<div id="pf1" class="pf w0 h0" data-page-no="1"><div class="pc pc1 w0 h0"><img class="bi x0 y0 w1 h0" alt="" src="https://files.passeidireto.com/adb72897-ef92-4b54-a0dc-9a438317dc1a/bg1.png"><div class="t m0 x1 h1 y1 ff1 fs0 fc0 sc0 ls0 ws0">This page in<span class="_0 blank"></span>ten<span class="_0 blank"></span>tionally left blank</div></div><div class="pi" data-data='{"ctm":[1.000000,0.000000,0.000000,1.000000,0.000000,0.000000]}'></div></div> <div id="pf2" class="pf w0 h0" data-page-no="2"><div class="pc pc2 w0 h0"><img class="bi x0 y0 w1 h0" alt="" src="https://files.passeidireto.com/adb72897-ef92-4b54-a0dc-9a438317dc1a/bg2.png"><div class="t m0 x2 h2 y2 ff2 fs1 fc0 sc0 ls1 ws1">[50] Dev<span class="_0 blank"></span>elop computer programs for simplifying sums</div><div class="t m0 x2 h2 y3 ff2 fs1 fc0 sc0 ls1 ws2">that<span class="_1 blank"> </span>in<span class="_0 blank"></span>v<span class="_2 blank"></span>olv<span class="_2 blank"></span>e<span class="_1 blank"> </span>binomial<span class="_1 blank"> </span>co e\ufb03cients<span class="_0 blank"></span>.</div><div class="t m0 x3 h1 y4 ff1 fs0 fc0 sc0 ls2 ws3">Exercise 1.2.6.63 in</div><div class="t m0 x4 h1 y5 ff3 fs0 fc0 sc0 ls3 ws4">The A<span class="_0 blank"></span>rt of Computer Pr<span class="_0 blank"></span>o<span class="_2 blank"></span>gr<span class="_0 blank"></span>am<span class="_0 blank"></span>ming, V<span class="_2 blank"></span>olume 1:<span class="_3 blank"> </span>F<span class="_2 blank"></span>undamen<span class="_0 blank"></span>tal A<span class="_0 blank"></span>lgorithms</div><div class="t m0 x5 h1 y6 ff1 fs0 fc0 sc0 ls4 ws5">b<span class="_0 blank"></span>y Do<span class="_0 blank"></span>nald E<span class="_0 blank"></span>. Kn<span class="_0 blank"></span>uth,</div><div class="t m0 x6 h1 y7 ff1 fs0 fc0 sc0 ls5 ws6">Addison W<span class="_2 blank"></span>esley<span class="_2 blank"></span>, Reading, M<span class="_0 blank"></span>assach<span class="_0 blank"></span>usetts, 1968.</div></div><div class="pi" data-data='{"ctm":[1.000000,0.000000,0.000000,1.000000,0.000000,0.000000]}'></div></div> <div id="pf3" class="pf w0 h0" data-page-no="3"><div class="pc pc3 w0 h0"><img fetchpriority="low" loading="lazy" class="bi x0 y0 w1 h0" alt="" src="https://files.passeidireto.com/adb72897-ef92-4b54-a0dc-9a438317dc1a/bg3.png"><div class="t m0 x7 h3 y8 ff4 fs2 fc0 sc0 lsb">A=B</div><div class="t m0 x8 h4 y9 ff5 fs3 fc0 sc0 lsc ws7">Marko Petk<span class="_0 blank"></span>ov</div><div class="t m0 x9 h4 ya ff5 fs3 fc0 sc0 lsd">\u02c7</div><div class="t m0 x9 h4 y9 ff5 fs3 fc0 sc0 ls6 ws8">sek</div><div class="t m0 xa h5 yb ff5 fs4 fc0 sc0 ls7 ws9">Universi<span class="_0 blank"></span>ty of Ljubljana</div><div class="t m0 xb h5 yc ff5 fs4 fc0 sc0 ls8 wsa">Ljubljana, Slo<span class="_2 blank"></span>venia</div><div class="t m0 xc h4 y9 ff5 fs3 fc0 sc0 lse wsb">Herber<span class="_2 blank"></span>t S. Wilf</div><div class="t m0 xd h5 yb ff5 fs4 fc0 sc0 lsf wsc">Univers<span class="_0 blank"></span>ity of Pennsyl<span class="_4 blank"></span>v<span class="_2 blank"></span>an<span class="_0 blank"></span>ia</div><div class="t m0 xe h5 yc ff5 fs4 fc0 sc0 ls9 wsd">Philadel<span class="_0 blank"></span>phia, P<span class="_4 blank"></span>A, USA</div><div class="t m0 xf h4 yd ff5 fs3 fc0 sc0 ls10 wse">Doron Zeilb<span class="_5 blank"> </span>erger</div><div class="t m0 x9 h5 ye ff5 fs4 fc0 sc0 ls9 wsf">Temple Uni<span class="_0 blank"></span>versity</div><div class="t m0 x10 h5 yf ff5 fs4 fc0 sc0 lsa ws10">Philadelphia, P<span class="_2 blank"></span>A, US<span class="_0 blank"></span>A</div><div class="t m0 x9 h4 y10 ff5 fs3 fc0 sc0 ls11 ws11">April 27, 1997</div></div><div class="pi" data-data='{"ctm":[1.000000,0.000000,0.000000,1.000000,0.000000,0.000000]}'></div></div> <div id="pf4" class="pf w0 h0" data-page-no="4"><div class="pc pc4 w0 h0"><img fetchpriority="low" loading="lazy" class="bi x0 y0 w1 h0" alt="" src="https://files.passeidireto.com/adb72897-ef92-4b54-a0dc-9a438317dc1a/bg4.png"><div class="t m0 x11 h1 y11 ff4 fs0 fc0 sc0 ls12">ii</div></div><div class="pi" data-data='{"ctm":[1.000000,0.000000,0.000000,1.000000,0.000000,0.000000]}'></div></div> <div id="pf5" class="pf w0 h0" data-page-no="5"><div class="pc pc5 w0 h0"><img fetchpriority="low" loading="lazy" class="bi x0 y0 w1 h0" alt="" src="https://files.passeidireto.com/adb72897-ef92-4b54-a0dc-9a438317dc1a/bg5.png"><div class="t m0 x12 h3 y12 ff4 fs2 fc0 sc0 ls14 ws13">Con<span class="_2 blank"></span>ten<span class="_2 blank"></span>ts</div><div class="t m0 x12 h1 y13 ff4 fs0 fc0 sc0 ls15 ws14">F<span class="_4 blank"></span>orew<span class="_0 blank"></span>ord vii</div><div class="t m0 x12 h1 y14 ff4 fs0 fc0 sc0 ls16 ws15">AQ<span class="_6 blank"></span>u<span class="_6 blank"></span>i<span class="_6 blank"></span>c<span class="_7 blank"></span>kS<span class="_6 blank"></span>t<span class="_6 blank"></span>a<span class="_6 blank"></span>r<span class="_6 blank"></span>t<span class="ff6 ls17 ws16 v0">... </span><span class="ls12">ix</span></div><div class="t m0 x12 h4 y15 ff4 fs3 fc0 sc0 ls18 ws17">I Bac<span class="_2 blank"></span>kground<span class="_8 blank"> </span>1</div><div class="t m0 x12 h1 y16 ff4 fs0 fc0 sc0 ls19 ws18">1<span class="_9 blank"> </span>Pro of<span class="_a blank"> </span>Mac<span class="_0 blank"></span>hines<span class="_b blank"> </span>3</div><div class="t m0 x13 h1 y17 ff1 fs0 fc0 sc0 ls13 ws19">1<span class="_c blank"></span>.<span class="_c blank"></span>1<span class="_1 blank"> </span>E<span class="_d blank"></span>v<span class="_d blank"></span>o<span class="_c blank"></span>l<span class="_c blank"></span>u<span class="_d blank"></span>t<span class="_c blank"></span>i<span class="_c blank"></span>o<span class="_c blank"></span>n<span class="_e blank"></span>o<span class="_d blank"></span>f<span class="_e blank"></span>t<span class="_c blank"></span>h<span class="_c blank"></span>e<span class="_e blank"></span>p<span class="_d blank"></span>r<span class="_c blank"></span>o<span class="_d blank"></span>v<span class="_d blank"></span>i<span class="_c blank"></span>n<span class="_f blank"></span>c<span class="_c blank"></span>e<span class="_10 blank"></span>o<span class="_c blank"></span>f<span class="_10 blank"></span>h<span class="_d blank"></span>u<span class="_c blank"></span>m<span class="_d blank"></span>a<span class="_c blank"></span>n<span class="_10 blank"></span>t<span class="_c blank"></span>h<span class="_f blank"></span>o<span class="_d blank"></span>u<span class="_c blank"></span>g<span class="_c blank"></span>h<span class="_d blank"></span>t ..............<span class="_11 blank"> </span>3</div><div class="t m0 x13 h1 y18 ff1 fs0 fc0 sc0 ls13 ws1a">1<span class="_c blank"></span>.<span class="_c blank"></span>2<span class="_1 blank"> </span>C<span class="_d blank"></span>a<span class="_c blank"></span>n<span class="_c blank"></span>o<span class="_c blank"></span>n<span class="_d blank"></span>i<span class="_c blank"></span>c<span class="_c blank"></span>a<span class="_c blank"></span>l<span class="_10 blank"></span>a<span class="_c blank"></span>n<span class="_c blank"></span>d<span class="_10 blank"></span>n<span class="_c blank"></span>o<span class="_c blank"></span>r<span class="_c blank"></span>m<span class="_c blank"></span>a<span class="_c blank"></span>l<span class="_10 blank"></span>f<span class="_c blank"></span>o<span class="_c blank"></span>r<span class="_c blank"></span>m<span class="_c blank"></span>s .......................<span class="_12 blank"> </span>7</div><div class="t m0 x13 h1 y19 ff1 fs0 fc0 sc0 ls13 ws1b">1<span class="_c blank"></span>.<span class="_c blank"></span>3<span class="_1 blank"> </span>P<span class="_13 blank"></span>o<span class="_c blank"></span>l<span class="_c blank"></span>y<span class="_c blank"></span>n<span class="_c blank"></span>o<span class="_c blank"></span>m<span class="_d blank"></span>i<span class="_c blank"></span>a<span class="_c blank"></span>l<span class="_e blank"></span>i<span class="_c blank"></span>d<span class="_d blank"></span>e<span class="_c blank"></span>n<span class="_d blank"></span>t<span class="_c blank"></span>i<span class="_c blank"></span>t<span class="_c blank"></span>i<span class="_c blank"></span>e<span class="_c blank"></span>s ...........................<span class="_12 blank"> </span>8</div><div class="t m0 x13 h1 y1a ff1 fs0 fc0 sc0 ls13 ws1c">1<span class="_c blank"></span>.<span class="_c blank"></span>4 P<span class="_d blank"></span>r<span class="_c blank"></span>o<span class="_14 blank"></span>o<span class="_d blank"></span>f<span class="_c blank"></span>s<span class="_e blank"></span>b<span class="_d blank"></span>y<span class="_10 blank"></span>e<span class="_c blank"></span>x<span class="_d blank"></span>a<span class="_c blank"></span>m<span class="_f blank"></span>p<span class="_c blank"></span>l<span class="_d blank"></span>e<span class="_c blank"></span>?.......................<span class="_0 blank"></span>.....<span class="_11 blank"> </span>9</div><div class="t m0 x13 h1 y1b ff1 fs0 fc0 sc0 ls13 ws1d">1<span class="_c blank"></span>.<span class="_c blank"></span>5<span class="_1 blank"> </span>T<span class="_15 blank"></span>r<span class="_c blank"></span>i<span class="_c blank"></span>g<span class="_c blank"></span>o<span class="_c blank"></span>n<span class="_d blank"></span>o<span class="_c blank"></span>m<span class="_c blank"></span>e<span class="_c blank"></span>t<span class="_c blank"></span>r<span class="_c blank"></span>i<span class="_c blank"></span>c<span class="_10 blank"></span>i<span class="_c blank"></span>d<span class="_c blank"></span>e<span class="_c blank"></span>n<span class="_d blank"></span>t<span class="_c blank"></span>i<span class="_c blank"></span>t<span class="_d blank"></span>i<span class="_c blank"></span>e<span class="_f blank"></span>s ....................<span class="_0 blank"></span>.....<span class="_16 blank"> </span>1<span class="_d blank"></span>1</div><div class="t m0 x13 h1 y1c ff1 fs0 fc0 sc0 ls13 ws1e">1<span class="_c blank"></span>.