Problems in the documentation of the rising factorial

[Peter Luschny]

http://docs.sympy.org/latest/modules/functions/combinatorial.html#risingfactorial

I executed the examples in SymPy-Live but got different

outputs from what the docs say. For example for 

>>> rf(x, k).rewrite(ff)

gives  nothing  instead of: FallingFactorial(k + x - 1, k)

>>> rf(x, k).rewrite(binomial)

gives  (x)^(k)  instead of: binomial(k + x - 1, k)*factorial(k)

>>> rf(n, k).rewrite(factorial)

gives  (n)^(k)  instead of: factorial(k + n - 1)/factorial(n - 1)

Also for rf(x**3, 2) the output is different, not

Poly(x**6 + 3*x**5 + 3*x**4 + x**3, x, domain='ZZ')

Peter

[Aaron Meurer]

We still haven't updated SymPy Live to SymPy 1.0, so the output of
some examples may be different.

Aaron Meurer

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[Peter Luschny]

We still haven't updated SymPy Live to SymPy 1.0, so the output of
some examples may be different.

Thanks! Maybe I expressed myself misleading. Also the output in my 

yupyter notebook did not correspond to what is in the documentation.

I have difficulty to understand the output of the three calls
below which are taken from the doc-pages I cited.
-----------------------------------------------------
from sympy import rf, symbols, factorial, ff, binomial
from sympy.abc import x
n, k = symbols('n k', integer=True)

rf(x**3, 2)                 # ? x**3*(x**3 + 1)

rf(x, k).rewrite(binomial)  # ? RisingFactorial(x, k)

rf(n, k).rewrite(factorial) # ? RisingFactorial(n, k)
-----------------------------------------------------

Perhaps someone can enlighten me what to expect 
and to tell me if the output of SymPy 1.0 is correct?

Peter

 

[Aaron Meurer]

Maybe this bit from the docstring is causing confusion:

When x is a polynomial f of a single variable y of order >= 1,
rf(x,k) = f(y) * f(y+1) * ... * f(x+k-1) as described in
Peter Paule, "Greatest Factorial Factorization and Symbolic Summation",
Journal of Symbolic Computation, vol. 20, pp. 235-268, 1995.

So rf(x**3, 2) is x**3*(x + 1)**3.

I'm not sure why this definition is made. It seems like a bad one,
since there are two different ways to interpret rf(a, b) if a is a
polynomial. It looks like this was changed in
https://github.com/sympy/sympy/pull/8941.

For the other two, I get the same thing as the docstring in SymPy 1.0

>>> rf(x, k).rewrite(binomial)

binomial(k + x - 1, k)*factorial(k)
>>> rf(n, k).rewrite(factorial)

factorial(k + n - 1)/factorial(n - 1)

These seem mathematically correct.

It seems all three of these changed from SymPy 0.7.6 to SymPy 1.0.

Aaron Meurer

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[Peter Luschny]

> I'm not sure why this definition is made. It seems like a bad one,
> since there are two different ways to interpret rf(a, b) if a is a
> polynomial.  

> For the other two, I get the same thing as the docstring in SymPy 1.0

> These seem mathematically correct.

Thank you very much.

I agree with your comments, however I cannot reproduce the results
in my computing environment (SMC) similarly as SymPy Live cannot. 

I will have to investigate further.

Peter

[Aaron Meurer]

Double check that

import sympy
sympy.__version__

gives '1.0'.

Aaron Meurer

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[Peter Luschny]

> Double check that
> import sympy
> sympy.__version__
> gives '1.0'.

Yes, this was the issue. Solved and thanks.

Peter