CoCalc -- Collaborative Calculation in the Cloud
Sharedwww / lectures / day4.psOpen in CoCalc
%!PS-Adobe-2.0
%%Creator: dvips(k) 5.92b Copyright 2002 Radical Eye Software
%%Pages: 6
%%PageOrder: Ascend
%%BoundingBox: 0 0 596 842
%%DocumentFonts: CMR17 CMBX12 CMR12 CMTI12 CMSY10 CMMI8 CMMI12 CMSY8
%%+ CMR8 EUFM10 CMEX10 CMTT12
%%EndComments
%DVIPSWebPage: (www.radicaleye.com)
%DVIPSCommandLine: dvips -O 0.0in,0.4in -Ppdf -f
%DVIPSParameters: dpi=8000, compressed
%DVIPSSource:  TeX output 2004.02.17:0927
%%BeginProcSet: tex.pro
%!
/TeXDict 300 dict def TeXDict begin/N{def}def/B{bind def}N/S{exch}N/X{S
N}B/A{dup}B/TR{translate}N/isls false N/vsize 11 72 mul N/hsize 8.5 72
mul N/landplus90{false}def/@rigin{isls{[0 landplus90{1 -1}{-1 1}ifelse 0
0 0]concat}if 72 Resolution div 72 VResolution div neg scale isls{
landplus90{VResolution 72 div vsize mul 0 exch}{Resolution -72 div hsize
mul 0}ifelse TR}if Resolution VResolution vsize -72 div 1 add mul TR[
matrix currentmatrix{A A round sub abs 0.00001 lt{round}if}forall round
exch round exch]setmatrix}N/@landscape{/isls true N}B/@manualfeed{
statusdict/manualfeed true put}B/@copies{/#copies X}B/FMat[1 0 0 -1 0 0]
N/FBB[0 0 0 0]N/nn 0 N/IEn 0 N/ctr 0 N/df-tail{/nn 8 dict N nn begin
/FontType 3 N/FontMatrix fntrx N/FontBBox FBB N string/base X array
/BitMaps X/BuildChar{CharBuilder}N/Encoding IEn N end A{/foo setfont}2
array copy cvx N load 0 nn put/ctr 0 N[}B/sf 0 N/df{/sf 1 N/fntrx FMat N
df-tail}B/dfs{div/sf X/fntrx[sf 0 0 sf neg 0 0]N df-tail}B/E{pop nn A
definefont setfont}B/Cw{Cd A length 5 sub get}B/Ch{Cd A length 4 sub get
}B/Cx{128 Cd A length 3 sub get sub}B/Cy{Cd A length 2 sub get 127 sub}
B/Cdx{Cd A length 1 sub get}B/Ci{Cd A type/stringtype ne{ctr get/ctr ctr
1 add N}if}B/CharBuilder{save 3 1 roll S A/base get 2 index get S
/BitMaps get S get/Cd X pop/ctr 0 N Cdx 0 Cx Cy Ch sub Cx Cw add Cy
setcachedevice Cw Ch true[1 0 0 -1 -.1 Cx sub Cy .1 sub]{Ci}imagemask
restore}B/D{/cc X A type/stringtype ne{]}if nn/base get cc ctr put nn
/BitMaps get S ctr S sf 1 ne{A A length 1 sub A 2 index S get sf div put
}if put/ctr ctr 1 add N}B/I{cc 1 add D}B/bop{userdict/bop-hook known{
bop-hook}if/SI save N @rigin 0 0 moveto/V matrix currentmatrix A 1 get A
mul exch 0 get A mul add .99 lt{/QV}{/RV}ifelse load def pop pop}N/eop{
SI restore userdict/eop-hook known{eop-hook}if showpage}N/@start{
userdict/start-hook known{start-hook}if pop/VResolution X/Resolution X
1000 div/DVImag X/IEn 256 array N 2 string 0 1 255{IEn S A 360 add 36 4
index cvrs cvn put}for pop 65781.76 div/vsize X 65781.76 div/hsize X}N
/p{show}N/RMat[1 0 0 -1 0 0]N/BDot 260 string N/Rx 0 N/Ry 0 N/V{}B/RV/v{
/Ry X/Rx X V}B statusdict begin/product where{pop false[(Display)(NeXT)
(LaserWriter 16/600)]{A length product length le{A length product exch 0
exch getinterval eq{pop true exit}if}{pop}ifelse}forall}{false}ifelse
end{{gsave TR -.1 .1 TR 1 1 scale Rx Ry false RMat{BDot}imagemask
grestore}}{{gsave TR -.1 .1 TR Rx Ry scale 1 1 false RMat{BDot}
imagemask grestore}}ifelse B/QV{gsave newpath transform round exch round
exch itransform moveto Rx 0 rlineto 0 Ry neg rlineto Rx neg 0 rlineto
fill grestore}B/a{moveto}B/delta 0 N/tail{A/delta X 0 rmoveto}B/M{S p
delta add tail}B/b{S p tail}B/c{-4 M}B/d{-3 M}B/e{-2 M}B/f{-1 M}B/g{0 M}
B/h{1 M}B/i{2 M}B/j{3 M}B/k{4 M}B/w{0 rmoveto}B/l{p -4 w}B/m{p -3 w}B/n{
p -2 w}B/o{p -1 w}B/q{p 1 w}B/r{p 2 w}B/s{p 3 w}B/t{p 4 w}B/x{0 S
rmoveto}B/y{3 2 roll p a}B/bos{/SS save N}B/eos{SS restore}B end

%%EndProcSet
%%BeginProcSet: alt-rule.pro
%!
% Patch by TVZ
% Makes dvips files draw rules with stroke rather than fill.
% Makes narrow rules more predictable at low resolutions
% after distilling to PDF.
% May have unknown consequences for very thick rules.
% Tested only with dvips 5.85(k).
TeXDict begin
/QV {
  gsave newpath /ruleY X /ruleX X
  Rx Ry gt
  { ruleX ruleY Ry 2 div sub moveto Rx 0 rlineto Ry }
  { ruleX Rx 2 div add ruleY moveto 0 Ry neg rlineto Rx }
  ifelse
  setlinewidth 0 setlinecap stroke grestore
} bind def
end

%%EndProcSet
%%BeginProcSet: texc.pro
%!
/TeXDict 300 dict def TeXDict begin/N{def}def/B{bind def}N/S{exch}N/X{S
N}B/A{dup}B/TR{translate}N/isls false N/vsize 11 72 mul N/hsize 8.5 72
mul N/landplus90{false}def/@rigin{isls{[0 landplus90{1 -1}{-1 1}ifelse 0
0 0]concat}if 72 Resolution div 72 VResolution div neg scale isls{
landplus90{VResolution 72 div vsize mul 0 exch}{Resolution -72 div hsize
mul 0}ifelse TR}if Resolution VResolution vsize -72 div 1 add mul TR[
matrix currentmatrix{A A round sub abs 0.00001 lt{round}if}forall round
exch round exch]setmatrix}N/@landscape{/isls true N}B/@manualfeed{
statusdict/manualfeed true put}B/@copies{/#copies X}B/FMat[1 0 0 -1 0 0]
N/FBB[0 0 0 0]N/nn 0 N/IEn 0 N/ctr 0 N/df-tail{/nn 8 dict N nn begin
/FontType 3 N/FontMatrix fntrx N/FontBBox FBB N string/base X array
/BitMaps X/BuildChar{CharBuilder}N/Encoding IEn N end A{/foo setfont}2
array copy cvx N load 0 nn put/ctr 0 N[}B/sf 0 N/df{/sf 1 N/fntrx FMat N
df-tail}B/dfs{div/sf X/fntrx[sf 0 0 sf neg 0 0]N df-tail}B/E{pop nn A
definefont setfont}B/Cw{Cd A length 5 sub get}B/Ch{Cd A length 4 sub get
}B/Cx{128 Cd A length 3 sub get sub}B/Cy{Cd A length 2 sub get 127 sub}
B/Cdx{Cd A length 1 sub get}B/Ci{Cd A type/stringtype ne{ctr get/ctr ctr
1 add N}if}B/id 0 N/rw 0 N/rc 0 N/gp 0 N/cp 0 N/G 0 N/CharBuilder{save 3
1 roll S A/base get 2 index get S/BitMaps get S get/Cd X pop/ctr 0 N Cdx
0 Cx Cy Ch sub Cx Cw add Cy setcachedevice Cw Ch true[1 0 0 -1 -.1 Cx
sub Cy .1 sub]/id Ci N/rw Cw 7 add 8 idiv string N/rc 0 N/gp 0 N/cp 0 N{
rc 0 ne{rc 1 sub/rc X rw}{G}ifelse}imagemask restore}B/G{{id gp get/gp
gp 1 add N A 18 mod S 18 idiv pl S get exec}loop}B/adv{cp add/cp X}B
/chg{rw cp id gp 4 index getinterval putinterval A gp add/gp X adv}B/nd{
/cp 0 N rw exit}B/lsh{rw cp 2 copy get A 0 eq{pop 1}{A 255 eq{pop 254}{
A A add 255 and S 1 and or}ifelse}ifelse put 1 adv}B/rsh{rw cp 2 copy
get A 0 eq{pop 128}{A 255 eq{pop 127}{A 2 idiv S 128 and or}ifelse}
ifelse put 1 adv}B/clr{rw cp 2 index string putinterval adv}B/set{rw cp
fillstr 0 4 index getinterval putinterval adv}B/fillstr 18 string 0 1 17
{2 copy 255 put pop}for N/pl[{adv 1 chg}{adv 1 chg nd}{1 add chg}{1 add
chg nd}{adv lsh}{adv lsh nd}{adv rsh}{adv rsh nd}{1 add adv}{/rc X nd}{
1 add set}{1 add clr}{adv 2 chg}{adv 2 chg nd}{pop nd}]A{bind pop}
forall N/D{/cc X A type/stringtype ne{]}if nn/base get cc ctr put nn
/BitMaps get S ctr S sf 1 ne{A A length 1 sub A 2 index S get sf div put
}if put/ctr ctr 1 add N}B/I{cc 1 add D}B/bop{userdict/bop-hook known{
bop-hook}if/SI save N @rigin 0 0 moveto/V matrix currentmatrix A 1 get A
mul exch 0 get A mul add .99 lt{/QV}{/RV}ifelse load def pop pop}N/eop{
SI restore userdict/eop-hook known{eop-hook}if showpage}N/@start{
userdict/start-hook known{start-hook}if pop/VResolution X/Resolution X
1000 div/DVImag X/IEn 256 array N 2 string 0 1 255{IEn S A 360 add 36 4
index cvrs cvn put}for pop 65781.76 div/vsize X 65781.76 div/hsize X}N
/p{show}N/RMat[1 0 0 -1 0 0]N/BDot 260 string N/Rx 0 N/Ry 0 N/V{}B/RV/v{
/Ry X/Rx X V}B statusdict begin/product where{pop false[(Display)(NeXT)
(LaserWriter 16/600)]{A length product length le{A length product exch 0
exch getinterval eq{pop true exit}if}{pop}ifelse}forall}{false}ifelse
end{{gsave TR -.1 .1 TR 1 1 scale Rx Ry false RMat{BDot}imagemask
grestore}}{{gsave TR -.1 .1 TR Rx Ry scale 1 1 false RMat{BDot}
imagemask grestore}}ifelse B/QV{gsave newpath transform round exch round
exch itransform moveto Rx 0 rlineto 0 Ry neg rlineto Rx neg 0 rlineto
fill grestore}B/a{moveto}B/delta 0 N/tail{A/delta X 0 rmoveto}B/M{S p
delta add tail}B/b{S p tail}B/c{-4 M}B/d{-3 M}B/e{-2 M}B/f{-1 M}B/g{0 M}
B/h{1 M}B/i{2 M}B/j{3 M}B/k{4 M}B/w{0 rmoveto}B/l{p -4 w}B/m{p -3 w}B/n{
p -2 w}B/o{p -1 w}B/q{p 1 w}B/r{p 2 w}B/s{p 3 w}B/t{p 4 w}B/x{0 S
rmoveto}B/y{3 2 roll p a}B/bos{/SS save N}B/eos{SS restore}B end

%%EndProcSet
%%BeginProcSet: f7b6d320.enc
% Thomas Esser, Dec 2002. public domain
%
% Encoding for:
%     cmb10 cmbx10 cmbx12 cmbx5 cmbx6 cmbx7 cmbx8 cmbx9 cmbxsl10
%     cmdunh10 cmr10 cmr12 cmr17cmr6 cmr7 cmr8 cmr9 cmsl10 cmsl12 cmsl8
%     cmsl9 cmss10cmss12 cmss17 cmss8 cmss9 cmssbx10 cmssdc10 cmssi10
%     cmssi12 cmssi17 cmssi8cmssi9 cmssq8 cmssqi8 cmvtt10
%
/TeXf7b6d320Encoding [
/Gamma /Delta /Theta /Lambda /Xi /Pi /Sigma /Upsilon /Phi /Psi /Omega
/ff /fi /fl /ffi /ffl /dotlessi /dotlessj /grave /acute /caron /breve
/macron /ring /cedilla /germandbls /ae /oe /oslash /AE /OE /Oslash
/suppress /exclam /quotedblright /numbersign /dollar /percent /ampersand
/quoteright /parenleft /parenright /asterisk /plus /comma /hyphen
/period /slash /zero /one /two /three /four /five /six /seven /eight
/nine /colon /semicolon /exclamdown /equal /questiondown /question /at
/A /B /C /D /E /F /G /H /I /J /K /L /M /N /O /P /Q /R /S /T /U /V /W /X
/Y /Z /bracketleft /quotedblleft /bracketright /circumflex /dotaccent
/quoteleft /a /b /c /d /e /f /g /h /i /j /k /l /m /n /o /p /q /r /s /t /u
/v /w /x /y /z /endash /emdash /hungarumlaut /tilde /dieresis /suppress
/.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef
/.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef
/.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef
/.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /space
/Gamma /Delta /Theta /Lambda /Xi /Pi /Sigma /Upsilon /Phi /Psi /.notdef
/.notdef /Omega /ff /fi /fl /ffi /ffl /dotlessi /dotlessj /grave /acute
/caron /breve /macron /ring /cedilla /germandbls /ae /oe /oslash /AE
/OE /Oslash /suppress /dieresis /.notdef /.notdef /.notdef /.notdef
/.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef
/.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef
/.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef
/.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef
/.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef
/.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef
/.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef
] def

%%EndProcSet
%%BeginProcSet: 74afc74c.enc
% Thomas Esser, Dec 2002. public domain
%
% Encoding for:
%     cmbxti10 cmff10 cmfi10 cmfib8 cmti10 cmti12 cmti7 cmti8cmti9 cmu10
%
/TeX74afc74cEncoding [
/Gamma /Delta /Theta /Lambda /Xi /Pi /Sigma /Upsilon /Phi /Psi /Omega
/ff /fi /fl /ffi /ffl /dotlessi /dotlessj /grave /acute /caron /breve
