Re: polcoeff() mystery

[Ilya Zakharevich <ilya@math.ohio-state.edu>]

On Sun, Jul 14, 2002 at 05:37:54PM +0200, Karim BELABAS wrote:
> > Which algorithsms assume that a poly is "filled"?

> Nearly everything operates on "filled" single variable polynomials. Once the
> higher level wrappers have done their stuff [ checking types, degrees, variable
> priorities, etc ], lower level routines assume everything is compatible (all args
> in sight are t_POL in the same variable) and operate on vectors of coefficients.

Do you mean here the support for base arithmetic, or higher-level
stuff?  If former, it is not out-of-hand to fix...

> > > Maybe a print function that output 'foo^0 as 'foo^0 not 1 could be useful.
> >
> > \x *must*.
> 
> \x *does*. Disable automatic simplification (\y) if you want \x to operate in the
> way you expect.

This confuses me again, when I felt almost unconfused...  Consider:

  ? aaa=x^2 + y*x + z;
  ? aaa
  %2 = x^2 + y*x + z
  ? \x
  [&=004854c4] POL(lg=5,CLONE):15000005  (+,varn=0,lgef=5):40000005  004854d8  004854fc  00485520  
    coef of degree 0 = [&=004854d8] POL(lg=4):14000004  (+,varn=3,lgef=4):40030004  004854e8  004854f0  
      coef of degree 0 = [&=004854e8] INT(lg=2):02000002  (0,lgef=2):00000002  
      coef of degree 1 = [&=004854f0] INT(lg=3):02000003  (+,lgef=3):40000003  00000001  
    coef of degree 1 = [&=004854fc] POL(lg=4):14000004  (+,varn=2,lgef=4):40020004  0048550c  00485514  
      coef of degree 0 = [&=0048550c] INT(lg=2):02000002  (0,lgef=2):00000002  
      coef of degree 1 = [&=00485514] INT(lg=3):02000003  (+,lgef=3):40000003  00000001  
    coef of degree 2 = [&=00485520] INT(lg=3):02000003  (+,lgef=3):40000003  00000001  

If every polynomial is filled, then aaa contains a filled poly, then
coefficient of degree 2 of aaa must be a polynomial in y - no matter
whether the simplifications are enabled or not.  Right?

If \x outputs 'foo^0 as 'foo^0 not 1, then we would see "coef of
degree 2" not as an INT.  Right?

Ilya