ApCoCoA-1:FGLM.FGLM: Difference between revisions
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<command> | |||
<title>FGLM.FGLM</title> | |||
<short_description>Performs a FGLM Groebner Basis conversion using ApCoCoAServer.</short_description> | |||
<syntax> | <syntax> | ||
FGLM( | FGLM(GBInput:LIST, M:MAT):LIST | ||
FGLM( | FGLM(GBInput:LIST):LIST | ||
</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/> | |||
The function <tt>FGLM</tt> calls the ApCoCoAServer to perform a | The function <tt>FGLM</tt> calls the ApCoCoAServer to perform a | ||
FGLM Groebner Basis conversion. Please note that the ideal generated by | FGLM Groebner Basis conversion. Please note that the ideal generated by | ||
the given Groebner Basis must be zero-dimensional. The Groebner | the given Groebner Basis must be zero-dimensional. The Groebner | ||
Basis contained in list | Basis contained in list GBInput 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>ApCoCoA-1:Ord|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>ApCoCoA-1:Ord|Ord</ref>(). Please note that the resulting polynomials belong | ||
to a different ring than the ones in | to a different ring than the ones in GBInput. | ||
<par/> | |||
The return value will be the transformed Groebner basis polynomials. | |||
<itemize> | |||
<item>@param <em>GBInput</em> A Groebner basis of a zero-dimensional ideal.</item> | |||
<item>@return A Groebner basis of the ideal generated by the polynomials of GBInput. The polynomials of the new Groebner basis will belong to the polynomial ring with term ordering specified by <tt>M</tt> or <ref>ApCoCoA-1:Ord|Ord</ref>() in case M is not given.</item> | |||
</itemize> | |||
The following parameter is optional. | |||
<itemize> | <itemize> | ||
<item>@param <em>M</em> A matrix representing a term ordering.</item> | |||
<item>@param <em>M</em> A matrix representing a term ordering | |||
</itemize> | </itemize> | ||
<example> | <example> | ||
Use | Use QQ[x, y, z], DegRevLex; | ||
GBInput := [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); | M := LexMat(3); | ||
GBNew := FGLM( | GBNew := FGLM.FGLM(GBInput, M); | ||
Use | Use QQ[x, y, z], Ord(M); | ||
-- New basis (Lex) | -- New basis (Lex) | ||
BringIn(GBNew); | BringIn(GBNew); | ||
------------------------------- | |||
[z^6 - z^5 - 4z^4 - 2z^3 + 1, y - 4/7z^5 + 5/7z^4 + 13/7z^3 + 10/7z^2 - 6/7z - 2/7, | |||
x + 4/7z^5 - 5/7z^4 - 13/7z^3 - 10/7z^2 - 1/7z + 2/7] | |||
------------------------------- | |||
</example> | </example> | ||
</description | </description> | ||
<see>ApCoCoA-1:GBasis5, and more|GBasis5, and more</see> | |||
<see>GBasis5, and more</see> | <see>ApCoCoA-1:Introduction to CoCoAServer|Introduction to CoCoAServer</see> | ||
</ | <types> | ||
<types> | <type>groebner</type> | ||
<type>ideal</type> | |||
<type>apcocoaserver</type> | |||
</types> | |||
< | <key>FGLM</key> | ||
</ | <key>FGLM.FGLM</key> | ||
<key>fglm</key> | <key>fglm.FGLM</key> | ||
<key> | <key>groebner basis conversion</key> | ||
<wiki-category>Package_fglm</wiki-category> | <wiki-category>ApCoCoA-1:Package_fglm</wiki-category> | ||
</command> | </command> | ||
Latest revision as of 10:00, 7 October 2020
| This article is about a function from ApCoCoA-1. |
FGLM.FGLM
Performs a FGLM Groebner Basis conversion using ApCoCoAServer.
Syntax
FGLM(GBInput:LIST, M:MAT):LIST FGLM(GBInput: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 GBInput 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 GBInput.
The return value will be the transformed Groebner basis polynomials.
@param GBInput A Groebner basis of a zero-dimensional ideal.
@return A Groebner basis of the ideal generated by the polynomials of GBInput. 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.
The following parameter is optional.
@param M A matrix representing a term ordering.
Example
Use QQ[x, y, z], DegRevLex; GBInput := [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.FGLM(GBInput, M); Use QQ[x, y, z], Ord(M); -- New basis (Lex) BringIn(GBNew); ------------------------------- [z^6 - z^5 - 4z^4 - 2z^3 + 1, y - 4/7z^5 + 5/7z^4 + 13/7z^3 + 10/7z^2 - 6/7z - 2/7, x + 4/7z^5 - 5/7z^4 - 13/7z^3 - 10/7z^2 - 1/7z + 2/7] -------------------------------
