Question

I m trying to solve this system of nonlinear equations with Python:

2y³ + y² - y⁵ - x⁴ + 2x³ - x² = 0
(-4x³ + 6x² - 2x) / (5y⁴ - 6y² - 2y) = 1

Here s my code:

from sympy import symbols, Eq, solve
x, y = symbols( x y )
eq1 = Eq(2*y**3 + y**2 - y**5 - x**4 + 2*x**3 - x**2, 0)
eq2 = Eq((-4*x**3 + 6*x**2 - 2*x)/(5*y**4 - 6*y**2 - 2*y), 1)
points = solve([eq1, eq2], [x,y])

I know that this system of equations have 5 solutions, however I get none with this code. Someone know how I can proceed instead?

顺便提一下,第二个公式是第一个公式的衍生结果/结果,因此,基本上Im试图在紧凑的等数1中找到所有点,其中斜体的斜坡度为1。第一个方程式的图表是这样。

图1

我已经用Geogebra和5个答案解决这一问题。我在试验沙尔时想看到,我是否能够利用任何沙尔图书馆来解决这个问题。

https://i.stack.imgur.com/NCQGj.png”rel=“nofollow noreferer”>。

Answer 1

解决办法(在5个以下2名排雷人员中,3个)可以通过格罗伯纳办法找到(尽管我不清楚如何在基础上处理2个X-y方程式):

>>> from sympy import *

# your equations go here, then

>>> n, d = fraction((eq2.lhs-eq2.rhs).normal())
>>> sols = list(groebner((eq1,n),x,y))
>>> yy = real_roots(sols[-1])
>>> xy=list(sorted(set([(s.n(4),yi.n(4)) for e in sols[:2] for yi in yy for s in solve(e.subs(y,yi.n()))])))
>>> [d.subs(dict(zip((x,y),i))) for i in xy]
[6.697, 0, -0.1917, -0.2850, 0, -0.2850, -0.1917, 6.697]
>>> xy = [xy[i] for i in range(len(xy)) if i not in (1,4)]
>>> [i for i in xy if all(abs(v)<1e-4 for v in Tuple(eq1.lhs,n).subs(dict(zip((x,y),i))))]
[(-0.7575, 1.453), (0.2267, -0.5028), (1.106, -0.5731)]

Those are just proof-of-concept, low precision values.

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