On November 3, 2006 9:48 AM David Harvey wrote:
>
> On Nov 3, 2006, at 9:37 AM, Bill Page wrote:
>
> >
> > Maybe it is interesting to consider how Axiom handles these
> > coercions? For example:
> >
> > sage: x = axiom('x::MPOLY([x],INT)')
> > sage: x.type()
> > MultivariatePolynomial([x],Integer)
> > sage: y = axiom('y::MPOLY([y],INT)')
> > sage: y.type()
> > MultivariatePolynomial([y],Integer)
> > sage: z = x*y
> > sage: z
> > y x
> > sage: z.type()
> > MultivariatePolynomial([x],MultivariatePolynomial([y],Integer))
> > sage: w = axiom('(x*y)::MPOLY([x,y],INT)')
> > sage: w
> > y x
> > sage: w.type()
> > MultivariatePolynomial([x,y],Integer)
>
> What would axiom do if you started off with x and y in a *univariate*
> polynomial ring?
>
sage: x=axiom('x::UP(x,INT)')
sage: y=axiom('y::UP(y,INT)')
sage: (x*y).type()
UnivariatePolynomial(x,UnivariatePolynomial(y,Integer))
In Axiom this can be coerced to MultivariatePolynomial
([x,y],Integer), but right now I do not yet have a method
in the Sage/Axiom interface that can easily apply Axiom's
:: coercion/conversion operator to an Sage Axiom ojbect.
So if you read my example above carefully and critically
you will see that the command:
axiom('(x*y)::MPOLY([x,y],INT)')
is actually bogus, although the result shown is correct.
In axiom.console():
(1) -> x:=x::UP(x,INT)
(1) x
Type:
UnivariatePolynomial(x,Integer)
(2) -> y:=y::UP(y,INT)
(2) y
Type:
UnivariatePolynomial(y,Integer)
(3) -> x*y
(3) y x
Type:
UnivariatePolynomial(x,UnivariatePolynomial(y,Integer))
(4) -> (x*y)::MPOLY([x,y],INT)
(4) y x
Type:
MultivariatePolynomial([x,y],Integer)
Regards,
Bill Page
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