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{SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 51 "restart; read `d:/Ae
k/Composition/Composition.txt`;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 38 "#some examples of important procedures" }}}{EXCHG {PARA 0 "> "
 0 "" {MPLTEXT 1 0 18 "# composition of n" }}}{EXCHG {PARA 0 "> " 0 ""
 {MPLTEXT 1 0 15 "Composition(3);" }}{PARA 11 "" 1 "" {XPPMATH 20 "<&7
%\"\"\"F$F$7$F$\"\"#7$F&F$7#\"\"$" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 57 "# each of the run (with position) of all composition \+
of n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "SetRun(3);" }}
{PARA 11 "" 1 "" {XPPMATH 20 "<(7$\"\"\"7%F$F$F$7$F$7$F$\"\"#7$F(F'7$F
$7$F(F$7$F(F+7$F$7#\"\"$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 79 
"# each of the part congruent to i mod m (with position) of all compos
ition of n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "SetPC(1,2,3);
" }}{PARA 11 "" 1 "" {XPPMATH 20 "<(7$\"\"\"7%F$F$F$7$F$7$F$\"\"#7$F(7
$F(F$7$F$7#\"\"$7$F(F%7$F-F%" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 36 "# Forward map in theorem 3.1, P to S" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 22 "PCtoSP(3,[2,1,2,2],2);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "7'\"\"#\"\"\"F$F$F#" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT
 1 0 81 "# Inverse map in theorem 3.1, S to P (element must correspond
 to the forward map)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "SPt
oPC(3,[2,1,1,1,2],2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "7&\"\"#\"\"\"F#
F#" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 115 "# Check the whole bi
jective map automatically. if works it will return the map, if not it \+
will return ERROR message" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
10 "Bi32(3,4);" }}{PARA 11 "" 1 "" {XPPMATH 20 "<$7%\"\"#7$\"\"\"\"\"$
7&F&F&F&F&7%F&7$F'F&F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 38 "#
 Below is the main result theorem 3.3" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 37 "# Forward map in theorem 3.3, OP to R" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "OPtoR(4,[3,1,6,7,4]);" }}{PARA 11 "
" 1 "" {XPPMATH 20 "7$\"\"%7(\"\"$\"\"\"\"\"'F#F%F#" }}}{EXCHG {PARA 0
 "> " 0 "" {MPLTEXT 1 0 82 "# Inverse map in theorem 3.3, PP to R (ele
ment must correspond to the forward map)" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 23 "RtoOP(4,[3,1,6,4,3,4]);" }}{PARA 11 "" 1 "" {XPPMATH 
20 "7$\"\"%7'\"\"$\"\"\"\"\"'\"\"(F#" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 115 "# Check the whole bijective map automatically. if wo
rks it will return the map, if not it will return ERROR message" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 52 "# I check up to n=13,  the b
ijective map works fine." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "
Bi33(3);" }}{PARA 11 "" 1 "" {XPPMATH 20 "<(7$7$\"\"\"7%F%F%F%7$F%7#\"
\"$7$7$F%7$F%\"\"#F+7$7$F-7$F-F%F/7$F'7$F%F07$7$F-F&7$F-F,7$7$F)F&F$" 
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