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