<span class="_c blank"></span>6<span class="_1 blank"> </span>F<span class="_d blank"></span>i<span class="_c blank"></span>b<span class="_c blank"></span>o<span class="_c blank"></span>n<span class="_c blank"></span>a<span class="_c blank"></span>c<span class="_c blank"></span>c<span class="_c blank"></span>i<span class="_e blank"></span>i<span class="_c blank"></span>d<span class="_d blank"></span>e<span class="_c blank"></span>n<span class="_d blank"></span>t<span class="_c blank"></span>i<span class="_c blank"></span>t<span class="_c blank"></span>i<span class="_c blank"></span>e<span class="_c blank"></span>s............................<span class="_16 blank"> </span>1<span class="_d blank"></span>2</div><div class="t m0 x13 h1 y1d ff1 fs0 fc0 sc0 ls13 ws1f">1<span class="_c blank"></span>.<span class="_c blank"></span>7<span class="_1 blank"> </span>S<span class="_d blank"></span>y<span class="_c blank"></span>m<span class="_c blank"></span>m<span class="_d blank"></span>e<span class="_c blank"></span>t<span class="_c blank"></span>r<span class="_c blank"></span>i<span class="_c blank"></span>c<span class="_10 blank"></span>f<span class="_c blank"></span>u<span class="_c blank"></span>n<span class="_c blank"></span>c<span class="_c blank"></span>t<span class="_c blank"></span>i<span class="_c blank"></span>o<span class="_c blank"></span>n<span class="_10 blank"></span>i<span class="_c blank"></span>d<span class="_c blank"></span>e<span class="_c blank"></span>n<span class="_d blank"></span>t<span class="_d blank"></span>i<span class="_c blank"></span>t<span class="_c blank"></span>i<span class="_f blank"></span>e<span class="_c blank"></span>s .................<span class="_0 blank"></span>.....<span class="_16 blank"> </span>1<span class="_d blank"></span>2</div><div class="t m0 x13 h1 y1e ff1 fs0 fc0 sc0 ls1a ws20">1.8<span class="_17 blank"> </span>Elliptic function identities<span class="_18 blank"> </span><span class="ls13 ws21">........................ 1<span class="_d blank"></span>3</span></div><div class="t m0 x12 h1 y1f ff4 fs0 fc0 sc0 ls1b ws22">2<span class="_9 blank"> </span>Tight<span class="_0 blank"></span>ening<span class="_a blank"> </span>the<span class="_a blank"> </span>T<span class="_4 blank"></span>arget<span class="_19 blank"> </span>17</div><div class="t m0 x13 h1 y20 ff1 fs0 fc0 sc0 ls13 ws1c">2<span class="_c blank"></span>.<span class="_c blank"></span>1 I<span class="_c blank"></span>n<span class="_13 blank"></span>t<span class="_c blank"></span>r<span class="_c blank"></span>o<span class="_f blank"></span>d<span class="_c blank"></span>u<span class="_c blank"></span>c<span class="_c blank"></span>t<span class="_c blank"></span>i<span class="_c blank"></span>o<span class="_c blank"></span>n<span class="_2 blank"></span>...........................<span class="_0 blank"></span>.....<span class="_16 blank"> </span>1<span class="_d blank"></span>7</div><div class="t m0 x13 h1 y21 ff1 fs0 fc0 sc0 ls13 ws1c">2<span class="_c blank"></span>.<span class="_c blank"></span>2 I<span class="_c blank"></span>d<span class="_d blank"></span>e<span class="_f blank"></span>n<span class="_13 blank"></span>t<span class="_c blank"></span>i<span class="_c blank"></span>t<span class="_c blank"></span>i<span class="_c blank"></span>e<span class="_c blank"></span>s<span class="_1a blank"></span>.............................<span class="_0 blank"></span>.....<span class="_16 blank"> </span>2<span class="_d blank"></span>1</div><div class="t m0 x13 h1 y22 ff1 fs0 fc0 sc0 ls13 ws1c">2<span class="_c blank"></span>.<span class="_c blank"></span>3 H<span class="_d blank"></span>u<span class="_c blank"></span>m<span class="_c blank"></span>a<span class="_c blank"></span>n<span class="_10 blank"></span>a<span class="_c blank"></span>n<span class="_c blank"></span>d<span class="_10 blank"></span>c<span class="_c blank"></span>o<span class="_c blank"></span>m<span class="_c blank"></span>p<span class="_c blank"></span>u<span class="_c blank"></span>t<span class="_c blank"></span>e<span class="_c blank"></span>r<span class="_10 blank"></span>p<span class="_c blank"></span>r<span class="_c blank"></span>o<span class="_f blank"></span>o<span class="_c blank"></span>f<span class="_d blank"></span>s<span class="_f blank"></span>;<span class="_10 blank"></span>a<span class="_c blank"></span>n<span class="_10 blank"></span>e<span class="_c blank"></span>x<span class="_c blank"></span>a<span class="_c blank"></span>m<span class="_c blank"></span>p<span class="_d blank"></span>l<span class="_c blank"></span>e<span class="_e blank"></span>................<span class="_16 blank"> </span>2<span class="_d blank"></span>3</div><div class="t m0 x13 h1 y23 ff1 fs0 fc0 sc0 ls13 ws1c">2<span class="_c blank"></span>.<span class="_c blank"></span>4 A<span class="_10 blank"></span>M<span class="_c blank"></span>a<span class="_c blank"></span>t<span class="_c blank"></span>h<span class="_d blank"></span>e<span class="_c blank"></span>m<span class="_c blank"></span>a<span class="_c blank"></span>t<span class="_c blank"></span>i<span class="_c blank"></span>c<span class="_c blank"></span>a<span class="_10 blank"></span>s<span class="_c blank"></span>e<span class="_c blank"></span>s<span class="_c blank"></span>s<span class="_c blank"></span>i<span class="_c blank"></span>o<span class="_c blank"></span>n.....................<span class="_0 blank"></span>.....<span class="_16 blank"> </span>2<span class="_d blank"></span>7</div><div class="t m0 x13 h1 y24 ff1 fs0 fc0 sc0 ls13 ws1c">2<span class="_c blank"></span>.<span class="_c blank"></span>5 A<span class="_10 blank"></span>M<span class="_c blank"></span>a<span class="_c blank"></span>p<span class="_d blank"></span>l<span class="_c blank"></span>e<span class="_e blank"></span>s<span class="_d blank"></span>e<span class="_f blank"></span>s<span class="_c blank"></span>s<span class="_c blank"></span>i<span class="_c blank"></span>o<span class="_d blank"></span>n<span class="_2 blank"></span>..............<span class="_0 blank"></span>................<span class="_16 blank"> </span>2<span class="_d blank"></span>9</div><div class="t m0 x13 h1 y25 ff1 fs0 fc0 sc0 ls13 ws1c">2<span class="_c blank"></span>.<span class="_c blank"></span>6 W<span class="_d blank"></span>h<span class="_c blank"></span>e<span class="_c blank"></span>r<span class="_c blank"></span>e<span class="_10 blank"></span>w<span class="_d blank"></span>e<span class="_10 blank"></span>a<span class="_c blank"></span>r<span class="_c blank"></span>e<span class="_e blank"></span>a<span class="_d blank"></span>n<span class="_f blank"></span>d<span class="_10 blank"></span>w<span class="_c blank"></span>h<span class="_d blank"></span>a<span class="_c blank"></span>t<span class="_10 blank"></span>h<span class="_c blank"></span>a<span class="_c blank"></span>p<span class="_c blank"></span>p<span class="_f blank"></span>e<span class="_c blank"></span>n<span class="_c blank"></span>s<span class="_10 blank"></span>n<span class="_c blank"></span>e<span class="_c blank"></span>x<span class="_c blank"></span>t<span class="_10 blank"></span>..................<span class="_16 blank"> </span>3<span class="_d blank"></span>0</div><div class="t m0 x13 h1 y26 ff1 fs0 fc0 sc0 ls13 ws1c">2<span class="_c blank"></span>.<span class="_c blank"></span>7 E<span class="_d blank"></span>x<span class="_f blank"></span>e<span class="_d blank"></span>r<span class="_c blank"></span>c<span class="_c blank"></span>i<span class="_c blank"></span>s<span class="_c blank"></span>e<span class="_c blank"></span>s<span class="_e blank"></span>..................<span class="_0 blank"></span>................<span class="_16 blank"> </span>3<span class="_d blank"></span>1</div><div class="t m0 x12 h1 y27 ff4 fs0 fc0 sc0 ls1c ws23">3<span class="_9 blank"> </span>The<span class="_1b blank"> </span>Hypergeometric<span class="_1b blank"> </span>Database<span class="_1c blank"> </span>33</div><div class="t m0 x13 h1 y28 ff1 fs0 fc0 sc0 ls13 ws1c">3<span class="_c blank"></span>.<span class="_c blank"></span>1 I<span class="_c blank"></span>n<span class="_13 blank"></span>t<span class="_c blank"></span>r<span class="_c blank"></span>o<span class="_f blank"></span>d<span class="_c blank"></span>u<span class="_c blank"></span>c<span class="_c blank"></span>t<span class="_c blank"></span>i<span class="_c blank"></span>o<span class="_c blank"></span>n<span class="_2 blank"></span>...........................<span class="_0 blank"></span>.....<span class="_16 blank"> </span>3<span class="_d blank"></span>3</div><div class="t m0 x13 h1 y29 ff1 fs0 fc0 sc0 ls13 ws1c">3<span class="_c blank"></span>.<span class="_c blank"></span>2 H<span class="_d blank"></span>y<span class="_c blank"></span>p<span class="_f blank"></span>e<span class="_c blank"></span>r<span class="_c blank"></span>g<span class="_c blank"></span>e<span class="_c blank"></span>o<span class="_c blank"></span>m<span class="_c blank"></span>e<span class="_c blank"></span>t<span class="_c blank"></span>r<span class="_c blank"></span>i<span class="_c blank"></span>c<span class="_10 blank"></span>s<span class="_c blank"></span>e<span class="_c blank"></span>r<span class="_c blank"></span>i<span class="_c blank"></span>e<span class="_d blank"></span>s<span class="_1a blank"></span>......................<span class="_0 blank"></span>.....<span class="_16 blank"> </span>3<span class="_d blank"></span>4</div><div class="t m0 x13 h1 y2a ff1 fs0 fc0 sc0 ls13 ws24">3<span class="_c blank"></span>.<span class="_c blank"></span>3<span class="_1 blank"> </span>H<span class="_d blank"></span>o<span class="_d blank"></span>w<span class="_10 blank"></span>t<span class="_c blank"></span>o<span class="_10 blank"></span>i<span class="_c blank"></span>d<span class="_c blank"></span>e<span class="_c blank"></span>n<span class="_d blank"></span>t<span class="_d blank"></span>i<span class="_c blank"></span>f<span class="_c blank"></span>y<span class="_e blank"></span>a<span class="_10 blank"></span>s<span class="_c blank"></span>e<span class="_c blank"></span>r<span class="_c blank"></span>i<span class="_d blank"></span>e<span class="_f blank"></span>s<span class="_10 blank"></span>a<span class="_c blank"></span>s<span class="_10 blank"></span>h<span class="_d blank"></span>y<span class="_c blank"></span>p<span class="_f blank"></span>e<span class="_c blank"></span>r<span class="_c blank"></span>g<span class="_d blank"></span>e<span class="_f blank"></span>o<span class="_c blank"></span>m<span class="_d blank"></span>e<span class="_c blank"></span>t<span class="_c blank"></span>r<span class="_c blank"></span>i<span class="_c blank"></span>c ...............