why no arg, abs methods for comlex type?

[Daniel Schüle]

Hello all,

I often have to deal with complex numbers
using python iteractive as calculator

I wonder why there are no methods like arg, abs

well one can use
c = 1+1j
abs(c)

In my opinion it would also be nice to have the
possibility to write it as
c.abs()
it looks more OO

unfortunately there is no arg method to get the angle
of the complex number
of course it easy to write one on your own
(that's what I have done for myself)
but differnt people will create and reinvite the wheel
over and over again
while reading alien code one will have to spend 2 seconds
remembering the function names etc

consider
c = 1+1j
c.arg(angle_mod e = cmath.GRAD) -> 45.0
or
c.arg(angle_mod e = cmath.RAD) -> 0.7853..

I would also like to see some more functions to make
calculations with complex number more convenient
e.g.
c = 27
c.pow(numerator = 1, denominator = 3,
mode = cmath.EULER, angle_mode = cmath.GRAD)
-> ((3,0), (3,120), (3,240))

what do you think about it?
maybe there exists some proposals aiming this goal?

--
Daniel

[Reinhold Birkenfeld]

Erik Max Francis wrote:

Daniel Schüle wrote:

maybe I confuse, in german one would say "45 Grad"
I took a freedom to translate it directly :)
well, my calculator shows a "D"
which most likely stands for Degree, I cannot tell for sure

Probably. In English, you have degrees and gradians, which aren't the
same thing; gradians are defined so that there are 400 gradians in a
circle (so 100 gradians in a right angle).

In German, they're "Altgrad" (degrees) and "Neugrad" or "Gon" (gradians).

Reinhold

[Terry Reedy]

"Daniel Schüle" <uv**@rz.uni-karlsruhe.de> wrote in message
news:dd******** **@news2.rz.uni-karlsruhe.de...

I agree that this is a deficiency. I would think .angle() should be a

I don't know what nomenclature is used in english speaking
mathematical world for angle of a complex number
I learned it in german as Arg(z) .. Arg standing for argument
you see, we would have named it differently, hence making
it difficult for the reader, eventually creating redundancy

I am aware of the usage of argument to mean the angle in polar
representation, but I don't like it. The word argument already has two
other meanings, one in common English, the other in math/CS. The latter
meaning is the inputs to a function, and that is how the word is used in
Python (though the former applies more to many c.l.p threads ;-) To me,
the polar angle has no connection with either meaning and so the usage is
'like Greek' to me. Whereas angle is exactly what it is.

As for Greek: I first learned r(adius),theta (versus x,y or real,imag) as
the names for polar coordinates or the polar representation for complex
numbers and only ran into arg much later in some contexts. And I have seen
complex number implementations that use the equivalent of c.r() and
c.theta(). But I did not suggest that for one of the reasons I don't like
'lambda': its fine if you already know it and arbitrary if you don't. (Is
theta used in Germany?)

It is possible that a cmath2 module, written in Python, could be
useful.

I hope so
I will google for cmath2, I never heard about it

That is because we have not written it yet. The allroots function could be
the first addition, if it is not present elsewhere. The 'could be' was
meant in the sense of 'if someone were to write it' rather than 'if you
were to read it' ;-)

Terry J. Reedy

[Daniel Schüle]

[...]

Derive your own subclass of complex and define those methods.

I think something as basic as an angle/arg of complex number
definetly belongs to the interface, and it would not even require a
great effort to put it there

most complex formulas out there use Euler representation
it's a waste of code lines (and programmers time)
to write 3 liner functions for the transformion between
a+bj <-> (r,angle)
Python makes things covenient
so we have complex numbers in the core language
the calculations where perfectly possible without them
using (re, im) tupels and many many sin/cos in the code
but imagine how ugly it would be ..
I would like see Python as a competitor to Matlab etc

Regards

--
Daniel

[Daniel Schüle]

[...]

I am aware of the usage of argument to mean the angle in polar
representation, but I don't like it. The word argument already has two
other meanings, one in common English, the other in math/CS. The latter
meaning is the inputs to a function, and that is how the word is used in
Python (though the former applies more to many c.l.p threads ;-) To me,
the polar angle has no connection with either meaning and so the usage is
'like Greek' to me. Whereas angle is exactly what it is.
..angle() would be also alright, as it is easy to grasp
As for Greek: I first learned r(adius),theta (versus x,y or real,imag) as
the names for polar coordinates or the polar representation for complex
numbers and only ran into arg much later in some contexts. And I have seen
complex number implementations that use the equivalent of c.r() and
c.theta(). But I did not suggest that for one of the reasons I don't like
'lambda': its fine if you already know it and arbitrary if you don't. (Is
theta used in Germany?)

yes, of course
the entire mathematic is full of them :)
as for the complex numbers, in our lessons we used R(adius) and
Phi for the angle for polar representation
I guess it's more a question of teacher's preference than a national
norm

[Dennis Lee Bieber]

