||
<short_description>Transforms a border basis into a Groebner basis.</short_description> | |||
<syntax> | <syntax> | ||
BB.TransformBBIntoGB(BB:LIST of POLY):LIST of POLY | BB.TransformBBIntoGB(BB:LIST of POLY):LIST of POLY | ||
</syntax> | </syntax> | ||
<description> | |||
<em>Please note:</em> The function(s) explained on this page is/are using the <em>ApCoCoAServer</em>. You will have to start the ApCoCoAServer in order to use it/them. | |||
<par/> | |||
Let <tt>BB</tt> be a list of polynomials that form a < | Let <tt>BB</tt> be a list of polynomials that form a <tt>O_sigma(I)</tt>-border basis of a zero-dimensional ideal <tt>I</tt>. This function extracts the reduced <tt>sigma</tt>-Groebner basis contained in the <tt>O_sigma(I)</tt>-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 <tt>BB</tt>.</item> | |||
</itemize> | |||
<example> | <example> | ||
Use | Use ZZ/(32003)[x,y,z],DegLex; | ||
I := Ideal( | I := Ideal( | ||
4*x+5*y+6, | 4*x+5*y+6, | ||
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x^2*y+3*x*y*z+x*z^2+15*x^2+x*y+9*y*z+7 | 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 | BB := BB.BBasis(I); -- compute a border basis of I | ||
GB := BB.TransformBBIntoGB(BB); | GB := BB.TransformBBIntoGB(BB); | ||
GB; | GB; | ||
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------------------------------- | ------------------------------- | ||
</example> | </example> | ||
</ | </description> | ||
<see>BBasis</see> | <types> | ||
<type>polynomial</type> | |||
<type>borderbasis</type> | |||
<type>groebner</type> | |||
<type>apcocoaserver</type> | |||
</types> | |||
<see>ApCoCoA-1:Introduction to CoCoAServer|Introduction to CoCoAServer</see> | |||
<see>ApCoCoA-1:Introduction to Groebner Basis in CoCoA|Introduction to Groebner Basis in CoCoA</see> | |||
<see>ApCoCoA-1:BB.BBasis|BB.BBasis</see> | |||
<see>ApCoCoA-1:GBasis|GBasis</see> | |||
<key>TransformBBIntoGB</key> | |||
<key>BB.TransformBBIntoGB</key> | |||
<key>borderbasis.TransformBBIntoGB</key> | |||
<wiki-category>ApCoCoA-1:Package_borderbasis</wiki-category> | |||
</command> | </command> | ||
Latest revision as of 09:43, 7 October 2020
| This article is about a function from ApCoCoA-1. |
BB.TransformBBIntoGB
Transforms 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 O_sigma(I)-border basis of a zero-dimensional ideal I. This function extracts the reduced sigma-Groebner basis contained in the O_sigma(I)-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 ZZ/(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 := 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] -------------------------------
Introduction to Groebner Basis in CoCoA