/macron /ring /cedilla /germandbls /ae /oe /oslash /AE /OE /Oslash
/suppress /exclam /quotedblright /numbersign /sterling /percent
/ampersand /quoteright /parenleft /parenright /asterisk /plus /comma
/hyphen /period /slash /zero /one /two /three /four /five /six /seven
/eight /nine /colon /semicolon /exclamdown /equal /questiondown /question
/at /A /B /C /D /E /F /G /H /I /J /K /L /M /N /O /P /Q /R /S /T /U /V /W
/X /Y /Z /bracketleft /quotedblleft /bracketright /circumflex /dotaccent
/quoteleft /a /b /c /d /e /f /g /h /i /j /k /l /m /n /o /p /q /r /s /t /u
/v /w /x /y /z /endash /emdash /hungarumlaut /tilde /dieresis /suppress
/.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef
/.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef
/.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef
/.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /space
/Gamma /Delta /Theta /Lambda /Xi /Pi /Sigma /Upsilon /Phi /Psi /.notdef
/.notdef /Omega /ff /fi /fl /ffi /ffl /dotlessi /dotlessj /grave /acute
/caron /breve /macron /ring /cedilla /germandbls /ae /oe /oslash /AE
/OE /Oslash /suppress /dieresis /.notdef /.notdef /.notdef /.notdef
/.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef
/.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef
/.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef
/.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef
/.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef
/.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef
/.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef
] def

%%EndProcSet
%%BeginProcSet: bbad153f.enc
% Thomas Esser, Dec 2002. public domain
%
% Encoding for:
%     cmsy10 cmsy5 cmsy6 cmsy7 cmsy8 cmsy9
%
/TeXbbad153fEncoding [
/minus /periodcentered /multiply /asteriskmath /divide /diamondmath
/plusminus /minusplus /circleplus /circleminus /circlemultiply
/circledivide /circledot /circlecopyrt /openbullet /bullet
/equivasymptotic /equivalence /reflexsubset /reflexsuperset /lessequal
/greaterequal /precedesequal /followsequal /similar /approxequal
/propersubset /propersuperset /lessmuch /greatermuch /precedes /follows
/arrowleft /arrowright /arrowup /arrowdown /arrowboth /arrownortheast
/arrowsoutheast /similarequal /arrowdblleft /arrowdblright /arrowdblup
/arrowdbldown /arrowdblboth /arrownorthwest /arrowsouthwest /proportional
/prime /infinity /element /owner /triangle /triangleinv /negationslash
/mapsto /universal /existential /logicalnot /emptyset /Rfractur /Ifractur
/latticetop /perpendicular /aleph /A /B /C /D /E /F /G /H /I /J /K
/L /M /N /O /P /Q /R /S /T /U /V /W /X /Y /Z /union /intersection
/unionmulti /logicaland /logicalor /turnstileleft /turnstileright
/floorleft /floorright /ceilingleft /ceilingright /braceleft /braceright
/angbracketleft /angbracketright /bar /bardbl /arrowbothv /arrowdblbothv
/backslash /wreathproduct /radical /coproduct /nabla /integral
/unionsq /intersectionsq /subsetsqequal /supersetsqequal /section
/dagger /daggerdbl /paragraph /club /diamond /heart /spade /arrowleft
/.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef
/.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef
/.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef
/.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef
/minus /periodcentered /multiply /asteriskmath /divide /diamondmath
/plusminus /minusplus /circleplus /circleminus /.notdef /.notdef
/circlemultiply /circledivide /circledot /circlecopyrt /openbullet
/bullet /equivasymptotic /equivalence /reflexsubset /reflexsuperset
/lessequal /greaterequal /precedesequal /followsequal /similar
/approxequal /propersubset /propersuperset /lessmuch /greatermuch
/precedes /follows /arrowleft /spade /.notdef /.notdef /.notdef /.notdef
/.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef
/.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef
/.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef
/.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef
/.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef
/.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef
/.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef
] def

%%EndProcSet
%%BeginProcSet: aae443f0.enc
% Thomas Esser, Dec 2002. public domain
%
% Encoding for:
%     cmmi10 cmmi12 cmmi5 cmmi6 cmmi7 cmmi8 cmmi9 cmmib10
%
/TeXaae443f0Encoding [
/Gamma /Delta /Theta /Lambda /Xi /Pi /Sigma /Upsilon /Phi /Psi /Omega
/alpha /beta /gamma /delta /epsilon1 /zeta /eta /theta /iota /kappa
/lambda /mu /nu /xi /pi /rho /sigma /tau /upsilon /phi /chi /psi
/omega /epsilon /theta1 /pi1 /rho1 /sigma1 /phi1 /arrowlefttophalf
/arrowleftbothalf /arrowrighttophalf /arrowrightbothalf /arrowhookleft
/arrowhookright /triangleright /triangleleft /zerooldstyle /oneoldstyle
/twooldstyle /threeoldstyle /fouroldstyle /fiveoldstyle /sixoldstyle
/sevenoldstyle /eightoldstyle /nineoldstyle /period /comma /less /slash
/greater /star /partialdiff /A /B /C /D /E /F /G /H /I /J /K /L /M /N
/O /P /Q /R /S /T /U /V /W /X /Y /Z /flat /natural /sharp /slurbelow
/slurabove /lscript /a /b /c /d /e /f /g /h /i /j /k /l /m /n /o /p
/q /r /s /t /u /v /w /x /y /z /dotlessi /dotlessj /weierstrass /vector
/tie /psi /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef
/.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef
/.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef
/.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef
/space /Gamma /Delta /Theta /Lambda /Xi /Pi /Sigma /Upsilon /Phi /Psi
/.notdef /.notdef /Omega /alpha /beta /gamma /delta /epsilon1 /zeta /eta
/theta /iota /kappa /lambda /mu /nu /xi /pi /rho /sigma /tau /upsilon
/phi /chi /psi /tie /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef
/.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef
/.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef
/.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef
/.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef
/.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef
/.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef
/.notdef /.notdef /.notdef /.notdef /.notdef
] def

%%EndProcSet
%%BeginProcSet: 09fbbfac.enc
% Thomas Esser, Dec 2002. public domain
%
% Encoding for:
%     cmsltt10 cmtt10 cmtt12 cmtt8 cmtt9
/TeX09fbbfacEncoding [
/Gamma /Delta /Theta /Lambda /Xi /Pi /Sigma /Upsilon /Phi /Psi
/Omega /arrowup /arrowdown /quotesingle /exclamdown /questiondown
/dotlessi /dotlessj /grave /acute /caron /breve /macron /ring /cedilla
/germandbls /ae /oe /oslash /AE /OE /Oslash /visiblespace /exclam
/quotedbl /numbersign /dollar /percent /ampersand /quoteright /parenleft
/parenright /asterisk /plus /comma /hyphen /period /slash /zero /one
/two /three /four /five /six /seven /eight /nine /colon /semicolon /less
/equal /greater /question /at /A /B /C /D /E /F /G /H /I /J /K /L /M /N
/O /P /Q /R /S /T /U /V /W /X /Y /Z /bracketleft /backslash /bracketright
/asciicircum /underscore /quoteleft /a /b /c /d /e /f /g /h /i /j /k /l
/m /n /o /p /q /r /s /t /u /v /w /x /y /z /braceleft /bar /braceright
/asciitilde /dieresis /visiblespace /.notdef /.notdef /.notdef /.notdef
/.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef
/.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef
/.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef
/.notdef /.notdef /.notdef /space /Gamma /Delta /Theta /Lambda /Xi /Pi
/Sigma /Upsilon /Phi /Psi /.notdef /.notdef /Omega /arrowup /arrowdown
/quotesingle /exclamdown /questiondown /dotlessi /dotlessj /grave /acute
/caron /breve /macron /ring /cedilla /germandbls /ae /oe /oslash /AE
/OE /Oslash /visiblespace /dieresis /.notdef /.notdef /.notdef /.notdef
/.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef
/.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef
/.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef
/.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef
/.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef
/.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef
/.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef
] def

%%EndProcSet
%%BeginProcSet: texps.pro
%!
TeXDict begin/rf{findfont dup length 1 add dict begin{1 index/FID ne 2
index/UniqueID ne and{def}{pop pop}ifelse}forall[1 index 0 6 -1 roll
exec 0 exch 5 -1 roll VResolution Resolution div mul neg 0 0]FontType 0
ne{/Metrics exch def dict begin Encoding{exch dup type/integertype ne{
pop pop 1 sub dup 0 le{pop}{[}ifelse}{FontMatrix 0 get div Metrics 0 get
div def}ifelse}forall Metrics/Metrics currentdict end def}{{1 index type
/nametype eq{exit}if exch pop}loop}ifelse[2 index currentdict end
definefont 3 -1 roll makefont/setfont cvx]cvx def}def/ObliqueSlant{dup
sin S cos div neg}B/SlantFont{4 index mul add}def/ExtendFont{3 -1 roll
mul exch}def/ReEncodeFont{CharStrings rcheck{/Encoding false def dup[
exch{dup CharStrings exch known not{pop/.notdef/Encoding true def}if}
forall Encoding{]exch pop}{cleartomark}ifelse}if/Encoding exch def}def
end

%%EndProcSet
%%BeginFont: CMTT12
%!PS-AdobeFont-1.1: CMTT12 1.0
%%CreationDate: 1991 Aug 20 16:45:46
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.0) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMTT12) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle 0 def
/isFixedPitch true def
end readonly def
/FontName /CMTT12 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 0 /.notdef put
readonly def
/FontBBox{-1 -234 524 695}readonly def
/UniqueID 5000833 def
currentdict end
currentfile eexec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0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
cleartomark
%%EndFont 
%%BeginFont: CMEX10
%!PS-AdobeFont-1.1: CMEX10 1.00
%%CreationDate: 1992 Jul 23 21:22:48
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.00) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMEX10) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle 0 def
/isFixedPitch false def
end readonly def
/FontName /CMEX10 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 81 /producttext put
readonly def
/FontBBox{-24 -2960 1454 772}readonly def
/UniqueID 5000774 def
currentdict end
currentfile eexec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0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
cleartomark
%%EndFont 
%%BeginFont: EUFM10
%!PS-AdobeFont-1.1: EUFM10 2.1
%%CreationDate: 1992 Nov 20 17:36:20
% Euler fonts were designed by Hermann Zapf.