<span class="_16 blank"> </span>3<span class="_d blank"></span>5</div><div class="t m0 x13 h1 y2b ff1 fs0 fc0 sc0 ls13 ws1c">3<span class="_c blank"></span>.<span class="_c blank"></span>4 S<span class="_d blank"></span>o<span class="_c blank"></span>f<span class="_c blank"></span>t<span class="_d blank"></span>w<span class="_d blank"></span>a<span class="_c blank"></span>r<span class="_c blank"></span>e<span class="_10 blank"></span>t<span class="_c blank"></span>h<span class="_c blank"></span>a<span class="_c blank"></span>t<span class="_10 blank"></span>i<span class="_c blank"></span>d<span class="_c blank"></span>e<span class="_c blank"></span>n<span class="_d blank"></span>t<span class="_c blank"></span>i<span class="_c blank"></span>\ufb01<span class="_c blank"></span>e<span class="_d blank"></span>s<span class="_e blank"></span>h<span class="_d blank"></span>y<span class="_c blank"></span>p<span class="_f blank"></span>e<span class="_d blank"></span>r<span class="_c blank"></span>g<span class="_c blank"></span>e<span class="_c blank"></span>o<span class="_c blank"></span>m<span class="_c blank"></span>e<span class="_c blank"></span>t<span class="_c blank"></span>r<span class="_c blank"></span>i<span class="_c blank"></span>c<span class="_10 blank"></span>s<span class="_c blank"></span>e<span class="_c blank"></span>r<span class="_c blank"></span>i<span class="_c blank"></span>e<span class="_c blank"></span>s<span class="_1a blank"></span>..............<span class="_1d blank"> </span>3<span class="_d blank"></span>9</div></div><div class="pi" data-data='{"ctm":[1.000000,0.000000,0.000000,1.000000,0.000000,0.000000]}'></div></div> <div id="pf6" class="pf w0 h0" data-page-no="6"><div class="pc pc6 w0 h0"><img fetchpriority="low" loading="lazy" class="bi x0 y0 w1 h0" alt="" src="https://files.passeidireto.com/adb72897-ef92-4b54-a0dc-9a438317dc1a/bg6.png"><div class="t m0 x11 h1 y11 ff4 fs0 fc0 sc0 ls12 ws25">iv <span class="ls1e ws26">CONTENTS</span></div><div class="t m0 xa h1 y1 ff1 fs0 fc0 sc0 ls13 ws1c">3<span class="_c blank"></span>.<span class="_c blank"></span>5 S<span class="_d blank"></span>o<span class="_c blank"></span>m<span class="_c blank"></span>e<span class="_10 blank"></span>e<span class="_c blank"></span>n<span class="_d blank"></span>t<span class="_c blank"></span>r<span class="_c blank"></span>i<span class="_c blank"></span>e<span class="_c blank"></span>s<span class="_10 blank"></span>i<span class="_c blank"></span>n<span class="_10 blank"></span>t<span class="_c blank"></span>h<span class="_c blank"></span>e<span class="_10 blank"></span>h<span class="_d blank"></span>y<span class="_c blank"></span>p<span class="_f blank"></span>e<span class="_c blank"></span>r<span class="_c blank"></span>g<span class="_c blank"></span>e<span class="_c blank"></span>o<span class="_c blank"></span>m<span class="_c blank"></span>e<span class="_d blank"></span>t<span class="_c blank"></span>r<span class="_c blank"></span>i<span class="_c blank"></span>c<span class="_10 blank"></span>d<span class="_c blank"></span>a<span class="_c blank"></span>t<span class="_c blank"></span>a<span class="_c blank"></span>b<span class="_c blank"></span>a<span class="_c blank"></span>s<span class="_c blank"></span>e<span class="_0 blank"></span>..............<span class="_1d blank"> </span>4<span class="_c blank"></span>2</div><div class="t m0 xa h1 y2c ff1 fs0 fc0 sc0 ls13 ws27">3<span class="_c blank"></span>.<span class="_c blank"></span>6<span class="_1 blank"> </span>U<span class="_d blank"></span>s<span class="_c blank"></span>i<span class="_d blank"></span>n<span class="_c blank"></span>g<span class="_e blank"></span>t<span class="_c blank"></span>h<span class="_c blank"></span>e<span class="_10 blank"></span>d<span class="_c blank"></span>a<span class="_c blank"></span>t<span class="_c blank"></span>a<span class="_d blank"></span>b<span class="_c blank"></span>a<span class="_c blank"></span>s<span class="_c blank"></span>e ............................<span class="_1d blank"> </span>4<span class="_c blank"></span>4</div><div class="t m0 xa h1 y2d ff1 fs0 fc0 sc0 ls13 ws28">3<span class="_c blank"></span>.<span class="_c blank"></span>7<span class="_1 blank"> </span>I<span class="_d blank"></span>s<span class="_10 blank"></span>t<span class="_c blank"></span>h<span class="_c blank"></span>e<span class="_c blank"></span>r<span class="_c blank"></span>e<span class="_10 blank"></span>r<span class="_c blank"></span>e<span class="_c blank"></span>a<span class="_c blank"></span>l<span class="_d blank"></span>l<span class="_c blank"></span>y<span class="_10 blank"></span>a<span class="_e blank"></span>h<span class="_d blank"></span>y<span class="_c blank"></span>p<span class="_c blank"></span>e<span class="_f blank"></span>r<span class="_c blank"></span>g<span class="_c blank"></span>e<span class="_d blank"></span>o<span class="_c blank"></span>m<span class="_c blank"></span>e<span class="_c blank"></span>t<span class="_c blank"></span>r<span class="_c blank"></span>i<span class="_c blank"></span>c<span class="_10 blank"></span>d<span class="_c blank"></span>a<span class="_c blank"></span>t<span class="_c blank"></span>a<span class="_c blank"></span>b<span class="_c blank"></span>a<span class="_c blank"></span>s<span class="_d blank"></span>e<span class="_f blank"></span>? ...............<span class="_9 blank"> </span>4<span class="_c blank"></span>8</div><div class="t m0 xa h1 y2e ff1 fs0 fc0 sc0 ls13 ws1c">3<span class="_c blank"></span>.<span class="_c blank"></span>8 E<span class="_d blank"></span>x<span class="_c blank"></span>e<span class="_c blank"></span>r<span class="_c blank"></span>c<span class="_c blank"></span>i<span class="_c blank"></span>s<span class="_c blank"></span>e<span class="_c blank"></span>s<span class="_10 blank"></span>..................................<span class="_9 blank"> </span>5<span class="_c blank"></span>0</div><div class="t m0 x2 h4 y2f ff4 fs3 fc0 sc0 ls1f ws29">I<span class="_5 blank"> </span>I<span class="_1e blank"> </span>The Fiv<span class="_0 blank"></span>e Basic Algo<span class="_5 blank"> </span>rithms<span class="_1f blank"> </span>53</div><div class="t m0 x2 h1 y30 ff4 fs0 fc0 sc0 ls20 ws2a">4<span class="_9 blank"> </span>Siste r<span class="_a blank"> </span>Celine\u2019s<span class="_a blank"> </span>Metho<span class="_20 blank"> </span>d<span class="_21 blank"> </span>55</div><div class="t m0 xa h1 y31 ff1 fs0 fc0 sc0 ls13 ws1c">4<span class="_c blank"></span>.<span class="_c blank"></span>1 I<span class="_c blank"></span>n<span class="_13 blank"></span>t<span class="_c blank"></span>r<span class="_c blank"></span>o<span class="_f blank"></span>d<span class="_c blank"></span>u<span class="_c blank"></span>c<span class="_c blank"></span>t<span class="_c blank"></span>i<span class="_c blank"></span>o<span class="_c blank"></span>n<span class="_2 blank"></span>.........................<span class="_0 blank"></span>.......<span class="_1d blank"> </span>5<span class="_c blank"></span>5</div><div class="t m0 xa h1 y32 ff1 fs0 fc0 sc0 ls13 ws2b">4<span class="_c blank"></span>.<span class="_c blank"></span>2<span class="_1 blank"> </span>S<span class="_d blank"></span>i<span class="_c blank"></span>s<span class="_d blank"></span>t<span class="_c blank"></span>e<span class="_f blank"></span>r<span class="_10 blank"></span>M<span class="_d blank"></span>a<span class="_c blank"></span>r<span class="_c blank"></span>y<span class="_e blank"></span>C<span class="_c blank"></span>e<span class="_c blank"></span>l<span class="_d blank"></span>i<span class="_c blank"></span>n<span class="_c blank"></span>e<span class="_10 blank"></span>F<span class="_13 blank"></span>a<span class="_c blank"></span>s<span class="_d blank"></span>e<span class="_c blank"></span>n<span class="_c blank"></span>m<span class="_d blank"></span>y<span class="_d blank"></span>e<span class="_c blank"></span>r ......................<span class="_9 blank"> </span>5<span class="_c blank"></span>7</div><div class="t m0 xa h1 y33 ff1 fs0 fc0 sc0 ls13 ws1c">4<span class="_c blank"></span>.<span class="_c blank"></span>3 S<span class="_d blank"></span>i<span class="_c blank"></span>s<span class="_c blank"></span>t<span class="_c blank"></span>e<span class="_c blank"></span>r<span class="_10 blank"></span>C<span class="_c blank"></span>e<span class="_c blank"></span>l<span class="_c blank"></span>i<span class="_c blank"></span>n<span class="_c blank"></span>e<span class="_c blank"></span>\u2019<span class="_c blank"></span>s<span class="_10 blank"></span>g<span class="_c blank"></span>e<span class="_c blank"></span>n<span class="_c blank"></span>e<span class="_d blank"></span>r<span class="_c blank"></span>a<span class="_c blank"></span>l<span class="_e blank"></span>a<span class="_c blank"></span>l<span class="_c blank"></span>g<span class="_d blank"></span>o<span class="_c blank"></span>r<span class="_c blank"></span>i<span class="_c blank"></span>t<span class="_c blank"></span>h<span class="_c blank"></span>m<span class="_4 blank"></span>.....................<span class="_1d blank"> </span>5<span class="_c blank"></span>8</div><div class="t m0 xa h1 y34 ff1 fs0 fc0 sc0 ls5 ws2c">4.4<span class="_17 blank"> </span>The F<span class="_2 blank"></span>undamen<span class="_0 blank"></span>tal Theorem<span class="_17 blank"> </span><span class="ls13 ws2d">....................... 6<span class="_d blank"></span>4</span></div><div class="t m0 xa h1 y35 ff1 fs0 fc0 sc0 ls21 ws2e">4.5<span class="_17 blank"> </span>Multiv<span class="_2 blank"></span>ariate and \u201c<span class="ff6 ls1d">q</span><span class="ls13 ws2f">\u201d<span class="_10 blank"></span>g<span class="_c blank"></span>e<span class="_c blank"></span>n<span class="_c blank"></span>e<span class="_c blank"></span>r<span class="_c blank"></span>a<span class="_c blank"></span>l<span class="_c blank"></span>i<span class="_c blank"></span>z<span class="_c blank"></span>a<span class="_c blank"></span>t<span class="_c blank"></span>i<span class="_d blank"></span>o<span class="_c blank"></span>n<span class="_c blank"></span>s ..................