Possibly unintentional conversion of real number to rational

[user202729]

Because QQ([element of RR]) tries to do a rational approximation, some part of the code that uses the constructor on user input has the following behavior…

sage: QuadraticField(pi.n())
Number Field in a with defining polynomial x^2 - 245850922/78256779 with a = 1.772453850905516?

sage: R.<x> = AsymptoticRing(growth_group='x^ZZ', coefficient_ring=ZZ)
sage: (1 + x)^(pi.n())
x^(245850922/78256779) + 245850922/78256779*x^(167594143/78256779) + 20601587289174923/6124123459454841*x^(89337364/78256779) + 1840491502630793355722972/1437762528405818857851417*x^(11080585/78256779) + 5098430634169557348880906924655/112514664439935388672910755005843*x^(-67176194/78256779) - 68498633075303442672509897293313532614/8805035229335182485655080241215399359697*x^(-145432973/78256779) + 4980979927288756272499089867645620034593240711/2067161088087893078113740853992180597265648907889*x^(-223689752/78256779) - 159170594950314274711966547531337367060627633645699096/161769368427893781189576754874137344728305890876260829531*x^(-301946531/78256779) + 6007626122806689076132415401891741471828772582757215638379497/12659549714031261070027065209722539002049849146701660082964140649*x^(-380203310/78256779) - 2284119337133569676886386334094220369253571089201542312095647795535070/8916260257894118369835704095222608474020660324910933528410817777243386139*x^(-458460089/78256779) + 104717755458887735895303392161722000487360506512316602734063646485366199482123/697757808508503026668072961689230627154962056480623119816535588003006898291386281*x^(-536716868/78256779) - 5109435066716738943030764777346834689842782240198560949438807023116814038100752595524/54604278615974240978794492118789587869297264407389641269773146055986362175064493795848899*x^(-614973647/78256779) + 785541979272120315935638662081031478279682412720434757807041439583840109007904194278527539007/12819464892314166137910792768472075576166030718100971371213749413114139115243944205185855219308963*x^(-693230426/78256779) - 41889353917822702810716721407423346015941075854991908158444781766335287806418143228222339116811863614/1003210030976088498023768431397117386035322733213639016282401349583452886516900872753560125823458050210177*x^(-771487205/78256779) + 2308364326665488334070391960384050247827590432575763751626804416553212448760293884316494965985096655029004205/78507985684678911874287982883020876516023937326775708282989284003654014597065191363982476229778549651068725039883*x^(-849743984/78256779) - 392303739892841898459699560171662605529040807859442574430029453222144458841593597253986709862424103253883933741890544/18431346256383243877519891376497042757702325666274012157011085572926562238355914187491655606559599536952636987773670350571*x^(-928000763/78256779) + 22753635621769426250560607286879206806844868021981194114109476418913929143826309649225898221511824553074692076619741868405317/1442377790658260855426177207554534869243061447451633122814529824230602364316764099913499057146645531291804846219429822643487270809*x^(-1006257542/78256779) - 1346824556019137914684670165324844676021493274771364609381686427070781920578166283680054973360038829336011070083897477716236573185342/112875839998051784287437300546432365710148156976642566481176518443723094261214494162064614831833409933640356361722905136620579141013064211*x^(-1084514321/78256779) + 730325259438610909274800496728115834122957380147366459793504942644792536767452967285184100338117799765489463260260743039518468921733993141391/79499696986502090221838879746968631936436181400005829383992146174558759123164278471137326719534183933939682299525341018630333218212422818657327321*x^(-1162771100/78256779) - 44694795014485209971024209255847244703714141482477445292484185000764333013099038472024080529087558208573575012291735287940959662023181532231982557900/6221390217639660057528506185966100149382028295424166788814779520918140235215700721010251655741381615063668317044166416994588869354008347574223540890159059*x^(-1241027879/78256779) + O(x^(-1319284658/78256779))

sage: B = Berkovich_Cp_Affine(Qp(3))
sage: B(3, power=pi.n())
Type II point centered at 3 + O(3^21) of radius 3^245850922/78256779

sage: Cusp(pi.n())
245850922/78256779

sage: Cusp(pi.n(), 2)
122925461/78256779

I've no idea what Berkovich_Cp_Affine is, but the rest surely doesn't seem intentional?

Originally posted by @user202729 in #38362 (comment)

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Edit: to be more conservative, we could probably use QQ.coerce().