We are certainly going to cause confusion if we don't implement this
symbolic simplification suggestion (+1):
sage: y=x-x
sage: y
0
sage: y==0
0 == 0
sage: 0==0
True
sage:
i.e. not all 0's ae the same. Now, I can understand why that is the
case (different rings) but it is not going to help beginner users.
John
2008/5/16 <[EMAIL PROTECTED]>:
>
>
>
>
> On Thu, 15 May 2008, William Stein wrote:
>
>>
>> On Thu, May 15, 2008 at 10:42 PM, John H Palmieri
>> <[EMAIL PROTECTED]> wrote:
>>>
>>>
>>>
>>> On May 15, 9:56 pm, "William Stein" <[EMAIL PROTECTED]> wrote:
>>>> On Thu, May 15, 2008 at 9:48 PM, John H Palmieri <[EMAIL PROTECTED]> wrote:
>>>>
>>>>
>>>>
>>>>> Is this a bug?
>>>>
>>>>> sage: 3 == pi
>>>>> 3 == pi
>>>>> sage: i == i
>>>>> I == I
>>>>
>>>>> Shouldn't this return "False" and "True", respectively?
>>>>
>>>> Those are symbolic equations:
>>>>
>>>> sage: type(I == I)
>>>> <class 'sage.calculus.equations.SymbolicEquation'>
>>>>
>>>> It's just a more general case of:
>>>>
>>>> sage: var('a,b,c,x')
>>>> (a, b, c, x)
>>>> sage: a*x^2 + b*x + c == 0
>>>> a*x^2 + b*x + c == 0
>>>> sage: type(a*x^2 + b*x + c == 0)
>>>> <class 'sage.calculus.equations.SymbolicEquation'>
>>>> sage: solve(a*x^2 + b*x + c == 0, x)
>>>> [x == (-sqrt(b^2 - 4*a*c) - b)/(2*a), x == (sqrt(b^2 - 4*a*c) - b)/(2*a)]
>>>
>>> Yes, except I, pi, and e are constants, not variables.
>>
>> They are elements of the symbolic ring:
>>
>> sage: parent(I)
>> Symbolic Ring
>> sage: parent(pi)
>> Symbolic Ring
>> sage: parent(e)
>> Symbolic Ring
>>
>> I'm not claiming to tell you the ultimate way things "should be". I'm only
>> explaining why they work the way they were and they do.
>>
>>> I suppose "bug" is not the right word, but I would content that this
>>> behavior is not at all what beginning users will expect. I mean, if I
>>> can do 'e**(i * pi)' and get -1, I would expect to be able to do '3 ==
>>> pi' and get "False".
>>>
>>> Or maybe I should say, if I can do 'a = 5; a == 7' and get "False", I
>>> would expect to be able to do '3 == pi' and get "False". Why is pi
>>> treated as a symbolic variable and not as a number?
>>
>> Pi is an element of the symbolic ring. What ring would you want
>> it to be part of? There is no "ring of numbers" in Sage. There could
>> be I suppose, but there isn't at present.
>>
>>> (Think about this from the beginning user's point of view. If they
>>> see odd behavior, they're going to be confused. A goal should be to
>>> not let this happen, or to provide a good way for them to figure out
>>> why the behavior was actually reasonable in the first place. How do
>>> you expect someone to react when they type in '3 == pi'? If they're
>>> puzzled, what do you reasonably expect them to be able to do to
>>> clarify things?)
>>
>> I would prefer "3 == pi" to return False. See below. Want to make
>> a Sage Enhancement Proposal and implement it? :-) It would
>> go something like this:
>>
>> Sage Enhancement Proposal: Change comparisons that involve
>> elements of the symbolic ring to return True or False if both sides
>> of the symbolic comparison are constants and the comparison can
>> be definitely determined. [...] There would be a discussion on sage-devel,
>> probably some voting, and then it would get done.
>
> +1! Robert Miller and I were discussing creating a language today. No
> matter what was input, it would return an affirmative answer. Perhaps this
> is a better idea:
>
> {{{
> class do_what_i_say:
> def eval(self,str):
> return str
> doit = do_what_i_say()
> }}}
>
> {{{
> %doit
> foo bar
> baz
> ///
> foo bar
> baz
> }}}
>
> Hey, check it out! Thanks to the Sage notebook, one can implement a
> feature-rich computer algebra system in 3 lines! It computes anything you
> ask for almost instantaneously!
>
> Seriously though, I understand *why* the following happens:
>
> sage: sqrt(2)
> sqrt(2)
> sage: sqrt(2) < 2
> sqrt(2) < 2
>
> I even know how to disable it. But it seriously drives me nuts every time I
> run into it.
>
>
>>
>>>
>>>> That said, maybe something so obvious as I == I would best be simplified
>>>> to True. But then people would argue that it is very inconsistent that
>>>> sometimes symbolic equations are simplified to True/False and sometimes
>>>> they aren't.
>>>>
>>>> In all cases you can do bool( a symbolic equation ) to get True or False.
>>>>
>>>> sage: bool(I == I)
>>>> True
>>>>
>>>>> I know this
>>>>> works:
>>>>
>>>>> sage: 3 == pi.n()
>>>>> False
>>>>> sage: 3 == RR(pi)
>>>>> False
>>>>
>>>>> but I sort of expect pi to act like the number pi when used with
>>>>> things like == or <, without using the .n() decoration.
>>>>
>>>> Nope. Pi is symbolic.
>>>>
>>>> I'm certainly open to doing some simplification to True/False of symbolic
>>>> equalities though, when we can do so. I think the main reason we don't
>>>> now is simply that nobody implemented it. Comments welcome.
>>>>
>>>> -- William
>>>>
>>>
>>
>>
>>
>> --
>> William Stein
>> Associate Professor of Mathematics
>> University of Washington
>> http://wstein.org
>>
>> >
>>
>
>
>
> >
>
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