<span class="_1d blank"> </span>7<span class="_c blank"></span>0</span></div><div class="t m0 xa h1 y36 ff1 fs0 fc0 sc0 ls13 ws1c">4<span class="_c blank"></span>.<span class="_c blank"></span>6 E<span class="_d blank"></span>x<span class="_c blank"></span>e<span class="_c blank"></span>r<span class="_c blank"></span>c<span class="_c blank"></span>i<span class="_c blank"></span>s<span class="_c blank"></span>e<span class="_c blank"></span>s<span class="_10 blank"></span>..................................<span class="_9 blank"> </span>7<span class="_c blank"></span>2</div><div class="t m0 x2 h1 y37 ff4 fs0 fc0 sc0 ls22 ws30">5<span class="_9 blank"> </span>Gosp er\u2019s<span class="_a blank"> </span>Algorithm<span class="_22 blank"> </span>73</div><div class="t m0 xa h1 y38 ff1 fs0 fc0 sc0 ls13 ws1c">5<span class="_c blank"></span>.<span class="_c blank"></span>1 I<span class="_c blank"></span>n<span class="_13 blank"></span>t<span class="_c blank"></span>r<span class="_c blank"></span>o<span class="_f blank"></span>d<span class="_c blank"></span>u<span class="_c blank"></span>c<span class="_c blank"></span>t<span class="_c blank"></span>i<span class="_c blank"></span>o<span class="_c blank"></span>n<span class="_2 blank"></span>.........................<span class="_0 blank"></span>.......<span class="_1d blank"> </span>7<span class="_c blank"></span>3</div><div class="t m0 xa h1 y39 ff1 fs0 fc0 sc0 ls13 ws31">5<span class="_c blank"></span>.<span class="_c blank"></span>2<span class="_1 blank"> </span>H<span class="_d blank"></span>y<span class="_c blank"></span>p<span class="_c blank"></span>e<span class="_c blank"></span>r<span class="_c blank"></span>g<span class="_c blank"></span>e<span class="_c blank"></span>o<span class="_c blank"></span>m<span class="_c blank"></span>e<span class="_c blank"></span>t<span class="_c blank"></span>r<span class="_c blank"></span>i<span class="_c blank"></span>c<span class="_c blank"></span>s<span class="_10 blank"></span>t<span class="_c blank"></span>o<span class="_10 blank"></span>r<span class="_c blank"></span>a<span class="_c blank"></span>t<span class="_c blank"></span>i<span class="_c blank"></span>o<span class="_c blank"></span>n<span class="_d blank"></span>a<span class="_c blank"></span>l<span class="_c blank"></span>s<span class="_10 blank"></span>t<span class="_c blank"></span>o<span class="_10 blank"></span>p<span class="_14 blank"></span>o<span class="_c blank"></span>l<span class="_c blank"></span>y<span class="_c blank"></span>n<span class="_c blank"></span>o<span class="_d blank"></span>m<span class="_c blank"></span>i<span class="_c blank"></span>a<span class="_c blank"></span>l<span class="_c blank"></span>s ..............<span class="_1d blank"> </span>7<span class="_c blank"></span>5</div><div class="t m0 xa h1 y3a ff1 fs0 fc0 sc0 ls13 ws32">5<span class="_c blank"></span>.<span class="_c blank"></span>3<span class="_1 blank"> </span>T<span class="_d blank"></span>h<span class="_c blank"></span>e<span class="_10 blank"></span>f<span class="_c blank"></span>u<span class="_c blank"></span>l<span class="_c blank"></span>l<span class="_10 blank"></span>a<span class="_c blank"></span>l<span class="_c blank"></span>g<span class="_d blank"></span>o<span class="_c blank"></span>r<span class="_c blank"></span>i<span class="_c blank"></span>t<span class="_c blank"></span>h<span class="_c blank"></span>m<span class="_c blank"></span>:<span class="_2 blank"></span>S<span class="_c blank"></span>t<span class="_c blank"></span>e<span class="_c blank"></span>p<span class="_10 blank"></span>2 ........................<span class="_9 blank"> </span>7<span class="_c blank"></span>9</div><div class="t m0 xa h1 y3b ff1 fs0 fc0 sc0 ls13 ws32">5<span class="_c blank"></span>.<span class="_c blank"></span>4<span class="_1 blank"> </span>T<span class="_d blank"></span>h<span class="_c blank"></span>e<span class="_10 blank"></span>f<span class="_c blank"></span>u<span class="_c blank"></span>l<span class="_c blank"></span>l<span class="_10 blank"></span>a<span class="_c blank"></span>l<span class="_c blank"></span>g<span class="_d blank"></span>o<span class="_c blank"></span>r<span class="_c blank"></span>i<span class="_c blank"></span>t<span class="_c blank"></span>h<span class="_c blank"></span>m<span class="_c blank"></span>:<span class="_2 blank"></span>S<span class="_c blank"></span>t<span class="_c blank"></span>e<span class="_c blank"></span>p<span class="_10 blank"></span>3 ........................<span class="_9 blank"> </span>8<span class="_c blank"></span>4</div><div class="t m0 xa h1 y3c ff1 fs0 fc0 sc0 ls13 ws33">5<span class="_c blank"></span>.<span class="_c blank"></span>5<span class="_1 blank"> </span>M<span class="_d blank"></span>o<span class="_c blank"></span>r<span class="_c blank"></span>e<span class="_10 blank"></span>e<span class="_c blank"></span>x<span class="_d blank"></span>a<span class="_c blank"></span>m<span class="_c blank"></span>p<span class="_c blank"></span>l<span class="_c blank"></span>e<span class="_c blank"></span>s ..............................<span class="_9 blank"> </span>8<span class="_c blank"></span>6</div><div class="t m0 xa h1 y3d ff1 fs0 fc0 sc0 ls13 ws1c">5<span class="_c blank"></span>.<span class="_c blank"></span>6 S<span class="_d blank"></span>i<span class="_c blank"></span>m<span class="_c blank"></span>i<span class="_c blank"></span>l<span class="_c blank"></span>a<span class="_c blank"></span>r<span class="_c blank"></span>i<span class="_c blank"></span>t<span class="_d blank"></span>y<span class="_10 blank"></span>a<span class="_c blank"></span>m<span class="_c blank"></span>o<span class="_c blank"></span>n<span class="_d blank"></span>g<span class="_e blank"></span>h<span class="_d blank"></span>y<span class="_c blank"></span>p<span class="_f blank"></span>e<span class="_c blank"></span>r<span class="_c blank"></span>g<span class="_c blank"></span>e<span class="_d blank"></span>o<span class="_c blank"></span>m<span class="_c blank"></span>e<span class="_c blank"></span>t<span class="_c blank"></span>r<span class="_c blank"></span>i<span class="_c blank"></span>c<span class="_10 blank"></span>t<span class="_c blank"></span>e<span class="_c blank"></span>r<span class="_c blank"></span>m<span class="_c blank"></span>s<span class="_2 blank"></span>..........<span class="_0 blank"></span>.......<span class="_1d blank"> </span>9<span class="_c blank"></span>1</div><div class="t m0 xa h1 y3e ff1 fs0 fc0 sc0 ls13 ws1c">5<span class="_c blank"></span>.<span class="_c blank"></span>7 E<span class="_d blank"></span>x<span class="_c blank"></span>e<span class="_c blank"></span>r<span class="_c blank"></span>c<span class="_c blank"></span>i<span class="_c blank"></span>s<span class="_c blank"></span>e<span class="_c blank"></span>s<span class="_10 blank"></span>..................................<span class="_9 blank"> </span>9<span class="_c blank"></span>5</div><div class="t m0 x2 h1 y3f ff4 fs0 fc0 sc0 ls5 ws34">6<span class="_9 blank"> </span>Zeilb erger\u2019s<span class="_a blank"> </span>Algorithm<span class="_23 blank"> </span>101</div><div class="t m0 xa h1 y40 ff1 fs0 fc0 sc0 ls13 ws35">6<span class="_c blank"></span>.<span class="_c blank"></span>1<span class="_1 blank"> </span>I<span class="_d blank"></span>n<span class="_d blank"></span>t<span class="_c blank"></span>r<span class="_d blank"></span>o<span class="_14 blank"></span>d<span class="_c blank"></span>u<span class="_c blank"></span>c<span class="_d blank"></span>t<span class="_c blank"></span>i<span class="_c blank"></span>o<span class="_c blank"></span>n<span class="_2 blank"></span>................................ 1<span class="_d blank"></span>0<span class="_c blank"></span>1</div><div class="t m0 xa h1 y41 ff1 fs0 fc0 sc0 ls13 ws35">6<span class="_c blank"></span>.<span class="_c blank"></span>2<span class="_1 blank"> </span>E<span class="_d blank"></span>x<span class="_d blank"></span>i<span class="_c blank"></span>s<span class="_f blank"></span>t<span class="_c blank"></span>e<span class="_d blank"></span>n<span class="_c blank"></span>c<span class="_c blank"></span>e<span class="_e blank"></span>o<span class="_d blank"></span>f<span class="_e blank"></span>t<span class="_c blank"></span>h<span class="_c blank"></span>e<span class="_10 blank"></span>t<span class="_c blank"></span>e<span class="_c blank"></span>l<span class="_c blank"></span>e<span class="_c blank"></span>s<span class="_d blank"></span>c<span class="_c blank"></span>o<span class="_c blank"></span>p<span class="_f blank"></span>e<span class="_c blank"></span>d<span class="_10 blank"></span>r<span class="_c blank"></span>e<span class="_c blank"></span>c<span class="_c blank"></span>u<span class="_c blank"></span>r<span class="_c blank"></span>r<span class="_c blank"></span>e<span class="_c blank"></span>n<span class="_c blank"></span>c<span class="_c blank"></span>e<span class="_1a blank"></span>.................. 1<span class="_d blank"></span>0<span class="_c blank"></span>4</div><div class="t m0 xa h1 y42 ff1 fs0 fc0 sc0 ls13 ws35">6<span class="_c blank"></span>.<span class="_c blank"></span>3<span class="_1 blank"> </span>H<span class="_d blank"></span>o<span class="_d blank"></span>w<span class="_10 blank"></span>t<span class="_c blank"></span>h<span class="_c blank"></span>e<span class="_10 blank"></span>a<span class="_d blank"></span>l<span class="_f blank"></span>g<span class="_c blank"></span>o<span class="_c blank"></span>r<span class="_d blank"></span>i<span class="_c blank"></span>t<span class="_c blank"></span>h<span class="_c blank"></span>m<span class="_10 blank"></span>w<span class="_d blank"></span>o<span class="_c blank"></span>r<span class="_c blank"></span>k<span class="_c blank"></span>s<span class="_24 blank"></span>......................... 1<span class="_d blank"></span>0<span class="_c blank"></span>6</div><div class="t m0 xa h1 y43 ff1 fs0 fc0 sc0 ls13 ws36">6<span class="_c blank"></span>.<span class="_c blank"></span>4<span class="_1 blank"> </span>E<span class="_d blank"></span>x<span class="_d blank"></span>a<span class="_c blank"></span>m<span class="_c blank"></span>p<span class="_c blank"></span>l<span class="_c blank"></span>e<span class="_c blank"></span>s .................................