coeff(f,x*y) does not work

[zimmermann6]

The following is ok:

sage: var('x,y,z')
sage: f=x*y*z^2
sage: f.coeff(z^2)
x*y

However the following is not:

sage: f.coeff(x*y)
0

Component: symbolics

Keywords: pynac

Stopgaps: #12699

Author: Paul Zimmermann

Branch/Commit: 06b3fc1

Reviewer: Ralf Stephan

Issue created by migration from https://trac.sagemath.org/ticket/9505

[zimmermann6]

comment:1

PS: I'm sorry if this is a duplicate. The trac search for "coeff" gives 295 entries!

[burcin]

Changed keywords from none to pynac

[burcin]

comment:2

I'm switching the component to symbolics since the problem involves symbolic expressions.

It seems that we inherited this behavior from GiNaC:

ginsh - GiNaC Interactive Shell (ginac V1.5.7)
  __,  _______  Copyright (C) 1999-2010 Johannes Gutenberg University Mainz,
 (__) *       | Germany.  This is free software with ABSOLUTELY NO WARRANTY.
  ._) i N a C | You are welcome to redistribute it under certain conditions.
<-------------' For details type `warranty;'.

Type ?? for a list of help topics.
> f = x*y*z^2;
y*z^2*x
> coeff(f, z^2,1);
y*x
> coeff(f, x*y,1);
0

I will report this to the ginac-list.

[jbalakrishnan]

Stopgaps: #12699

[williamstein]

comment:4

Since I don't know how to fix this, at least I can point out some related facts.

Maxima does exactly the same thing as GINAC (and Sage):

sage: !maxima
;;; Loading #P"/Users/wstein/sage/install/sage-5.0.beta2/local/lib/ecl/sb-bsd-sockets.fas"
;;; Loading #P"/Users/wstein/sage/install/sage-5.0.beta2/local/lib/ecl/sockets.fas"
;;; Loading #P"/Users/wstein/sage/install/sage-5.0.beta2/local/lib/ecl/defsystem.fas"
;;; Loading #P"/Users/wstein/sage/install/sage-5.0.beta2/local/lib/ecl/cmp.fas"
Maxima 5.24.0 http://maxima.sourceforge.net
using Lisp ECL 11.1.1
Distributed under the GNU Public License. See the file COPYING.
Dedicated to the memory of William Schelter.
The function bug_report() provides bug reporting information.
(%i1) f : x*y*z;
(%o1)                                x y z
(%i2) coeff(f, x);
(%o2)                                 y z
(%i3) coeff(f, x*y);
(%o3)                                  0

Maple raises an error in this case:

> f := x*y*z 
> ;
                                                                     f := x y z

> coeff(f, x);
                                                                         y z

> coeff(f, x*y);
Error, invalid input: coeff received x*y, which is not valid for its 2nd argument, x

Mathematica does what you expect:

In[1]:= f := x*y*z;

In[2]:= Coefficient[f,x] 

Out[2]= y z

In[3]:= Coefficient[f,x*y]

Out[3]= z

Sage multivariate polynomials (hence Singular) do what you expect:

sage: R.<x,y,z>=QQ[]
sage: f = x*y*z^2
sage: f.coefficient(x)
y*z^2
sage: f.coefficient(x*y)
z^2

[zimmermann6]

comment:5

a possible fix would be that f.coeff(x<sup>n*y</sup>m) automatically calls
f.coeff(x,n).coeff(y,m) which gives the expected answer:

sage: var('x,y,z')
(x, y, z)
sage: f=x*y*z^2
sage: f.coeff(x,1).coeff(y,1)
z^2

Paul

[burcin]

comment:6

We might need to expand the expression before doing recursive calls to coefficient():

sage: var('x,y,z')
(x, y, z)
sage: g = x*y*(z^2 + y*z)
sage: g.coeff(x,1).coeff(y,1)
z

Compare to MMA:

In[12]:= Coefficient[x*y*(z^2 + y*z), x*y]

          2
Out[12]= z

[zimmermann6]

Author: Paul Zimmermann

[zimmermann6]

comment:8

Attachment: trac_9505.patch.gz

attached is a temporary fix that calls coeff in turn for each term x^n in s.
In addition it checks the extra argument n is only used for a single symbol.

Paul

[rwst]

Branch: u/rws/ticket/9505

[rwst]

Commit: 850abdc

[rwst]

comment:11

Patch applies cleanly, looks good, tests OK in symbolics/

Not sure if the stopgap is still necessary. My tests were satisfying but hey.

---

New commits:

850abdc

trac 9505: coeff(f,x*y) does not work

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1 and set ticket back to needs_review. New commits:

0c57d9a

Merge branch 'develop' into ticket/9505

[sagetrac-git]

Changed commit from 850abdc to 0c57d9a

[vbraun]

Reviewer: Ralf Stephan

[vbraun]

comment:15

Documentation does not build

[calculus ] docstring of sage.symbolic.expression.Expression.coeff:57: WARNING: Literal block expected; none found.
[calculus ] docstring of sage.symbolic.expression.Expression.coeff:57: WARNING: Literal block expected; none found.
Traceback (most recent call last):
  File "/home/buildslave-sage/slave/sage_git/build/src/doc/common/builder.py", line 83, in f
    execfile(sys.argv[0])
  File "/home/buildslave-sage/slave/sage_git/build/src/doc/common/custom-sphinx-build.py", line 185, in <module>
    sphinx.cmdline.main(sys.argv)
  File "/home/buildslave-sage/slave/sage_git/build/local/lib/python2.7/site-packages/Sphinx-1.1.2-py2.7.egg/sphinx/cmdline.py", line 206, in main
    print >>error
  File "/home/buildslave-sage/slave/sage_git/build/src/doc/common/custom-sphinx-build.py", line 165, in write
    self._write(str)
  File "/home/buildslave-sage/slave/sage_git/build/src/doc/common/custom-sphinx-build.py", line 139, in _write
    self._log_line(line)
  File "/home/buildslave-sage/slave/sage_git/build/src/doc/common/custom-sphinx-build.py", line 108, in _log_line
    raise OSError(line)
OSError: [calculus ] docstring of sage.symbolic.expression.Expression.coeff:57: WARNING: Literal block expected; none found.

[zimmermann6]

comment:16

sorry with the change to git I don't know how yet how to submit a patch, thus I won't be able to work on this in the near future.

Paul

[sagetrac-git]

Changed commit from 0c57d9a to 06b3fc1

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1 and set ticket back to needs_review. New commits:

06b3fc1

Trac #9505: reviewer's patch: fix doc

[vbraun]

Changed branch from u/rws/ticket/9505 to 06b3fc1