from __future__ import division
from sympy import *
x,y,z = symbols('xyz')
def hyperplot( a2 = 5.10125066033543, b2 = 1.844025414703168, c2 =
2.303750131640994, d2 = 0, e2 = 3):
"""e2 is the distance between foci and a2,b2,c2,d2 are the times
of arrival the foci, c2 is at the center"""
a = ((a2 - c2)/2)**2
b = ((b2 - c2)/2)**2
c = ((d2 - c2)/2)**2
e = e2/2
eq1 = y**2/(e**2 - a) - (x + e)**2/a + 1
eq2 = x**2/(e**2 - b) - (y - e)**2/b + 1
eq3 = y**2/(e**2 - c) - (x - e)**2/c + 1
# returns the correct 4 solutions
# return solve([eq1, eq3], [x, y])
# sympy seems to have issues with eq2,
# these should have 4 real solutions each, but the returned
solutions have small imaginary components
#return solve([eq2, eq3], [x, y])
#return solve([eq1, eq2], [x, y])
# this did not return in a reasonable time frame
#return solve([eq1, eq2, eq3], [x, y])
# This is the best I have come up with, is there a better way?
s = solve([eq1, eq3], [x, y])
bestError = 1
best = None
for each in s:
error = eq2.evalf(subs={x:each[0], y:each[1]})
if error < bestError:
bestError = error
best = each
return best
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