Curve translation in Python does not reach expected value-CodePudding

Suppose I have two curves, f(x) and g(x), and I want to evaluate if g(x) is a translation of f(x). I used Sympy Curve to do the job with the function translate. However, I need help to reach the correct result. Consider the two functions:

f(x) = -x^2 and g(x) = -(x 5)^2 8

Notice that g is vertically translated by 8 and horizontally translated by 5. Why at is not equal to b in the following Python code?

from sympy import expand, Symbol, Curve, oo

x = Symbol('x')
f = -x**2
g = -(x 5)**2 8

a = Curve((x, f), (x, -oo, oo))
at = a.translate(5,8)
b = Curve((x, g), (x, -oo, oo))

a, at, b, at == b

>>> (Curve((x, -x**2), (x, -10, 10)),
 Curve((x   5, 8 - x**2), (x, -10, 10)),
 Curve((x, 8 - (x   5)**2), (x, -10, 10)),
 False)

How could I make this analysis work using this or any other method?

CodePudding user response：

Curve is probably not the right way to do this. If you have univariate functions for which you want to know a x and y translation will make them equal, you could use something like the following:

>>> dx,dy = Symbols('dx dy')
>>> eq = Eq(f.subs(x,x-dx) dy)
>>> solve_undetermined_coeffs(eq,g),(dx,dy),x)
[(-5, 8)]

If there are no values of dx and dy that will solve the equality, then an empty list will be returned.

CodePudding user response：

Thanks to @smichr for the reference about solve_undetermined_coeffs. Here you can find a full answer to my initial problem in Python 3.8.10 and Sympy 1.11.1.

from sympy import symbols, Eq, solve_undetermined_coeffs

x, dx, dy = symbols('x dx dy')
f = -x**2
g = -(x 5)**2 8

eq = Eq(f.subs(x,x-dx) dy,g)
solve_undetermined_coeffs(eq,[dx,dy],x)