Updates:
Summary: Ellipse.tangent_lines needs to be more robust
Comment #4 on issue 716 by [email protected]: Ellipse.tangent_lines needs to
be more robust
http://code.google.com/p/sympy/issues/detail?id=716
The name of the method is now tangent_lines. The intersection detection
could perhaps use checksol in solvers.py to do the checking to see if the
point satisfies the original equation.
Sometimes a tangent line is found and sometimes not, so it needs to be more
robust in that area, too:
e = Ellipse(Point(0,0), 3, 2)
t = e.tangent_lines(e.random_point())
t
[]
e.tangent_lines(e.random_point())
[]
e.tangent_lines(e.random_point())
[]
e.tangent_lines(e.random_point())
[]
e.tangent_lines(e.random_point())
[]
e.tangent_lines(e.random_point())
[]
e.tangent_lines(e.random_point())
Traceback (most recent call last):
File "<stdin>", line 1, in <module>
File "sympy\geometry\ellipse.py", line 528, in tangent_lines
tangent_points = solve([w.as_numer_denom()[0] for w in [slope - dydx,
eq]],
[x, y])
File "sympy\solvers\solvers.py", line 483, in solve
solution = _solve(f, *symbols, **flags)
File "sympy\solvers\solvers.py", line 883, in _solve
result = solve_poly_system(polys, *symbols)
File "sympy\solvers\polysys.py", line 40, in solve_poly_system
return solve_biquadratic(f, g, opt)
File "sympy\solvers\polysys.py", line 48, in solve_biquadratic
G = groebner([f, g])
File "sympy\polys\polytools.py", line 5460, in groebner
return GroebnerBasis(F, *gens, **args)
File "sympy\polys\polytools.py", line 5496, in __new__
raise DomainError("can't compute a Groebner basis over %s" % opt.domain)
sympy.polys.polyerrors.DomainError: can't compute a Groebner basis over RR
e.tangent_lines(e.random_point())
[]
e.tangent_lines(e.random_point())
Traceback (most recent call last):
File "<stdin>", line 1, in <module>
File "sympy\geometry\ellipse.py", line 528, in tangent_lines
tangent_points = solve([w.as_numer_denom()[0] for w in [slope - dydx,
eq]],
[x, y])
File "sympy\solvers\solvers.py", line 483, in solve
solution = _solve(f, *symbols, **flags)
File "sympy\solvers\solvers.py", line 883, in _solve
result = solve_poly_system(polys, *symbols)
File "sympy\solvers\polysys.py", line 40, in solve_poly_system
return solve_biquadratic(f, g, opt)
File "sympy\solvers\polysys.py", line 48, in solve_biquadratic
G = groebner([f, g])
File "sympy\polys\polytools.py", line 5460, in groebner
return GroebnerBasis(F, *gens, **args)
File "sympy\polys\polytools.py", line 5496, in __new__
raise DomainError("can't compute a Groebner basis over %s" % opt.domain)
sympy.polys.polyerrors.DomainError: can't compute a Groebner basis over RR
e.tangent_lines(e.random_point())
Traceback (most recent call last):
File "<stdin>", line 1, in <module>
File "sympy\geometry\ellipse.py", line 528, in tangent_lines
tangent_points = solve([w.as_numer_denom()[0] for w in [slope - dydx,
eq]],
[x, y])
File "sympy\solvers\solvers.py", line 483, in solve
solution = _solve(f, *symbols, **flags)
File "sympy\solvers\solvers.py", line 883, in _solve
result = solve_poly_system(polys, *symbols)
File "sympy\solvers\polysys.py", line 40, in solve_poly_system
return solve_biquadratic(f, g, opt)
File "sympy\solvers\polysys.py", line 48, in solve_biquadratic
G = groebner([f, g])
File "sympy\polys\polytools.py", line 5460, in groebner
return GroebnerBasis(F, *gens, **args)
File "sympy\polys\polytools.py", line 5496, in __new__
raise DomainError("can't compute a Groebner basis over %s" % opt.domain)
sympy.polys.polyerrors.DomainError: can't compute a Groebner basis over RR
e.tangent_lines(e.random_point())
[]
e.tangent_lines(e.random_point())
[]
e.tangent_lines(e.random_point())
[]
e.tangent_lines(e.random_point())
[]
e.tangent_lines(e.random_point())
[Line(Point(-1.54497514980999, -1.71439030775370), Point(-16.9744879195933,
4.46
551029148626))]
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