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).
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?
Aaron Meurer
On Sat, Jul 6, 2013 at 12:16 PM, Amit Saha <amitsaha...@gmail.com> wrote:
> Hello,
>
> I have been playing a bit with the number classes, and I have come
> across Integer, Real and Rational classes. Comparing to their "native"
> counterparts in CPython, I understand they correspond to int, float
> and the Fraction (from the fractions) objects respectively. Good so
> far, I also looked around in the code and understand how the
> comparison works.
>
> One thing I haven't found out (after fair searching around) is how do
> I create a complex number (not a symbol as complex)? For example, I
> can do this to create a SymPy floating point number:
>
> >>> from sympy import Float
> >>> f=Float(1.4)
>
> How can I create a number such as 1+4j?
>
> Also, considering this:
>
> >>> f.is_complex
> True
>
> which is fair, I understand, how do I assign the imaginary component
> if that's the way i want to go about it?
>
>
> Regarding declaring symbols as complex:
>
> With explicit complex assumption set:
>
> >>> x=Symbol('x',complex=True)
> >>> x1 = x+1j
>
>
> Generic symbol:
>
> >>> x=Symbol('x')
> >>> x2=x+1j
>
> How are the above two different? I know they are:
>
> >>> x1==x2
> False
>
> Even though the structure of both the above expressions are the same,
> the test evaluates to False.
>
> Thanks in advance for clarifying my doubts.
>
> Best,
> Amit.
>
> --
> http://echorand.me
>
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