# Revision history [back]

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


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


You get a fast numerical representation of your complex number

With

sage: z = 1+2*ComplexIntervalField(1000)(I)


You get a certified numerical representation of your complex number with high precision

With

sage: z = 1+2*QQbar(I)


You get an algebraic (hence exact) representation of your complex number.

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 numbernumber.

With

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


You get a certified numerical representation of your complex number with high precisionprecision.

With

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


You get an algebraic (hence exact) representation of your complex number.

With

sage: z = 1+2*ZZ[i].basis()[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.

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.number (you should prefer CDF to CC since both have the same precision, but CDF takes the advantage of the CPU floating-point arithmetics).

With

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


You get a certified numerical representation of your complex number with high precision.

With

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


You get an algebraic (hence exact) representation of your complex number.

With

sage: z = 1+2*ZZ[i].basis()[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.

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 to CC since both have the same precision, but CDF takes the advantage of the CPU floating-point arithmetics).

With

sage: z = 1+2*ComplexIntervalField(1000)(I)
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.

With

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


You get an algebraic (hence exact) representation of your complex number.

With

sage: z = 1+2*ZZ[i].basis()[1]
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.

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 to CC since both have the same precision, but CDF takes the advantage of the CPU floating-point arithmetics).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.

With

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


You get an algebraic (hence exact) representation of your complex number.

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.

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 to 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.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.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.

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 to 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.