Precision for inverse polynomials
This might be an obvious question, but how do you change the number of terms shown for in inverse polynomial? I have a polynomial, which I name eisen in my code, which is:
1 + 240*q + 2160*q^2 + 6720*q^3 + 17520*q^4 + 30240*q^5 + 60480*q^6 + 82560*q^7 + 140400*q^8 + 181680*q^9 + 272160*q^10 + 319680*q^11 + 490560*q^12 + 527520*q^13 + 743040*q^14 + 846720*q^15 + 1123440*q^16 + 1179360*q^17 + 1635120*q^18 + 1646400*q^19 + 2207520*q^20 + 2311680*q^21 + 2877120*q^22 + 2920320*q^23 + 3931200*q^24 + 3780240*q^25 + 4747680*q^26 + 4905600*q^27 + 6026880*q^28 + 5853600*q^29
And I would like to calculate the inverse of this polynomial, up to O(q^30). However, what I get when I enter (eisen)^(-1) is:
1 - 240*q + 55440*q^2 - 12793920*q^3 + 2952385680*q^4 - 681306078240*q^5 + 157221316739520*q^6 - 36281112432850560*q^7 + 8372395974330234000*q^8 - 1932052510261208053680*q^9 + 445849302141400152457440*q^10 - 102886230661038692118348480*q^11 + 23742498662203277988768469440*q^12 - 5478927929451211228257360565920*q^13 + 1264342548070079096527645691391360*q^14 - 291765487599771712002077691406849920*q^15 + 67329142631696181086152506843238511760*q^16 - 15537181881284423393192481036645057742560*q^17 + 3585431380474292447563107175964481073840080*q^18 - 827390596461696991629836522119620115607496000*q^19 + O(q^20)
I'm just not sure where to specify the precision, since there is nowhere to enter arguments, since exponentiation is just done by ^.
Never mind, I figured it out. I changed the precision of the PowerSeriesRing, but it still didn't work. However, after changing the precision, if I then recalculate eisen itself, then recalculate the inverse, it gives the right precision.
For future user's sake, you should write up your answer to your own question and post it as such.
Perusing archives is a great way to get the hang of Sage...