ApCoCoA-1:FGLM.FGLM: Difference between revisions
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<command> | |||
<title>FGLM.FGLM</title> | |||
<short_description>Perform a FGLM Groebner Basis conversion using ApCoCoAServer.</short_description> | |||
<syntax> | <syntax>FGLM(GBOld:LIST, M:MAT):LIST | ||
FGLM(GBOld:LIST, M:MAT):LIST | FGLM(GBOld:LIST):LIST</syntax> | ||
FGLM(GBOld:LIST):LIST | <description> | ||
</syntax> | |||
<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/> | ||
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the given Groebner Basis must be zero-dimensional. The Groebner | the given Groebner Basis must be zero-dimensional. The Groebner | ||
Basis contained in list GBOld will be converted into a Groebner | Basis contained in list GBOld will be converted into a Groebner | ||
Basis with respect to term ordering Ord(M), i.e. M must be a matrix | Basis with respect to term ordering <ref>Ord</ref>(M), i.e. M must be a matrix | ||
specifying a term ordering. If the parameter M is not specified, | specifying a term ordering. If the parameter M is not specified, ApCoCoA | ||
will assume M = Ord(). Please note that the resulting polynomials belong | will assume M = <ref>Ord</ref>(). Please note that the resulting polynomials belong | ||
to a different ring than the ones in GBOld. | to a different ring than the ones in GBOld. | ||
<par/> | |||
The return value will be the transformed Groebner basis polynomials. | |||
<itemize> | <itemize> | ||
<item>@param <em>GBOld</em> A Groebner basis of a zero-dimensional ideal.</item> | <item>@param <em>GBOld</em> A Groebner basis of a zero-dimensional ideal.</item> | ||
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BringIn(GBNew); | BringIn(GBNew); | ||
</example> | </example> | ||
</description | </description> | ||
<see>GBasis5, and more</see> | <see>GBasis5, and more</see> | ||
<types> | |||
<types> | <type>groebner</type> | ||
<type>matrix</type> | |||
<type>list</type> | |||
<type>apcocoaserver</type> | |||
</types> | |||
</types> | <key>FGLM</key> | ||
<key>FGLM</key> | <key>FGLM.FGLM</key> | ||
<key>FGLM.FGLM</key> | <key>fglm.FGLM</key> | ||
<key>fglm.FGLM</key> | <key>groebner basis conversion</key> | ||
<key>groebner basis conversion</key> | <wiki-category>Package_fglm</wiki-category> | ||
<wiki-category>Package_fglm</wiki-category> | |||
</command> | </command> | ||
Revision as of 11:43, 24 April 2009
FGLM.FGLM
Perform a FGLM Groebner Basis conversion using ApCoCoAServer.
Syntax
FGLM(GBOld:LIST, M:MAT):LIST FGLM(GBOld:LIST):LIST
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.
The function FGLM calls the ApCoCoAServer to perform a
FGLM Groebner Basis conversion. Please note that the ideal generated by
the given Groebner Basis must be zero-dimensional. The Groebner Basis contained in list GBOld will be converted into a Groebner Basis with respect to term ordering Ord(M), i.e. M must be a matrix specifying a term ordering. If the parameter M is not specified, ApCoCoA will assume M = Ord(). Please note that the resulting polynomials belong to a different ring than the ones in GBOld.
The return value will be the transformed Groebner basis polynomials.
@param GBOld A Groebner basis of a zero-dimensional ideal.
@param M A matrix representing a term ordering.
@return A Groebner basis of the ideal generated by the polynomials of GBOld. The polynomials of the new Groebner basis will belong to the polynomial ring with term ordering specified by M or Ord() in case M is not given.
Example
Use QQ[x, y, z], DegRevLex; GBOld := [z^4 -3z^3 - 4yz + 2z^2 - y + 2z - 2, yz^2 + 2yz - 2z^2 + 1, y^2 - 2yz + z^2 - z, x + y - z]; M := LexMat(3); GBNew := FGLM(GBOld, M); Use QQ[x, y, z], Ord(M); -- New basis (Lex) BringIn(GBNew);
