Did you just try using solve? Sympifying the equations you give for h13 and
h23 gives the following result for me:
>>> solve((h23,h13),x,y)
[(-0.557666440391888 + 4.91385686350788e-31*I, -1.35411398328542 -
2.27087209183
879e-32*I), (-0.555228172386711 + 2.35128780795143e-29*I,
0.0820809601337735 - 1
.08661602193259e-30*I), (0.871420006337371 + 4.47416209082826e-30*I,
-0.28263412
4887546 - 2.06767454992846e-31*I), (2.00000355907055 -
2.84784242544466e-29*I, 5
.70736401553117e-7 + 6.42623143478428e-34*I)]
/c
On Thursday, July 30, 2015 at 3:09:19 AM UTC-5, Russell Young wrote:
>
> I'm a newbie with sympy, so this may be something I am doing wrong.
>
> I've written code that finds the intersection of 2 hyperbolas. The
> equations are correct - when I plot them they are as expected. Using test
> data where I know there is a solution, sometimes it finds it, sometimes it
> doesn't. I've found and fixed a few issues so far: no division of python
> numbers, normalizing the graphs so no numbers are too small, adding a
> .simplify() call to the equations being solved. Still, it ends up missing
> solutions. The order the equations are passed to the solve function also
> affects the solutions found.
>
> Here is some output that describes the hyperbolas, shows the equations,
> and gives the results:
>
> $ python hyperbola.py -1 0 10.033445 1 1 4.729811 0 -1 7.478488
> h12
> a = 0.792893, b = 0.788239, c = 1.118034
> foci are Point(-1, 0) and Point(1, 1)
> center is Point(0, 1/2)
> equation is -1.60947597191687*(-sqrt(5)*x/5 + 2*sqrt(5)*(y - 1/2)/5)**2
> + 1.59063495669236*(2*sqrt(5)*x/5 + sqrt(5)*(y - 1/2)/5)**2 == 1
> h13
> a = 0.381966, b = 0.595065, c = 0.707107
> foci are Point(-1, 0) and Point(0, -1)
> center is Point(-1/2, -1/2)
> equation is 6.8540998039692*(sqrt(2)*(x + 1/2)/2 - sqrt(2)*(y + 1/2)/2
> )**2 - 2.82404568540787*(sqrt(2)*(x + 1/2)/2 + sqrt(2)*(y + 1/2)/2)**2 ==
> 1
> h23
> a = 0.410927, b = 1.039778, c = 1.118034
> foci are Point(1, 1) and Point(0, -1)
> center is Point(1/2, 0)
> equation is -0.924950593916484*(-sqrt(5)*y/5 - 2*sqrt(5)*(x - 1/2)/5)**2
> + 5.92202447335121*(2*sqrt(5)*y/5 - sqrt(5)*(x - 1/2)/5)**2 == 1
> h12 and h13: [(2.00000069353477, -1.05724449909221e-7)]
> h13 and h13: []
>
> h12 and h23: [(-0.872442811259504, -1.67266454797664), (-0.671975994196070
> , 0.0582722523367054), (0.819499463572107, 0.688825355380073), (
> 2.00000032674867, 4.62032762769592e-8)]
> h23 and h12: [(2.00000032674867, 4.62032762919501e-8)]
>
> h13 and h23: []
> h23 and h13: []
> $
>
> Parameters for these 3 equations were chosen so that the point (2, 0) is
> nearly on all of them. It is found in one of the orderings of the first
> pair, in both of the second pair, and in neither of the third pair.
>
> Following is an excerpt of the code that makes and solves the equation:
> _x, _y, _a, _b = symbols('x, y, a, b')
> _standard = Eq(_x**2/_a**2 - _y**2/_b**2, 1)
> _degenerate = Eq(_x, 0)
>
>
> class Hyperbola(object):
> def __init__(self, f0, f1, diff):
> self.foci = [Point(f0), Point(f1)]
> self.a = S(diff)/2
> self.c = self.foci[0].distance(self.foci[1])/2
> try:
> self.b = sqrt(self.c**2 - self.a**2)
> except ValueError:
> print 'Computed minor axis for %s %s %f is imaginary' % (str(
> f0), str(f1), diff)
> exit(1)
> ...
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