<span class="_3 blank"> </span>1<span class="_d blank"></span>0<span class="_c blank"></span>9</div><div class="t m0 xa h1 y44 ff1 fs0 fc0 sc0 ls13 ws35">6<span class="_c blank"></span>.<span class="_c blank"></span>5<span class="_1 blank"> </span>U<span class="_d blank"></span>s<span class="_c blank"></span>e<span class="_10 blank"></span>o<span class="_c blank"></span>f<span class="_10 blank"></span>t<span class="_c blank"></span>h<span class="_c blank"></span>e<span class="_10 blank"></span>p<span class="_c blank"></span>r<span class="_c blank"></span>o<span class="_c blank"></span>g<span class="_c blank"></span>r<span class="_c blank"></span>a<span class="_c blank"></span>m<span class="_d blank"></span>s<span class="_1 blank"> </span>........<span class="_0 blank"></span>................... 1<span class="_d blank"></span>1<span class="_c blank"></span>2</div><div class="t m0 xa h1 y45 ff1 fs0 fc0 sc0 ls13 ws35">6<span class="_c blank"></span>.<span class="_c blank"></span>6<span class="_1 blank"> </span>E<span class="_d blank"></span>x<span class="_d blank"></span>e<span class="_f blank"></span>r<span class="_c blank"></span>c<span class="_c blank"></span>i<span class="_d blank"></span>s<span class="_f blank"></span>e<span class="_d blank"></span>s<span class="_e blank"></span>.................................. 1<span class="_d blank"></span>1<span class="_c blank"></span>8</div><div class="t m0 x2 h1 y46 ff4 fs0 fc0 sc0 ls23 ws37">7<span class="_9 blank"> </span>The WZ Phenomenon<span class="_25 blank"> </span>121</div><div class="t m0 xa h1 y47 ff1 fs0 fc0 sc0 ls13 ws35">7<span class="_c blank"></span>.<span class="_c blank"></span>1<span class="_1 blank"> </span>I<span class="_d blank"></span>n<span class="_d blank"></span>t<span class="_c blank"></span>r<span class="_d blank"></span>o<span class="_14 blank"></span>d<span class="_c blank"></span>u<span class="_c blank"></span>c<span class="_d blank"></span>t<span class="_c blank"></span>i<span class="_c blank"></span>o<span class="_c blank"></span>n<span class="_2 blank"></span>................................ 1<span class="_d blank"></span>2<span class="_c blank"></span>1</div><div class="t m0 xa h1 y48 ff1 fs0 fc0 sc0 ls13 ws38">7<span class="_c blank"></span>.<span class="_c blank"></span>2<span class="_1 blank"> </span>W<span class="_d blank"></span>Z<span class="_10 blank"></span>p<span class="_c blank"></span>r<span class="_c blank"></span>o<span class="_f blank"></span>o<span class="_d blank"></span>f<span class="_f blank"></span>s<span class="_10 blank"></span>o<span class="_c blank"></span>f<span class="_10 blank"></span>t<span class="_c blank"></span>h<span class="_c blank"></span>e<span class="_10 blank"></span>h<span class="_d blank"></span>y<span class="_c blank"></span>p<span class="_f blank"></span>e<span class="_c blank"></span>r<span class="_c blank"></span>g<span class="_c blank"></span>e<span class="_d blank"></span>o<span class="_c blank"></span>m<span class="_c blank"></span>e<span class="_c blank"></span>t<span class="_c blank"></span>r<span class="_c blank"></span>i<span class="_c blank"></span>c<span class="_10 blank"></span>d<span class="_c blank"></span>a<span class="_c blank"></span>t<span class="_c blank"></span>a<span class="_c blank"></span>b<span class="_c blank"></span>a<span class="_c blank"></span>s<span class="_c blank"></span>e ...............<span class="_3 blank"> </span>1<span class="_d blank"></span>2<span class="_c blank"></span>6</div><div class="t m0 xa h1 y49 ff1 fs0 fc0 sc0 ls13 ws39">7<span class="_c blank"></span>.<span class="_c blank"></span>3<span class="_1 blank"> </span>S<span class="_d blank"></span>p<span class="_c blank"></span>i<span class="_c blank"></span>n<span class="_d blank"></span>o<span class="_c blank"></span>\ufb00<span class="_c blank"></span>s<span class="_e blank"></span>f<span class="_c blank"></span>r<span class="_c blank"></span>o<span class="_d blank"></span>m<span class="_10 blank"></span>t<span class="_c blank"></span>h<span class="_c blank"></span>e<span class="_10 blank"></span>W<span class="_c blank"></span>Z<span class="_e blank"></span>m<span class="_c blank"></span>e<span class="_d blank"></span>t<span class="_c blank"></span>h<span class="_c blank"></span>o<span class="_f blank"></span>d ......................<span class="_3 blank"> </span>1<span class="_d blank"></span>2<span class="_c blank"></span>7</div><div class="t m0 xa h1 y4a ff1 fs0 fc0 sc0 ls13 ws3a">7<span class="_c blank"></span>.<span class="_c blank"></span>4<span class="_1 blank"> </span>D<span class="_d blank"></span>i<span class="_c blank"></span>s<span class="_c blank"></span>c<span class="_c blank"></span>o<span class="_d blank"></span>v<span class="_d blank"></span>e<span class="_d blank"></span>r<span class="_c blank"></span>i<span class="_c blank"></span>n<span class="_c blank"></span>g<span class="_10 blank"></span>n<span class="_c blank"></span>e<span class="_c blank"></span>w<span class="_10 blank"></span>h<span class="_d blank"></span>y<span class="_c blank"></span>p<span class="_f blank"></span>e<span class="_c blank"></span>r<span class="_c blank"></span>g<span class="_c blank"></span>e<span class="_c blank"></span>o<span class="_c blank"></span>m<span class="_c blank"></span>e<span class="_d blank"></span>t<span class="_c blank"></span>r<span class="_c blank"></span>i<span class="_c blank"></span>c<span class="_10 blank"></span>i<span class="_c blank"></span>d<span class="_c blank"></span>e<span class="_c blank"></span>n<span class="_d blank"></span>t<span class="_c blank"></span>i<span class="_c blank"></span>t<span class="_c blank"></span>i<span class="_c blank"></span>e<span class="_c blank"></span>s ...............<span class="_3 blank"> </span>1<span class="_d blank"></span>3<span class="_c blank"></span>5</div><div class="t m0 xa h1 y4b ff1 fs0 fc0 sc0 ls13 ws35">7<span class="_c blank"></span>.<span class="_c blank"></span>5<span class="_1 blank"> </span>S<span class="_d blank"></span>o<span class="_c blank"></span>f<span class="_d blank"></span>t<span class="_c blank"></span>w<span class="_13 blank"></span>a<span class="_c blank"></span>r<span class="_c blank"></span>e<span class="_e blank"></span>f<span class="_c blank"></span>o<span class="_d blank"></span>r<span class="_e blank"></span>t<span class="_c blank"></span>h<span class="_c blank"></span>e<span class="_10 blank"></span>W<span class="_c blank"></span>Z<span class="_10 blank"></span>m<span class="_c blank"></span>e<span class="_c blank"></span>t<span class="_c blank"></span>h<span class="_d blank"></span>o<span class="_14 blank"></span>d<span class="_24 blank"></span>....................... 1<span class="_d blank"></span>3<span class="_c blank"></span>7</div><div class="t m0 xa h1 y4c ff1 fs0 fc0 sc0 ls13 ws35">7<span class="_c blank"></span>.<span class="_c blank"></span>6<span class="_1 blank"> </span>E<span class="_d blank"></span>x<span class="_d blank"></span>e<span class="_f blank"></span>r<span class="_c blank"></span>c<span class="_c blank"></span>i<span class="_d blank"></span>s<span class="_f blank"></span>e<span class="_d blank"></span>s<span class="_e blank"></span>.................................. 1<span class="_d blank"></span>4<span class="_c blank"></span>0</div></div><div class="pi" data-data='{"ctm":[1.000000,0.000000,0.000000,1.000000,0.000000,0.000000]}'></div></div> <div id="pf7" class="pf w0 h0" data-page-no="7"><div class="pc pc7 w0 h0"><img fetchpriority="low" loading="lazy" class="bi x0 y0 w1 h0" alt="" src="https://files.passeidireto.com/adb72897-ef92-4b54-a0dc-9a438317dc1a/bg7.png"><div class="t m0 x12 h1 y11 ff4 fs0 fc0 sc0 ls24 ws3b">CONTENTS <span class="lsd">v</span></div><div class="t m0 x12 h1 y1 ff4 fs0 fc0 sc0 ls1a ws3c">8<span class="_9 blank"> </span>Algorithm<span class="_1b blank"> </span>Hyp er<span class="_26 blank"> </span>141</div><div class="t m0 x13 h1 y4d ff1 fs0 fc0 sc0 ls13 ws35">8<span class="_c blank"></span>.<span class="_c blank"></span>1<span class="_1 blank"> </span>I<span class="_d blank"></span>n<span class="_d blank"></span>t<span class="_c blank"></span>r<span class="_d blank"></span>o<span class="_14 blank"></span>d<span class="_c blank"></span>u<span class="_c blank"></span>c<span class="_c blank"></span>t<span class="_c blank"></span>i<span class="_c blank"></span>o<span class="_d blank"></span>n<span class="_2 blank"></span>................................ 1<span class="_d blank"></span>4<span class="_c blank"></span>1</div><div class="t m0 x13 h1 y4e ff1 fs0 fc0 sc0 ls13 ws35">8<span class="_c blank"></span>.<span class="_c blank"></span>2<span class="_1 blank"> </span>T<span class="_d blank"></span>h<span class="_c blank"></span>e<span class="_10 blank"></span>r<span class="_c blank"></span>i<span class="_c blank"></span>n<span class="_c blank"></span>g<span class="_10 blank"></span>o<span class="_c blank"></span>f<span class="_10 blank"></span>s<span class="_c blank"></span>e<span class="_c blank"></span>q<span class="_c blank"></span>u<span class="_d blank"></span>e<span class="_f blank"></span>n<span class="_c blank"></span>c<span class="_d blank"></span>e<span class="_c blank"></span>s<span class="_4 blank"></span>........................... 1<span class="_d blank"></span>4<span class="_c blank"></span>4</div><div class="t m0 x13 h1 y4f ff1 fs0 fc0 sc0 ls13 ws3d">8<span class="_c blank"></span>.<span class="_c blank"></span>3<span class="_1 blank"> </span>P<span class="_13 blank"></span>o<span class="_c blank"></span>l<span class="_c blank"></span>y<span class="_c blank"></span>n<span class="_c blank"></span>o<span class="_c blank"></span>m<span class="_d blank"></span>i<span class="_c blank"></span>a<span class="_c blank"></span>l<span class="_e blank"></span>s<span class="_d blank"></span>o<span class="_c blank"></span>l<span class="_c blank"></span>u<span class="_c blank"></span>t<span class="_c blank"></span>i<span class="_c blank"></span>o<span class="_c blank"></span>n<span class="_c blank"></span>s ...........................<span class="_3 blank"> </span>1<span class="_d blank"></span>4<span class="_c blank"></span>8</div><div class="t m0 x13 h1 y50 ff1 fs0 fc0 sc0 ls13 ws35">8<span class="_c blank"></span>.