Ralf Hemmecke <[email protected]> writes:
>>>> It would be nicer to have a domain specifically for finite series, I
>>>> think. But no time...
>>>
>>> But this is one of the most fundamental domains: List. And it's
>>> already done. ;-)
>>
>> Not series: sequences! Thus: it's SparseUnivariatePolynomial, but lazy.
>
> You want what. Lists, that evaluate lazily like stream, but are
> always supposed to be finite. So you want to be able to call expand
> on a lazy list like [n for n in 0..10^(10^10))]?
why are you exaggerating?
> What do you gain?
equality for reasonable cases. But, to be honest, I do not know why
++ Author: Clifton J. Williamson
decided to use UPXS instead of SUP as representation. The only reason I
can think of is lazyness.
ExponentialOfUnivariatePuiseuxSeries(FE,var,cen):_
Exports == Implementation where
FE : Join(Field, Comparable)
var : Symbol
cen : FE
UPXS ==> UnivariatePuiseuxSeries(FE,var,cen)
Exports ==> Join(UnivariatePuiseuxSeriesCategory(FE),OrderedAbelianMonoid) _
with
exponential : UPXS -> %
++ exponential(f(x)) returns \spad{exp(f(x))}.
++ Note: the function does NOT check that \spad{f(x)} has no
++ non-negative terms.
exponent : % -> UPXS
++ exponent(exp(f(x))) returns \spad{f(x)}
exponentialOrder: % -> Fraction Integer
++ exponentialOrder(exp(c * x ^(-n) + ...)) returns \spad{-n}.
++ exponentialOrder(0) returns \spad{0}.
Implementation ==> UPXS add
Rep := UPXS
exponential f == complete f
exponent f == f pretend UPXS
exponentialOrder f == order(exponent f,0)
zero? f == empty? entries complete terms f
f = g ==
-- we redefine equality because we know that we are dealing with
-- a FINITE series, so there is no danger in computing all terms
(entries complete terms f) = (entries complete terms g)
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