#18393: make Expression.series return an element of SR[[]]
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Reporter: rws | Owner:
Type: enhancement | Status: new
Priority: major | Milestone: sage-6.7
Component: calculus | Resolution:
Keywords: | Merged in:
Authors: | Reviewers:
Report Upstream: N/A | Work issues:
Branch: | Commit:
Dependencies: | Stopgaps:
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Comment (by rws):
Replying to [comment:4 nbruin]:
> That's ambiguous and not what happens by default in our current
coercion:
> {{{
> sage: R=PowerSeriesRing(SR,name='x',default_prec=10)
> sage: F=1/(1-R.0)
> sage: F-x
> -x + 1 + x + x^2 + x^3 + x^4 + x^5 + x^6 + x^7 + x^8 + x^9 + O(x^10)
> sage: F-R.0
> 1 + x^2 + x^3 + x^4 + x^5 + x^6 + x^7 + x^8 + x^9 + O(x^10)
> }}}
> You see that SR('x') doesn't coerce to R.0 in R. You'd have to override
that somehow and that will be extremely messy: where does `sin(x)` coerce?
To `sin(R.0)`, where is the problem? Of course it would expand to
{{{
x - 1/6*x^3 + 1/120*x^5 - 1/5040*x^7 + 1/362880*x^9 - 1/39916800*x^11 +
1/6227020800*x^13 - 1/1307674368000*x^15 + 1/355687428096000*x^17 -
1/121645100408832000*x^19 + Order(x^20)
}}}
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Ticket URL: <http://trac.sagemath.org/ticket/18393#comment:5>
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