On 15 June 2010 05:21, Tom Coates <t.coa...@imperial.ac.uk> wrote:
>
> Dear sage-devel,
>
> I believe that the following:
>
> sage: gamma(x).full_simplify()
> factorial(x - 1)
>
> is not correct, because in Sage factorial(x) is defined only if x is a
> non-negative integer.  The problem arises because behind the scenes
> full_simplify() uses Maxima, and for Maxima factorial(x) is equivalent
> to gamma(x+1).
>
> I can think of two ways to fix this.  Given a symbolic expression
> symb, we could:
>
> a)  make symb.full_simplify() return an expression in terms of gamma()
> rather than an expression in terms of factorial();
>
> b)  check whether symb contains any subexpression of the form
> gamma(foo).  If so, symb.full_simplify() should return an expression
> in terms of gamma(); if not, symb.full_simplify() should return an
> expression in terms of factorial().
>
> Option (a) is easy to implement but I think it is the wrong way to
> go.  There may be many Sage users who would want to simplify
> expressions containing factorials (e.g. combinations of binomial
> coefficients) but who don't know what the gamma function is.

I'd agree with that.

Dave

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