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (2.1) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (EUFM10) readonly def
/FamilyName (Euler) readonly def
/Weight (Medium) readonly def
/ItalicAngle 0 def
/isFixedPitch false def
end readonly def
/FontName /EUFM10 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 112 /p put
dup 113 /q put
readonly def
/FontBBox{-26 -224 1055 741}readonly def
/UniqueID 5031986 def
currentdict end
currentfile eexec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0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
cleartomark
%%EndFont 
%%BeginFont: CMR8
%!PS-AdobeFont-1.1: CMR8 1.0
%%CreationDate: 1991 Aug 20 16:39:40
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.0) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMR8) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle 0 def
/isFixedPitch false def
end readonly def
/FontName /CMR8 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 0 /.notdef put
readonly def
/FontBBox{-36 -250 1070 750}readonly def
/UniqueID 5000791 def
currentdict end
currentfile eexec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0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
cleartomark
%%EndFont 
%%BeginFont: CMSY8
%!PS-AdobeFont-1.1: CMSY8 1.0
%%CreationDate: 1991 Aug 15 07:22:10
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.0) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMSY8) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle -14.035 def
/isFixedPitch false def
end readonly def
/FontName /CMSY8 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 0 /.notdef put
readonly def
/FontBBox{-30 -955 1185 779}readonly def
/UniqueID 5000818 def
currentdict end
currentfile eexec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0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
cleartomark
%%EndFont 
%%BeginFont: CMMI12
%!PS-AdobeFont-1.1: CMMI12 1.100
%%CreationDate: 1996 Jul 27 08:57:55
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.100) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMMI12) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle -14.04 def
/isFixedPitch false def
end readonly def
/FontName /CMMI12 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 0 /.notdef put
readonly def
/FontBBox{-30 -250 1026 750}readonly def
/UniqueID 5087386 def
currentdict end
currentfile eexec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0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
cleartomark
%%EndFont 
%%BeginFont: CMBX12
%!PS-AdobeFont-1.1: CMBX12 1.0
%%CreationDate: 1991 Aug 20 16:34:54
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.0) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMBX12) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Bold) readonly def
/ItalicAngle 0 def
/isFixedPitch false def
end readonly def
/FontName /CMBX12 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 0 /.notdef put
readonly def
/FontBBox{-53 -251 1139 750}readonly def
/UniqueID 5000769 def
currentdict end
currentfile eexec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0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
cleartomark
%%EndFont 
%%BeginFont: CMMI8
%!PS-AdobeFont-1.1: CMMI8 1.100
%%CreationDate: 1996 Jul 23 07:53:54
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.100) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMMI8) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle -14.04 def
/isFixedPitch false def
end readonly def
/FontName /CMMI8 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 0 /.notdef put
readonly def
/FontBBox{-24 -250 1110 750}readonly def
/UniqueID 5087383 def
currentdict end
currentfile eexec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0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
cleartomark
%%EndFont 
%%BeginFont: CMSY10
%!PS-AdobeFont-1.1: CMSY10 1.0
%%CreationDate: 1991 Aug 15 07:20:57
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.0) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMSY10) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle -14.035 def
/isFixedPitch false def
end readonly def
/FontName /CMSY10 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 0 /.notdef put
readonly def
/FontBBox{-29 -960 1116 775}readonly def
/UniqueID 5000820 def
currentdict end
currentfile eexec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0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
cleartomark
%%EndFont 
%%BeginFont: CMTI12
%!PS-AdobeFont-1.1: CMTI12 1.0
%%CreationDate: 1991 Aug 18 21:06:53
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.0) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMTI12) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle -14.04 def
/isFixedPitch false def
end readonly def
/FontName /CMTI12 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 0 /.notdef put
readonly def
/FontBBox{-36 -251 1103 750}readonly def
/UniqueID 5000829 def
currentdict end
currentfile eexec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0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
cleartomark
%%EndFont 
%%BeginFont: CMR12
%!PS-AdobeFont-1.1: CMR12 1.0
%%CreationDate: 1991 Aug 20 16:38:05
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.0) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMR12) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle 0 def
/isFixedPitch false def
end readonly def
/FontName /CMR12 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 0 /.notdef put
readonly def
/FontBBox{-34 -251 988 750}readonly def
/UniqueID 5000794 def
currentdict end
currentfile eexec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0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
cleartomark
%%EndFont 
%%BeginFont: CMR17
%!PS-AdobeFont-1.1: CMR17 1.0
%%CreationDate: 1991 Aug 20 16:38:24
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.0) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMR17) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle 0 def
/isFixedPitch false def
end readonly def
/FontName /CMR17 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 0 /.notdef put
readonly def
/FontBBox{-33 -250 945 749}readonly def
/UniqueID 5000795 def
currentdict end
currentfile eexec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0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
cleartomark
%%EndFont 
TeXDict begin 39158280 55380996 1000 8000 8000 () @start
/Fa 137[684 684 684 684 684 1[684 684 1[684 684 3[684
1[684 684 684 684 1[684 38[684 10[684 684 46[{
 TeX09fbbfacEncoding ReEncodeFont }18 1328.35 /CMTT12
rf /Fb 174[1255 81[{}1 1328.35 /CMEX10 rf /Fc 142[650
665 112[{}2 1328.35 /EUFM10 rf /Fd 205[470 470 470 48[{
 TeXf7b6d320Encoding ReEncodeFont }3 885.568 /CMR8 rf
/Fe 255[732{ TeXbbad153fEncoding ReEncodeFont }1 885.568
/CMSY8 rf /Ff 135[739 7[653 1[776 1138 3[444 2[641 1[676
560 553 683 13[800 990 6[1107 719 574 11[650 1012 361
361 46[827 11[{ TeXaae443f0Encoding ReEncodeFont }20
1328.35 /CMMI12 rf /Fg 134[789 2[789 830 581 589 610
1[830 747 830 1245 415 789 1[415 830 747 457 682 830
664 1[726 6[913 4[1148 1039 1[1115 1122 1021 3[898 1170
1[557 2[939 1[1145 1079 8[415 747 747 747 747 747 747
747 747 747 747 1[415 4[581 581 27[830 12[{
 TeXf7b6d320Encoding ReEncodeFont }47 1328.35 /CMBX12
rf /Fh 134[1136 3[1196 837 849 879 2[1076 1196 1793 598
1136 1[598 1196 1076 658 982 1196 956 1196 1046 11[1654
1497 5[1683 2041 5[1691 2[1649 2[1625 13[1076 1076 1076
49[{ TeXf7b6d320Encoding ReEncodeFont }29 1912.83 /CMBX12
rf /Fi 145[571 832 3[320 29[793 75[{ TeXaae443f0Encoding ReEncodeFont }
4 885.568 /CMMI8 rf /Fj 143[1107 8[664 664 9[886 12[1058
24[0 3[886 22[1033 1033 10[664 6[1033 6[369 1033{
 TeXbbad153fEncoding ReEncodeFont }13 1328.35 /CMSY10
rf /Fk 133[531 631 598 863 598 697 432 531 548 598 664
664 731 1063 332 598 1[399 664 598 399 598 664 598 598
664 12[930 731 2[881 1[966 1[815 2[501 2[848 881 981
930 914 966 6[399 2[664 5[664 2[399 1[399 2[531 531 399
26[731 12[{ TeX74afc74cEncoding ReEncodeFont }46 1328.35
/CMTI12 rf /Fl 133[578 686 686 939 686 723 506 513 506
686 723 650 723 1084 361 686 1[361 723 650 397 578 723
578 723 650 3[361 1[361 1[975 1[1336 2[939 723 957 1[885
1012 975 1192 813 2[469 975 1021 849 885 993 939 921
975 3[1012 1[361 361 650 650 650 650 650 650 650 650
650 650 1[361 434 361 1012 1[506 506 361 2[650 2[361
18[1084 1[723 12[{ TeXf7b6d320Encoding ReEncodeFont }70
1328.35 /CMR12 rf /Fm 134[824 3[867 607 616 607 3[867
1301 434 2[434 3[694 867 1[867 780 9[1604 2[1127 867
12[1019 14[780 2[780 1[780 780 780 3[434 44[{
 TeXf7b6d320Encoding ReEncodeFont }23 1594.02 /CMR12
rf /Fn 138[1435 1004 1[1055 12[1178 1[1148 22[1552 23[1291
52[{ TeXf7b6d320Encoding ReEncodeFont }7 2295.84 /CMBX12
rf /Fo 134[1113 3[1173 813 1[813 2[1053 1[1773 573 2[573
1173 1053 1[933 1[933 1173 1053 12[1533 5[1592 1952 11[1592
6[573 1053 6[1053 1053 49[{ TeXf7b6d320Encoding ReEncodeFont }22
2295.84 /CMR17 rf end
%%EndProlog
%%BeginSetup
%%Feature: *Resolution 8000dpi
TeXDict begin
%%PaperSize: A4
 end
%%EndSetup
%%Page: 1 1
TeXDict begin 1 0 bop 8651 11017 a Fo(Math)693 b(129:)932
b(Algebraic)693 b(Num)-60 b(b)60 b(er)692 b(Theory)20551
13785 y Fn(Lecture)862 b(4)21199 17728 y Fm(William)518
b(Stein)16545 20844 y(T)-130 b(uesda)-43 b(y)-130 b(,)519
b(F)-130 b(ebruary)520 b(17,)g(2004)4109 25839 y Fl(Note:)507
b(There's)291 b(a)f(b)36 b(o)g(ok)291 b(called)g Fk(A)-33
b(lgebr)-66 b(aic)331 b(Numb)-66 b(er)332 b(The)-66 b(ory)332
b(and)h(F)-100 b(ermat's)333 b(L)-66 b(ast)333 b(The)-66
b(or)g(em)2158 27444 y Fl(b)-36 b(y)609 b(Stew)-36 b(art)607
b(and)h(T)-108 b(all,)653 b(whic)-36 b(h)608 b(app)36
b(ears)608 b(to)g(ha)-36 b(v)g(e)609 b(a)f(detailed)h(in)-36
