Dear William,
> > Or my student's :). That was my intention ! The obvious question is now the
> > naming convention. It seems to me that we should stick as close as possible
> > to
> > polynomials:
> >
> > sage: ring = ZZ['x1,x2']
> > sage: x1 = ring.gens()[0] # why x1 is not defined ???
>
> What do you mean by "why x1 is not defined?" There is inject_on(),
> but that only works with PolynomialRing:
>
> sage: inject_on()
> Redefining: FiniteField Frac FractionField FreeMonoid GF
> LaurentSeriesRing NumberField PolynomialRing quo quotient
Ok !!! In forgot about this mantra. Thanks for pointing this out.
> sage: PolynomialRing(ZZ, 'x1,x2')
> Defining x1, x2
> Multivariate Polynomial Ring in x1, x2 over Integer Ring
> sage: (x1+x2)^3
> x1^3 + 3*x1^2*x2 + 3*x1*x2^2 + x2^3
>
>
> It might be possible to fix ZZ['x1,x2'] to also work with inject_on -- not
> sure.
And I also thought after asking the debugger that the call
PolynomialRing(ZZ, 'x1,x2')
and
ZZ['x1,x2']
where strictly equivalent:
sage: trace("ZZ['x,y']")
> <string>(1)<module>()
ipdb> s
--Call--
> /usr/local/sage/sage-3.4.2/local/lib/python2.5/site-packages/sage/rings/polynomial/polynomial_ring_constructor.py(41)PolynomialRing()
40
---> 41 def PolynomialRing(base_ring, arg1=None, arg2=None,
42 sparse=False, order='degrevlex',
But inject_on seems to change the first one without telling the second one...
> > sage: truc = x1^8 + 2*x1^4 + 2
> > sage: truc
> > x1^8 + 2*x1^4 + 2
> > sage: type(truc)
> > <type
> > 'sage.rings.polynomial.multi_polynomial_libsingular.MPolynomial_libsingular'>
> > sage: truc.dict()
> > {(0, 0): 2, (4, 0): 2, (8, 0): 1}
> > sage: truc.coefficients()
> > [1, 2, 2]
> > sage: truc.monomials()
> > [x1^8, x1^4, 1]
> >
> > Should we stick to this interface ?
> >
>
> I've cc'd David Kohel -- original author of FreeAlgebra, since he
> might have some thoughts.
Awaiting for comments...
Cheers,
Florent
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