Ilya Zakharevich on Wed, 7 Nov 2001 13:27:12 -0500

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Re: subst() broken

On Tue, Nov 06, 2001 at 04:37:24PM +0100, Bill Allombert wrote:
> (1+y)*Mod(1,P(z)) is a polynomial, belonging to the ring {Q[z]/P(z)Q[z]}[y]
> Mod(1+y,P(z)) is a coset, belonging to the quotient ring Q(z)[y]/P(z)Q(z)[y],
> which is isomorphic to the null ring since P(z) is invertible in Q(z)[y]
> > The next question is how I can deduce that these expressions will
> > result in elements of these rings.  [Preferably deduce basing on the
> > documentation. ;-]
> You can probably *deduce* it... with some effort :-)
> Please read 
> ?? POL
> and
> ??"Multivariate objects"@4

I did.  Many times.  With a very low yield.

> The big thing is that each polynomial euclidean division is done as univariate
> polynomials division in the higher priority variables, because euclidean division
> does not make sense for multivariate polynomials.

IMO, what is needed is some explicit explanation; with ample crosslinks
to it from all the places which mention POLMOD and variable priorities...