"Testing numerics"

clear

check(infixform(1) == "1")
check(infixform(12) == "12")
check(infixform(123) == "123")
check(infixform(1234) == "1234")
check(infixform(12345) == "12345")
check(infixform(123456) == "123456")
check(infixform(1234567) == "1234567")
check(infixform(12345678) == "12345678")
check(infixform(123456789) == "123456789")
check(infixform(1234567890) == "1234567890")
check(infixform(12345678901) == "12345678901")
check(infixform(123456789012) == "123456789012")
check(infixform(1234567890123) == "1234567890123")
check(infixform(12345678901234) == "12345678901234")
check(infixform(123456789012345) == "123456789012345")
check(infixform(1234567890123456) == "1234567890123456")
check(infixform(12345678901234567) == "12345678901234567")
check(infixform(123456789012345678) == "123456789012345678")
check(infixform(1234567890123456789) == "1234567890123456789")
check(infixform(12345678901234567890) == "12345678901234567890")

N = 13/4000000

T = N^(3/2)
check(prefixform(T) == "(* 13/8000000000 (^ 13 1/2))")

T = N^(5/2)
check(prefixform(T) == "(* 169/32000000000000000 (^ 13 1/2))")

T = N^(-3/2)
check(prefixform(T) == "(* 8000000000/13 (^ 13 -1/2))")

T = N^(-5/2)
check(prefixform(T) == "(* 32000000000000000/169 (^ 13 -1/2))")

T = sqrt(102)
check(infixform(T)="2^(1/2) 3^(1/2) 17^(1/2)")

T = sqrt(204)
check(infixform(T)="2 3^(1/2) 17^(1/2)")

T = sqrt(408)
check(infixform(T)="2 2^(1/2) 3^(1/2) 17^(1/2)")

T = sqrt(816)
check(infixform(T)="4 3^(1/2) 17^(1/2)")

T = sqrt(2146654199) -- 46327 46337 (less than 2^31)
check(infixform(T) == "46327^(1/2) 46337^(1/2)")

T = sqrt(2147673613) -- 46337 46349 (greater than 2^31)
check(infixform(T) == "2147673613^(1/2)")

for(k,1,100,
N=2^31-k,
M=sqrt(N),
check(N/M=M))

check(1000! ==
402387260077093773543702433923003985719374864210714632543799910429938512398629020592044208486969404800479988610197196058631666872994808558901323829669944590997424504087073759918823627727188732519779505950995276120874975462497043601418278094646496291056393887437886487337119181045825783647849977012476632889835955735432513185323958463075557409114262417474349347553428646576611667797396668820291207379143853719588249808126867838374559731746136085379534524221586593201928090878297308431392844403281231558611036976801357304216168747609675871348312025478589320767169132448426236131412508780208000261683151027341827977704784635868170164365024153691398281264810213092761244896359928705114964975419909342221566832572080821333186116811553615836546984046708975602900950537616475847728421889679646244945160765353408198901385442487984959953319101723355556602139450399736280750137837615307127761926849034352625200015888535147331611702103968175921510907788019393178114194545257223865541461062892187960223838971476088506276862967146674697562911234082439208160153780889893964518263243671616762179168909779911903754031274622289988005195444414282012187361745992642956581746628302955570299024324153181617210465832036786906117260158783520751516284225540265170483304226143974286933061690897968482590125458327168226458066526769958652682272807075781391858178889652208164348344825993266043367660176999612831860788386150279465955131156552036093988180612138558600301435694527224206344631797460594682573103790084024432438465657245014402821885252470935190620929023136493273497565513958720559654228749774011413346962715422845862377387538230483865688976461927383814900140767310446640259899490222221765904339901886018566526485061799702356193897017860040811889729918311021171229845901641921068884387121855646124960798722908519296819372388642614839657382291123125024186649353143970137428531926649875337218940694281434118520158014123344828015051399694290153483077644569099073152433278288269864602789864321139083506217095002597389863554277196742822248757586765752344220207573630569498825087968928162753848863396909959826280956121450994871701244516461260379029309120889086942028510640182154399457156805941872748998094254742173582401063677404595741785160829230135358081840096996372524230560855903700624271243416909004153690105933983835777939410970027753472000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000)
