# Ticket #4498(closed enhancement: fixed)

Opened 5 years ago

## Implement a symbolic version of the arg function

Reported by: Owned by: TimothyClemans somebody major sage-5.0 symbolics beginner, sd35.5 kcrisman, ktkohl N/A Karl-Dieter Crisman, Burcin Erocal Karen T. Kohl, Burcin Erocal sage-5.0.beta4

It would be nice if there were a symbolic arg function, just like the symbolic sin, cos, etc., functions. Then the following would happen:

```sage: f = arg(x); f
arg(x)
sage: f.subs(x=1+I)
arg(1+I)
```

Now we have

```sage: arg(1+I)
0.785398163397
sage: type(arg(1+I))
<type 'sage.rings.real_double.RealDoubleElement'>
```

I.e., the arg in Sage is currently the numerical person's arg, not the symbolic person's. It just casts to CDF.

"The function should return the argument of a complex function." - Ronan Paixão

Apply

## Change History

### comment:1 Changed 5 years ago by TimothyClemans

```arg(x)
///

Traceback (most recent call last):
File "<stdin>", line 1, in <module>
line 6, in <module>
exec compile(ur'arg(x)' + '\n', '', 'single')
File
"/home/ronan/progs/sage/local/lib/python2.5/site-packages/ZODB3-3.7.0-py2.5-linux-i686.egg/", line 1, in <module>

File
"/home/ronan/progs/sage/local/lib/python2.5/site-packages/sage/misc/functional.py", line 67, in arg
except AttributeError: return CDF(x).arg()
File "complex_double.pyx", line 286, in
sage.rings.complex_double.ComplexDoubleField_class.__call__
(sage/rings/complex_double.c:3324)
File
"/home/ronan/progs/sage/local/lib/python2.5/site-packages/sage/calculus/calculus.py", line 1454, in _complex_double_
raise TypeError
TypeError
```

### comment:2 Changed 5 years ago by mabshoff

Please post a complete session. As is the above is not very clear.

Cheers,

Michael

### comment:3 Changed 5 years ago by was

• Summary changed from The argument function does not work with variables. to Implement a symbolic version of the arg function; the current one is only for actual numbers
• Type changed from defect to enhancement
• Description modified (diff)
• Milestone changed from sage-3.2.1 to sage-wishlist

### comment:4 Changed 5 years ago by ronanpaixao

Is this really an enchancement? As it is, just using arg(x) already raises an error and everything that needs arg() must be implemented numerically.

### comment:5 Changed 5 years ago by was

Is this really an enchancement? As it is, just using arg(x) already raises an error and everything that needs arg() must be implemented numerically.

Yes, this is an enhancement since it is implementing new functionality. It would be a bug fix if there were a bug in the existing arg function, where it produced invalid results on supported input.

-- William

### comment:6 Changed 3 years ago by kcrisman

• Component changed from basic arithmetic to symbolics
• Report Upstream set to N/A

### comment:7 Changed 3 years ago by burcin

• Summary changed from Implement a symbolic version of the arg function; the current one is only for actual numbers to Implement a symbolic version of the arg function

This was also reported in #6220. I will close that as duplicate.

### comment:9 Changed 17 months ago by ktkohl

• Keywords beginner, sd35.5 added; beginner removed

### Changed 17 months ago by ktkohl

symbolic arg function

### comment:10 Changed 17 months ago by ktkohl

• Status changed from new to needs_review
• Authors set to Karen T. Kohl

### comment:11 Changed 17 months ago by kcrisman

• Status changed from needs_review to needs_work
• Reviewers set to Karl-Dieter Crisman

There are a few small formatting issues, and it would be good to add an example showing that arg(sqrt(2)+i) remaining symbolic (as opposed to arctan(1/sqrt(2))) still evaluates correctly numerically. Otherwise looks fine. Currently running tests, as arg is likely used in a lot of places in Sage...

### comment:12 Changed 17 months ago by kcrisman

```File "/Users/karl-dietercrisman/Downloads/sage-4.8.alpha5/devel/sage-main/sage/symbolic/random_tests.py", line 16:
sage: [f for (one,f,arity) in _mk_full_functions()]
Expected:
[Ei, abs, arccos, arccosh, arccot, arccoth, arccsc, arccsch,
arcsec, arcsech, arcsin, arcsinh, arctan, arctan2, arctanh,
binomial, ceil, conjugate, cos, cosh, cot, coth, csc, csch,
dickman_rho, dilog, dirac_delta, elliptic_e, elliptic_ec,
elliptic_eu, elliptic_f, elliptic_kc, elliptic_pi, erf, exp,
factorial, floor, heaviside, imag_part, integrate,
kronecker_delta, log, polylog, real_part, sec, sech, sgn, sin,
sinh, tan, tanh, unit_step, zeta, zetaderiv]
Got:
[Ei, abs, arccos, arccosh, arccot, arccoth, arccsc, arccsch, arcsec, arcsech, arcsin, arcsinh, arctan, arctan2, arctanh, arg, binomial, ceil, conjugate, cos, cosh, cot, coth, csc, csch, dickman_rho, dilog, dirac_delta, elliptic_e, elliptic_ec, elliptic_eu, elliptic_f, elliptic_kc, elliptic_pi, erf, exp, factorial, floor, heaviside, imag_part, integrate, kronecker_delta, log, polylog, real_part, sec, sech, sgn, sin, sinh, tan, tanh, unit_step, zeta, zetaderiv]
**********************************************************************
sage: random_expr(5, verbose=True)
Expected:
About to apply dirac_delta to [1]
About to apply arccsch to [0]
arccsch(0)
Got:
About to apply dirac_delta to [1]
About to apply arcsec to [0]
arcsec(0)
```

