Difference between revisions of "ApCoCoA-1:CharP.GBasisF2"
From ApCoCoAWiki
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<item>@return The Groebner Basis of the given ideal.</item> | <item>@return The Groebner Basis of the given ideal.</item> | ||
</itemize> | </itemize> | ||
| + | |||
| + | <example> | ||
| + | Use R::=QQ[x,y,z]; | ||
| + | I:=Ideal(x-y^2,x^2+xy,y^3); | ||
| + | GBasis(I); | ||
| + | [x^2 + xy, -y^2 + x, -xy] | ||
| + | ------------------------------- | ||
| + | Use Z::=ZZ[x,y,z]; | ||
| + | -- WARNING: Coeffs are not in a field | ||
| + | -- GBasis-related computations could fail to terminate or be wrong | ||
| + | |||
| + | ------------------------------- | ||
| + | I:=Ideal(x-y^2,x^2+xy,y^3); | ||
| + | Char2.GBasisF2(I); | ||
| + | -- WARNING: Coeffs are not in a field | ||
| + | -- GBasis-related computations could fail to terminate or be wrong | ||
| + | -- CoCoAServer: computing Cpu Time = 0 | ||
| + | ------------------------------- | ||
| + | [y^2 + x, x^2, xy] | ||
| + | ------------------------------- | ||
| + | </example> | ||
| + | |||
</description> | </description> | ||
<seealso> | <seealso> | ||
Revision as of 13:02, 13 July 2009
Char2.GBasisF2
Computing a Groebner Basis of a given ideal in F_2.
Syntax
Char2.GBasisF2(Ideal:IDEAL):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.
This command computes a Groebner Basis in the field F_2 = Z/(2).
@param Ideal An Ideal in a Ring over Z, where the elements 0,1 represent the elements of the field.
@return The Groebner Basis of the given ideal.
Example
Use R::=QQ[x,y,z]; I:=Ideal(x-y^2,x^2+xy,y^3); GBasis(I); [x^2 + xy, -y^2 + x, -xy] ------------------------------- Use Z::=ZZ[x,y,z]; -- WARNING: Coeffs are not in a field -- GBasis-related computations could fail to terminate or be wrong ------------------------------- I:=Ideal(x-y^2,x^2+xy,y^3); Char2.GBasisF2(I); -- WARNING: Coeffs are not in a field -- GBasis-related computations could fail to terminate or be wrong -- CoCoAServer: computing Cpu Time = 0 ------------------------------- [y^2 + x, x^2, xy] -------------------------------
See also
Introduction to Groebner Basis in CoCoA
Representation of finite fields
