Using Sage Symbolic Functions in Scipy fsolve

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The original scenario involves two variables and only one equation. Because ff accepts two variables but does not return a list (or tuple, or array, ...) of length 2, the "shape mismatch" error is thrown. Here is a working example (with two equations and minimal modifications):

import scipy.optimize

var('x,y')
f = x^2 + y^2 - 1
g = x - y^2

def ff(v):
    x, y = map(float, v)
    return [f(x=x, y=y), g(x=x, y=y)]

print scipy.optimize.fsolve(ff, [1, 1])

Here is a more compact version using lambda functions and the trick described link:here

import scipy.optimize

var('x,y')
f(x,y) = (x^2 + y^2 - 1, x - y^2)

print scipy.optimize.fsolve(lambda v: f(*map(float, v)), (1, 1))

Since you said you have a large number of variables and equations, here is a slightly more "scale-friendly" approach (but somewhat kludgy):

import scipy.optimize

# Create symbolic variables "x_0" and "x_1".
# This is a pretty messy kludge
x = tuple(
    SR.var(
        "".join(['x_', str(t)])
    )
    for t in range(2)
)

# Represent system of equations using "x" as defined above.
# I use the intermediate "exprs" variable to allow breaking up the tuple
# over multiple lines.
exprs = (
    x[0]^2 + x[1]^2 - 1,
    x[0] - x[1]^2
)

f(*x) = exprs

# Guess values
guess = (1, 1)

print scipy.optimize.fsolve(lambda v: f(*map(float, v)), guess)

In all cases, the result should look like: [ 0.61803399 0.78615138]