Rat to dec with PARI/GP

rat2dec_with_PARI-GP.gp

\\ So we have a rational number with nominator called 'p' and denom called 'q'.
\\ The person that gave us these numbers claims that the rational approximates Pi.
\\ We want to test this hypothesis.
\\
\\ Using the following version of PARI/GP:
\\   GP/PARI CALCULATOR Version 2.9.4 (released)
\\   amd64 running linux (x86-64/GMP-6.1.2 kernel) 64-bit version
\\   compiled: Dec 19 2017, gcc version 7.3.0 (Ubuntu 7.3.0-1ubuntu1)
\\   threading engine: pthread
\\   (readline v7.0 disabled, extended help enabled)
\\
\\    For a more recent version check here: http://pari.math.u-bordeaux.fr/download.html
\\
\\ To run: 
\\ From Linux console type: `gq < rat2dec_with_PARI-GP.gp`
\\
\\ ================================================== C O D E =============================================================
\\
\\ First define the nominator.
p = 169621521599715008276219171512587640647841095442456069002320644182266868459617619753889122898655162183404136973947180752187359905902753260425513050548229467432513862416424894942454713985465278932529328431801828096801920887765994271135011232692744581328925613143089416369332765923820914844366872416498286310709782023849335976275636317740764835591903828756560907312090101454770517747287108619058818385005663195977504011488807928750255014263206030308478008789858365581938685005925857190843815093499376975642422198241136503493946530984537459852215831260865709362658168293949557761906738505201661019132792725659665127352812617496756168506523926285934972259335392327959749209119904008499118043974118384243889708663618255952472658431205999918317575607657740236649567997214307671993864889895393839141039506162002967032097850104329360630620037199839999142283857127423583660420412640713389114512448981659186654920369410109397250843678564086072047059266513900405454076350312323975218753628513160246104286440957540497492228327530693076123214774002565781816122426929452997664845839935152576597214412838642199080522538526785632514871374048614455166761773227562170331518842728241937247564343923818495125376084747425403562295453185186235744629977833817398516530400483769490658446407168075399793934693849926911293460509164677.
\\ %01 = 1.6962152159971500827621917151258764065 E1307

\\ Then define the denominator
q = 53992207234726675278961941928450302452822047623718564385150323747724701281112300190300106635808547972512609385998185753170427113716200847706128220369404709717036269053644161045979852353945911645945115429379410105679831222022124449171708573935148545356552619360430097618490856349218462434207739425221688438345427657734945388360754851355876703517025241721040065222250907032187978825511851598073604902050405347475910190484449194196262402616451203465800884163477391039657283777500697293141096800015886292794390305130398878990902018844921870933047995171901635986345004445034969192966427479779117696471307624934148805180535413821861248354813884290062923803439746267128219005135975738755802559525508507324875485007341328779475078894735722877157533192681548668962657606446758705361666748320254297731413043617929690439214061599103967718073490431270227525555253221083788818740709945739088997644645878720664836566515847158951628965993677079199266744574662134053159976336619213638568983033487260628088204640814188076260382314091548602410696939680031879020944602729449902120056631834098794391928608779141524686795239077451960200846097922780695588801746583663247036517735360081178649014537721782789452025926453581219061848116302188155364930920220240513762484943105388217395949984758122066857243133095444913227856394518646.
\\ %02 = 5.3992207234726675278961941928450302453 E1306

\\ Then do the division
p / q
\\ %03 = 3.1415926535897932384626433832795028842

\\ Compare the result of the division with the value of Pi in the current precision of the system.
Pi
\\ %04 = 3.1415926535897932384626433832795028842

\\ Checking again.
Pi - (p / q)
\\ %05 = 0.E-37

\\ Checking again.
Pi - (p / q) == 0
\\ %06 = 1
\\ 
\\ ================================================= END CODE ===============================================================
\\
\\ EXACTLY what you'll see after typing `gp < rat2dec_with_PARI-GP.gp` in your Linux terminal:
\\
\\ Reading GPRC: /etc/gprc ...Done.
\\
\\                  GP/PARI CALCULATOR Version 2.9.4 (released)
\\          amd64 running linux (x86-64/GMP-6.1.2 kernel) 64-bit version
\\        compiled: Dec 19 2017, gcc version 7.3.0 (Ubuntu 7.3.0-1ubuntu1)
\\                           threading engine: pthread
\\                (readline v7.0 disabled, extended help enabled)
\\
\\                     Copyright (C) 2000-2017 The PARI Group
\\
\\PARI/GP is free software, covered by the GNU General Public License, and comes 
\\WITHOUT ANY WARRANTY WHATSOEVER.
\\
\\Type ? for help, \q to quit.
\\Type ?15 for how to get moral (and possibly technical) support.
\\
\\parisize = 8000000, primelimit = 500000, nbthreads = 2
\\%1 = 1.6962152159971500827621917151258764065 E1307
\\%2 = 5.3992207234726675278961941928450302453 E1306
\\%3 = 3.1415926535897932384626433832795028842
\\%4 = 3.1415926535897932384626433832795028842
\\%5 = 0.E-37
\\%6 = 1
\\Goodbye!
\\
\\ ========================================================================================================================
\\ CONCLUSION: 
\\ ----------
\\ According to the above results its apparent that the rational p/q approximates Pi with accuracy of 37 decimal digits. 
\\
\\ Next Actions: PARI/GP, I  Choose  YOU !
\\
\\ =========================================================================================================================