Unable to solve the following set of equations

[Shishir Kushwaha]

In the following piece of code I am  unable to get the values of a,b and c after solving them.

Is there a different way to solve it and what am i doing wrong. Take x1 = 0 , y1=10, x2=0, y2=10, length = 20.

def get_lowest_point(self):

a, b, c, x = symbols('a b c x')

x1, y1 = self._left_support

x2, y2 = self._right_support

length = self._length

eq1 = Eq(a * x1**2 + b * x1 + c, y1)

eq2 = Eq(a * x2**2 + b * x2 + c, y2)

arc_length_expr = integrate(sqrt(1 + (2 * a * x + b)**2),

(x, x1, x2))

eq3 = Eq(arc_length_expr, length)

solution = solve((eq1, eq2, eq3), (a, b, c))

# Print the solution to debug

print("Solution:", solution)

return solution

[Aaron Meurer]

With x1 = x2 = 0, arc_length_expr is equal to 0, meaning your eq3 is
invalid. You can see this if you print eq3. It gets set to False,
because it is 0 = 10.

Aaron Meurer

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[Shishir Kushwaha]

I'm sorry , I meant to write x1=0, x2=10. It gives

Eq(Piecewise(((5 + b/(4*a))*sqrt(400*a**2 + 40*a*b + b**2 + 1) - log(4*a*b + 4*sqrt(b**2 + 1)*sqrt(a**2))/(4*sqrt(a**2)) + log(80*a**2 + 4*a*b + 4*sqrt(400*a**2 + 40*a*b + b**2 + 1)*sqrt(a**2))/(4*sqrt(a**2)) - b*sqrt(b**2 + 1)/(4*a), ((a > -oo) & (a < oo) & Ne(a, 0)) | (Ne(a**2, 0) & Ne(a*b, 0))), (-(b**2 + 1)**(3/2)/(6*a*b) + (40*a*b + b**2 + 1)**(3/2)/(6*a*b), Ne(a*b, 0)), (10*sqrt(b**2 + 1), True)), 20) 

but the solution I got is empty i.e. [ ]

Thanks

Shishir Kushwaha

[Chris Smith]

`nsolve(eqs,list(ordered(eqs.free_symbols)),(.4,3,10))` (with eqs defined with  x1= 0,y1=10, x2=10, y2=10, length = 20) gives  `Matrix([[0.326920231236118], [-3.26920231236118], [10.0000000000000]])`

I doubt there is a closed form solution. You can easily solve the first two equations for `a` and `c` and then you only have the last equation in `b`.

/c

[Aaron Meurer]

Just to clarify what Chris is saying, sympy.solve() *only* returns
symbolic closed-form solutions. If the equation doesn't have any, or
if it just doesn't have the algorithms to find them, it might return
an empty solution set. That doesn't mean the equation has no
solutions. It just means it couldn't find any closed-form ones.

If you just need a numerical answer, you are better off using nsolve()
or a solver from a numeric library like scipy. See
https://docs.sympy.org/latest/guides/solving/solve-numerically.html.

If you really do want a symbolic solution here, and are convinced one
exists, you'll have to do some work yourself manipulating the
equations yourself to help SymPy find it, because it doesn't yet have
the algorithms to find it on its own. If you find that a closed-form
solution does exist, you can open an issue for SymPy to improve its
solvers for this equation.

Aaron Meurer

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