There have been several questions about solving equations where it seems
that we haven't featured nsolve enough: nsolve is a great way to get a
numerical solution to an equation. You can use sympy to do the derivations
of some equation that you want to solve and then use nsolve to process it
for given parameters.
On Stock Overflow, a question asked about how to find the distance from a
point to a function, f.
>>> f=1/(1+exp(-x))
>>> perp_slope = -1/f.diff(x)
>>> line_from_ab = b + perp_slope*(x - a) # or solve(Line((a,b),
slope=perp_slope).equation(x, y), y)[0]
>>> xcross = Eq(f, line_from_ab)
>>> dist = Point(a, b).distance(Point(x,y))
>>> reps = {a:a, b:b, x: x, y:y}
>>> reps[a]=1;reps[b]=2
>>> reps[x] = nsolve(xcross.subs(reps),x,1)
>>> reps[y] = f.subs(reps)
>>> dist.subs(reps).n(3)
1.25
Now try from (2,2)
>>> reps[a]=2; reps[x]=x; reps[y]=y
>>> reps[x] = nsolve(xcross.subs(reps),x,2)
>>> reps[y] = f.subs(reps)
>>> dist.subs(reps).n(3)
1.11
So...when you want a numeric answer, don't feel stymied if you can't solve
the expression symbolically for x.
/c
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