Hi all,
Thanks for the quick reply. I thought that a sensible solution might
be to introduce a new floating point type (for example, Float) which
does the round off by itself (with given precision). Basically, one
could write the equation like this:
expr = (Float(2.1,digits=1)*(1-y**2)+2*x)/x**3
Is it now possible in sympy? If not, would it be hard to implement it?
BTW Your are doing great job with sympy! Thanks a lot!
Cheers,
Bartosz
On May 24, 2011, at 9:54 PM, Aaron S. Meurer wrote:
That's basically correct. The problem is that certain polynomial
algorithms (in this case, polynomial division) rely on the ability
to determine zero equivalence in the coefficients. But floating
point numbers, as we all know, have the problem where they will
often give something like 1e-14 instead of 0.
The solution is to replace the RR domain with RR(eps) domain, where
eps is the cutoff for zero (if 0 <= a < eps, then consider a == 0).
By the way, if anyone is interested, the problem comes from while
loop at line 1268 of densearith.py. The loop breaks when the degree
of r is less than the degree of g, but in this case, on the final
iteration where it should be less, the leading term of r has a
coefficient somewhere on the order of 1e-13 instead of 0, so it goes
through the loop one too many times. Since the loop decrements N
each time, this ends up becoming negative. This is the "negative
power" it complains about later.
Mateusz, would a suitable temporary fix for this be to put chop=True
in key places in the RR domain? I think a lot of people use
floating point coefficients, and they won't be happy to see errors
like this one.
Aaron Meurer
On May 24, 2011, at 1:20 PM, Tom Bachmann wrote:
Presumably mateusz (or aaron) know better than me, but the problem
is simply that polys does not really work well with Floats.
There is also an open issue (2384) related to this.
On 24.05.2011 20:13, Chris Smith wrote:
Andy Ray Terrel wrote:
Quite strange indeed.
On my Mac Python 2.7, sympy.__version__ = 0.6.7 I get:
In [17]: expr = (2.1 - 2.1*y**2 + 2*x)/x**3
In [18]: sympy.simplify(expr)
Out[18]: -inf
This raises an error for me:
raise ValueError("can't raise polynomial to a negative power")
ValueError: can't raise polynomial to a negative power
But if I nsimplify(..., rational=True) everthing works ok:
h[12]>>> e1= (2.1 - 2.1*y**2 + 2*x)/x**3
h[12]>>> e2= (2.1*x*(1-y)**2+2*y*x)/ x**3
h[12]>>> e3= (sympy.Rational(21,10)*x*(1-y)**2 + 2*y*x) / X**3
h[12]>>> for e in [e1,e2,e3]:
... print simplify(nsimplify(e,rational=True))
...
(20*x - 21*y**2 + 21)/(10*x**3)
(21*y**2 - 22*y + 21)/(10*x**2)
x*(21*y**2 - 22*y + 21)/(10*X**3)
CAUTION: you used an X instead of an x in the last equation.
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