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{USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 
1 0 0 0 0 }{PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 
0 0 0 0 0 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }}
{SECT 0 {EXCHG {PARA 0 "" 0 "" {TEXT -1 75 "This defines a shift regis
ter. Note that the formula goes into the c4 cell." }}{PARA 0 "" 0 "" 
{TEXT -1 50 "The other cells are shifted one step to the right." }}
{PARA 0 "> " 0 "" {MPLTEXT 1 0 43 "f:=(c4,c3,c2,c1)->((c3+c1 mod 2),c4
,c3,c2);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 59 "This is how we get th
e next state after the state (1,0,0,0)" }{TEXT -1 0 "" }}{PARA 0 "> " 
0 "" {MPLTEXT 1 0 11 "f(1,0,0,0);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 
92 "% stands for the previous result. (Only on release 5. On release 4
 or 3, use \" instead of %)" }}{PARA 0 "" 0 "" {TEXT -1 52 "So f(%) is
 the next state after the previous result." }}{PARA 0 "> " 0 "" 
{MPLTEXT 1 0 5 "f(\");" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 66 "(f@@2) \+
is Maple's notation for applying a function twice in a row." }{TEXT 
-1 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "(f@@2)(1,0,0,0);" }}}
{EXCHG {PARA 0 "" 0 "" {TEXT -1 64 "Now we execute a loop printing out
 all the states in succession." }{TEXT -1 0 "" }}{PARA 0 "> " 0 "" 
{MPLTEXT 1 0 51 "c:=(1,0,0,0);\nfor i from 0 to 10 do\n    c:=f(c) od;
" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 26 "A nonlinear shift register" }
{TEXT -1 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 63 "f:=(c4,c3,c2,c1)->(
( (c4+1)*c3 + (c3+1)*c2+c1 mod 2),c4,c3,c2);" }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 51 "c:=(1,0,0,0);\nfor i from 0 to 20 do\n    c:=f(c
) od;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "with(linalg):" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 339 "runshift:=proc(f,m)\n   loc
al x,ans,c0,c;\n   if nargs > 2 then \n      c0:=args[3];\n   else\n  \+
    c0:=[1,0$(m-1)];\n   fi;\n   ans:=[c0];\n   for x from 1 to 2^m do
\n        c:=[f(c0) mod 2,op(c0[1..(m-1)])];\n        if member(c, ans
) then break fi;\n        ans:=[op(ans),c];\n        c0:=c;\n   od;\n \+
  ans:=[op(ans),c];\n   RETURN(evalm(ans))\nend:" }}}{EXCHG {PARA 0 ">
 " 0 "" {MPLTEXT 1 0 49 "m:=13;\nrunshift( c->(c[m-1]+c[m]), m):\nrowd
im(\");" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 51 "runshift( c-> (c
[1]+1)*c[2]+(c[2]+1)*c[3]+c[4], 4);" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 63 "m:=5;\nrunshift( c->(c[1]*c[3]+c[5]), m,[1,1,1,1,0]);
\nrowdim(\");" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}
{MARK "0 2 0" 31 }{VIEWOPTS 1 1 0 1 1 1803 }