Status: Accepted
Owner: ----
Labels: Type-Defect Priority-Medium
New issue 2834 by [email protected]: naive radical removal can lead to
multiplying by 0/0
http://code.google.com/p/sympy/issues/detail?id=2834
There is an unguided attempt at removing of a radical from the denominator
that leads to an interesting 0/0 situation. A match for a+b*sqrt(c) is made
and the sqrt(c) is cleared by multiplying by a - b*sqrt(c). This usually
works but not if a = b*sqrt(c) because then you multiply numer and denom by
0 and that leads to weird results. Here is a case where it arose:
p1=Polygon(*RegularPolygon((0,0),1,5).vertices)
x=p1.centroid.x # modified so the point coordinates are not simplified
[w.n() for w in x.as_numer_denom()]
[.0e-128, 3921366368769.96]
[w.n() for w in simplify(x).as_numer_denom()]
[.0e-131, -.0e-120]
# oops! the denominator shouldn't be zero after simplifying
...
n,d=x.as_numer_denom()
a, b, c = map(Wild, 'abc')
r = d.match(a + b*sqrt(c))
a, b, c = r[a], r[b], r[c]
(d-(a+b*sqrt(c))).n() # the match is correct
0
conj_like = a-b*sqrt(c)
(d*conj_like - (a**2-c*b**2)).n() # is the new denom a**2 - c*b**2?
.0e-108
# yep, it is BUT...it is zero!
...
conj_like.n() # this is what the numer and denom were mutliplied by
.0e-123
# and that's the oops. Let's see what a, b and c were
...
a
103079215104*sqrt(10)*sqrt(sqrt(5) + 5) +
206158430208*sqrt(10)*sqrt(-sqrt(5) +
5)
b
515396075520*sqrt(2)
c
sqrt(5) + 5
pprint(d.as_content_primitive()[1])
___________ _____________ ___________
____ / ___ ____ / ___ ___ / ___
\/ 10 *\/ \/ 5 + 5 + 2*\/ 10 *\/ - \/ 5 + 5 + 5*\/ 2 *\/ \/ 5 + 5
d.args
(206158430208*sqrt(10)*sqrt(-sqrt(5) + 5),
103079215104*sqrt(10)*sqrt(sqrt(5) +
5), 515396075520*sqrt(2)*sqrt(sqrt(5) + 5))
A,B,C=(d.as_content_primitive()[1]).args
A
2*sqrt(10)*sqrt(-sqrt(5) + 5)
B
sqrt(10)*sqrt(sqrt(5) + 5)
C
5*sqrt(2)*sqrt(sqrt(5) + 5)
a=A+B;b=5*sqrt(2);c=sqrt(sqrt(5) + 5);(a**2-c*b**2).n()
227.303696482198
So there is a way to remove a radical without multiplying by 0/0...this
part of simplify needs to be smarter so this doesn't happen.
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