# Should I use numpy and cython for complex numbers? Anonymous

Here is the problem:

if I try this:

var('z')
z = 1+2*I
type(z)
<type 'sage.symbolic.expression.Expression'>


So, it isn't a complex number. BUT, if I do this:

I = CC.0
z = 1+2*I
type(z)


then I get a complex number

<type 'sage.rings.complex_number.ComplexNumber'>


Should I use numpy and cython for complex numbers?

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It depends on what kind of complex number you want. Sage provide tons, you do not need numpy, cython or whatever. Here are some examples (these are not the only ones):

With

sage: z = 1+2*I
sage: z.parent()
Symbolic Ring


You indeed get symbolic representation of a complex number, so you can do symboloc things such as:

sage: exp(pi*z).simplify()
e^pi


WIth

sage: z = 1+2*CDF.0
sage: z.parent()
Complex Double Field


You get a fast numerical representation of your complex number (you should prefer CDF over CC since both have the same precision, but CDF takes the advantage of the CPU floating-point arithmetics, and the functions you will call from it will use optimized libraries).

With

sage: z = 1+2*ComplexIntervalField(1000).0
sage: z.parent()
Complex Interval Field with 1000 bits of precision


You get a certified numerical representation of your complex number with high precision (interval arithmetics).

With

sage: z = 1+2*QQbar.0
sage: z.parent()
Algebraic Field


You get an algebraic (hence exact) representation of your complex number (but pi does not exist here).

With

sage: z = 1+2*ZZ[i].1
sage: z.parent()
Gaussian Integers in Number Field in I with defining polynomial x^2 + 1


You get a Gaussian integer.

And so on...

Now, you just have to decide what do you want to do with z to select an appropriate representation.

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