b(tro)36 b(duction)607 b(to)h(algebraic)2158 29050 y(n)-36
b(um)g(b)36 b(er)447 b(theory)i(and)f(assumes)g(little)h(bac)-36
b(kground)448 b(on)h(the)f(part)g(of)h(the)f(reader.)623
b(There)448 b(is)h(a)2158 30655 y(discussion)394 b(of)h(the)f
(de\257nition)f(of)i(mo)36 b(dule,)402 b(and)393 b(pro)36
b(ofs)395 b(of)g(basic)f(facts)h(ab)36 b(out)394 b(n)-36
b(um)g(b)36 b(er)392 b(\257elds,)2158 32260 y(and)513
b(man)-36 b(y)514 b(exercises.)819 b(If)514 b(y)-36 b(ou)514
b(\257nd)f(Swinnerton-Dy)-36 b(er's)513 b(b)36 b(o)g(ok)514
b(di\261cult,)533 b(y)-36 b(ou)514 b(migh)-36 b(t)513
b(w)-36 b(an)g(t)2158 33865 y(to)513 b(try)g(to)g(get)g(y)-36
b(our)513 b(hands)f(on)h(Stew)-36 b(art)512 b(and)g(T)-108
b(all,)534 b(whic)-36 b(h)513 b(costs)g(ab)36 b(out)512
b($38)i(new.)816 b(\(Hand)2158 35470 y(around)433 b(a)h(cop)-36
b(y)-108 b(.\))4109 37075 y(T)g(o)36 b(da)-36 b(y)440
b(w)-36 b(e)440 b(will)g(deduce,)g(with)g(complete)f(pro)36
b(ofs,)442 b(the)c(most)i(imp)36 b(ortan)-36 b(t)438
b(basic)i(prop)36 b(ert)-36 b(y)2158 38680 y(of)415 b(the)f(ring)g(of)g
(in)-36 b(tegers)414 b Fj(O)15807 38879 y Fi(K)17132
38680 y Fl(of)h(an)e(algebraic)j(n)-36 b(um)g(b)36 b(er,)416
b(namely)f(that)e(ev)-36 b(ery)415 b(nonzero)f(ideals)2158
40285 y(can)391 b(b)36 b(e)391 b(written)g(uniquely)g(as)g(pro)36
b(ducts)390 b(of)i(prime)e(ideals.)565 b(After)391 b(pro)-36
b(ving)391 b(this)g(fundamen)-36 b(tal)2158 41890 y(theorem,)432
b(w)-36 b(e)432 b(will)h(compute)e(some)h(examples)g(using)g(MA)-36
b(GMA.)431 b(On)f(Th)-36 b(ursda)g(y)432 b(the)f(lecture)2158
43495 y(will)294 b(consist)e(mostly)h(of)g(examples)g(illustrating)f
(the)g(substan)-36 b(tial)291 b(theory)h(w)-36 b(e)293
b(will)g(ha)-36 b(v)g(e)292 b(already)2158 45100 y(dev)-36
b(elop)36 b(ed,)434 b(so)g(hang)g(in)f(there!)2158 49538
y Fh(1)2152 b(Dedekind)716 b(Domains)2158 52458 y Fg(Corollary)521
b(1.1.)554 b Fk(The)465 b(ring)f(of)g(inte)-66 b(gers)463
b Fj(O)24509 52657 y Fi(K)25885 52458 y Fk(of)i(a)g(numb)-66
b(er)463 b(\257eld)i(is)g(No)-66 b(etherian.)2158 55170
y(Pr)g(o)g(of.)650 b Fl(As)415 b(w)-36 b(e)415 b(sa)-36
b(w)416 b(b)36 b(efore)416 b(using)f(norms,)k(the)c(ring)g
Fj(O)29972 55369 y Fi(K)31298 55170 y Fl(is)h(\257nitely)f(generated)g
(as)h(a)f(mo)36 b(dule)2158 56775 y(o)-36 b(v)g(er)511
b Fg(Z)p Fl(,)531 b(so)511 b(it)f(is)h(certainly)g(\257nitely)g
(generated)f(as)h(a)g(ring)f(o)-36 b(v)g(er)511 b Fg(Z)p
Fl(.)810 b(By)511 b(the)f(Hilb)36 b(ert)510 b(Basis)2158
58380 y(Theorem,)434 b Fj(O)9069 58579 y Fi(K)10414 58380
y Fl(is)g(No)36 b(etherian.)p 48707 58380 45 878 v 48752
57547 781 45 v 48752 58380 V 49532 58380 45 878 v 4109
60982 a(If)471 b Ff(R)481 b Fl(is)471 b(an)f(in)-36 b(tegral)471
b(domain,)479 b(the)470 b Fk(\257eld)498 b(of)h(fr)-66
b(actions)468 b Fl(of)j Ff(R)481 b Fl(is)471 b(the)f(\257eld)f(of)i
(all)h(elemen)-36 b(ts)2158 62587 y Ff(a=b)p Fl(,)424
b(where)c Ff(a;)221 b(b)369 b Fj(2)g Ff(R)11 b Fl(.)574
b(The)420 b(\257eld)g(of)h(fractions)g(of)g Ff(R)432
b Fl(is)420 b(the)g(smallest)h(\257eld)f(that)g(con)-36
b(tains)420 b Ff(R)11 b Fl(.)2158 64192 y(F)-108 b(or)434
b(example,)g(the)f(\257eld)g(of)i(fractions)f(of)g Fg(Z)g
Fl(is)g Fg(Q)g Fl(and)f(of)h Fg(Z)p Fl([\(1)296 b(+)35537
63093 y Fj(p)p 36644 63093 651 54 v 1099 x Fl(5\))p Ff(=)p
Fl(2])434 b(is)g Fg(Q)p Fl(\()42831 63093 y Fj(p)p 43938
63093 V 1099 x Fl(5)q(\).)2158 66904 y Fg(De\257nition)502
b(1.2)e(\(In)-42 b(tegrally)501 b(Closed\).)556 b Fl(An)434
b(in)-36 b(tegral)435 b(domain)g Ff(R)446 b Fl(is)436
b Fk(inte)-66 b(gr)g(al)66 b(ly)464 b(close)-66 b(d)466
b(in)2158 68509 y(its)517 b(\257eld)g(of)f(fr)-66 b(actions)489
b Fl(if)i(whenev)-36 b(er)490 b Ff(\256)498 b Fl(is)491
b(in)f(the)g(\257eld)f(of)i(fractions)g(of)g Ff(R)501
b Fl(and)490 b Ff(\256)499 b Fl(satis\257es)490 b(a)2158
70114 y(monic)434 b(p)36 b(olynomial)435 b Ff(f)511 b
Fj(2)369 b Ff(R)11 b Fl([)p Ff(x)p Fl(],)434 b(then)f
Ff(\256)378 b Fj(2)368 b Ff(R)11 b Fl(.)2158 72826 y
Fg(Prop)42 b(osition)507 b(1.3.)557 b Fk(If)469 b Ff(K)565
b Fk(is)470 b(any)g(numb)-66 b(er)469 b(\257eld,)i(then)e
Fj(O)31842 73025 y Fi(K)33223 72826 y Fk(is)h(inte)-66
b(gr)g(al)66 b(ly)469 b(close)-66 b(d.)613 b(A)-33 b(lso,)471
b(the)2158 74431 y(ring)p 4898 73360 914 54 v 464 w Fg(Z)465
b Fk(of)g(al)66 b(l)466 b(algebr)-66 b(aic)463 b(inte)-66
b(gers)463 b(is)i(inte)-66 b(gr)g(al)66 b(ly)463 b(close)-66
b(d.)25578 78073 y Fl(1)p eop end
%%Page: 2 2
TeXDict begin 2 1 bop 2158 5648 a Fk(Pr)-66 b(o)g(of.)650
b Fl(W)-108 b(e)458 b(\257rst)g(pro)-36 b(v)g(e)458 b(that)p
17573 4578 914 54 v 458 w Fg(Z)h Fl(is)f(in)-36 b(tegrally)460
b(closed.)653 b(Supp)36 b(ose)458 b Ff(c)411 b Fj(2)p
37895 4578 1123 54 v 411 w Fg(Q)458 b Fl(is)h(in)-36
b(tegral)459 b(o)-36 b(v)g(er)p 48373 4578 914 54 v 459
w Fg(Z)p Fl(,)2158 7254 y(so)474 b(there)e(is)h(a)g(monic)g(p)36
b(olynomial)474 b Ff(f)142 b Fl(\()p Ff(x)p Fl(\))435
b(=)g Ff(x)25411 6772 y Fi(n)26360 7254 y Fl(+)321 b
Ff(a)28376 7453 y Fi(n)p Fe(\241)p Fd(1)30205 7254 y
Ff(x)30944 6772 y Fi(n)p Fe(\241)p Fd(1)33094 7254 y
Fl(+)h Fj(\242)221 b(\242)g(\242)322 b Fl(+)g Ff(a)38316
7453 y Fd(1)38841 7254 y Ff(x)g Fl(+)g Ff(a)41919 7453
y Fd(0)42917 7254 y Fl(with)473 b Ff(a)46602 7453 y Fi(i)47413
7254 y Fj(2)p 48734 6183 V 435 w Fg(Z)2158 8859 y Fl(and)545
b Ff(f)142 b Fl(\()p Ff(c)p Fl(\))558 b(=)h(0.)913 b(The)545
b Ff(a)14675 9058 y Fi(i)15596 8859 y Fl(all)h(lie)g(in)f(the)f(ring)h
(of)h(in)-36 b(tegers)545 b Fj(O)33700 9058 y Fi(K)35156
8859 y Fl(of)h(the)f(n)-36 b(um)g(b)36 b(er)543 b(\257eld)i
Ff(K)654 b Fl(=)2158 10464 y Fg(Q)p Fl(\()p Ff(a)4469
10663 y Fd(0)4995 10464 y Ff(;)221 b(a)6260 10663 y Fd(1)6786
10464 y Ff(;)g(:)g(:)g(:)j(a)9800 10663 y Fi(n)p Fe(\241)p
Fd(1)11629 10464 y Fl(\),)436 b(and)g Fj(O)16522 10663
y Fi(K)17869 10464 y Fl(is)h(\257nitely)f(generated)g(as)h(a)f
Fg(Z)p Fl(-mo)36 b(dule,)437 b(so)g Fg(Z)p Fl([)p Ff(a)42025
10663 y Fd(0)42551 10464 y Ff(;)221 b(:)g(:)g(:)i(;)e(a)46146
10663 y Fi(n)p Fe(\241)p Fd(1)47975 10464 y Fl(])437
b(is)2158 12069 y(\257nitely)310 b(generated)g(as)g(a)g
Fg(Z)p Fl(-mo)36 b(dule.)537 b(Since)309 b Ff(f)142 b
Fl(\()p Ff(c)p Fl(\))369 b(=)f(0,)335 b(w)-36 b(e)311
b(can)e(write)h Ff(c)37575 11587 y Fi(n)38511 12069 y
Fl(as)g(a)h Fg(Z)p Fl([)p Ff(a)42902 12268 y Fd(0)43428
12069 y Ff(;)221 b(:)g(:)g(:)i(;)e(a)47023 12268 y Fi(n)p
Fe(\241)p Fd(1)48852 12069 y Fl(]-)2158 13674 y(linear)485
b(com)-36 b(bination)484 b(of)g Ff(c)15370 13192 y Fi(i)16230
13674 y Fl(for)g Ff(i)455 b(<)f(n)p Fl(,)497 b(so)485
b(the)e(ring)h Fg(Z)p Fl([)p Ff(a)30885 13873 y Fd(0)31411
13674 y Ff(;)221 b(:)g(:)g(:)j(;)d(a)35007 13873 y Fi(n)p
Fe(\241)p Fd(1)36836 13674 y Ff(;)g(c)p Fl(])484 b(is)h(also)g
(\257nitely)f(gen-)2158 15279 y(erated)512 b(as)h(a)g
Fg(Z)p Fl(-mo)36 b(dule.)814 b(Th)-36 b(us)512 b Fg(Z)p
Fl([)p Ff(c)p Fl(])h(is)g(\257nitely)f(generated)g(as)h
Fg(Z)p Fl(-mo)36 b(dule)512 b(b)36 b(ecause)512 b(it)g(is)h(a)2158
16884 y(submo)36 b(dule)413 b(of)h(a)f(\257nitely)g(generated)g
Fg(Z)p Fl(-mo)36 b(dule,)417 b(whic)-36 b(h)413 b(implies)h(that)e
Ff(c)h Fl(is)h(in)-36 b(tegral)413 b(o)-36 b(v)g(er)414
b Fg(Z)p Fl(.)4109 18489 y(Supp)36 b(ose)536 b Ff(c)544
b Fj(2)f Ff(K)632 b Fl(is)536 b(in)-36 b(tegral)537 b(o)-36
b(v)g(er)537 b Fj(O)23775 18688 y Fi(K)24686 18489 y
Fl(.)887 b(Then)536 b(since)p 32722 17418 V 536 w Fg(Z)h
Fl(is)g(in)-36 b(tegrally)537 b(closed,)g Ff(c)g Fl(is)f(an)2158
20094 y(elemen)-36 b(t)434 b(of)p 8445 19024 V 434 w
Fg(Z)p Fl(,)g(so)g Ff(c)369 b Fj(2)f Ff(K)390 b Fj(\\)p
16611 19024 V 295 w Fg(Z)369 b Fl(=)g Fj(O)20332 20293
y Fi(K)21243 20094 y Fl(,)434 b(as)g(required.)p 48707
20094 45 878 v 48752 19261 781 45 v 48752 20094 V 49532
20094 45 878 v 2158 22806 a Fg(De\257nition)400 b(1.4)f(\(Dedekind)h
(Domain\).)489 b Fl(An)346 b(in)-36 b(tegral)347 b(domain)g
Ff(R)358 b Fl(is)347 b(a)g Fk(De)-66 b(dekind)384 b(domain)2158
24411 y Fl(if)407 b(it)f(is)h(No)36 b(etherian,)411 b(in)-36
b(tegrally)408 b(closed)e(in)g(its)g(\257eld)f(of)i(fractions,)413
b(and)405 b(ev)-36 b(ery)407 b(nonzero)f(prime)2158 26017
y(ideal)435 b(of)f Ff(R)444 b Fl(is)434 b(maximal.)4109
28729 y(The)450 b(ring)f Fg(Q)307 b Fj(\251)f Fg(Q)450
b Fl(is)g(No)36 b(etherian,)454 b(in)-36 b(tegrally)450
b(closed)g(in)f(its)h(\257eld)f(of)h(fractions,)455 b(and)449
b(the)2158 30334 y(t)-36 b(w)g(o)479 b(prime)f(ideals)h(are)f(maximal.)
714 b(Ho)-36 b(w)g(ev)g(er,)491 b(it)478 b(is)h(not)f(a)h(Dedekind)f
(domain)g(b)36 b(ecause)479 b(it)f(is)2158 31939 y(not)427
b(an)g(in)-36 b(tegral)427 b(domain.)577 b(The)427 b(ring)g
Fg(Z)p Fl([)22727 30840 y Fj(p)p 23834 30840 651 54 v
1099 x Fl(5)q(])g(is)g(not)g(a)g(Dedekind)g(domain)g(b)36
b(ecause)427 b(it)g(is)h(not)2158 33544 y(in)-36 b(tegrally)477
b(closed)e(in)g(its)g(\257eld)g(of)h(fractions,)486 b(as)476
b(\(1)323 b(+)29841 32445 y Fj(p)p 30948 32445 V 1099
x Fl(5\))p Ff(=)p Fl(2)475 b(is)h(in)-36 b(tegrally)476
b(o)-36 b(v)g(er)476 b Fg(Z)f Fl(and)g(lies)2158 35149
y(in)525 b Fg(Q)p Fl(\()5395 34050 y Fj(p)p 6503 34050
V 6503 35149 a Fl(5\),)548 b(but)524 b(not)h(in)g Fg(Z)p
Fl([)16331 34050 y Fj(p)p 17438 34050 V 1099 x Fl(5)q(].)853
b(The)525 b(ring)g Fg(Z)h Fl(is)f(a)h(Dedekind)f(domain,)548
b(as)526 b(is)f(an)-36 b(y)525 b(ring)h(of)2158 36754
y(in)-36 b(tegers)407 b Fj(O)8002 36953 y Fi(K)9320 36754
y Fl(of)g(a)g(n)-36 b(um)g(b)36 b(er)405 b(\257eld,)412
b(as)407 b(w)-36 b(e)407 b(will)h(see)f(b)36 b(elo)-36
b(w.)570 b(Also,)413 b(an)-36 b(y)407 b(\257eld)g Ff(K)501
b Fl(is)407 b(a)g(Dedekind)2158 38359 y(domain,)504 b(since)490
b(it)g(is)f(a)h(domain,)504 b(it)490 b(is)g(trivially)h(in)-36
b(tegrally)491 b(closed)f(in)f(itself,)505 b(and)489
b(there)g(are)2158 39964 y(no)434 b(nonzero)f(prime)g(ideals)i(so)f
