I'm bumping this up since I can't figure it out and I'm talking to Mike at
the Sage booth at JMMS. Can anyone answer this?
-Marshall
On Sunday, December 30, 2012 11:01:00 PM UTC-8, Mike wrote:
>
> For varying values of n, I'd like to find values of a so that int_0^z
> (x-a)^n dx has a root on the unit circle.
>
> As I'd like high precision, mpmath seems right.
>
> I can set things up as follows:
>
> sage: from mpmath import *; mp.dps=30; mp.pretty=true
> sage: var("a b c", domain="real")
> sage: p=integral((x-a)^2, x)
> sage: print p.subs(x=b+c*I).real()
> sage: print p.subs(x=b+c*I).imag()
> a^2*b - a*b^2 + a*c^2 + 1/3*b^3 - b*c^2
> a^2*c - 2*a*b*c + b^2*c - 1/3*c^3
>
> and then copy-and-paste the equations into a function
> and solve:
>
> sage: def f(a, b, c):
> ... return (a^2*b - a*b^2 + a*c^2 + 1/3*b^3 - b*c^2,
> ... a^2*c - 2*a*b*c + b^2*c - 1/3*c^3,
> ... b^2+c^2-1 )
> ...
> sage: findroot(f, (0.57, 0.85, 0.49))
> ...
> [0.577350269189625764509148780502]
> [0.866025403784438646763723170753]
> [ 0.5]
>
> which works, but I need to eliminate the manual copy-and-paste.
>
> What can I do to avoid the following error?
>
> sage: def g(a, b, c):
> ... return (p.subs(x=b+c*I).real(),
> ... p.subs(x=b+c*I).imag(),
> ... b^2+c^2-1 )
> ...
> sage: findroot(g, (0.57, 0.85, 0.49))
> Traceback (most recent call last):
> ...
> TypeError: g() takes exactly 3 arguments (1 given)
>
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