On Sun, Jul 7, 2013 at 12:03 PM, Aaron Meurer <asmeu...@gmail.com> wrote:
>
>
>
> On Sat, Jul 6, 2013 at 5:45 PM, Amit Saha <amitsaha...@gmail.com> wrote:
>>
>> On Sun, Jul 7, 2013 at 4:50 AM, Aaron Meurer <asmeu...@gmail.com> wrote:
>> > I think you are confusing the assumptions system and the numeric classes
>> > in
>> > SymPy.
>> >
>> > First, for the numeric classes, SymPy does not have a complex type.
>> > Rather,
>> > we just have the object I, which represents sqrt(-1). If you want 12 +
>> > 3*I,
>> > you just type exactly that. Internally, it is represented as Add(12,
>> > Mul(3,
>> > I)). One difference you'll notice here is that, because it is just an
>> > Add,
>> > things like (12 + 3*I)**2 or 1/(12 + 2*I) are not reevaluated to real +
>> > imag*I by default. You can use expand_complex() to do that (or
>> > as_real_imag
>> > if you want to pull out the real and imaginary parts).
>>
>> Thanks for the explanation. Here is what I tried:
>>
>> >>> from sympy import Symbol
>> >>>
>> >>> i=Symbol('i')
>> >>> c = 1 + 2*i
>> >>> c.as_real_imag(c)
>> (2*re(i) + 1, 2*im(i))
>>
>> Good so far, I understand that the real and imaginary components are
>> being expressed as multiples of the real and and imaginary components
>> of i, respectively.
>>
>> Now, I tried to to add this to a native CPython complex number:
>>
>> >>> c = c + 1+2j
>> >>> c.as_real_imag(c)
>> (2*re(i) + 2, 2*im(i) + 2.0)
>>
>> Here the real part is clear to me: 2*re(i) + 2 = 2*0 + 2 = 2
>>
>> But, I don't quite understand what the imaginary part: 2*im(i) + 2 is
>> supposed to mean. I was expecting it to be 4*im(i).
>
>
> Why? Symbol('i') has nothing to do with sqrt(-1). It's just a symbol named
> i. If you want sqrt(-1), use I (not Symbol('I'), just I).
>
> If you look, your c is 2 + 2*i + 2*I. The i is Symbol('i') and the I is
> sqrt(-1), which comes from the 2j.
>
> It's also clear if you enable unicode pretty printing, because I is printed
> as ⅈ.
My mistake, I assumed that i and I both would be understood as
denoting an imaginary object.
Thanks, it's clear now.
>
> Aaron Meurer
>
>>
>>
>>
>> >
>> > Now, for the assumptions. Symbol('x', complex=True) means that the
>> > symbol is
>> > assumed to be complex. This is in contrast to Symbol('x', real=True),
>> > which
>> > is assumed to be real. This matters for things like x.is_real, and
>> > affects
>> > how things are simplified. For example, sqrt(x**2) == x only when x is
>> > positive, so it will remain unevaluated by default, but if you create
>> > Symbol('x', positive=True), then sqrt(x**2) will simplify to just x.
>> >
>> > Symbols are assumed to be complex by default, so actually Symbol('x',
>> > complex=True) is unnecessary. Actually, this isn't entirely true;
>> > apparently
>> > Symbol('x', complex=True) is different from just Symbol('x'), which I
>> > don't
>> > entirely understand why. I think this might be a bug. Could you open an
>> > issue for it?
>>
>>
>> Filed: https://github.com/sympy/sympy/issues/2260
>>
>> I hope I got the description right.
>>
>> Thanks,
>> Amit.
>>
>>
>>
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