(that)f(condition)g(that)g(they)h(b)36 b(e)433 b(maximal)i(is)f(empt)
-36 b(y)-108 b(.)2158 42676 y Fg(Prop)42 b(osition)459
b(1.5.)526 b Fk(The)431 b(ring)g(of)g(inte)-66 b(gers)430
b Fj(O)25722 42875 y Fi(K)27064 42676 y Fk(of)i(a)g(numb)-66
b(er)430 b(\257eld)h(is)h(a)g(De)-66 b(dekind)429 b(domain.)2158
45388 y(Pr)-66 b(o)g(of.)650 b Fl(By)459 b(Prop)36 b(osition)460
b(1.3,)467 b(the)459 b(ring)g Fj(O)23833 45587 y Fi(K)25204
45388 y Fl(is)g(in)-36 b(tegrally)461 b(closed,)466 b(and)459
b(b)-36 b(y)459 b(Prop)36 b(osition)460 b(1.1)2158 46993
y(it)516 b(is)g(No)36 b(etherian.)823 b(Supp)36 b(ose)514
b(that)h Fc(p)g Fl(is)h(a)g(nonzero)f(prime)g(ideal)h(of)g
Fj(O)38720 47192 y Fi(K)39631 46993 y Fl(.)823 b(Let)515
b Ff(\256)i Fj(2)508 b Fc(p)515 b Fl(b)36 b(e)515 b(a)2158
48599 y(nonzero)434 b(elemen)-36 b(t,)433 b(and)g(let)h
Ff(f)142 b Fl(\()p Ff(x)p Fl(\))369 b Fj(2)f Fg(Z)p Fl([)p
Ff(x)p Fl(])435 b(b)36 b(e)433 b(the)g(minimal)h(p)36
b(olynomial)435 b(of)g Ff(\256)8 b Fl(.)579 b(Then)13408
51532 y Ff(f)142 b Fl(\()p Ff(\256)8 b Fl(\))369 b(=)g
Ff(\256)18623 50984 y Fi(n)19545 51532 y Fl(+)295 b Ff(a)21535
51731 y Fi(n)p Fe(\241)p Fd(1)23363 51532 y Ff(\256)24198
50984 y Fi(n)p Fe(\241)p Fd(1)26323 51532 y Fl(+)g Fj(\242)221
b(\242)g(\242)296 b Fl(+)e Ff(a)31464 51731 y Fd(1)31990
51532 y Ff(\256)304 b Fl(+)295 b Ff(a)35111 51731 y Fd(0)36005
51532 y Fl(=)369 b(0)p Ff(;)2158 54465 y Fl(so)501 b
Ff(a)4505 54664 y Fd(0)5512 54465 y Fl(=)482 b Fj(\241)p
Fl(\()p Ff(\256)9380 53983 y Fi(n)10347 54465 y Fl(+)340
b Ff(a)12382 54664 y Fi(n)p Fe(\241)p Fd(1)14210 54465
y Ff(\256)15045 53983 y Fi(n)p Fe(\241)p Fd(1)17215 54465
y Fl(+)g Fj(\242)221 b(\242)g(\242)341 b Fl(+)f Ff(a)22492
54664 y Fd(1)23018 54465 y Ff(\256)8 b Fl(\))482 b Fj(2)g
Fc(p)p Fl(.)777 b(Since)499 b Ff(f)642 b Fl(is)500 b(irreducible,)517
b Ff(a)41690 54664 y Fd(0)42715 54465 y Fl(is)500 b(a)g(nonzero)2158
56071 y(elemen)-36 b(t)517 b(of)h Fg(Z)g Fl(that)e(lies)i(in)f
Fc(p)p Fl(.)829 b(Ev)-36 b(ery)518 b(elemen)-36 b(t)517
b(of)h(the)f(\257nitely)g(generated)g(ab)36 b(elian)518
b(group)2158 57676 y Fj(O)3216 57875 y Fi(K)4127 57676
y Ff(=)p Fc(p)463 b Fl(is)h(killed)g(b)-36 b(y)462 b
Ff(a)13295 57875 y Fd(0)13821 57676 y Fl(,)471 b(so)463
b Fj(O)17337 57875 y Fi(K)18248 57676 y Ff(=)p Fc(p)g
Fl(is)g(a)g(\257nite)g(set.)666 b(Since)463 b Fc(p)f
Fl(is)i(prime,)470 b Fj(O)39486 57875 y Fi(K)40397 57676
y Ff(=)p Fc(p)463 b Fl(is)g(an)g(in)-36 b(tegral)2158
59281 y(domain.)850 b(Ev)-36 b(ery)524 b(\257nite)f(in)-36
b(tegral)524 b(domain)g(is)g(a)g(\257eld,)547 b(so)524
b Fc(p)f Fl(is)h(maximal,)549 b(whic)-36 b(h)523 b(completes)2158
60886 y(the)433 b(pro)36 b(of.)p 48707 60886 45 878 v
48752 60052 781 45 v 48752 60886 V 49532 60886 45 878
v 4109 63487 a(If)524 b Ff(I)627 b Fl(and)523 b Ff(J)646
b Fl(are)523 b(ideals)g(in)g(a)g(ring)h Ff(R)11 b Fl(,)545
b(the)523 b(pro)36 b(duct)521 b Ff(I)104 b(J)646 b Fl(is)524
b(the)e(ideal)i(generated)e(b)-36 b(y)523 b(all)2158
65092 y(pro)36 b(ducts)433 b(of)h(elemen)-36 b(ts)434
b(in)f Ff(I)538 b Fl(with)433 b(elemen)-36 b(ts)434 b(in)f
Ff(J)123 b Fl(:)17735 68026 y Ff(I)104 b(J)492 b Fl(=)369
b(\()p Ff(ab)f Fl(:)i Ff(a)e Fj(2)h Ff(I)104 b(;)221
b(b)370 b Fj(2)e Ff(J)123 b Fl(\))369 b Fj(\275)g Ff(R)11
b(:)2158 70959 y Fl(Note)445 b(that)f(the)g(set)h(of)g(all)h(pro)36
b(ducts)443 b Ff(ab)p Fl(,)k(with)e Ff(a)387 b Fj(2)h
Ff(I)548 b Fl(and)444 b Ff(b)388 b Fj(2)f Ff(J)123 b
Fl(,)448 b(need)c(not)g(b)36 b(e)444 b(an)h(ideal,)j(so)2158
72564 y(it)396 b(is)f(imp)36 b(ortan)-36 b(t)395 b(to)g(tak)-36
b(e)395 b(the)g(ideal)h(generated)f(b)-36 b(y)395 b(that)f(set.)566
b(\(See)394 b(the)h(homew)-36 b(ork)396 b(problems)2158
74169 y(for)435 b(examples.\))25578 78073 y(2)p eop end
%%Page: 3 3
TeXDict begin 3 2 bop 2158 5648 a Fg(De\257nition)485
b(1.6)e(\(F)-125 b(ractional)486 b(Ideal\).)543 b Fl(A)421
b Fk(fr)-66 b(actional)450 b(ide)-66 b(al)420 b Fl(is)g(an)g
Fj(O)38221 5847 y Fi(K)39132 5648 y Fl(-submo)36 b(dule)419
b(of)i Ff(I)473 b Fj(\275)2158 7254 y Ff(K)529 b Fl(that)433
b(is)h(\257nitely)g(generated)f(as)h(an)f Fj(O)22678
7453 y Fi(K)23589 7254 y Fl(-mo)36 b(dule.)4109 9966
y(T)-108 b(o)515 b(a)-36 b(v)g(oid)516 b(confusion,)535
b(w)-36 b(e)516 b(will)f(sometimes)h(call)f(a)g(gen)-36
b(uine)514 b(ideal)i Ff(I)611 b Fj(\275)507 b(O)42166
10165 y Fi(K)43592 9966 y Fl(an)515 b Fk(inte)-66 b(gr)g(al)2158
11571 y(ide)g(al)p Fl(.)610 b(Also,)447 b(since)d(fractional)i(ideals)e
(are)h(\257nitely)f(generated,)j(w)-36 b(e)444 b(can)g(clear)h
(denominators)2158 13176 y(of)430 b(a)g(generating)f(set)g(to)h(see)f
(that)g(ev)-36 b(ery)430 b(fractional)g(ideal)g(is)g(of)g(the)e(form)i
Ff(aI)473 b Fl(=)368 b Fj(f)p Ff(ab)h Fl(:)g Ff(b)g Fj(2)g
Ff(I)104 b Fj(g)2158 14781 y Fl(for)435 b(some)e Ff(a)369
b Fj(2)g Ff(K)528 b Fl(and)433 b(ideal)h Ff(I)474 b Fj(\275)369
b(O)20490 14980 y Fi(K)21401 14781 y Fl(.)4109 16386
y(F)-108 b(or)420 b(example,)k(the)419 b(collection)19998
15863 y Fd(1)p 19998 16080 471 54 v 19998 16844 a(2)20601
16386 y Fg(Z)h Fl(of)h(rational)g(n)-36 b(um)g(b)36 b(ers)419
b(with)h(denominator)f(1)i(or)f(2)h(is)f(a)2158 17991
y(fractional)435 b(ideal)f(of)h Fg(Z)p Fl(.)2158 20703
y Fg(Theorem)554 b(1.7.)578 b Fk(The)507 b(set)h(of)g(nonzer)-66
b(o)507 b(fr)-66 b(actional)506 b(ide)-66 b(als)508 b(of)g(a)g(De)-66
b(dekind)506 b(domain)i Ff(R)519 b Fk(is)508 b(an)2158
22308 y(ab)-66 b(elian)464 b(gr)-66 b(oup)465 b(under)g(ide)-66
b(al)464 b(multiplic)-66 b(ation.)4109 25020 y Fl(Before)469
b(pro)-36 b(ving)469 b(Theorem)f(1.7)h(w)-36 b(e)469
b(pro)-36 b(v)g(e)468 b(a)g(lemma.)683 b(F)-108 b(or)468
b(the)f(rest)h(of)h(this)f(section)g Fj(O)48736 25219
y Fi(K)2158 26625 y Fl(is)434 b(the)f(ring)h(of)g(in)-36
b(tegers)434 b(of)g(a)g(n)-36 b(um)g(b)36 b(er)432 b(\257eld)h
Ff(K)95 b Fl(.)2158 29337 y Fg(De\257nition)481 b(1.8)f(\(Divides)g
(for)g(Ideals\).)542 b Fl(Supp)36 b(ose)416 b(that)h
Ff(I)104 b(;)221 b(J)540 b Fl(are)418 b(ideals)g(of)g
Fj(O)43745 29536 y Fi(K)44655 29337 y Fl(.)573 b(Then)417
b Ff(I)2158 30943 y Fk(divides)433 b Ff(J)557 b Fl(if)434
b Ff(I)473 b Fj(\276)369 b Ff(J)123 b Fl(.)4109 33655
y(T)-108 b(o)613 b(see)g(that)f(this)g(notion)h(of)g(divides)g(is)g
(sensible,)657 b(supp)36 b(ose)612 b Ff(K)769 b Fl(=)673
b Fg(Q)p Fl(,)658 b(so)613 b Fj(O)45103 33854 y Fi(K)46688
33655 y Fl(=)673 b Fg(Z)p Fl(.)2158 35260 y(Then)473
b Ff(I)539 b Fl(=)435 b(\()p Ff(n)p Fl(\))473 b(and)f
Ff(J)559 b Fl(=)435 b(\()p Ff(m)p Fl(\))472 b(for)h(some)g(in)-36
b(teger)472 b Ff(n)h Fl(and)f Ff(m)p Fl(,)483 b(and)472
b Ff(I)577 b Fl(divides)473 b Ff(J)595 b Fl(means)473
b(that)2158 36865 y(\()p Ff(n)p Fl(\))369 b Fj(\276)h
Fl(\()p Ff(m)p Fl(\),)380 b(i.e.,)h(that)367 b(there)g(exists)g(an)h
(in)-36 b(teger)367 b Ff(c)g Fl(suc)-36 b(h)366 b(that)h
Ff(m)h Fl(=)h Ff(cn)p Fl(,)381 b(whic)-36 b(h)367 b(exactly)h(means)
2158 38470 y(that)434 b Ff(n)g Fl(divides)f Ff(m)p Fl(,)h(as)g(exp)36
b(ected.)2158 41182 y Fg(Lemma)504 b(1.9.)556 b Fk(Supp)-66
b(ose)469 b Ff(I)572 b Fk(is)469 b(an)f(ide)-66 b(al)468
b(of)g Fj(O)25346 41381 y Fi(K)26257 41182 y Fk(.)608
b(Then)468 b(ther)-66 b(e)468 b(exist)f(prime)h(ide)-66
b(als)468 b Fc(p)44917 41381 y Fd(1)45443 41182 y Ff(;)221
b(:)g(:)g(:)j(;)d Fc(p)49021 41381 y Fi(n)2158 42787
y Fk(such)467 b(that)f Fc(p)8438 42986 y Fd(1)9260 42787
y Fj(\242)296 b Fc(p)10590 42986 y Fd(2)11337 42787 y
Fj(\242)221 b(\242)g(\242)h Fc(p)13773 42986 y Fi(n)14770
42787 y Fj(\275)371 b Ff(I)104 b Fk(.)601 b(In)465 b(other)h(wor)-66
b(ds,)466 b Ff(I)570 b Fk(divides)466 b(a)g(pr)-66 b(o)g(duct)465
b(of)h(prime)f(ide)-66 b(als.)600 b(\(By)2158 44392 y(c)-66
b(onvention)414 b(the)i(empty)g(pr)-66 b(o)g(duct)416
b(is)h(the)f(unit)g(ide)-66 b(al.)580 b(A)-33 b(lso,)426
b(if)415 b Ff(I)473 b Fl(=)369 b(0)p Fk(,)426 b(then)416
b(we)h(take)f Fc(p)45312 44591 y Fd(1)46206 44392 y Fl(=)369
b(\(0\))p Fk(,)2158 45997 y(which)465 b(is)g(a)g(prime)f(ide)-66
b(al.\))2158 48709 y(Pr)g(o)g(of.)650 b Fl(The)551 b(k)-36
b(ey)552 b(idea)g(is)f(to)h(use)f(that)f Fj(O)23843 48908
y Fi(K)25306 48709 y Fl(is)h(No)36 b(etherian)552 b(to)f(deduce)f(that)
h(the)g(set)g Ff(S)629 b Fl(of)2158 50314 y(ideals)480
b(that)e(do)g(not)g(satisfy)i(the)e(lemma)h(is)g(empt)-36
b(y)-108 b(.)712 b(If)479 b Ff(S)556 b Fl(is)479 b(nonempt)-36
b(y)-108 b(,)488 b(then)478 b(b)36 b(ecause)478 b Fj(O)48736
50513 y Fi(K)2158 51919 y Fl(is)435 b(No)36 b(etherian,)435
b(there)f(is)h(an)g(ideal)g Ff(I)474 b Fj(2)370 b Ff(S)512
b Fl(that)434 b(is)h(maximal)h(as)f(an)f(elemen)-36 b(t)435
b(of)g Ff(S)77 b Fl(.)581 b(If)436 b Ff(I)538 b Fl(w)-36
b(ere)2158 53525 y(prime,)573 b(then)543 b Ff(I)649 b
Fl(w)-36 b(ould)545 b(trivially)h(con)-36 b(tain)545
b(a)g(pro)36 b(duct)543 b(of)j(primes,)572 b(so)545 b
Ff(I)648 b Fl(is)545 b(not)g(prime.)911 b(By)2158 55130
y(de\257nition)553 b(of)h(prime)f(ideal,)585 b(there)552
b(exists)j Ff(a;)221 b(b)573 b Fj(2)g(O)29147 55329 y
Fi(K)30611 55130 y Fl(suc)-36 b(h)553 b(that)g Ff(ab)572
b Fj(2)h Ff(I)657 b Fl(but)553 b Ff(a)573 b Fj(62)f Ff(I)658
b Fl(and)2158 56735 y Ff(b)397 b Fj(62)e Ff(I)104 b Fl(.)626
b(Let)449 b Ff(J)9119 56934 y Fd(1)10041 56735 y Fl(=)396
b Ff(I)410 b Fl(+)306 b(\()p Ff(a)p Fl(\))448 b(and)h
Ff(J)19158 56934 y Fd(2)20080 56735 y Fl(=)396 b Ff(I)410
b Fl(+)306 b(\()p Ff(b)p Fl(\).)625 b(Then)449 b(neither)g
Ff(J)34896 56934 y Fd(1)35871 56735 y Fl(nor)h Ff(J)38919
56934 y Fd(2)39894 56735 y Fl(is)g(in)f Ff(S)77 b Fl(,)454
b(since)449 b Ff(I)554 b Fl(is)2158 58340 y(maximal,)402
b(so)392 b(b)36 b(oth)390 b Ff(J)13099 58539 y Fd(1)14016
58340 y Fl(and)h Ff(J)17222 58539 y Fd(2)18139 58340
y Fl(con)-36 b(tain)391 b(a)h(pro)36 b(duct)390 b(of)i(prime)f(ideals.)
