Difference between revisions of "ApCoCoA-1:BB.TransformGBIntoBB"
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<command> | <command> | ||
<title>BB.TransformGBIntoBB</title> | <title>BB.TransformGBIntoBB</title> | ||
| − | <short_description> | + | <short_description>Transforms a Groebner basis into a border basis.</short_description> |
| − | <syntax>BB.TransformGBIntoBB(GB:LIST of POLY):LIST of POLY</syntax> | + | |
| + | <syntax> | ||
| + | BB.TransformGBIntoBB(GB:LIST of POLY):LIST of POLY | ||
| + | </syntax> | ||
<description> | <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. | <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/> | <par/> | ||
| − | Let <tt>GB</tt> be a list of polynomials that form a <tt>sigma</tt>-Groebner basis of a zero-dimensional ideal <tt>I</tt>. This function computes the O_sigma(I)-border basis of <tt>I</tt> by using the information provided by the given <tt>sigma</tt>-Groebner basis. | + | Let <tt>GB</tt> be a list of polynomials that form a <tt>sigma</tt>-Groebner basis of a zero-dimensional ideal <tt>I</tt>. This function computes the <tt>O_sigma(I)</tt>-border basis of <tt>I</tt> by using the information provided by the given <tt>sigma</tt>-Groebner basis. |
<itemize> | <itemize> | ||
| − | <item>@param <em>GB</em> A | + | <item>@param <em>GB</em> A Groebner basis of a zero-dimensional ideal.</item> |
| − | <item>@return A list of polynomials that represents the border basis of the zero-dimensional ideal generated by the input polynomials in GB.</item> | + | <item>@return A list of polynomials that represents the border basis of the zero-dimensional ideal generated by the input polynomials in <tt>GB</tt>.</item> |
</itemize> | </itemize> | ||
<example> | <example> | ||
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</description> | </description> | ||
<types> | <types> | ||
| − | |||
| − | |||
<type>polynomial</type> | <type>polynomial</type> | ||
| + | <type>groebner</type> | ||
<type>borderbasis</type> | <type>borderbasis</type> | ||
<type>apcocoaserver</type> | <type>apcocoaserver</type> | ||
</types> | </types> | ||
| − | <see>BB.BBasis</see> | + | |
| − | <see>GBasis</see> | + | <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>TransformGBIntoBB</key> | <key>TransformGBIntoBB</key> | ||
<key>BB.TransformGBIntoBB</key> | <key>BB.TransformGBIntoBB</key> | ||
<key>borderbasis.TransformGBIntoBB</key> | <key>borderbasis.TransformGBIntoBB</key> | ||
| − | <wiki-category>Package_borderbasis</wiki-category> | + | <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.TransformGBIntoBB
Transforms a Groebner basis into a border basis.
Syntax
BB.TransformGBIntoBB(GB: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 GB be a list of polynomials that form a sigma-Groebner basis of a zero-dimensional ideal I. This function computes the O_sigma(I)-border basis of I by using the information provided by the given sigma-Groebner basis.
@param GB A Groebner basis of a zero-dimensional ideal.
@return A list of polynomials that represents the border basis of the zero-dimensional ideal generated by the input polynomials in GB.
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 ); GB := GBasis(I); -- compute a Groebner basis of I BB := BB.TransformGBIntoBB(GB); BB; ------------------------------- [x + 8002y - 16000, xz + 8002yz - 16000z, xy + 8002y^2 - 16000y, y^2z - 5614yz^2 + 6179y^2 - 2246yz - 4492y - 3370z, y^3 + 12128yz^2 + 2045y^2 - 10508yz + 10240z^2 + 3337y - 8088z - 11495, xz^2 + 8002yz^2 - 16000z^2, xyz - 8984yz^2 + 277y^2 + 2809yz + 5615y - 11789z, xy^2 - 15160yz^2 + 5446y^2 + 13135yz - 12800z^2 - 12172y + 10110z + 6368, 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, y^2z^2 + 1958yz^2 - 11982z^3 + 13714y^2 + 3833yz - 12303z^2 - 11335y + 4481z + 7925, xz^3 + 4083yz^2 - 14176z^3 - 8440y^2 - 10130yz + 10863z^2 - 14814y - 5151z - 9107, xyz^2 - 2446yz^2 - 1024z^3 - 1141y^2 - 12792yz + 7378z^2 + 6168y - 13602z + 14096] -------------------------------
Introduction to Groebner Basis in CoCoA
