On Jul 10, 2013, at 9:21 AM, Amit Saha <[email protected]> wrote:
> On Sun, Jul 7, 2013 at 12:03 PM, Aaron Meurer <[email protected]> wrote: >> >> >> >> On Sat, Jul 6, 2013 at 5:45 PM, Amit Saha <[email protected]> wrote: >>> >>> On Sun, Jul 7, 2013 at 4:50 AM, Aaron Meurer <[email protected]> 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. Symbol('I') wouldn't be the same as I either. Symbols and objects are completely different. Objects in SymPy are compared by type, not by their string representation. Also, don't confuse symbol names and python variable names. Aaron Meurer > > > >> >> 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. >>> >>> >>> >>> -- >>> http://echorand.me >>> >>> -- >>> You received this message because you are subscribed to the Google Groups >>> "sympy" group. >>> To unsubscribe from this group and stop receiving emails from it, send an >>> email to [email protected]. >>> To post to this group, send email to [email protected]. >>> Visit this group at http://groups.google.com/group/sympy. >>> For more options, visit https://groups.google.com/groups/opt_out. >>> >>> >> >> -- >> You received this message because you are subscribed to the Google Groups >> "sympy" group. >> To unsubscribe from this group and stop receiving emails from it, send an >> email to [email protected]. >> To post to this group, send email to [email protected]. >> Visit this group at http://groups.google.com/group/sympy. >> For more options, visit https://groups.google.com/groups/opt_out. >> >> > > > > -- > http://echorand.me > > -- > You received this message because you are subscribed to the Google Groups > "sympy" group. > To unsubscribe from this group and stop receiving emails from it, send an > email to [email protected]. > To post to this group, send email to [email protected]. > Visit this group at http://groups.google.com/group/sympy. > For more options, visit https://groups.google.com/groups/opt_out. > > -- You received this message because you are subscribed to the Google Groups "sympy" group. 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