On Wed, Aug 26, 2009 at 8:42 PM, kenji<[email protected]> wrote:
>
> Hi all,
>
> I want to expand and reduce Lagrange Resolvent in Galois theory under a
> restriction.
>
> The below equation is expanding and reducing operations in Maxima.
>
> (C1) L1(w, x0,x1,x2):= x0 + w*x1 + w^2*x2;
> (C2) expand(ratsubst(0,1+w+w^2, L1(w, x0,x1,x2)^3) );
>
> 3 2 2 2 2
> (D2) x2 - 3 w x1 x2 - 3 x1 x2 + 3 w x0 x2 + 3 w x1 x2 + 6 x0 x1 x2
>
> 2 2 3 2 2 2
> 3
> - 3 w x0 x2 - 3 x0 x2 + x1 - 3 w x0 x1 - 3 x0 x1 + 3 w x0 x1 + x0
>
>
> I want to manipulate this operations in sympy. I tried fraction, collect match
> and others, but can't manipulate them
>
> Does sympy manipulate this expanding and reducing operations under a
> restriction ?
I think we can't --- do you know the algorithm for it? E.g. I just
take an expression:
In [1]: L1 = S("x0 + w*x1 + w^2*x2")
In [2]: L1
Out[2]:
2
x₀ + w⋅x₁ + x₂⋅w
cube it, expand it:
In [3]: (L1**3).expand()
Out[3]:
2 2 2 4 2 5 2 2 2 4
3⋅w⋅x₁⋅x₀ + 3⋅x₀⋅w ⋅x₁ + 3⋅x₀⋅w ⋅x₂ + 3⋅x₁⋅w ⋅x₂ + 3⋅x₂⋅w ⋅x₀ + 3⋅x₂⋅w ⋅x
2 3 3 3 6 3 3
₁ + x₀ + w ⋅x₁ + w ⋅x₂ + 6⋅x₀⋅x₁⋅x₂⋅w
and then I should somehow substitute 1+w+w^2 for 0, right? E.g.
something like this, except that it doesn't work:
In [3]: e = (L1**3).expand()
In [6]: w = S("w")
In [11]: e.subs(1+w+w**2, 0)
Out[11]:
2 2 2 4 2 5 2 2 2 4
3⋅w⋅x₁⋅x₀ + 3⋅x₀⋅w ⋅x₁ + 3⋅x₀⋅w ⋅x₂ + 3⋅x₁⋅w ⋅x₂ + 3⋅x₂⋅w ⋅x₀ + 3⋅x₂⋅w ⋅x
2 3 3 3 6 3 3
₁ + x₀ + w ⋅x₁ + w ⋅x₂ + 6⋅x₀⋅x₁⋅x₂⋅w
If you know some algorithm for it, maybe it's not difficult to implement this.
Ondrej
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