565 b(Th)-36 b(us)391 b(so)h(do)36 b(es)391 b Ff(I)104
b Fl(,)400 b(since)15942 61273 y Ff(J)16661 61472 y Fd(1)17187
61273 y Ff(J)17906 61472 y Fd(2)18800 61273 y Fl(=)369
b Ff(I)20859 60725 y Fd(2)21680 61273 y Fl(+)295 b Ff(I)104
b Fl(\()p Ff(b)p Fl(\))295 b(+)f(\()p Ff(a)p Fl(\))p
Ff(I)399 b Fl(+)295 b(\()p Ff(ab)p Fl(\))368 b Fj(\275)i
Ff(I)104 b(;)2158 64207 y Fl(whic)-36 b(h)434 b(is)g(a)g(con)-36
b(tradiction.)578 b(Th)-36 b(us)433 b Ff(S)511 b Fl(is)433
b(empt)-36 b(y)-108 b(,)434 b(whic)-36 b(h)433 b(completes)h(the)f(pro)
36 b(of.)p 48707 64207 45 878 v 48752 63373 781 45 v
48752 64207 V 49532 64207 45 878 v 4109 66808 a(W)-108
b(e)434 b(are)g(no)-36 b(w)434 b(ready)f(to)h(pro)-36
b(v)g(e)434 b(the)f(theorem.)2158 69409 y Fk(Pr)-66 b(o)g(of)465
b(of)f(The)-66 b(or)g(em)464 b(1.7.)649 b Fl(The)518
b(pro)36 b(duct)517 b(of)i(t)-36 b(w)g(o)518 b(fractional)h(ideals)f
(is)g(again)h(\257nitely)f(gener-)2158 71014 y(ated,)447
b(so)e(it)f(is)g(a)h(fractional)g(ideal,)i(and)d Ff(I)104
b Fj(O)24339 71213 y Fi(K)25637 71014 y Fl(=)386 b Fj(O)28093
71213 y Fi(K)29448 71014 y Fl(for)445 b(an)-36 b(y)444
b(nonzero)g(ideal)h Ff(I)104 b Fl(,)447 b(so)d(to)g(pro)-36
b(v)g(e)2158 72620 y(that)524 b(the)g(set)h(of)g(fractional)g(ideals)h
(under)d(m)-36 b(ultiplication)524 b(is)h(a)g(group)f(it)g(su\261ces)h
(to)f(sho)-36 b(w)2158 74225 y(the)507 b(existence)h(of)h(in)-36
b(v)g(erses.)800 b(W)-108 b(e)508 b(will)h(\257rst)d(pro)-36
b(v)g(e)508 b(that)f(if)h Fc(p)g Fl(is)f(a)h(prime)f(ideal,)527
b(then)507 b Fc(p)g Fl(has)25578 78073 y(3)p eop end
%%Page: 4 4
TeXDict begin 4 3 bop 2158 5648 a Fl(an)430 b(in)-36
b(v)g(erse,)431 b(then)d(w)-36 b(e)430 b(will)h(pro)-36
b(v)g(e)430 b(that)f(nonzero)g(in)-36 b(tegral)430 b(ideals)g(ha)-36
b(v)g(e)430 b(in)-36 b(v)g(erses,)431 b(and)e(\257nally)2158
7254 y(observ)-36 b(e)434 b(that)f(ev)-36 b(ery)435 b(fractional)g
(ideal)f(has)f(an)h(in)-36 b(v)g(erse.)4109 8859 y(Supp)36
b(ose)433 b Fc(p)g Fl(is)h(a)g(nonzero)f(prime)h(ideal)g(of)g
Fj(O)26874 9058 y Fi(K)27785 8859 y Fl(.)578 b(W)-108
b(e)434 b(will)h(sho)-36 b(w)434 b(that)f(the)g Fj(O)42760
9058 y Fi(K)43671 8859 y Fl(-mo)36 b(dule)19177 11463
y Ff(I)473 b Fl(=)369 b Fj(f)p Ff(a)g Fj(2)f Ff(K)464
b Fl(:)370 b Ff(a)p Fc(p)e Fj(\275)h(O)31053 11662 y
Fi(K)31964 11463 y Fj(g)2158 14068 y Fl(is)434 b(a)g(fractional)h
(ideal)f(of)h Fj(O)16014 14267 y Fi(K)17358 14068 y Fl(suc)-36
b(h)433 b(that)g Ff(I)104 b Fc(p)369 b Fl(=)f Fj(O)27260
14267 y Fi(K)28171 14068 y Fl(,)434 b(so)g(that)f Ff(I)538
b Fl(is)434 b(an)f(in)-36 b(v)g(erse)434 b(of)g Fc(p)p
Fl(.)4109 15673 y(F)-108 b(or)436 b(the)g(rest)g(of)h(the)f(pro)36
b(of,)438 b(\257x)f(a)f(nonzero)h(elemen)-36 b(t)436
b Ff(b)373 b Fj(2)h Fc(p)p Fl(.)586 b(Since)436 b Ff(I)541
b Fl(is)436 b(an)h Fj(O)43787 15872 y Fi(K)44698 15673
y Fl(-mo)36 b(dule,)2158 17278 y Ff(bI)756 b Fj(\275)651
b(O)6783 17477 y Fi(K)8294 17278 y Fl(is)599 b(an)h Fj(O)12798
17477 y Fi(K)14308 17278 y Fl(ideal,)642 b(hence)599
b Ff(I)703 b Fl(is)600 b(a)g(fractional)h(ideal.)1076
b(Since)599 b Fj(O)40477 17477 y Fi(K)42039 17278 y Fj(\275)652
b Ff(I)703 b Fl(w)-36 b(e)600 b(ha)-36 b(v)g(e)2158 18883
y Fc(p)536 b Fj(\275)h Ff(I)104 b Fc(p)536 b Fj(\275)g(O)9435
19082 y Fi(K)10346 18883 y Fl(,)556 b(hence)531 b(either)h
Fc(p)k Fl(=)f Ff(I)104 b Fc(p)532 b Fl(or)g Ff(I)104
b Fc(p)536 b Fl(=)g Fj(O)29554 19082 y Fi(K)30464 18883
y Fl(.)873 b(If)533 b Ff(I)104 b Fc(p)536 b Fl(=)f Fj(O)37581
19082 y Fi(K)38492 18883 y Fl(,)557 b(w)-36 b(e)532 b(are)g(done)f
(since)2158 20488 y(then)476 b Ff(I)580 b Fl(is)477 b(an)f(in)-36
b(v)g(erse)476 b(of)h Fc(p)p Fl(.)706 b(Th)-36 b(us)476
b(supp)36 b(ose)476 b(that)f Ff(I)104 b Fc(p)442 b Fl(=)f
Fc(p)p Fl(.)706 b(Our)475 b(strategy)i(is)g(to)f(sho)-36
b(w)477 b(that)2158 22093 y(there)505 b(is)g(some)g Ff(d)491
b Fj(2)f Ff(I)609 b Fl(not)505 b(in)g Fj(O)19020 22292
y Fi(K)19930 22093 y Fl(;)541 b(suc)-36 b(h)505 b(a)g
Ff(d)g Fl(w)-36 b(ould)505 b(lea)-36 b(v)g(e)506 b Fc(p)e
Fl(in)-36 b(v)-72 b(arian)-36 b(t)505 b(\(i.e.,)524 b
Ff(d)p Fc(p)490 b Fj(\275)h Fc(p)p Fl(\),)523 b(so)2158
23698 y(since)434 b Fc(p)f Fl(is)h(an)g Fj(O)10616 23897
y Fi(K)11527 23698 y Fl(-mo)36 b(dule)433 b(it)g(will)i(follo)-36
b(w)436 b(that)d Ff(d)369 b Fj(2)f(O)30239 23897 y Fi(K)31150
23698 y Fl(,)434 b(a)g(con)-36 b(tradiction.)4109 25303
y(By)435 b(Lemma)e(1.9,)i(w)-36 b(e)434 b(can)f(c)-36
b(ho)36 b(ose)434 b(a)g(pro)36 b(duct)433 b Fc(p)28302
25502 y Fd(1)28827 25303 y Ff(;)221 b(:)g(:)g(:)j(;)d
Fc(p)32405 25502 y Fi(m)33293 25303 y Fl(,)434 b(with)f
Ff(m)h Fl(minimal,)g(suc)-36 b(h)433 b(that)19873 27908
y Fc(p)20538 28107 y Fd(1)21064 27908 y Fc(p)21729 28107
y Fd(2)22476 27908 y Fj(\242)221 b(\242)g(\242)h Fc(p)24912
28107 y Fi(m)26168 27908 y Fj(\275)370 b Fl(\()p Ff(b)p
Fl(\))e Fj(\275)h Fc(p)p Ff(:)2158 30512 y Fl(If)456
b(no)e Fc(p)5972 30711 y Fi(i)6802 30512 y Fl(is)h(con)-36
b(tained)454 b(in)h Fc(p)p Fl(,)460 b(then)453 b(w)-36
b(e)455 b(can)g(c)-36 b(ho)36 b(ose)455 b(for)g(eac)-36
b(h)454 b Ff(i)h Fl(an)f Ff(a)36902 30711 y Fi(i)37683
30512 y Fj(2)404 b Fc(p)39638 30711 y Fi(i)40468 30512
y Fl(with)455 b Ff(a)44135 30711 y Fi(i)44915 30512 y
Fj(62)404 b Fc(p)p Fl(;)465 b(but)2158 32117 y(then)5187
31121 y Fb(Q)6663 32117 y Ff(a)7346 32316 y Fi(i)8202
32117 y Fj(2)481 b Fc(p)p Fl(,)516 b(whic)-36 b(h)499
b(con)-36 b(tradicts)499 b(that)g Fc(p)h Fl(is)f(a)h(prime)f(ideal.)777
b(Th)-36 b(us)499 b(some)g Fc(p)43139 32316 y Fi(i)43515
32117 y Fl(,)516 b(sa)-36 b(y)500 b Fc(p)47370 32316
y Fd(1)47896 32117 y Fl(,)516 b(is)2158 33722 y(con)-36
b(tained)342 b(in)g Fc(p)p Fl(,)361 b(whic)-36 b(h)342
b(implies)g(that)g Fc(p)22114 33921 y Fd(1)23009 33722
y Fl(=)368 b Fc(p)342 b Fl(since)g(ev)-36 b(ery)343 b(nonzero)f(prime)g
(ideal)h(is)f(maximal.)2158 35327 y(Because)495 b Ff(m)e
Fl(is)i(minimal,)510 b Fc(p)16354 35526 y Fd(2)17101
35327 y Fj(\242)221 b(\242)g(\242)h Fc(p)19537 35526
y Fi(m)20918 35327 y Fl(is)494 b(not)g(a)g(subset)g(of)g(\()p
Ff(b)p Fl(\),)509 b(so)495 b(there)e(exists)i Ff(c)471
b Fj(2)h Fc(p)45577 35526 y Fd(2)46324 35327 y Fj(\242)221
b(\242)g(\242)h Fc(p)48760 35526 y Fi(m)2158 36932 y
Fl(that)447 b(do)36 b(es)447 b(not)f(lie)i(in)e(\()p
Ff(b)p Fl(\).)618 b(Then)447 b Fc(p)p Fl(\()p Ff(c)p
Fl(\))390 b Fj(\275)i Fl(\()p Ff(b)p Fl(\),)450 b(so)d(b)-36
b(y)447 b(de\257nition)f(of)i Ff(I)550 b Fl(w)-36 b(e)448
b(ha)-36 b(v)g(e)447 b Ff(d)391 b Fl(=)g Ff(c=b)h Fj(2)f
Ff(I)104 b Fl(.)2158 38538 y(Ho)-36 b(w)g(ev)g(er,)491
b Ff(d)445 b Fj(62)f(O)11323 38737 y Fi(K)12234 38538
y Fl(,)490 b(since)478 b(if)h(it)g(w)-36 b(ere)478 b(then)f
Ff(c)h Fl(w)-36 b(ould)479 b(b)36 b(e)478 b(in)g(\()p
Ff(b)p Fl(\).)712 b(W)-108 b(e)478 b(ha)-36 b(v)g(e)479
b(th)-36 b(us)477 b(found)h(our)2158 40143 y(elemen)-36
b(t)515 b Ff(d)508 b Fj(2)f Ff(I)619 b Fl(that)515 b(do)36
b(es)515 b(not)g(lie)h(in)f Fj(O)23597 40342 y Fi(K)24508
40143 y Fl(.)823 b(T)-108 b(o)515 b(\257nish)f(the)h(pro)36
b(of)515 b(that)g Fc(p)g Fl(has)g(an)g(in)-36 b(v)g(erse,)2158
41748 y(w)g(e)441 b(observ)-36 b(e)440 b(that)f Ff(d)h
Fl(preserv)-36 b(es)439 b(the)h Fj(O)21547 41947 y Fi(K)22457
41748 y Fl(-mo)36 b(dule)440 b Fc(p)p Fl(,)h(and)e(is)i(hence)e(in)g
Fj(O)39003 41947 y Fi(K)39914 41748 y Fl(,)j(a)e(con)-36
b(tradiction.)2158 43353 y(More)361 b(precisely)-108
b(,)375 b(if)361 b Ff(b)12629 43552 y Fd(1)13155 43353
y Ff(;)221 b(:)g(:)g(:)j(;)d(b)16621 43552 y Fi(n)17608
43353 y Fl(is)361 b(a)g(basis)f(for)h Fc(p)f Fl(as)h(a)f
Fg(Z)p Fl(-mo)36 b(dule,)375 b(then)360 b(the)g(action)g(of)h
Ff(d)g Fl(on)f Fc(p)g Fl(is)2158 44958 y(giv)-36 b(en)431
b(b)-36 b(y)430 b(a)h(matrix)g(with)f(en)-36 b(tries)430