On Fri, 05 Aug 2005 18:24:26 +0200, Daniel Schüle
<uv**@rz.uni-karlsruhe.de> declaimed the following in comp.lang.pytho n:

c = 1+1j
c.arg(angle_m ode = cmath.GRAD) -> 45.0

Is that right? The result looks more like Degrees...

maybe I confuse, in german one would say "45 Grad"
I took a freedom to translate it directly :)
well, my calculator shows a "D"
which most likely stands for Degree, I cannot tell for sure

45 Degrees => 50 Grad

2PI => 360 Degree => 400 Grad

(and military protractors are the only place I've seen Grads
used)
-- =============== =============== =============== =============== == <
wl*****@ix.netc om.com | Wulfraed Dennis Lee Bieber KD6MOG <
wu******@dm.net | Bestiaria Support Staff <
=============== =============== =============== =============== == <
Home Page: <http://www.dm.net/~wulfraed/> <
Overflow Page: <http://wlfraed.home.ne tcom.com/> <

[Robert Kern]

Daniel Schüle wrote:

[...]

> Derive your own subclass of complex and define those methods.
I think something as basic as an angle/arg of complex number
definetly belongs to the interface, and it would not even require a
great effort to put it there

<shrug> Okay. Write a patch. Personally, I would prefer that it be a
function in cmath rather than a method because then it could be made to
work on integers and regular floats, too.
most complex formulas out there use Euler representation
it's a waste of code lines (and programmers time)
to write 3 liner functions for the transformion between
a+bj <-> (r,angle)
It's a very, very tiny outlay of effort on the programmer's part that
only has to happen once in their career.
Python makes things covenient
so we have complex numbers in the core language
the calculations where perfectly possible without them
using (re, im) tupels and many many sin/cos in the code
but imagine how ugly it would be ..
I don't have to imagine. It's not all that ugly.
I would like see Python as a competitor to Matlab etc

I think it is already.

--
Robert Kern
rk***@ucsd.edu

"In the fields of hell where the grass grows high
Are the graves of dreams allowed to die."
-- Richard Harter

[Daniel Schüle]

[...]

<shrug> Okay. Write a patch. Personally, I would prefer that it be a
function in cmath rather than a method because then it could be made to
work on integers and regular floats, too.

Ok, but what semantic should angle/arg have, say for 3 respectively
for 3.0?
the same as for arg(3+0j)?

[tiissa]

Daniel Schüle wrote:

<shrug> Okay. Write a patch. Personally, I would prefer that it be a
function in cmath rather than a method because then it could be made
to work on integers and regular floats, too.

Ok, but what semantic should angle/arg have, say for 3 respectively
for 3.0?
the same as for arg(3+0j)?

As a potential user, that's what I would expect.

See Dan Bishop's implementation (earlier in this thread).

[Bengt Richter]

On Sat, 06 Aug 2005 06:44:03 GMT, Dennis Lee Bieber <wl*****@ix.net com.com> wrote:

On Fri, 05 Aug 2005 18:24:26 +0200, Daniel Schüle
<uv**@rz.uni-karlsruhe.de> declaimed the following in comp.lang.pytho n:

>>c = 1+1j
>>c.arg(angle_m ode = cmath.GRAD) -> 45.0
>
>
> Is that right? The result looks more like Degrees...

maybe I confuse, in german one would say "45 Grad"
I took a freedom to translate it directly :)
well, my calculator shows a "D"
which most likely stands for Degree, I cannot tell for sure

45 Degrees => 50 Grad

2PI => 360 Degree => 400 Grad

(and military protractors are the only place I've seen Grads
used)

No one seems to have mentioned 2PI => 1 circle as in unit circles.
IIRC, back in the day before math chips, we implemented all the trig
functions in terms of angles where some number of bits respresented
one circle, for best resolution of angles with a given number of bits.
Also for compatibility with angular input devices. Also for the natural
modulo 2PI effect of representing an angle as an int, with unsigned interval
[0..2PI) or signed interval [-PI..PI). IIRC, FFTs involve phase in steps of
2PI/2**n also (for power-of-2 decimation effectively dividing the unit circle
in terms of powers of e**-i*(2*pi/2**n)) (where i is imaginary 0+1j). Hm, let' see,
for 45-degree deltas (2PI/2**3) ...

import cmath
(cmath.e+0j)**(-2j*cmath.pi/2**3) (0.707106781186 54757-0.7071067811865 4746j)
for c in [((cmath.e+0j)** (-2j*cmath.pi/2**3))**i for i in xrange(8)]: print c

...
(1+0j)
(0.707106781187-0.707106781187j )
(1.5701957963e-016-1j)
(-0.707106781187-0.707106781187j )
(-1-3.1403915926e-016j)
(-0.707106781187+ 0.707106781187j )
(-4.71058738891e-016+1j)
(0.707106781187 +0.707106781187 j)

Regards,
Bengt Richter