On Fri, 6 May 2011 15:22:25 -0700 (PDT)
tvn <nguyenthanh...@gmail.com> wrote:

> given a list of equality expressions, is there a way to remove all the
> members that can be inferred by others in the list so that the final
> list contains only independent expressions and they imply all the ones
> that were removed.
> 
> For example
> 
> [x == 2,  x^2 = 4]   =>  [x == 2]
> 
> ([x*x-y*y==0,x-y==0,x*x-y*y==0,2*x*y-2*y*y==0]  => [-x + y == 0]
> 
> 
> 
> I tried to use Grobner basis
> 
> Q = PolynomialRing(QQ,[x,y,z ...])
> result = (Q*input_list).groebner_basis()
> 
> but it's not the right approach for this because
> 
> [a*y - b == 0,a*r - a*x + b*q == 0,q*y + r - x == 0]  =>  [a*y - b ==
> 0, q*y + r - x == 0, -a*r + a*x - b*q == 0]   even though a*r - a*x +
> b*q == 0 can be implied from the other two.
> 
> 
> Any suggestion ?

You can try qepcad, see:

sage: qepcad?

You will need to install the experimental package before you can use
any of it.

sage: install_package('qepcad')


Cheers,
Burcin

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