On Fri, Aug 9, 2013 at 12:03 PM, Manoj Kumar
<manojkumarsivaraj...@gmail.com> wrote:
> Hi, I came across this while working on the lie group methods, Is this a bug
> or am I missing something quite obvious?
>
> r, x = Symbols("r x")
> eq = Integral(1/sqrt(a0 + a1*x + a2*x**2 + a3*x**3 + a4*x**4), x)
> eq = eq.subs(x, r)
> print(eq.doit())
> x/sqrt(a0 + a1*r + a2*r**2 + a3*r**3 + a4*r**4)
>
>
> This is because subs does not substitute for the variable with respect to
> which I am integrating. I would want eq = Integral(1/sqrt(a0 + a1*r +
> a2*r**2 + a3*r**3 + a4*r**4), r) rather than eq = Integral(1/sqrt(a0 + a1*r
> + a2*r**2 + a3*r**3 + a4*r**4), x) .
>
> Is there a possible workaround?
Integral.transform() is what you want. Here is how to use it:
In [10]: var("a0:5")
Out[10]: (a₀, a₁, a₂, a₃, a₄)
In [11]: eq = Integral(1/sqrt(a0 + a1*x + a2*x**2 + a3*x**3 + a4*x**4), x)
In [12]: eq
Out[12]:
⌠
⎮ 1
⎮ ────────────────────────────────────── dx
⎮ ___________________________________
⎮ ╱ 2 3 4
⎮ ╲╱ a₀ + a₁⋅x + a₂⋅x + a₃⋅x + a₄⋅x
⌡
In [13]: eq.transform(x, r)
Out[13]:
⌠
⎮ 1
⎮ ────────────────────────────────────── dr
⎮ ___________________________________
⎮ ╱ 2 3 4
⎮ ╲╱ a₀ + a₁⋅r + a₂⋅r + a₃⋅r + a₄⋅r
⌡
Ondrej
>
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