On Sep 3, 2009, at 12:49 PM, kcrisman wrote:
>
>
>
> On Sep 3, 2:28 pm, William Stein <wst...@gmail.com> wrote:
>> Hi Sage-Devel,
>>
>> What do you think of this:
>>
>> sage: var('x, i')
>> sage: solve(x^2 + i == 0, x)
>> [x == -sqrt(-I), x == sqrt(-I)]
>>
>> Basically, I make a purely symbolic variable which I happen to call
>> "i", and it gets treated somewhere (presumably in Maxima) as if it
>> were sqrt(-1).
>>
>> Here is another instance of this:
>>
>> sage: var('i')
>> i
>> sage: a = i^2
>> sage: a
>> i^2
>> sage: a.simplify_full()
>> -1
>>
>> So Ginac treats things fine, but our use of Maxima messes it up.
>>
>> This came up for me just now when doing some symbolic calculation
>> with
>> a quaternion algebra where the generators are called "i,j,k", and
>> this
>> i has nothing to do with sqrt(-1).
>>
>> Thoughts?
>>
>> William
>>
>
> I see your point. I guess to me it's another instance of the "should
> x be predefined" question - on the whole, it's better to make this
> available.
I think my email must have not been clear. I think it's an instance
of a *HUGE BUG* in Sage. No more, no less. It's a bug, because
irregardless of anything being predefined, it makes no sense that
simplifying via *maxima* would just happen to decide that the formal
variable "i" is sqrt(-1), even though it isn't with Ginac.
William
> It is also annoying when doing [f(i) for i in indexset],
> but unless we can come up with another way to represent this, it will
> be hard to do things with complexes very easily. Luckily for me, I
> don't usually need that, but others may very often. Does this happen
> with 'e' as well, or is that defined as a constant rather than a
> variable? It seems like both are "symbolic.expression.Expression.
>
> What do the other major systems do with this - do they insist on sqrt
> (-1) or CC(i) or something like that? If everyone expects this coming
> in, it is an argument for it - not decisive, but a significant
> argument.
>
> - kcrisman
> >
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