Hello,
I developed a package to work with infinite power series.
You can work with the power series mostly like with functions, the
actual value of a coefficient is computed when requested.
For example (the working title is PowerSeriesRingI, "I" like
infinite):
sage: PQ = PowerSeriesRingI(QQ)
sage: #Predefined
PowerSeries
sage: expps = PQ.exp
sage: expps.poly(10,x)
1/362880*x^9 + 1/40320*x^8 + 1/5040*x^7 + 1/720*x^6 +
1/120*x^5 + 1/24*x^4 + 1/6*x^3 + 1/2*x^2 + x + 1
sage: expps
[1, 1, 1/2, 1/6, 1/24, 1/120, 1/720, 1/5040, 1/40320,
1/362880, 1/3628800, ...]
sage: PQ.zero
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, ...]
sage: PQ.one
[1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, ...]
sage: PQ.id
[0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, ...]
sage: #finite
powerseries
sage: p = PQ([1,2,3,4])
sage: p.poly(10,x)
4*x^3 + 3*x^2 + 2*x + 1
sage: p
[1, 2, 3, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, ...]
sage: one = PQ([1])
sage: id = PQ([0,1])
sage: #power series are just functions that map the index to
the coefficient
sage: expps[30]
1/265252859812191058636308480000000
sage: #power series
operations
sage: p+p
[2, 4, 6, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, ...]
sage: p-p
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, ...]
sage: p*p
[1, 4, 10, 20, 25, 24, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, ...]
sage: one/p
[1, -2, 1, 0, 5, -14, 13, -4, 25, -90, 121, -72, 141, -550,
965, -844, 993, ...]
sage: p.rcp()/p*p*p
[1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, ...]
sage: p**2
[1, 4, 10, 20, 25, 24, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, ...]
sage: #composition only works for coefficient 0 being 0 in the
second operand
sage: dexp = expps - one
sage: expps.o(dexp)
[1, 1, 1, 5/6, 5/8, 13/30, 203/720, 877/5040, 23/224,
1007/17280, ...]
Beneath composition it can also perform (fractional) iteration
sage: #we come into interesting
regions ...
sage: dexp.o(dexp)
[0, 1, 1, 5/6, 5/8, 13/30, 203/720, 877/5040, 23/224,
1007/17280, ...]
sage: dexp.nit(2)
[0, 1, 1, 5/6, 5/8, 13/30, 203/720, 877/5040, 23/224,
1007/17280, ...]
sage: dexp.it(-1)
[0, 1, -1/2, 1/3, -1/4, 1/5, -1/6, 1/7, -1/8, 1/9, -1/10,
1/11, -1/12, ...]
sage: dexp.it(-1).o(dexp)
[0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, ...]
sage: hdexp = dexp.it(1/2)
sage: hdexp
[0, 1, 1/4, 1/48, 0, 1/3840, -7/92160, 1/645120, 53/3440640,
-281/30965760, ...]
sage: #verifying that shoudl be
Zero
sage: hdexp.it(2) - dexp
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, ...]
My question is about making this a standard SAGE package.
Is there any guideline how to do so and what are the criteria and
requirements?
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