<span class="_c blank"></span>4<span class="_1 blank"> </span>H<span class="_d blank"></span>y<span class="_c blank"></span>p<span class="_c blank"></span>e<span class="_f blank"></span>r<span class="_c blank"></span>g<span class="_d blank"></span>e<span class="_f blank"></span>o<span class="_c blank"></span>m<span class="_d blank"></span>e<span class="_c blank"></span>t<span class="_c blank"></span>r<span class="_c blank"></span>i<span class="_c blank"></span>c<span class="_10 blank"></span>s<span class="_c blank"></span>o<span class="_c blank"></span>l<span class="_c blank"></span>u<span class="_c blank"></span>t<span class="_c blank"></span>i<span class="_c blank"></span>o<span class="_c blank"></span>n<span class="_c blank"></span>s<span class="_10 blank"></span>......................... 1<span class="_d blank"></span>5<span class="_c blank"></span>1</div><div class="t m0 x13 h1 y51 ff1 fs0 fc0 sc0 ls13 ws35">8<span class="_c blank"></span>.<span class="_c blank"></span>5<span class="_1 blank"> </span>A<span class="_1a blank"></span>M<span class="_c blank"></span>a<span class="_c blank"></span>t<span class="_c blank"></span>h<span class="_c blank"></span>e<span class="_c blank"></span>m<span class="_c blank"></span>a<span class="_c blank"></span>t<span class="_c blank"></span>i<span class="_c blank"></span>c<span class="_c blank"></span>a<span class="_10 blank"></span>s<span class="_c blank"></span>e<span class="_c blank"></span>s<span class="_d blank"></span>s<span class="_f blank"></span>i<span class="_c blank"></span>o<span class="_c blank"></span>n.....................<span class="_0 blank"></span>..... 1<span class="_c blank"></span>5<span class="_c blank"></span>6</div><div class="t m0 x13 h1 y52 ff1 fs0 fc0 sc0 ls13 ws35">8<span class="_c blank"></span>.<span class="_c blank"></span>6<span class="_1 blank"> </span>F<span class="_d blank"></span>i<span class="_c blank"></span>n<span class="_c blank"></span>d<span class="_c blank"></span>i<span class="_d blank"></span>n<span class="_c blank"></span>g<span class="_e blank"></span>a<span class="_c blank"></span>l<span class="_d blank"></span>l<span class="_e blank"></span>h<span class="_d blank"></span>y<span class="_c blank"></span>p<span class="_f blank"></span>e<span class="_c blank"></span>r<span class="_c blank"></span>g<span class="_c blank"></span>e<span class="_d blank"></span>o<span class="_c blank"></span>m<span class="_c blank"></span>e<span class="_c blank"></span>t<span class="_c blank"></span>r<span class="_c blank"></span>i<span class="_c blank"></span>c<span class="_10 blank"></span>s<span class="_c blank"></span>o<span class="_c blank"></span>l<span class="_c blank"></span>u<span class="_c blank"></span>t<span class="_c blank"></span>i<span class="_c blank"></span>o<span class="_c blank"></span>n<span class="_c blank"></span>s .................. 1<span class="_d blank"></span>5<span class="_c blank"></span>7</div><div class="t m0 x13 h1 y53 ff1 fs0 fc0 sc0 ls13 ws35">8<span class="_c blank"></span>.<span class="_c blank"></span>7<span class="_1 blank"> </span>F<span class="_d blank"></span>i<span class="_c blank"></span>n<span class="_c blank"></span>d<span class="_c blank"></span>i<span class="_d blank"></span>n<span class="_c blank"></span>g<span class="_e blank"></span>a<span class="_c blank"></span>l<span class="_d blank"></span>l<span class="_e blank"></span>c<span class="_c blank"></span>l<span class="_c blank"></span>o<span class="_c blank"></span>s<span class="_c blank"></span>e<span class="_c blank"></span>d<span class="_10 blank"></span>f<span class="_c blank"></span>o<span class="_d blank"></span>r<span class="_c blank"></span>m<span class="_e blank"></span>s<span class="_c blank"></span>o<span class="_d blank"></span>l<span class="_c blank"></span>u<span class="_f blank"></span>t<span class="_c blank"></span>i<span class="_c blank"></span>o<span class="_d blank"></span>n<span class="_c blank"></span>s<span class="_e blank"></span>................<span class="_0 blank"></span>..... 1<span class="_c blank"></span>5<span class="_c blank"></span>8</div><div class="t m0 x13 h1 y54 ff1 fs0 fc0 sc0 ls13 ws3e">8<span class="_c blank"></span>.<span class="_c blank"></span>8<span class="_1 blank"> </span>S<span class="_d blank"></span>o<span class="_c blank"></span>m<span class="_c blank"></span>e<span class="_10 blank"></span>f<span class="_c blank"></span>a<span class="_c blank"></span>m<span class="_c blank"></span>o<span class="_c blank"></span>u<span class="_d blank"></span>s<span class="_e blank"></span>s<span class="_d blank"></span>e<span class="_f blank"></span>q<span class="_d blank"></span>u<span class="_c blank"></span>e<span class="_c blank"></span>n<span class="_c blank"></span>c<span class="_c blank"></span>e<span class="_c blank"></span>s<span class="_10 blank"></span>t<span class="_c blank"></span>h<span class="_c blank"></span>a<span class="_c blank"></span>t<span class="_10 blank"></span>d<span class="_c blank"></span>o<span class="_10 blank"></span>n<span class="_c blank"></span>o<span class="_c blank"></span>t<span class="_10 blank"></span>h<span class="_c blank"></span>a<span class="_d blank"></span>v<span class="_d blank"></span>e<span class="_10 blank"></span>c<span class="_c blank"></span>l<span class="_c blank"></span>o<span class="_c blank"></span>s<span class="_c blank"></span>e<span class="_c blank"></span>d<span class="_10 blank"></span>f<span class="_c blank"></span>o<span class="_c blank"></span>r<span class="_c blank"></span>m .........<span class="_3 blank"> </span>1<span class="_d blank"></span>5<span class="_c blank"></span>9</div><div class="t m0 x13 h1 y55 ff1 fs0 fc0 sc0 ls13 ws35">8<span class="_c blank"></span>.<span class="_c blank"></span>9<span class="_1 blank"> </span>I<span class="_d blank"></span>n<span class="_c blank"></span>h<span class="_c blank"></span>o<span class="_c blank"></span>m<span class="_d blank"></span>o<span class="_c blank"></span>g<span class="_c blank"></span>e<span class="_c blank"></span>n<span class="_c blank"></span>e<span class="_c blank"></span>o<span class="_c blank"></span>u<span class="_c blank"></span>s<span class="_10 blank"></span>r<span class="_c blank"></span>e<span class="_c blank"></span>c<span class="_c blank"></span>u<span class="_c blank"></span>r<span class="_c blank"></span>r<span class="_c blank"></span>e<span class="_c blank"></span>n<span class="_d blank"></span>c<span class="_c blank"></span>e<span class="_c blank"></span>s<span class="_1a blank"></span>........................ 1<span class="_c blank"></span>6<span class="_d blank"></span>1</div><div class="t m0 x13 h1 y56 ff1 fs0 fc0 sc0 ls13 ws3f">8<span class="_c blank"></span>.<span class="_c blank"></span>1<span class="_c blank"></span>0F<span class="_27 blank"></span>a<span class="_c blank"></span>c<span class="_c blank"></span>t<span class="_d blank"></span>o<span class="_c blank"></span>r<span class="_c blank"></span>i<span class="_c blank"></span>z<span class="_f blank"></span>a<span class="_d blank"></span>t<span class="_c blank"></span>i<span class="_c blank"></span>o<span class="_c blank"></span>n<span class="_10 blank"></span>o<span class="_c blank"></span>f<span class="_10 blank"></span>o<span class="_c blank"></span>p<span class="_14 blank"></span>e<span class="_d blank"></span>r<span class="_c blank"></span>a<span class="_c blank"></span>t<span class="_c blank"></span>o<span class="_c blank"></span>r<span class="_c blank"></span>s<span class="_28 blank"> </span>........................<span class="_28 blank"> </span>1<span class="_c blank"></span>6<span class="_c blank"></span>2</div><div class="t m0 x13 h1 y57 ff1 fs0 fc0 sc0 ls13 ws3f">8<span class="_c blank"></span>.<span class="_c blank"></span>1<span class="_c blank"></span>1E<span class="_c blank"></span>x<span class="_c blank"></span>e<span class="_c blank"></span>r<span class="_c blank"></span>c<span class="_c blank"></span>i<span class="_d blank"></span>s<span class="_f blank"></span>e<span class="_d blank"></span>s<span class="_e blank"></span>..................................<span class="_28 blank"> </span>1<span class="_c blank"></span>6<span class="_c blank"></span>4</div><div class="t m0 x12 h4 y58 ff4 fs3 fc0 sc0 ls25 ws40">III E<span class="_0 blank"></span>p<span class="_2 blank"></span>il<span class="_2 blank"></span>o<span class="_0 blank"></span>g<span class="_0 blank"></span>u<span class="_2 blank"></span>e<span class="_29 blank"> </span>1<span class="_0 blank"></span>6<span class="_0 blank"></span>9</div><div class="t m0 x12 h1 y59 ff4 fs0 fc0 sc0 ls12 ws41">9<span class="_9 blank"> </span>An<span class="_1b blank"> </span>Op era tor<span class="_1b blank"> </span>Algebra<span class="_a blank"> </span>Viewp oint<span class="_2a blank"> </span>171</div><div class="t m0 x13 h1 y5a ff1 fs0 fc0 sc0 ls13 ws42">9<span class="_c blank"></span>.<span class="_c blank"></span>1<span class="_1 blank"> </span>E<span class="_d blank"></span>a<span class="_c blank"></span>r<span class="_c blank"></span>l<span class="_c blank"></span>y<span class="_10 blank"></span>h<span class="_c blank"></span>i<span class="_d blank"></span>s<span class="_f blank"></span>t<span class="_c blank"></span>o<span class="_d blank"></span>r<span class="_c blank"></span>y ............................... 1<span class="_d blank"></span>7<span class="_c blank"></span>1</div><div class="t m0 x13 h1 y5b ff1 fs0 fc0 sc0 ls13 ws43">9<span class="_c blank"></span>.<span class="_c blank"></span>2<span class="_1 blank"> </span>L<span class="_d blank"></span>i<span class="_c blank"></span>n<span class="_c blank"></span>e<span class="_d blank"></span>a<span class="_c blank"></span>r<span class="_e blank"></span>d<span class="_c blank"></span>i<span class="_c blank"></span>\ufb00<span class="_c blank"></span>e<span class="_d blank"></span>r<span class="_c blank"></span>e<span class="_c blank"></span>n<span class="_c blank"></span>c<span class="_c blank"></span>e<span class="_10 blank"></span>o<span class="_c blank"></span>p<span class="_f blank"></span>e<span class="_c blank"></span>r<span class="_c blank"></span>a<span class="_c blank"></span>t<span class="_c blank"></span>o<span class="_c blank"></span>r<span class="_c blank"></span>s ........................