Ilya Zakharevich on Fri, 2 Nov 2001 18:50:33 -0500

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Re: subst() broken

On Sat, Nov 03, 2001 at 12:31:02AM +0100, Bill Allombert wrote:
> > > Probably you mean (1+y)*Mod(1,z), but it is not the same thing:
> > > it is a polynomial not a POLMOD.

> > I have no slightest idea what you mean by this sentence.  Can it be
> > expressed algebraically, or it is just some "implementation detail"?
> Both.

[Can't understand your examples, but I hope one can replace Z by Z^3
 to get something more friendly.]

> (1+y)*Mod(1,z) is an object living in the ring (Q[Z]/(Z))[Y],
> so it is a polynomial in Y whose coeffcients are cosets in Z.

You mean the coefficients are in Q[Z]/(Z) == Z?

> Mod(1+y,z) is an object living in Q(Z)[Y]/(Z) so it is a coset,
> but the ideal (Z) being trivial because Z is invertible, this quotient
> is the null ring.

The next question is how I can deduce that these expressions will
result in elements of these rings.  [Preferably deduce basing on the
documentation. ;-]