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{SECT 0 {EXCHG {PARA 0 "" 0 "" {TEXT -1 232 "( Oops.  I realized I neg
lected to save my worksheet from  class on 3-03-98.  So, I will attemp
t to recreate it here.  Note that, as usual, there will be no running \+
commentary, so you can just pretend that it is the REAL worksheet)." }
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{PARA 11 "" 1 "" {XPPMATH 20 "6#7$\"#s\"$0\"" }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 30 "convert([66, 121, 101],bytes);" }}{PARA 11 "" 1 
"" {XPPMATH 20 "6#%$ByeG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 33 
"convert([seq(i,i=1..255)],bytes);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#
%jz|\"|#|$|%|&|'|(|)|*|+|,|-|.|/|0|1|2|3|4|5|6|7|8|9|:|;|<|=|>|?|@~!\"
#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\\]^_`abcdefg
hijklmnopqrstuvwxyz|fr|gr|hr|ir|jr|[s|\\s|]s|^s|_s|`s|as|bs|cs|ds|es|f
s|gs|hs|is|js|[t|\\t|]t|^t|_t|`t|at|bt|ct|dt|et|ft|gt|ht|it|jt|[u|\\u|
]u|^u|_u|`u|au|bu|cu|du|eu|fu|gu|hu|iu|ju|[v|\\v|]v|^v|_v|`v|av|bv|cv|
dv|ev|fv|gv|hv|iv|jv|[w|\\w|]w|^w|_w|`w|aw|bw|cw|dw|ew|fw|gw|hw|iw|jw|
[x|\\x|]x|^x|_x|`x|ax|bx|cx|dx|ex|fx|gx|hx|ix|jx|[y|\\y|]y|^y|_y|`y|ay
|by|cy|dy|ey|fy|gy|hy|iy|jy|[z|\\z|]z|^z|_z|`z|az|bz|cz|dz|ez|fz|gz|hz
|iz|jzG" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 87 "Using this, we can sta
rt to write a little function to do a Caesar, or shift, cipher.  " }}
{PARA 0 "" 0 "" {TEXT 256 106 "But first, we have to figure out how we
 can \"add 5\" to every element in a list of numbers. We can use the \+
" }{TEXT 257 5 " map " }{TEXT -1 20 "function to do that:" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "map(sqrt,[0,1,2,3,4,5]);" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#7(\"\"!\"\"\"*$\"\"##F%F'*$\"\"$F(F'*$\"\"&F
(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "map(x->x^2+2, [0,1,2,3
,4,5]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7(\"\"#\"\"$\"\"'\"#6\"#=\"
#F" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 57 "Now we're ready.  Read this
 function from the middle out:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 127 "Encode:= plain -> \n  convert(map(x->(x+4) mod 255 + 1,\n    \+
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" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'EncodeG:6#%&plainG6\"6$%)operat
orG%&arrowGF(-%(convertG6$-%$mapG6$:6#%\"xGF(F)F(,&-%$modG6$,&9$\"\"\"
\"\"%F;\"$b#F;F;F;F(F(-F-6$F:%&bytesGF@F(F(" }}}{EXCHG {PARA 0 "> " 0 
"" {MPLTEXT 1 0 13 "Encode(`Hi`);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%
#MnG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 60 "Encode(`Who put the
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{XPPMATH 20 "6#%R\\mt%uzy%ymj%gjs|jrjiwnsj%ns%Rwx3%Rzwum|ir,x%T|frfqyn
sjDG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 115 "Encode148:= plain \+
-> \n  convert(map(x->(x+147) mod 255 + 1,\n              convert(plai
n,bytes)),\n          bytes); " }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 98 "E
ncode148(`The quick brown fox jumped over the lazy dog, and then got e
aten by the hungry lion.`);" }}{PARA 11 "" 0 "" {TEXT -1 0 "" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#>%*Encode148G:6#%&plainG6\"6$%)operatorG%&ar
rowGF(-%(convertG6$-%$mapG6$:6#%\"xGF(F)F(,&-%$modG6$,&9$\"\"\"\"$Z\"F
;\"$b#F;F;F;F(F(-F-6$F:%&bytesGF@F(F(" }}{PARA 12 "" 1 "" {XPPMATH 20 
"6#%_p|cy|gz|dz|_v|'|+|hz|bz|jz|_v|az|(|%|-|$|_v|ez|%|.|_v|iz|+|#|&|dz
|cz|_v|%|,|dz|(|_v|*|gz|dz|_v|\"|`z|0|/|_v|cz|%|fz|[w|_v|`z|$|cz|_v|*|
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" 0 "" {TEXT -1 90 "This is not fully satifactory.  Now we diverge int
o a discussion about writing procedures." }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 20 "sqr := x -> sqrt(x);" }}{PARA 11 "" 1 "" {XPPMATH 20 
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;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"&" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 32 "sqr2 := proc(x)\n   sqrt(x);\nend;" }}{PARA 11 "" 
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{PARA 0 "> " 0 "" {MPLTEXT 1 0 122 "sqr3 := proc(x)\n  if (x >= 0) the
n\n     sqrt(x);\n  else\n     print(`Square root of `,x,`is not a rea
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(25);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"&" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 77 "try:= proc(x)\n  y := x^2;\n  if ( y>5) then\n
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"Warning, `y` is implicitly declared local" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%$tryG:6#%\"xG6#%\"yG6\"F*C$>8$*$9$\"\"#@%2\"\"&F-\"#D
F-F*F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "y:=35;" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#>%\"yG\"#N" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 8 "try(19);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"#D" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 2 "y;" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#\"#N" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 91 "try2
:= proc(x)\n  global y;\n\n  y := x^2;\n  if ( y>5) then\n     25;\n  \+
else\n     y;\n  fi;\nend;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%try2G
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{PARA 0 "> " 0 "" {MPLTEXT 1 0 2 "y;" }}{PARA 11 "" 1 "" {XPPMATH 20 "
6#\"#N" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "try2(19);" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#\"#D" }}}{EXCHG {PARA 0 "> " 0 "" 
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