<span class="_28 blank"> </span>1<span class="_c blank"></span>7<span class="_c blank"></span>2</div><div class="t m0 x13 h1 y5c ff1 fs0 fc0 sc0 ls13 ws44">9<span class="_c blank"></span>.<span class="_c blank"></span>3<span class="_1 blank"> </span>E<span class="_d blank"></span>l<span class="_c blank"></span>i<span class="_c blank"></span>m<span class="_c blank"></span>i<span class="_c blank"></span>n<span class="_d blank"></span>a<span class="_c blank"></span>t<span class="_c blank"></span>i<span class="_c blank"></span>o<span class="_c blank"></span>n<span class="_10 blank"></span>i<span class="_c blank"></span>n<span class="_10 blank"></span>t<span class="_d blank"></span>w<span class="_d blank"></span>o<span class="_10 blank"></span>v<span class="_13 blank"></span>a<span class="_c blank"></span>r<span class="_c blank"></span>i<span class="_c blank"></span>a<span class="_c blank"></span>b<span class="_c blank"></span>l<span class="_c blank"></span>e<span class="_c blank"></span>s .......................<span class="_3 blank"> </span>1<span class="_d blank"></span>7<span class="_c blank"></span>7</div><div class="t m0 x13 h1 y5d ff1 fs0 fc0 sc0 ls13 ws45">9<span class="_c blank"></span>.<span class="_c blank"></span>4<span class="_1 blank"> </span>M<span class="_d blank"></span>o<span class="_f blank"></span>d<span class="_c blank"></span>i<span class="_c blank"></span>\ufb01<span class="_c blank"></span>e<span class="_c blank"></span>d<span class="_10 blank"></span>e<span class="_c blank"></span>l<span class="_c blank"></span>i<span class="_c blank"></span>m<span class="_d blank"></span>i<span class="_c blank"></span>n<span class="_c blank"></span>a<span class="_c blank"></span>t<span class="_c blank"></span>i<span class="_c blank"></span>o<span class="_c blank"></span>n<span class="_10 blank"></span>p<span class="_c blank"></span>r<span class="_c blank"></span>o<span class="_c blank"></span>b<span class="_c blank"></span>l<span class="_c blank"></span>e<span class="_c blank"></span>m .................<span class="_0 blank"></span>.....<span class="_3 blank"> </span>1<span class="_c blank"></span>8<span class="_c blank"></span>0</div><div class="t m0 x13 h1 y5e ff1 fs0 fc0 sc0 ls13 ws35">9<span class="_c blank"></span>.<span class="_c blank"></span>5<span class="_1 blank"> </span>D<span class="_d blank"></span>i<span class="_c blank"></span>s<span class="_c blank"></span>c<span class="_c blank"></span>r<span class="_d blank"></span>e<span class="_f blank"></span>t<span class="_d blank"></span>e<span class="_e blank"></span>h<span class="_c blank"></span>o<span class="_c blank"></span>l<span class="_d blank"></span>o<span class="_c blank"></span>n<span class="_c blank"></span>o<span class="_c blank"></span>m<span class="_c blank"></span>i<span class="_c blank"></span>c<span class="_10 blank"></span>f<span class="_c blank"></span>u<span class="_c blank"></span>n<span class="_c blank"></span>c<span class="_c blank"></span>t<span class="_c blank"></span>i<span class="_c blank"></span>o<span class="_c blank"></span>n<span class="_c blank"></span>s<span class="_e blank"></span>....................... 1<span class="_c blank"></span>8<span class="_d blank"></span>4</div><div class="t m0 x13 h1 y5f ff1 fs0 fc0 sc0 ls13 ws43">9<span class="_c blank"></span>.<span class="_c blank"></span>6<span class="_1 blank"> </span>E<span class="_d blank"></span>l<span class="_c blank"></span>i<span class="_c blank"></span>m<span class="_c blank"></span>i<span class="_c blank"></span>n<span class="_d blank"></span>a<span class="_c blank"></span>t<span class="_c blank"></span>i<span class="_c blank"></span>o<span class="_c blank"></span>n<span class="_10 blank"></span>i<span class="_c blank"></span>n<span class="_10 blank"></span>t<span class="_c blank"></span>h<span class="_c blank"></span>e<span class="_10 blank"></span>r<span class="_c blank"></span>i<span class="_c blank"></span>n<span class="_c blank"></span>g<span class="_10 blank"></span>o<span class="_c blank"></span>f<span class="_e blank"></span>o<span class="_d blank"></span>p<span class="_f blank"></span>e<span class="_f blank"></span>r<span class="_c blank"></span>a<span class="_d blank"></span>t<span class="_c blank"></span>o<span class="_c blank"></span>r<span class="_c blank"></span>s ...................<span class="_3 blank"> </span>1<span class="_c blank"></span>8<span class="_d blank"></span>5</div><div class="t m0 x13 h1 y60 ff1 fs0 fc0 sc0 ls13 ws35">9<span class="_c blank"></span>.<span class="_c blank"></span>7<span class="_1 blank"> </span>B<span class="_d blank"></span>e<span class="_c blank"></span>y<span class="_d blank"></span>o<span class="_c blank"></span>n<span class="_d blank"></span>d<span class="_e blank"></span>t<span class="_c blank"></span>h<span class="_c blank"></span>e<span class="_10 blank"></span>h<span class="_c blank"></span>o<span class="_c blank"></span>l<span class="_c blank"></span>o<span class="_c blank"></span>n<span class="_d blank"></span>o<span class="_c blank"></span>m<span class="_c blank"></span>i<span class="_c blank"></span>c<span class="_10 blank"></span>p<span class="_c blank"></span>a<span class="_c blank"></span>r<span class="_c blank"></span>a<span class="_c blank"></span>d<span class="_c blank"></span>i<span class="_c blank"></span>g<span class="_c blank"></span>m<span class="_24 blank"></span>................<span class="_0 blank"></span>..... 1<span class="_c blank"></span>8<span class="_c blank"></span>5</div><div class="t m0 x13 h1 y61 ff1 fs0 fc0 sc0 ls13 ws35">9<span class="_c blank"></span>.<span class="_c blank"></span>8<span class="_1 blank"> </span>B<span class="_d blank"></span>i<span class="_c blank"></span>-<span class="_d blank"></span>b<span class="_f blank"></span>a<span class="_d blank"></span>s<span class="_f blank"></span>i<span class="_c blank"></span>c<span class="_10 blank"></span>e<span class="_c blank"></span>q<span class="_c blank"></span>u<span class="_c blank"></span>a<span class="_c blank"></span>t<span class="_c blank"></span>i<span class="_d blank"></span>o<span class="_c blank"></span>n<span class="_c blank"></span>s<span class="_10 blank"></span>........................<span class="_0 blank"></span>..... 1<span class="_c blank"></span>8<span class="_d blank"></span>7</div><div class="t m0 x13 h1 y62 ff1 fs0 fc0 sc0 ls13 ws35">9<span class="_c blank"></span>.<span class="_c blank"></span>9<span class="_1 blank"> </span>C<span class="_d blank"></span>r<span class="_c blank"></span>e<span class="_c blank"></span>a<span class="_d blank"></span>t<span class="_c blank"></span>i<span class="_c blank"></span>v<span class="_d blank"></span>e<span class="_e blank"></span>a<span class="_c blank"></span>n<span class="_13 blank"></span>t<span class="_c blank"></span>i<span class="_c blank"></span>-<span class="_c blank"></span>s<span class="_c blank"></span>y<span class="_c blank"></span>m<span class="_c blank"></span>m<span class="_c blank"></span>e<span class="_c blank"></span>t<span class="_c blank"></span>r<span class="_c blank"></span>i<span class="_c blank"></span>z<span class="_c blank"></span>i<span class="_c blank"></span>n<span class="_d blank"></span>g<span class="_10 blank"></span>........................ 1<span class="_c blank"></span>8<span class="_d blank"></span>8</div><div class="t m0 x13 h1 y63 ff1 fs0 fc0 sc0 ls13 ws3f">9<span class="_c blank"></span>.<span class="_c blank"></span>1<span class="_c blank"></span>0W<span class="_27 blank"></span>a<span class="_d blank"></span>v<span class="_d blank"></span>e<span class="_c blank"></span>l<span class="_d blank"></span>e<span class="_f blank"></span>t<span class="_d blank"></span>s.......<span class="_0 blank"></span>...........................<span class="_28 blank"> </span>1<span class="_c blank"></span>9<span class="_c blank"></span>0</div><div class="t m0 x13 h1 y64 ff1 fs0 fc0 sc0 ls13 ws3f">9<span class="_c blank"></span>.<span class="_c blank"></span>1<span class="_c blank"></span>1A<span class="_c blank"></span>b<span class="_f blank"></span>e<span class="_c blank"></span>l<span class="_c blank"></span>-<span class="_c blank"></span>t<span class="_d blank"></span>y<span class="_c blank"></span>p<span class="_c blank"></span>e<span class="_e blank"></span>i<span class="_c blank"></span>d<span class="_c blank"></span>e<span class="_c blank"></span>n<span class="_13 blank"></span>t<span class="_c blank"></span>i<span class="_c blank"></span>t<span class="_c blank"></span>i<span class="_c blank"></span>e<span class="_c blank"></span>s<span class="_0 blank"></span>............<span class="_0 blank"></span>................<span class="_3 blank"> </span>1<span class="_c blank"></span>9<span class="_d blank"></span>1</div><div class="t m0 x13 h1 y65 ff1 fs0 fc0 sc0 ls13 ws3f">9<span class="_c blank"></span>.<span class="_c blank"></span>1<span class="_c blank"></span>2A<span class="_c blank"></span>n<span class="_c blank"></span>o<span class="_c blank"></span>t<span class="_c blank"></span>h<span class="_c blank"></span>e<span class="_d blank"></span>r<span class="_e blank"></span>s<span class="_c blank"></span>e<span class="_c blank"></span>m<span class="_c blank"></span>i<span class="_d blank"></span>-<span class="_f blank"></span>h<span class="_c blank"></span>o<span class="_c blank"></span>l<span class="_d blank"></span>o<span class="_c blank"></span>n<span class="_c blank"></span>o<span class="_c blank"></span>m<span class="_c blank"></span>i<span class="_c blank"></span>c<span class="_10 blank"></span>i<span class="_c blank"></span>d<span class="_c blank"></span>e<span class="_c blank"></span>n<span class="_d blank"></span>t<span class="_c blank"></span>i<span class="_c blank"></span>t<span class="_d blank"></span>y<span class="_1 blank"> </span>...............<span class="_0 blank"></span>.....<span class="_3 blank"> </span>1<span class="_c blank"></span>9<span class="_d blank"></span>3</div><div class="t m0 x13 h1 y66 ff1 fs0 fc0 sc0 ls13 ws3f">9<span class="_c blank"></span>.<span class="_c blank"></span>1<span class="_c blank"></span>3T<span class="_c blank"></span>h<span class="_c blank"></span>e<span class="_10 blank"></span>a<span class="_c blank"></span>r<span class="_c blank"></span>t<span class="_2b blank"> </span>.............................<span class="_0 blank"></span>.....