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{SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "with(numtheory);" }}
{PARA 7 "" 1 "" {TEXT -1 69 "Warning, the protected name order has bee
n redefined and unprotected\n" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#7Q%&G
IgcdG%)bigomegaG%&cfracG%)cfracpolG%+cyclotomicG%)divisorsG%)factorEQG
%*factorsetG%'fermatG%)imagunitG%&indexG%/integral_basisG%)invcfracG%'
invphiG%*issqrfreeG%'jacobiG%*kroneckerG%'lambdaG%)legendreG%)mcombine
G%)mersenneG%(migcdexG%*minkowskiG%(mipolysG%%mlogG%'mobiusG%&mrootG%&
msqrtG%)nearestpG%*nthconverG%)nthdenomG%)nthnumerG%'nthpowG%&orderG%)
pdexpandG%$phiG%#piG%*pprimrootG%)primrootG%(quadresG%+rootsunityG%*sa
feprimeG%&sigmaG%*sq2factorG%(sum2sqrG%$tauG%%thueG" }}}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 21 "2&^4500000003 mod 31;" }}{PARA 11 "" 1 "
" {XPPMATH 20 "6#\"\")" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 33 "1
456&^45923984287912803 mod 1007;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"
$X'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 43 "4141457&^24082398438
7349723 mod (2^100+17);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"@yZY1M9?f
!*4_uVv<\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "521^1008 mod \+
1009;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"\"" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 24 "seq( a^6 mod 9 ,a=1..8);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6*\"\"\"F#\"\"!F#F#F$F#F#" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 26 "seq( a^8 mod 15, a=1..14);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "60\"\"\"F#\"\"'F#\"#5F$F#F#F$F%F#F$F#F#" }}}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 13 "with(linalg):" }}{PARA 7 "" 1 "" {TEXT 
-1 80 "Warning, the protected names norm and trace have been redefined
 and unprotected\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 44 "mtx:=
 matrix( 3,3, [1,2,3, 4,5,7, 9,12,13]);" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6#>%$mtxGK%'matrixG6#7%7%\"\"\"\"\"#\"\"$7%\"\"%\"\"&\"\"(7%\"\"*
\"#7\"#8Q(pprint06\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "inv
m:=inverse(mtx);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%invmGK%'matrixG
6#7%7%#!#>\"#7#\"\"&\"\"'#!\"\"F,7%#\"#6F,#!\"(F/#F.F,7%#\"\"\"\"\"%#F
:\"\"##F1F;Q(pprint26\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "d
et(mtx);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"#7" }}}{EXCHG {PARA 0 ">
 " 0 "" {MPLTEXT 1 0 24 "numerm:= evalm(12*invm);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%'numermGK%'matrixG6#7%7%!#>\"#5!\"\"7%\"#6!#9\"\"&7%
\"\"$\"\"'!\"$Q(pprint36\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
16 "12&^(-1) mod 31;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"#8" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "bob:=evalm( 13*numerm);" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$bobGK%'matrixG6#7%7%!$Z#\"$I\"!#87%
\"$V\"!$#=\"#l7%\"#R\"#y!#RQ(pprint66\"" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 30 "evalm(map( x->x mod 31, bob));" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#K%'matrixG6#7%7%\"\"\"\"\"'\"#=7%\"#>\"\"%\"\"$7%\"\")
\"#;\"#BQ(pprint86\"" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 25 "Note that
 if you explore " }{TEXT 256 5 "Maple" }{TEXT -1 86 " a bit, you can f
ind quicker (but less instructive) ways to invert a matrix modulo m. \+
" }{MPLTEXT 1 0 0 "" }}}}{MARK "15 0 1" 5 }{VIEWOPTS 1 1 0 1 1 1803 1 
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