Hmm, poles are not so bad.
We can imagine, that you do something like with rational functions:
define two expressions are equal, if they are equal on some open and
dense subset.
If you have something like
sin[x] and cos[x-Pi/2]
you should add a relation, that they are equal.
And I suppose, there many such hidden relations in the symbolic ring.
Michael
On 12 Aug., 13:43, Martin Albrecht <m...@informatik.uni-bremen.de>
wrote:
> > > I think one should treat it like a field for this purpose. It is of
> > > course not really
> > > a field, since functions have poles, etc.; also, their are floating
> > > point numbers in
> > > SR and floating point numbers don't form a field either. But they are
> > > supposed to approximately model one.
>
> > If I have understood this correctly, and the suggestion is to use
> > Buchberger's algorithm to compute Grobner bases in Sage's symbolic
> > ring, which includes limited precision floating point numbers
>
> This is not what William meant (well, I think :). You can compute in the
> symbolic ring with exact coefficients:
>
> sage: var('x,y,z')
> (x, y, z)
> sage: 1/2*x
> 1/2*x
> sage: (1/2*x)^1000
> 1/10715086071862673209484250490600018105614048117055336074437503883703510511249361224931983788156958581275946729175531468251871452856923140435984577574698574803934567774824230985421074605062371141877954182153046474983581941267398767559165543946077062914571196477686542167660429831652624386837205668069376*x^1000
>
> Cheers,
> Martin
>
> --
> name: Martin Albrecht
> _pgp:http://pgp.mit.edu:11371/pks/lookup?op=get&search=0x8EF0DC99
> _otr: 47F43D1A 5D68C36F 468BAEBA 640E8856 D7951CCF
> _www:http://www.informatik.uni-bremen.de/~malb
> _jab: martinralbre...@jabber.ccc.de
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