b(in)g Fg(Z)p Fl(,)h(so)g(the)e(minimal)i(p)36 b(olynomial)432
b(of)f Ff(d)f Fl(has)g(co)36 b(e\261cien)-36 b(ts)2158
46563 y(in)403 b Fg(Z)p Fl(.)568 b(This)403 b(implies)f(that)g
Ff(d)h Fl(is)f(in)-36 b(tegral)403 b(o)-36 b(v)g(er)403
b Fg(Z)p Fl(,)409 b(so)403 b Ff(d)369 b Fj(2)f(O)32010
46762 y Fi(K)32921 46563 y Fl(,)409 b(since)402 b Fj(O)37904
46762 y Fi(K)39218 46563 y Fl(is)g(in)-36 b(tegrally)404
b(closed)2158 48168 y(b)-36 b(y)427 b(Prop)36 b(osition)427
b(1.3.)577 b(\(Note)427 b(ho)-36 b(w)427 b(this)f(argumen)-36
b(t)426 b(dep)36 b(ends)425 b(strongly)i(on)g(the)f(fact)h(that)f
Fj(O)48736 48367 y Fi(K)2158 49773 y Fl(is)434 b(in)-36
b(tegrally)435 b(closed!\))4109 51378 y(So)542 b(far)g(w)-36
b(e)541 b(ha)-36 b(v)g(e)542 b(pro)-36 b(v)g(ed)541 b(that)f(if)i
Fc(p)g Fl(is)f(a)h(prime)f(ideal)h(of)g Fj(O)35277 51577
y Fi(K)36188 51378 y Fl(,)568 b(then)541 b Fc(p)40853
50896 y Fe(\241)p Fd(1)42662 51378 y Fl(=)552 b Fj(f)p
Ff(a)h Fj(2)f Fg(K)g Fl(:)2158 52983 y Ff(a)p Fc(p)654
b Fj(\275)g(O)6905 53182 y Fi(K)7816 52983 y Fj(g)602
b Fl(is)f(the)g(in)-36 b(v)g(erse)601 b(of)h Fc(p)f Fl(in)g(the)f
(monoid)h(of)h(nonzero)f(fractional)h(ideals)g(of)g Fj(O)48375
53182 y Fi(K)49286 52983 y Fl(.)2158 54588 y(As)510 b(men)-36
b(tioned)509 b(after)h(De\257nition)f(1.6,)530 b(ev)-36
b(ery)510 b(nonzero)f(fractional)i(ideal)f(is)g(of)g(the)f(form)h
Ff(aI)2158 56194 y Fl(for)631 b Ff(a)702 b Fj(2)g Ff(K)724
b Fl(and)629 b Ff(I)734 b Fl(an)630 b(in)-36 b(tegral)629
b(ideal,)680 b(so)630 b(since)f(\()p Ff(a)p Fl(\))g(has)h(in)-36
b(v)g(erse)629 b(\(1)p Ff(=a)p Fl(\),)679 b(it)630 b(su\261ces)f(to)
2158 57799 y(sho)-36 b(w)612 b(that)f(ev)-36 b(ery)612
b(in)-36 b(tegral)611 b(ideal)h Ff(I)716 b Fl(has)611
b(an)g(in)-36 b(v)g(erse.)1112 b(If)612 b(not,)655 b(then)611
b(there)f(is)i(a)f(nonzero)2158 59404 y(in)-36 b(tegral)463
b(ideal)h Ff(I)566 b Fl(that)462 b(is)h(maximal)h(among)f(all)h
(nonzero)e(in)-36 b(tegral)463 b(ideals)g(that)f(do)h(not)f(ha)-36
b(v)g(e)2158 61009 y(an)436 b(in)-36 b(v)g(erse.)586
b(Ev)-36 b(ery)436 b(ideal)h(is)f(con)-36 b(tained)435
b(in)h(a)g(maximal)i(ideal,)f(so)f(there)g(is)g(a)g(nonzero)g(prime)
2158 62614 y(ideal)570 b Fc(p)e Fl(suc)-36 b(h)568 b(that)g
Ff(I)703 b Fj(\275)600 b Fc(p)p Fl(.)983 b(Then)568 b
Ff(I)703 b Fj(\275)600 b Fc(p)24681 62132 y Fe(\241)p
Fd(1)25938 62614 y Ff(I)703 b Fj(\275)599 b(O)29905 62813
y Fi(K)30816 62614 y Fl(.)984 b(If)569 b Ff(I)703 b Fl(=)599
b Fc(p)37149 62132 y Fe(\241)p Fd(1)38407 62614 y Ff(I)104
b Fl(,)602 b(then)568 b(\(arguing)h(as)2158 64219 y(in)576
b(the)f(previous)h(paragraph\))f(eac)-36 b(h)576 b(elemen)-36
b(t)575 b(of)i Fc(p)28683 63737 y Fe(\241)p Fd(1)30516
64219 y Fl(preserv)-36 b(es)575 b(that)g Fj(O)40254 64418
y Fi(K)41165 64219 y Fl(-ideal)h Ff(I)680 b Fl(and)575
b(is)2158 65824 y(hence)499 b(in)-36 b(tegral,)517 b(so)499
b Fc(p)13341 65342 y Fe(\241)p Fd(1)15080 65824 y Fj(\275)481
b(O)17652 66023 y Fi(K)18563 65824 y Fl(,)516 b(whic)-36
b(h)499 b(implies)g(that)g Fj(O)31649 66023 y Fi(K)33041
65824 y Fl(=)481 b Fc(pp)35864 65342 y Fe(\241)p Fd(1)37602
65824 y Fj(\275)g Fc(p)p Fl(,)516 b(a)499 b(con)-36 b(tradiction.)2158
67429 y(Th)g(us)528 b Ff(I)633 b Fj(6)p Fl(=)529 b Fc(p)8961
66947 y Fe(\241)p Fd(1)10218 67429 y Ff(I)104 b Fl(.)861
b(Because)528 b Ff(I)632 b Fl(is)528 b(maximal)h(among)g(ideals)f(that)
f(do)h(not)f(ha)-36 b(v)g(e)528 b(an)g(in)-36 b(v)g(erse,)2158
69034 y(the)553 b(ideal)h Fc(p)8410 68552 y Fe(\241)p
Fd(1)9668 69034 y Ff(I)657 b Fl(do)36 b(es)554 b(ha)-36
b(v)g(e)553 b(an)g(in)-36 b(v)g(erse,)584 b(call)554
b(it)g Ff(J)123 b Fl(.)937 b(Then)553 b Fc(p)p Ff(J)677
b Fl(is)553 b(the)g(in)-36 b(v)g(erse)553 b(of)i Ff(I)104
b Fl(,)583 b(since)2158 70639 y Fj(O)3216 70838 y Fi(K)4496
70639 y Fl(=)369 b(\()p Fc(p)p Ff(J)123 b Fl(\)\()p Fc(p)9567
70157 y Fe(\241)p Fd(1)10824 70639 y Ff(I)104 b Fl(\))368
b(=)h Ff(J)123 b(I)104 b Fl(.)p 48707 70639 45 878 v
48752 69806 781 45 v 48752 70639 V 49532 70639 45 878
v 4109 73147 a(W)-108 b(e)376 b(can)g(\257nally)h(deduce)e(the)g
(crucial)i(Theorem)f(1.11,)389 b(whic)-36 b(h)376 b(will)h(allo)-36
b(w)378 b(us)d(to)i(sho)-36 b(w)376 b(that)2158 74752
y(an)-36 b(y)566 b(nonzero)f(ideal)g(of)h(a)f(Dedekind)g(domain)h(can)f
(b)36 b(e)564 b(expressed)h(uniquely)h(as)f(a)g(pro)36
b(duct)25578 78073 y(4)p eop end
%%Page: 5 5
TeXDict begin 5 4 bop 2158 5648 a Fl(of)527 b(primes)e(\(up)f(to)h
(order\).)854 b(Th)-36 b(us)524 b(unique)h(factorization)i(holds)e(for)
h(ideals)g(in)g(a)f(Dedekind)2158 7254 y(domain,)442
b(and)e(it)g(is)g(this)g(unique)g(factorization)h(that)f(initially)h
(motiv)-72 b(ated)441 b(the)e(in)-36 b(tro)36 b(duction)2158
8859 y(of)435 b(rings)e(of)i(in)-36 b(tegers)433 b(of)h(n)-36
b(um)g(b)36 b(er)432 b(\257elds)i(o)-36 b(v)g(er)434
b(a)f(cen)-36 b(tury)433 b(ago.)2158 11058 y Fg(Theorem)549
b(1.10.)576 b Fk(Supp)-66 b(ose)504 b Ff(I)608 b Fk(is)504
b(an)g(inte)-66 b(gr)g(al)501 b(ide)-66 b(al)504 b(of)f
Fj(O)32081 11257 y Fi(K)32992 11058 y Fk(.)715 b(Then)503
b Ff(I)609 b Fk(c)-66 b(an)503 b(b)-66 b(e)503 b(written)g(as)h(a)2158
12663 y(pr)-66 b(o)g(duct)22452 14268 y Ff(I)473 b Fl(=)369
b Fc(p)25545 14467 y Fd(1)26292 14268 y Fj(\242)221 b(\242)g(\242)h
Fc(p)28728 14467 y Fi(n)2158 16336 y Fk(of)461 b(prime)g(ide)-66
b(als)461 b(of)g Fj(O)13580 16535 y Fi(K)14490 16336
y Fk(,)h(and)f(this)g(r)-66 b(epr)g(esentation)459 b(is)i(unique)f(up)i
(to)f(or)-66 b(der.)596 b(\(Exc)-66 b(eption:)594 b(If)2158
17941 y Ff(I)474 b Fl(=)368 b(0)p Fk(,)465 b(then)f(the)h(r)-66
b(epr)g(esentation)462 b(is)j(not)f(unique.\))2158 20141
y(Pr)-66 b(o)g(of.)650 b Fl(Supp)36 b(ose)611 b Ff(I)717
b Fl(is)613 b(an)g(ideal)h(that)e(is)h(maximal)h(among)g(the)e(set)h
(of)g(all)h(ideals)g(in)e Fj(O)48736 20340 y Fi(K)2158
21746 y Fl(that)651 b(can)g(not)g(b)36 b(e)650 b(written)h(as)h(a)f
(pro)36 b(duct)650 b(of)i(primes.)1230 b(Ev)-36 b(ery)652
b(ideal)f(is)h(con)-36 b(tained)650 b(in)h(a)2158 23351
y(maximal)602 b(ideal,)642 b(so)601 b Ff(I)704 b Fl(is)600
b(con)-36 b(tained)600 b(in)f(a)i(nonzero)e(prime)h(ideal)h
Fc(p)p Fl(.)1077 b(If)601 b Ff(I)104 b Fc(p)41864 22869
y Fe(\241)p Fd(1)43773 23351 y Fl(=)652 b Ff(I)104 b
Fl(,)642 b(then)2158 24956 y(b)-36 b(y)455 b(Theorem)g(1.7)h(w)-36
b(e)455 b(can)g(cancel)g Ff(I)559 b Fl(from)455 b(b)36
b(oth)454 b(sides)h(of)h(this)e(equation)i(to)f(see)g(that)f
Fc(p)46973 24474 y Fe(\241)p Fd(1)48636 24956 y Fl(=)2158
26561 y Fj(O)3216 26760 y Fi(K)4127 26561 y Fl(,)607
b(a)572 b(con)-36 b(tradiction.)994 b(Th)-36 b(us)571
b Ff(I)676 b Fl(is)572 b(strictly)h(con)-36 b(tained)571
b(in)h Ff(I)104 b Fc(p)34896 26079 y Fe(\241)p Fd(1)36154
26561 y Fl(,)607 b(so)572 b(b)-36 b(y)572 b(our)f(maximalit)-36
b(y)2158 28166 y(assumption)620 b(on)g Ff(I)725 b Fl(there)619
b(are)i(maximal)h(ideals)f Fc(p)28351 28365 y Fd(1)28876
28166 y Ff(;)221 b(:)g(:)g(:)j(;)d Fc(p)32454 28365 y
Fi(n)33701 28166 y Fl(suc)-36 b(h)619 b(that)h Ff(I)104
b Fc(p)41169 27684 y Fe(\241)p Fd(1)43113 28166 y Fl(=)687
b Fc(p)45477 28365 y Fd(1)46224 28166 y Fj(\242)221 b(\242)g(\242)h
Fc(p)48660 28365 y Fi(n)49286 28166 y Fl(.)2158 29771
y(Then)408 b Ff(I)473 b Fl(=)368 b Fc(p)242 b Fj(\242)g
Fc(p)10139 29970 y Fd(1)10886 29771 y Fj(\242)221 b(\242)g(\242)h
Fc(p)13322 29970 y Fi(n)13948 29771 y Fl(,)413 b(a)408
b(con)-36 b(tradiction.)569 b(Th)-36 b(us)407 b(ev)-36
b(ery)409 b(ideal)f(can)f(b)36 b(e)407 b(written)h(as)g(a)f(pro)36
b(duct)2158 31376 y(of)435 b(primes.)4109 32982 y(Supp)36
b(ose)451 b Fc(p)9894 33181 y Fd(1)10641 32982 y Fj(\242)221
b(\242)g(\242)h Fc(p)13077 33181 y Fi(n)14102 32982 y
Fl(=)399 b Fc(q)16163 33181 y Fd(1)16910 32982 y Fj(\242)221
b(\242)g(\242)h Fc(q)19331 33181 y Fi(m)20219 32982 y
