If you create an actual power series element, you can easily write the
coefficients to a file:
sage: f = taylor(sin(x), x, 0, 10); f
1/362880*x^9 - 1/5040*x^7 + 1/120*x^5 - 1/6*x^3 + x
sage: power_series = RR[['x']](f); power_series
0.000000000000000 + 1.00000000000000*x + 0.000000000000000*x^2 -
0.166666666666667*x^3 + 0.000000000000000*x^4 +
0.00833333333333333*x^5 + 0.000000000000000*x^6 -
0.000198412698412698*x^7 + 0.000000000000000*x^8 +
2.75573192239859e-6*x^9
sage: list(power_series)
[0.000000000000000, 1.00000000000000, 0.000000000000000,
-0.166666666666667, 0.000000000000000, 0.00833333333333333,
0.000000000000000, -0.000198412698412698, 0.000000000000000,
2.75573192239859e-6]
sage: ",".join(str(a) for a in list(power_series))
'0.000000000000000,1.00000000000000,0.000000000000000,-0.166666666666667,0.000000000000000,0.00833333333333333,0.000000000000000,-0.000198412698412698,0.000000000000000,2.75573192239859e-6'
sage: open("file.txt", "w").write("\n".join(str(a) for a in list(power_series)))
sage: open("file.txt", "w").write("\n".join(str(a) for a in list(power_series)))
sage: !cat file.txt
0.000000000000000
1.00000000000000
0.000000000000000
-0.166666666666667
0.000000000000000
0.00833333333333333
0.000000000000000
-0.000198412698412698
0.000000000000000
2.75573192239859e-6
Note that ZZ[[x]], QQ[[x]], RR[[x]] are *much* faster to compute with as well
sage: R.<t> = PowerSeriesRing(ZZ, 't', 1000)
sage: f = 1/(t+1)
sage: f + O(t^10) # this is really O(t^1000), don't want to print it all
1 - t + t^2 - t^3 + t^4 - t^5 + t^6 - t^7 + t^8 - t^9 + O(t^10)
sage: timeit("f^100")
25 loops, best of 3: 28.2 ms per loop
- Robert
On Tue, Dec 6, 2011 at 3:33 AM, Julie <juliewilliams...@googlemail.com> wrote:
> Thank you very much to everyone for all your help.
> I've now solved the issue I was having trouble with - the reason
> finding the coefficients of the y terms didn't give me the required
> results was because the generating function was really in terms of one
> variable (p), not two, and required values to be substituted in for
> y's rather than finding the various coefficients.
>
> Now I have completed this work, wondered if you knew the best way to
> export the outputted coefficients by the internet version of sage to
> another package such as Excel? Or indeed, if this is even possible?
>
> Many thanks,
> Julie
>
> On Dec 3, 8:57 pm, Anton Sherwood <bro...@pobox.com> wrote:
>> On 2011-12-02 08:17, Julie wrote:> Unfortunately, having the
>> Tayorseriesapproach out, don't think it's
>> > really appropriate for my problem afterall, as what I esentially need
>> > to do is find the coefficientsof p^0*y^0, p, y, p^2*y etc in the
>> > formula
>> > (0.030*0.248244^y)y+0.05721*(0.248244^y)p +0.08838*(0.248244^y)
>>
>> > [...]
>>
>> Since this is not a polynomial in p and y, what does it mean to obtain
>> thecoefficientsof p^j y^k *if not* those of something very similar to
>> a Taylorseries?
>>
>> --
>> Anton Sherwood *\\*www.bendwavy.org*\\*www.zazzle.com/tamfang
>
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