Implement a symbolic version of the arg function

[TimothyClemans]

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

• attachment: trac_4498-symbolic_arg.cleanup.patch
• attachment: trac_4498-arg_evalf.patch

CC: @kcrisman @sagetrac-ktkohl

Component: symbolics

Keywords: sd35.5

Author: Karen Kohl, Burcin Erocal

Reviewer: Karl-Dieter Crisman, Burcin Erocal

Merged: sage-5.0.beta4

Issue created by migration from https://trac.sagemath.org/ticket/4498

[TimothyClemans]

comment:1

arg(x)
///

Traceback (most recent call last):
 File "<stdin>", line 1, in <module>
 File "/home/ronan/.sage/sage_notebook/worksheets/admin/0/code/127.py",
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

[sagetrac-mabshoff]

comment:2

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

Cheers,

Michael

[williamstein]

Description changed:

--- 
+++ 
@@ -1 +1,22 @@
+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

[sagetrac-ronanpaixao]

comment:4

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.

[williamstein]

comment:5

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