Difference between revisions of "ApCoCoA-1:CharP.XLSolve"
| Line 1: | Line 1: | ||
<command> | <command> | ||
<title>CharP.GBasisF2</title> | <title>CharP.GBasisF2</title> | ||
| − | <short_description>Computing the unique <tt>F_2-</tt>rational | + | <short_description>Computing the unique <tt>F_2-</tt>rational zero of a given polynomial system over <tt>F_2</tt>.</short_description> |
<syntax> | <syntax> | ||
CharP.XLSolve(F:LIST):LIST | CharP.XLSolve(F:LIST):LIST | ||
</syntax> | </syntax> | ||
<description> | <description> | ||
| + | |||
| + | This function computes the unique zero in <tt>F_2^n</tt> of a polynomial system over <tt>F_2 </tt>. It uses XL-Algorithm to find the unique zero. If the given polynomial system has more than one zeros in <tt>F_2^n </tt> then this function does not find any zero. Because XL-Algorithm is impelemented only to find a unique solution. | ||
| + | |||
<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/> | ||
| − | This command computes the unique <tt>F_2-</tt>rational | + | This command computes the unique <tt>F_2-</tt>rational zero of a polynomial system over <tt>F_2 </tt>. |
<itemize> | <itemize> | ||
| − | <item>@param <em>F</em> A system of polynomial | + | <item>@param <em>F</em> A system of polynomial over <tt>F_2</tt> having a unique zero in <tt>F_2^n</tt>. </item> |
| − | <item>@return The unique solution of the given system in <tt>F_2</tt>. </item> | + | <item>@return The unique solution of the given system in <tt>F_2^n</tt>. </item> |
</itemize> | </itemize> | ||
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<see>CharP.GBasisF16</see> | <see>CharP.GBasisF16</see> | ||
<see>CharP.GBasisF32</see> | <see>CharP.GBasisF32</see> | ||
| − | + | ||
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</seealso> | </seealso> | ||
Revision as of 15:54, 6 December 2010
CharP.GBasisF2
Computing the unique F_2-rational zero of a given polynomial system over F_2.
Syntax
CharP.XLSolve(F:LIST):LIST
Description
This function computes the unique zero in F_2^n of a polynomial system over F_2 . It uses XL-Algorithm to find the unique zero. If the given polynomial system has more than one zeros in F_2^n then this function does not find any zero. Because XL-Algorithm is impelemented only to find a unique solution.
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 the unique F_2-rational zero of a polynomial system over F_2 .
@param F A system of polynomial over F_2 having a unique zero in F_2^n.
@return The unique solution of the given system in F_2^n.
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); CharP.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
