hermann on Tue, 01 Oct 2024 01:56:09 +0200 |
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What is the Mathematica "PowerMod[a, 1/2, m]" equivalent in PARI/GP? |
https://reference.wolfram.com/language/ref/PowerMod.html I found this mailing list post from 2000: https://pari.math.u-bordeaux.fr/archives/pari-users-0004/msg00001.html But its function does not work for non-prime modulus: hermann@7950x:~$ gp -q ? powermod(a,k,n)=lift(Mod(a,n)^k) (a,k,n)->lift(Mod(a,n)^k)? powermod(41,1/2,71641520761751435455133616475667090434063332228247871795429)
*** at top-level: powermod(41,1/2,716415207617514354551336164756 *** ^---------------------------------------------- *** in function powermod: lift(Mod(a,n)^k) *** ^---*** _^_: not a prime number in gpow: 71641520761751435455133616475667090434063332228247871795429.
*** Break loop: type 'break' to go back to GP prompt break>PowerMod[] can deal with non-prime modulus — how can this be computed with PARI/GP?
pi@raspberrypi5:~ $ time wolframscript -code "PowerMod[41,1/2,71641520761751435455133616475667090434063332228247871795429]"
15567422879070002639383923810785206745982804843948310703484 real 0m59.452s user 0m0.341s sys 0m0.071s pi@raspberrypi5:~ $ Regards, Hermann.