Difference between revisions of "ApCoCoA-1:CharP.XLSolve"
| Line 18: | Line 18: | ||
<example> | <example> | ||
| − | Use | + | Use Z/(2)[x[1..4]]; |
| − | + | F:=[ | |
| − | + | x[1]x[2] + x[2]x[3] + x[2]x[4] + x[3]x[4] + x[1] + x[3] + 1, | |
| − | [x | + | x[1]x[2] + x[1]x[3] + x[1]x[4] + x[3]x[4] + x[2] + x[3] + 1, |
| − | ------------------------------- | + | x[1]x[2] + x[1]x[3] + x[2]x[3] + x[3]x[4] + x[1] + x[4] + 1, |
| − | + | x[1]x[3] + x[2]x[3] + x[1]x[4] + x[2]x[4] + 1 | |
| − | -- | + | ]; |
| − | -- | + | |
| + | -- Then we compute the solution with | ||
| + | CharP.XLSolve(F); | ||
| + | |||
| + | -- And we achieve the following information on the screen together with the solution at the end. | ||
| + | ---------------------------------------- | ||
| + | The size of Matrix is: | ||
| + | No. of Rows=4 | ||
| + | No. of Columns=11 | ||
| + | Appling Gaussian Elimination... | ||
| + | -- CoCoAServer: computing Cpu Time = 0 | ||
------------------------------- | ------------------------------- | ||
| − | + | Gaussian Elimination Completed. | |
| − | + | The variables found till now, if any are: | |
| − | + | [x[1], x[2], x[3], x[4]] | |
| − | + | The size of Matrix is: | |
| + | No. of Rows=16 | ||
| + | No. of Columns=15 | ||
| + | Appling Gaussian Elimination... | ||
-- CoCoAServer: computing Cpu Time = 0 | -- CoCoAServer: computing Cpu Time = 0 | ||
------------------------------- | ------------------------------- | ||
| − | [ | + | Gaussian Elimination Completed. |
| − | + | The variables found till now, if any are: | |
| + | [0, 1, 0, 1] | ||
| + | [0, 1, 0, 1] | ||
| + | |||
</example> | </example> | ||
Revision as of 16:13, 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. The XL-Algorithm is impelemented only to find a unique solution. If the given polynomial system has more than one zeros in F_2^n then this function does not find any zero. In this case a massage for non-uniqueness will be displayed to the screen after reaching the maximum degree bound.
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.
@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 Z/(2)[x[1..4]];
F:=[
x[1]x[2] + x[2]x[3] + x[2]x[4] + x[3]x[4] + x[1] + x[3] + 1,
x[1]x[2] + x[1]x[3] + x[1]x[4] + x[3]x[4] + x[2] + x[3] + 1,
x[1]x[2] + x[1]x[3] + x[2]x[3] + x[3]x[4] + x[1] + x[4] + 1,
x[1]x[3] + x[2]x[3] + x[1]x[4] + x[2]x[4] + 1
];
-- Then we compute the solution with
CharP.XLSolve(F);
-- And we achieve the following information on the screen together with the solution at the end.
----------------------------------------
The size of Matrix is:
No. of Rows=4
No. of Columns=11
Appling Gaussian Elimination...
-- CoCoAServer: computing Cpu Time = 0
-------------------------------
Gaussian Elimination Completed.
The variables found till now, if any are:
[x[1], x[2], x[3], x[4]]
The size of Matrix is:
No. of Rows=16
No. of Columns=15
Appling Gaussian Elimination...
-- CoCoAServer: computing Cpu Time = 0
-------------------------------
Gaussian Elimination Completed.
The variables found till now, if any are:
[0, 1, 0, 1]
[0, 1, 0, 1]
See also
Introduction to Groebner Basis in CoCoA
