Status: Valid
Owner: ----
Labels: Type-Defect Priority-Medium Solvers WrongResult
New issue 3956 by skirpic...@gmail.com: Failures in rsolve_hyper from
test_rsolve_bulk()
http://code.google.com/p/sympy/issues/detail?id=3956
I had observed a lot of wrong answers from rsolve_hyper() after
uncommenting the "if p.is_hypergeometric(n)" branch in the file
test_recurr.py.
For example:
In [12]: def recurrence_term(c, f):
....: """Compute RHS of recurrence in f(n) with coefficients in c."""
....: return sum(c[i]*f.subs(n, n + i) for i in range(len(c)))
....:
In [13]: f=Function('f')
In [14]: c=[-2, 1]
In [15]: p=n
In [16]: q=recurrence_term(c, p)
In [17]: s=rsolve_hyper(c, q, n)
In [18]: s
Out[18]:
n
2 ⋅C₀ + C₀⋅(-n + 1)
In [19]: eq=Eq(sum(c[i]*f(n + i) for i in range(len(c))),q)
In [20]: eq
Out[20]: -2⋅f(n) + f(n + 1) = -n + 1
In [21]: k=Symbol('k',integer=True)
In [22]: eq.subs(f,Lambda(k,s.subs(n,k))).simplify()
Out[22]: C₀⋅(n - 2) = -n + 1
Mathematica's answer:
In[9]:= (f[n]/.RSolve[-2 f[n] + f[n + 1] == -n + 1,f[n],n])[[1]]
Out[9]=
n
-2 + 2 n -1 + n
--------- + 2 C[1]
2
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