Fl(.)631 b(If)453 b(no)e Fc(q)25004 33181 y Fi(i)25831
32982 y Fl(is)g(con)-36 b(tained)451 b(in)h Fc(p)35264
33181 y Fd(1)35789 32982 y Fl(,)k(then)451 b(for)h(eac)-36
b(h)451 b Ff(i)g Fl(there)g(is)2158 34587 y(an)479 b
Ff(a)4693 34786 y Fi(i)5515 34587 y Fj(2)445 b Fc(q)7496
34786 y Fi(i)8350 34587 y Fl(suc)-36 b(h)478 b(that)h
Ff(a)14876 34786 y Fi(i)15697 34587 y Fj(62)446 b Fc(p)17694
34786 y Fd(1)18219 34587 y Fl(.)714 b(But)479 b(the)f(pro)36
b(duct)478 b(of)h(the)f Ff(a)33625 34786 y Fi(i)34480
34587 y Fl(is)h(in)g(the)f Fc(p)40346 34786 y Fd(1)41093
34587 y Fj(\242)221 b(\242)g(\242)h Fc(p)43529 34786
y Fi(n)44155 34587 y Fl(,)490 b(whic)-36 b(h)479 b(is)2158
36192 y(a)451 b(subset)e(of)h Fc(p)9426 36391 y Fd(1)9952
36192 y Fl(,)k(whic)-36 b(h)449 b(con)-36 b(tradicts)450
b(the)f(fact)i(that)e Fc(p)29549 36391 y Fd(1)30524 36192
y Fl(is)h(a)h(prime)e(ideal.)628 b(Th)-36 b(us)449 b
Fc(q)44273 36391 y Fi(i)45045 36192 y Fl(=)396 b Fc(p)47118
36391 y Fd(1)48094 36192 y Fl(for)2158 37797 y(some)502
b Ff(i)p Fl(.)780 b(W)-108 b(e)502 b(can)f(th)-36 b(us)500
b(cancel)h Fc(q)19378 37996 y Fi(i)20255 37797 y Fl(and)f
Fc(p)23516 37996 y Fd(1)24543 37797 y Fl(from)h(b)36
b(oth)501 b(sides)g(of)h(the)e(equation.)782 b(Rep)36
b(eating)2158 39402 y(this)434 b(argumen)-36 b(t)433
b(\257nishes)f(the)h(pro)36 b(of)435 b(of)f(uniqueness.)p
48707 39402 45 878 v 48752 38568 781 45 v 48752 39402
V 49532 39402 45 878 v 2158 41601 a Fg(Corollary)774
b(1.11.)666 b Fk(If)h Ff(I)771 b Fk(is)667 b(a)g(fr)-66
b(actional)665 b(ide)-66 b(al)667 b(of)g Fj(O)30723 41800
y Fi(K)32301 41601 y Fk(then)f(ther)-66 b(e)666 b(exists)g(prime)h(ide)
-66 b(als)2158 43206 y Fc(p)2823 43405 y Fd(1)3349 43206
y Ff(;)221 b(:)g(:)g(:)j(;)d Fc(p)6927 43405 y Fi(n)8018
43206 y Fk(and)465 b Fc(q)11192 43405 y Fd(1)11718 43206
y Ff(;)221 b(:)g(:)g(:)j(;)d Fc(q)15281 43405 y Fi(m)16169
43206 y Fk(,)464 b(unique)g(up)i(to)f(or)-66 b(der,)464
b(such)h(that)18278 45542 y Ff(I)473 b Fl(=)369 b(\()p
Fc(p)21877 45741 y Fd(1)22624 45542 y Fj(\242)221 b(\242)g(\242)h
Fc(p)25060 45741 y Fi(n)25686 45542 y Fl(\)\()p Fc(q)27348
45741 y Fd(1)28094 45542 y Fj(\242)f(\242)g(\242)h Fc(q)30515
45741 y Fi(m)31403 45542 y Fl(\))31909 44993 y Fe(\241)p
Fd(1)33166 45542 y Ff(:)2158 47877 y Fk(Pr)-66 b(o)g(of.)650
b Fl(W)-108 b(e)600 b(ha)-36 b(v)g(e)600 b Ff(I)757 b
Fl(=)652 b(\()p Ff(a=b)p Fl(\))p Ff(J)723 b Fl(for)601
b(some)f Ff(a;)221 b(b)653 b Fj(2)g(O)29784 48076 y Fi(K)31295
47877 y Fl(and)599 b(in)-36 b(tegral)601 b(ideal)g Ff(J)123
b Fl(.)1078 b(Applying)2158 49482 y(Theorem)486 b(1.11)h(to)f(\()p
Ff(a)p Fl(\),)499 b(\()p Ff(b)p Fl(\),)g(and)485 b Ff(J)609
b Fl(giv)-36 b(es)486 b(an)g(expression)g(as)g(claimed.)736
b(F)-108 b(or)485 b(uniqueness,)499 b(if)2158 51087 y(one)525
b(has)f(t)-36 b(w)g(o)524 b(suc)-36 b(h)523 b(pro)36
b(duct)523 b(expressions,)548 b(m)-36 b(ultiply)524 b(through)f(b)-36
b(y)524 b(the)g(denominators)g(and)2158 52692 y(use)434
b(the)f(uniqueness)g(part)g(of)h(Theorem)g(1.11)p 48707
52692 V 48752 51858 781 45 v 48752 52692 V 49532 52692
45 878 v 2158 57041 a Fh(2)2152 b(Using)716 b(MA)-60
b(GMA)2158 59961 y Fl(This)540 b(section)g(is)h(a)f(\257rst)f(in)-36
b(tro)36 b(duction)538 b(to)i(MA)-36 b(GMA,)540 b(whic)-36
b(h)539 b(is)h(an)g(excellen)-36 b(t)540 b(pac)-36 b(k)-72
b(age)541 b(for)2158 61566 y(doing)635 b(algebraic)i(n)-36
b(um)g(b)36 b(er)633 b(theory)i(computations.)1182 b(Y)-108
b(ou)634 b(can)h(use)g(it)g(via)h(the)e(w)-36 b(eb)635
b(page)2158 63172 y Fa(http://modular.fas.harvard.edu/calc)p
Fl(.)857 b(MA)-36 b(GMA)531 b(is)h(not)f(free,)557 b(but)531
b(if)h(y)-36 b(ou)532 b(w)-36 b(ould)2158 64777 y(lik)g(e)403
b(a)e(cop)-36 b(y)402 b(for)f(y)-36 b(our)402 b(p)36
b(ersonal)401 b(computer,)407 b(send)401 b(me)g(an)g(email,)409
b(and)400 b(I)i(can)f(arrange)g(for)h(y)-36 b(ou)2158
66382 y(to)333 b(obtain)g(a)g(legal)h(cop)-36 b(y)333
b(for)h(free.)545 b(\(Sa)-36 b(y)333 b(something)g(ab)36
b(out)332 b(m)-36 b(y)333 b(visiting)h(MA)-36 b(GMA)332
b(in)h(Sydney)2158 67987 y(three)433 b(times,)h(and)f(ho)-36
b(w)434 b(MA)-36 b(GMA)433 b(compares)g(to)h(Maple,)g(Mathematica,)g
(and)f(P)-108 b(ARI.\))3748 70347 y(1.)651 b(MA)-36 b(GMA)433
b(w)-36 b(eb)433 b(page)3748 72888 y(2.)651 b(Example)432
b(co)36 b(de)431 b(to)g(illustrate)h(things)e(so)i(far)f(in)g(course,)h
(and)f(relev)-72 b(an)-36 b(t)431 b(to)g(eac)-36 b(h)431
b(home-)5410 74494 y(w)-36 b(ork)435 b(problems.)577
b(Exp)36 b(erimen)-36 b(t)434 b(with)f(studen)-36 b(ts)432
b(suggesting)i(what)g(examples)g(to)g(try)-108 b(.)25578
78073 y(5)p eop end
%%Page: 6 6
TeXDict begin 6 5 bop 2158 5648 a Fh(3)2152 b(Algorithms)716
b(for)h(Algebraic)g(Num)-60 b(b)60 b(er)716 b(Theory)2158
8569 y Fl(The)555 b(b)36 b(est)554 b(o)-36 b(v)g(erall)556
b(reference)e(for)h(algorithms)g(for)g(doing)g(basic)g(algebraic)g(n)
-36 b(um)g(b)36 b(er)553 b(theory)2158 10174 y(computations)438
b(is)g(Henri)g(Cohen's)g(b)36 b(o)g(ok)439 b Fk(A)469
b(Course)g(in)f(Computational)h(A)-33 b(lgebr)-66 b(aic)467
b(Numb)-66 b(er)2158 11779 y(The)g(ory)p Fl(,)434 b(Springer,)f(GTM)g
(138.)4109 13384 y(Our)593 b(main)g(long-term)g(algorithmic)h(goals)h
(for)e(this)g(course)g(are)h(to)f(understand)e(go)36
b(o)g(d)2158 14989 y(algorithms)435 b(for)f(solving)h(the)e(follo)-36
b(wing)435 b(problems)f(in)f(particular)h(cases:)4096
17701 y Fj(\262)650 b Fg(Ring)411 b(of)f(in)-42 b(tegers:)541
b Fl(Giv)-36 b(en)357 b(a)h(n)-36 b(um)g(b)36 b(er)355
b(\257eld)i Ff(K)452 b Fl(\(b)-36 b(y)357 b(giving)h(a)g(p)36
b(olynomial\),)374 b(compute)5410 19307 y(the)433 b(full)h(ring)g
Fj(O)13658 19506 y Fi(K)15002 19307 y Fl(of)h(in)-36
b(tegers.)4096 22019 y Fj(\262)650 b Fg(Decomp)42 b(osition)566
b(of)d(primes:)693 b Fl(Giv)-36 b(en)490 b(a)h(prime)f(n)-36
b(um)g(b)36 b(er)489 b Ff(p)465 b Fj(2)h Fg(Z)p Fl(,)505
b(\257nd)489 b(the)h(decom-)5410 23624 y(p)36 b(osition)434
b(of)g(the)f(ideal)i Ff(p)p Fj(O)18907 23823 y Fi(K)20251
23624 y Fl(as)f(a)g(pro)36 b(duct)432 b(of)i(prime)g(ideals)g(of)g
Fj(O)39135 23823 y Fi(K)40046 23624 y Fl(.)4096 26336
y Fj(\262)650 b Fg(Class)551 b(group:)669 b Fl(Compute)478
b(the)g(group)f(of)i(equiv)-72 b(alence)480 b(classes)f(of)g(nonzero)f
(ideals)h(of)5410 27941 y Fj(O)6468 28140 y Fi(K)7379
27941 y Fl(,)371 b(where)355 b Ff(I)460 b Fl(and)354
b Ff(J)478 b Fl(are)356 b(equiv)-72 b(alen)-36 b(t)356
b(if)f(there)g(exists)h Ff(\256)378 b Fj(2)368 b(O)36050
28140 y Fi(K)37316 27941 y Fl(suc)-36 b(h)355 b(that)f
Ff(I)104 b(J)44431 27459 y Fe(\241)p Fd(1)46058 27941
y Fl(=)369 b(\()p Ff(\256)8 b Fl(\).)4096 30653 y Fj(\262)650
b Fg(Units:)580 b Fl(Compute)433 b(generators)h(for)g(the)f(group)g(of)
h(units)f(of)i Fj(O)37090 30852 y Fi(K)38000 30653 y
Fl(.)4109 33365 y(As)559 b(w)-36 b(e)558 b(will)h(see,)590
b(somewhat)558 b(surprisingly)h(it)f(turns)f(out)h(that)f
(algorithmically)k(b)-36 b(y)558 b(far)2158 34970 y(the)428
b(most)g(time-consuming)g(step)f(in)i(computing)e(the)h(ring)g(of)h(in)
-36 b(tegers)428 b Fj(O)39899 35169 y Fi(K)41238 34970
y Fl(is)h(to)f(factor)h(the)2158 36575 y(discriminan)-36
b(t)390 b(of)h(a)f(p)36 b(olynomial)392 b(whose)e(ro)36
b(ot)390 b(generates)h(the)e(\257eld)h Ff(K)95 b Fl(.)563
b(The)390 b(algorithm\(s\))h(for)2158 38180 y(computing)448
b Fj(O)9662 38379 y Fi(K)11022 38180 y Fl(are)h(quite)f(complicated)h
(to)g(describ)36 b(e,)452 b(but)c(the)g(\257rst)g(step)g(is)h(to)f
(factor)i(this)2158 39785 y(discriminan)-36 b(t,)578
b(and)548 b(it)g(tak)-36 b(es)550 b(m)-36 b(uc)g(h)547
b(longer)i(in)g(practice)f(than)g(all)i(the)e(other)g(complicated)2158
41390 y(steps.)25578 78073 y(6)p eop end
%%Trailer

userdict /end-hook known{end-hook}if
%%EOF