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{SECT 0 {EXCHG {PARA 0 "" 0 "" {TEXT -1 131 "This worksheet the contin
ued fraction convergents to sqrt(2) and checks whether close to their \+
denominators is where disc gets bad." }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 11 "Digits:=30:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 43 "with(numtheory): cfrac(sqrt(2),'periodic');" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#,&\"\"\"F$*&\"\"\"F&,&\"\"#F$*&F&F&,&F(F$%$...GF$!\"\"F
$F,F$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 42 "a[0]:=1: for i fro
m 1 to 14 do a[i]:=2 od:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "a[0]+1/(a[1]+1/(a[2]+1/a[3])
);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6##\"#<\"#7" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 37 "p[-1]:=0: p[0]:=1: q[-1]:=1: q[0]:=0:" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 82 "for i from 1 to 14 do p[i]:=
a[i-1]*p[i-1]+p[i-2]: q[i]:=a[i-1]*q[i-1]+q[i-2]:  od:" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "for i from 1 to 14 do p[i]/q[i] od:
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "evalf(sqrt(2)-p[14]/q[1
4]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$!4KM^'*)o`$yT&!#H" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 85 "N:=18000: Digits:=30: alpha:=evalf(
sqrt(2)): A:=[seq(evalf(frac(i^2*alpha)),i=1..N)]:" }}{PARA 0 "> " 0 "
" {MPLTEXT 1 0 11 "B:=sort(A):" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "C
:=[seq(N*(B[i+1]-B[i]),i=1..N-1)]:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 
19 "E:=sort(C): disc();" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#$\">bS>S!\\TV:EmECP5!#I" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 111 "disc:=proc() tempvar:=0: for j fro
m 1 to N-1 do tempvar:=max(tempvar,abs(j/N-(1-exp(-E[j])))) od: tempva
r; end:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}{PARA 7 "" 1 "" 
{TEXT -1 47 "Warning, `tempvar` is implicitly declared local" }}{PARA 
7 "" 1 "" {TEXT -1 41 "Warning, `j` is implicitly declared local" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "disc();" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#$\">V2.Ctn4?DxXBLB\"!#I" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 23 "evalf((80782+33461)/2);" }}{PARA 11 "" 1 "" {XPPMATH 
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