Status: New
Owner: pr...@goodok.ru
Labels: Type-Defect Priority-Medium Polynomial Simplify
New issue 2245 by pr...@goodok.ru: assumption while canceling the
polynomials
http://code.google.com/p/sympy/issues/detail?id=2245
Consider simplification:
>>> a = (x**2 - 3*x + 2)/(x - 1)
>>> a.cancel()
-2 + x
It seems that result is correct: `(x**2 - 3*x + 2)` is equal to `(x - 1)*(x
- 2)`,
so `(x - 1)` is canceling, and `(x - 2)` is obtained.
But no one told to the SymPy that `x` might not to be equals to the one.
And mathematically, it brings the incorrect behavior, when someone wants to
consider the value of expression at some point:
>>> a.subs(x, 1)
nan
>>> a.cancel().subs(x, 1)
-1
The answer must be `nan` in both.
Or, while solving equation:
>>> solve((x**2 - 3*x + 2)/(x - 1))
[1, 2]
The right answer is 2 only.
For this aims, it seems that would be convenient a few variants:
1) while simplification like cancel, return the `Piecewise`:
E.g.:
>>> a.cancel()
Piecewise(-2 + x, x<>1)
2) while simplification set assumption about `x` somehow:
E.g.:
>>> a.cancel(a, assume=(x<>1) )
-2 + x
>>> a.cancel(a, assume=(x==1) )
nan
The same with simplify.
or use assumption attached to `x` symbol.
It seems that 1) is easy, and 2) can use 1) implementation.
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