### comment:13 Changed 17 months ago by kcrisman

I think the Maxima translation may not be correct.

``` -- Function: carg (<z>)
Returns the complex argument of <z>.  The complex argument is an
angle `theta' in `(-%pi, %pi]' such that `r exp (theta %i) = <z>'
where `r' is the magnitude of <z>.

`carg' is a computational function, not a simplifying function.

`realpart', and `imagpart'.

Examples:

(%i1) carg (1);
(%o1)                           0
(%i2) carg (1 + %i);
%pi
(%o2)                          ---
4
(%i3) carg (exp (%i));
(%o3)                           1
(%i4) carg (exp (%pi * %i));
(%o4)                          %pi
(%i5) carg (exp (3/2 * %pi * %i));
%pi
(%o5)                         - ---
2
(%i6) carg (17 * exp (2 * %i));
(%o6)                           2

(%o3)                                true
```

### comment:14 Changed 17 months ago by kcrisman

• Work issues set to random tests, Maxima

Otherwise, all tests pass!

### comment:15 Changed 17 months ago by kcrisman

Do this to check the fix works.

```sage: maxima(arg(x))
atan2(0,x)
sage: maxima(arg(2+i))
atan(1/2)
sage: maxima(arg(sqrt(2)+i))
atan(1/sqrt(2))
sage: arg(2+i)
arctan(1/2)
sage: arg(sqrt(2)+i)
arg(sqrt(2) + I)
```

It also seems to help with the sqrt(2) issue, in a manner of speaking. One could tell someone to do

```sage: arg(sqrt(2)+i).simplify()
arctan(1/2*sqrt(2))
```

### Changed 17 months ago by ktkohl

revision of arg function--apply instead of the previous patch

### comment:16 Changed 17 months ago by ktkohl

• Status changed from needs_work to needs_review

### Changed 17 months ago by ktkohl

symbolic arg--fixed whitespace issues--use this one instead of others

### comment:17 Changed 16 months ago by burcin

• Reviewers changed from Karl-Dieter Crisman to Karl-Dieter Crisman, Burcin Erocal

I uploaded a new patch with minor modifications to Karen's. In particular, it

• removes the duplicate commands that appear in the EXAMPLES and TESTS blocks for Function_arg.
• import CC directly instead of calling ComplexField in _evalf_().

I give a positive review to Karen's patch. If someone can take a quick look at my changes to check if I didn't mess anything up, this can be merged.

### comment:18 Changed 16 months ago by kcrisman

• Status changed from needs_review to needs_work

It doesn't appear that you messed anything up, except ...

```sage: arg(3.0)
---------------------------------------------------------------------------
<snip>
1426             return x.arg()
1427         except AttributeError:
-> 1428             from sage.rings.complex_field import CC
1429             x = CC(x)
1430             return x.arg()

ImportError: cannot import name CC
```

So apparently that won't work. Otherwise the changes are fine.

### comment:19 Changed 16 months ago by burcin

• Status changed from needs_work to needs_review
• Description modified (diff)
• Authors changed from Karen T. Kohl to Karen T. Kohl, Burcin Erocal

Apparently I didn't run tests, latex output was also broken.

attachment:trac_4498-arg_evalf.patch , to be applied after attachment:trac_4498-symbolic_arg.cleanup.patch , implements a new _evalf_() function which keeps the precision of the input. This one needs a real review. :)

### comment:20 Changed 16 months ago by kcrisman

This makes a lot more sense. Running tests...

Why parent_d and not parent? Just wondering in case there is a convention I should be aware of.

### comment:21 Changed 16 months ago by burcin

• Milestone changed from sage-wishlist to sage-5.0

Using parent as the name of the keyword argument masks the imported parent() function, which I used in the function body.

### comment:22 Changed 16 months ago by kcrisman

• Status changed from needs_review to positive_review

I wondered; that makes sense.

All looks well. Just a question - do you want to include any of the following as tests?

```sage: arg(long(1000))
0
sage: arg(1j)
1.57079632679490
sage: arg(1J)
1.57079632679490
sage: arg(complex(0,1))
1.57079632679490
sage: arg(complex(1,0))
0.000000000000000
sage: arg(int(10))
0
```

It's not a big deal to me either way, I just wanted to test them.

### comment:23 Changed 16 months ago by jdemeyer

• Status changed from positive_review to needs_work

This patch conflicts with #9130. Either this one or #9130 should be rebased.

### comment:24 Changed 15 months ago by jdemeyer

• Status changed from needs_work to positive_review
• Work issues random tests, Maxima deleted

### comment:25 Changed 15 months ago by jdemeyer

• Status changed from positive_review to closed
• Resolution set to fixed
• Merged in set to sage-5.0.beta4
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