︠ddc97992-3ab2-48de-ada8-663f40afbdb5s︠ R = PowerSeriesRing(QQ, 'x'); R ︡b7e188a5-88ed-444c-a32c-129dab5bce64︡{"stdout":"Power Series Ring in x over Rational Field\n"}︡{"done":true}︡ ︠e64fae0c-2a21-4290-88ed-d334bdf2d02bs︠ g=R.random_element(6);g ︡61ad62ef-5d04-4a75-a559-975a9ae07276︡{"stdout":"-1/2 - 7/3*x^2 + 9*x^4 - 5*x^5 + O(x^6)\n"}︡{"done":true}︡ ︠52e8ed1a-993e-4f93-bfff-08a46c8d7cf9︠ g^(-1) ︡a351af0f-57fd-4bd9-b2a2-a0524ee8ddb2︡ ︠158e2cfb-b7ee-4909-831d-323394c7b234s︠ f*f ︡dc6acc13-46d7-48cc-8972-15b1a2728735︡{"stdout":"x^2 + 4*x^3 + 10*x^4 + 20*x^5 + 35*x^6 + 56*x^7 + 70*x^8 + 76*x^9 + 73*x^10 + 60*x^11 + 36*x^12\n"}︡{"done":true}︡ ︠82d569a3-64da-4f79-ab8c-c51320edaceds︠ def (i) =0 forjn(1+1): s+=j*2^(-j) rturn d(20) ︡bf617240-b87a-434e-9c95-6cdd06453b31︡ ︠feb5d246-38c5-4140-8559-aee21ea4c74d︠ rn(1,21) ︡3f309458-30dc-4a7a-ad2a-074fd3a1f1b8︡ ︠1a306ac9-cfdc-43f2-950b-ed903dc1ad9b︠