Am 03.06.2012 14:38, schrieb [email protected]:
@Joachim: I really do not understand what are you talking about.
I don't know how to phrase it so it's clearer.
> As of
this moment the solvers in sympy do indeed require you to set your
assumptions if you wish solve(x**2-1) to return only +1 and
solve(x**2+1) to return None. It would be awful if sympy starts
guessing what assumptions the user wants.
I can't remember having written anything that involves guessing on
SymPy's side, so I'm not sure what you mean with that.
> Every single CAS I know is
very explicit about this as it should be.
First, "explicit about this" is quite unspecific, so this is an
unfalsifiable statement.
Second, just because everybody is doing something in a specific way does
not always mean it's the best way.
Be specific if you're in a technical argument.
Moreover, my inquiry is not at all concerned with this question. It is
whether solve(x+1) should return [-1] or -1.
Yes, and my stance is "it shouldn't matter because mathematicians don't
usually care".
> Even if the abuse of
notation of set_of_one_element = the_element_itself is as widely used
as you suggest
Decrying it as an "abuse" isn't valid unless agreed to, or supported by
arguments.
Which I have yet to see.
> (I do not think so)
Maybe textbooks have become more rigorous in the last 30 years or so.
Those that I saw in my university time generally ignored the issue. sin
was defined for reals and liberally applied to vector, other functions
(which sometimes are regarded and handled as vectors with an infinite
dimensionality), etc. etc.
Rigor seems to be reserved for school, and is thrown out of the window
in the first semester of engineering and seems to get abandoned even in
math (in exploratory thinking, anyway - it's still required for proof,
as it should be to make sure that the handwavy parts didn't introduce an
error).
> it is not an abuse of notation that
is so important to be supported in a CAS. Your comparison with
Principia Mathematica is extreme and I do not think that it is valid.
How so?
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