solve() has issues with equations like these currently because it
wants to treat them as polynomials. But the degree of the polynomial
is related to the numerator and denominator of the exponent:
In [14]: Rational(0.45)
Out[14]:
8106479329266893
─────────────────
18014398509481984
If you use rational numbers, and solve for a manually in the second
equation, you get a degree 20 polynomial (after multiplying by b**20):
In [24]: expr = a * b**Rational(45, 100) - a + 1 - 4.5 * b
In [25]: expr.subs(solve([0.45 * a * b**(Rational(45, 100) - 1) - 4.5], [a]))
Out[25]:
11
──
20
- 10.0⋅b + 5.5⋅b + 1
I was able to get solutions with solve(expr.subs(solve([0.45 * a *
b**(Rational(45, 100) - 1) - 4.5], [a]))*b**20, rational=True), but
none are expressible exactly.
I recommend trying nsolve, which can give you numeric solutions to
this system, and quite fast:
In [30]: nsolve([a * b**0.45 - a + 1 - 4.5 * b, 0.45 * a * b**(0.45 -
1) - 4.5], [a, b], [1, 1])
Out[30]:
⎡ 1.09929682680944 ⎤
⎢ ⎥
⎣0.0180539685108078⎦
Aaron Meurer
On Sun, Apr 16, 2017 at 4:51 PM, pdknsk <[email protected]> wrote:
> I've been trying to get the solution for the following equations.
>
> 4.5*b = a*b^0.45-a+1
> 4.5 = 0.45*a*b^(0.45-1)
>
> I think this should do it.
>
> ab = sympy.solve([a * b**0.45 - a + 1 - 4.5 * b, 0.45 * a * b**(0.45 - 1) -
> 4.5])
>
> After waiting 100 minutes I cancelled it. It's not clear to me if it will
> eventually find a solution, or if it has reached a broken internal state
> which will make it compute indefinitely.
>
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