On Jun 17, 10:32 am, Robert Dodier <robert.dod...@gmail.com> wrote: > On Jun 16, 11:24 am, Tom Coates <t.coa...@imperial.ac.uk> wrote: > > > A) factorial(x) should raise an error; > > > B) factorial(x) should return gamma(x+1). > > More generally, the question is what to do with something > which doesn't make sense according to whatever rules have > been established so far. I claim the "mathematical" attitude > is to let it stand; then someone who has greater imagination > can figure out what to do with it. Barfing out an error makes > it pretty much impossible to reinterpret the expression in > an interesting way.
This is an option if you are working in a symbolic domain, where "gamma(x+1)" can be represented as such. The original question was what should happen if a numerical argument gets passed in, for instance factorial(ZZ(-3)) It would be rather bad form if the return value were to lie in what is referred to as the "symbolic ring" for this input, whereas factorial(ZZ(3)) would return the integer 6. In general, the *parent* of the return value should not depend on the *value* of the argument; only on the *parent* of the argument. This kind of issue points at a fundamental difference between symbolic algebra systems where everything is an "expression tree", such as maple and maxima, and systems more fundamentally based on categories, where objects have a parent. In fact, William Stein's vote for "B" in favor of backwards compatibility is only partly based on reality: sage: factorial(-1) ValueError: factorial -- self = (-1) must be nonnegative sage: factorial(-1.1) ValueError: factorial -- must be nonnegative sage: gamma(-1.1+1) -10.6862870211932 but: sage: factorial(1.1) 1.04648584685356 sage: gamma(1.1+1) 1.04648584685356 I'd say factorial( <integer> ) should return an integer (or an error if it can't). factorial( <float> ) would be expected to return a float and hence can safely use gamma. This probably violates Python's duck typing, though. Perhaps return integer output on anything that can be canonically coerced into the integers? -- To post to this group, send an email to sage-devel@googlegroups.com To unsubscribe from this group, send an email to sage-devel+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-devel URL: http://www.sagemath.org