<span class="_3 blank"> </span>1<span class="_c blank"></span>9<span class="_d blank"></span>3</div><div class="t m0 x13 h1 y67 ff1 fs0 fc0 sc0 ls13 ws3f">9<span class="_c blank"></span>.<span class="_c blank"></span>1<span class="_c blank"></span>4E<span class="_c blank"></span>x<span class="_c blank"></span>e<span class="_c blank"></span>r<span class="_c blank"></span>c<span class="_c blank"></span>i<span class="_d blank"></span>s<span class="_f blank"></span>e<span class="_d blank"></span>s<span class="_e blank"></span>..................................<span class="_28 blank"> </span>1<span class="_c blank"></span>9<span class="_c blank"></span>5</div><div class="t m0 x12 h1 y68 ff4 fs0 fc0 sc0 ls26 ws46">A<span class="_2c blank"> </span>The WWW sites and<span class="_a blank"> </span>the sof<span class="_5 blank"> </span>t<span class="_0 blank"></span>w<span class="_0 blank"></span>are<span class="_2d blank"> </span>197</div><div class="t m0 x13 h1 y69 ff1 fs0 fc0 sc0 lsd ws47">A.1<span class="_2e blank"> </span>The Maple pac<span class="_2 blank"></span>k<span class="_0 blank"></span>ages <span class="ff7 ls27 ws48">EKHAD<span class="_2f blank"> </span></span><span class="ls28 ws20">and <span class="ff7 ls27 ws48">qEKHAD<span class="_2b blank"> </span></span><span class="ls13 ws35">................. 1<span class="_d blank"></span>9<span class="_c blank"></span>8</span></span></div><div class="t m0 x13 h1 y47 ff1 fs0 fc0 sc0 ls13 ws49">A<span class="_c blank"></span>.<span class="_c blank"></span>2 M<span class="_c blank"></span>a<span class="_c blank"></span>t<span class="_c blank"></span>h<span class="_d blank"></span>e<span class="_c blank"></span>m<span class="_c blank"></span>a<span class="_c blank"></span>t<span class="_c blank"></span>i<span class="_c blank"></span>c<span class="_c blank"></span>a<span class="_10 blank"></span>p<span class="_c blank"></span>r<span class="_c blank"></span>o<span class="_c blank"></span>g<span class="_c blank"></span>r<span class="_c blank"></span>a<span class="_c blank"></span>m<span class="_c blank"></span>s..........<span class="_0 blank"></span>................<span class="_3 blank"> </span>1<span class="_d blank"></span>9<span class="_c blank"></span>9</div><div class="t m0 x12 h1 y6a ff4 fs0 fc0 sc0 ls29 ws4a">Bibliograph<span class="_0 blank"></span>y<span class="_30 blank"> </span>201</div><div class="t m0 x12 h1 y6b ff4 fs0 fc0 sc0 ls2a ws4b">Index<span class="_31 blank"> </span>208</div></div><div class="pi" data-data='{"ctm":[1.000000,0.000000,0.000000,1.000000,0.000000,0.000000]}'></div></div> <div id="pf8" class="pf w0 h0" data-page-no="8"><div class="pc pc8 w0 h0"><img fetchpriority="low" loading="lazy" class="bi x0 y0 w1 h0" alt="" src="https://files.passeidireto.com/adb72897-ef92-4b54-a0dc-9a438317dc1a/bg8.png"><div class="t m0 x11 h1 y11 ff4 fs0 fc0 sc0 ls2b ws4c">vi <span class="ls1e ws26">CONTENTS</span></div></div><div class="pi" data-data='{"ctm":[1.000000,0.000000,0.000000,1.000000,0.000000,0.000000]}'></div></div> <div id="pf9" class="pf w0 h0" data-page-no="9"><div class="pc pc9 w0 h0"><img fetchpriority="low" loading="lazy" class="bi x0 y0 w1 h0" alt="" src="https://files.passeidireto.com/adb72897-ef92-4b54-a0dc-9a438317dc1a/bg9.png"><div class="t m0 x12 h3 y6c ff4 fs2 fc0 sc0 ls47 ws4d">Fo<span class="_32 blank"> </span>r<span class="_32 blank"> </span>e<span class="_32 blank"> </span>w o<span class="_32 blank"> </span>r<span class="_32 blank"> </span>d</div><div class="t m0 x13 h1 y6d ff1 fs0 fc0 sc0 ls22 ws4e">Science is what we understand w<span class="_0 blank"></span>ell enough to explain to a computer.<span class="_33 blank"> </span>Art is</div><div class="t m0 x12 h1 y6e ff1 fs0 fc0 sc0 ls48 ws4f">ev<span class="_0 blank"></span>erything els<span class="_5 blank"> </span>e w<span class="_0 blank"></span>e do.<span class="_28 blank"> </span>During the past sev<span class="_0 blank"></span>eral y<span class="_0 blank"></span>ears an imp<span class="_5 blank"> </span>ortant part of mathematics</div><div class="t m0 x12 h1 y6f ff1 fs0 fc0 sc0 ls1a ws50">has b<span class="_5 blank"> </span>een transformed<span class="_34 blank"> </span>from an Art to a Science:<span class="_28 blank"> </span>No longer do we need to get a brillian<span class="_0 blank"></span>t</div><div class="t m0 x12 h1 y70 ff1 fs0 fc0 sc0 ls49 ws51">insight<span class="_2f blank"> </span>in<span class="_2f blank"> </span>order<span class="_2f blank"> </span>to<span class="_1b blank"> </span>ev<span class="_2 blank"></span>aluate<span class="_2f blank"> </span>sum s<span class="_2f blank"> </span>of<span class="_1b blank"> </span>binomial<span class="_2f blank"> </span>co<span class="_5 blank"> </span>e \ufb03ci ents,<span class="_2f blank"> </span>and<span class="_2f blank"> </span>many<span class="_2f blank"> </span>similar<span class="_2f blank"> </span>fo rmulas</div><div class="t m0 x12 h1 y71 ff1 fs0 fc0 sc0 ls1a ws52">that arise frequently in practice;<span class="_35 blank"> </span>w<span class="_0 blank"></span>e can no<span class="_0 blank"></span>w follo<span class="_0 blank"></span>w a mechanical procedure a<span class="_5 blank"> </span>nd</div><div class="t m0 x12 h1 y72 ff1 fs0 fc0 sc0 ls1e ws53">disco<span class="_0 blank"></span>v<span class="_0 blank"></span>er the answers quite s<span class="_0 blank"></span>ystematically<span class="_2 blank"></span>.</div><div class="t m0 x13 h1 y73 ff1 fs0 fc0 sc0 ls49 ws54">I fell in lo<span class="_0 blank"></span>v<span class="_0 blank"></span>e with these pro<span class="_5 blank"> </span>ced<span class="_5 blank"> </span>ures as so<span class="_5 blank"> </span>on as I learned them, b<span class="_20 blank"> </span>ecause they w<span class="_0 blank"></span>orked</div><div class="t m0 x12 h1 y74 ff1 fs0 fc0 sc0 ls15 ws55">for me immediately<span class="_4 blank"></span>.<span class="_3 blank"> </span>Not on<span class="_0 blank"></span>ly did they disp<span class="_5 blank"> </span>ose of sums that I had wrestled with long</div><div class="t m0 x12 h1 y75 ff1 fs0 fc0 sc0 ls4a ws56">and hard in the past, they also kno<span class="_5 blank"> </span>c<span class="_0 blank"></span>k<span class="_0 blank"></span>ed o\ufb00 t<span class="_0 blank"></span>w<span class="_0 blank"></span>o new problems that I w<span class="_0 blank"></span>as w<span class="_0 blank"></span>orking on</div><div class="t m0 x12 h1 y76 ff1 fs0 fc0 sc0 lse ws57">at the time I \ufb01rst tried<span class="_2f blank"> </span>them.<span class="_28 blank"> </span>The success rate wa<span class="_0 blank"></span>s astonishing.</div><div class="t m0 x13 h1 y77 ff1 fs0 fc0 sc0 ls24 ws58">In fact, like a c<span class="_0 blank"></span>hild with a new to<span class="_0 blank"></span>y<span class="_4 blank"></span>, I can\u2019t resis<span class="_5 blank"> </span>t mentio<span class="_0 blank"></span>ning how I used the new</div><div class="t m0 x12 h6 y78 ff1 fs0 fc0 sc0 ls22 ws59">metho<span class="_5 blank"> </span>ds just yes<span class="_0 blank"></span>terday<span class="_4 blank"></span>.<span class="_28 blank"> </span>Long ago I had run into the sum <span class="ff8 fs5 lsd ws5a v1">P<span class="_0 blank"></span><span class="ff9 fs6 ls2c v2">k<span class="ff8 fs5 lsd v3">³</span><span class="ffa ls2d v1">2<span class="ff9 lsd ws5b">n<span class="ffb ws5c">\u2212</span></span>2<span class="ff9 lsd">k</span></span></span></span></div><div class="t m0 x14 h7 y79 ff9 fs6 fc0 sc0 lsd ws5b">n<span class="ffb ws5c">\u2212</span><span class="ls2e">k<span class="ff8 fs5 ls4b ws5d v4">´³<span class="_0 blank"></span><span class="ffa fs6 ls2d v5">2<span class="ff9 lsd">k</span></span></span></span></div><div class="t m0 x15 h7 y79 ff9 fs6 fc0 sc0 ls2f">k<span class="ff8 fs5 ls30 v4">´</span><span class="ff1 fs0 ls4c ws5e v6">,w<span class="_36 blank"></span>h<span class="_36 blank"></span>i<span class="_36 blank"></span>c<span class="_36 blank"></span>ht<span class="_36 blank"></span>a<span class="_36 blank"></span>k<span class="_37 blank"></span>e<span class="_36 blank"></span>s</span></div><div class="t m0 x12 h1 y7a ff1 fs0 fc0 sc0 ls4d ws5f">the v<span class="_2 blank"></span>alues 1, 4, 16, 64 for <span class="ff6 ls31">n</span><span class="ls4e ws60">=<span class="_0 blank"></span>0<span class="_37 blank"></span>,1<span class="_36 blank"></span>,2<span class="_36 blank"></span>,3s<span class="_37 blank"></span>oi<span class="_37 blank"></span>tm<span class="_37 blank"></span>u<span class="_37 blank"></span>s<span class="_36 blank"></span>tb<span class="_38 blank"></span>e4</span></div><div class="t m0 x16 h8 y7b ff9 fs6 fc0 sc0 ls32">n<span class="ff1 fs0 ls4f ws61 v7">.<span class="_28 blank"> </span>Ev<span class="_0 blank"></span>entually I learned a<span class="_39 blank"> </span>tric<span class="_0 blank"></span>ky</span></div><div class="t m0 x12 h9 y7c ff1 fs0 fc0 sc0 ls4f ws62">w<span class="_0 blank"></span>a<span class="_0 blank"></span>y to<span class="_34 blank"> </span>pro<span class="_0 blank"></span>v<span class="_0 blank"></span>e that it is,<span class="_34 blank"> </span>indeed,<span class="_34 blank"> </span>4<span class="ff9 fs6 ls32 v8">n</span><span class="ls23 ws63">;<span class="_39 blank"> </span>but if I had known the methods<span class="_34 blank"> </span>in this b<span class="_5 blank"> </span>o<span class="_20 blank"> </span>ok I could</span></div><div class="t m0 x12 h1 y7d ff1 fs0 fc0 sc0 ls50 ws64">ha<span class="_0 blank"></span>ve pro<span class="_2 blank"></span>ved the identit<span class="_2 blank"></span>y i<span class="_5 blank"> </span>mmediately<span class="_2 blank"></span>.<span class="_28 blank"> </span>Y<span class="_2 blank"></span>esterday I w<span class="_2 blank"></span>as working on a harder problem</div><div class="t m0 x12 h6 y7e ff1 fs0 fc0 sc0 ls51 ws65">whose answ<span class="_0 blank"></span>er w<span class="_0 blank"></span>as <span class="ff6 lsd ws66">S<span class="ff9 fs6 ls33 v9">n</span></span><span class="ls34">=<span class="ff8 fs5 ls35 v1">P</span><span class="ff9 fs6 ls36 va">k</span><span class="ff8 fs5 lsd ws5a vb">³</span><span class="ffa fs6 ls2d vc">2<span class="ff9 lsd ws5b">n<span class="ffb ws5c">\u2212<span class="_0 blank"></span><span class="ffa ls2d">2<span class="ff9 lsd">k</span></span></span></span></span></span></div><div class="t m0 x17 ha y7f ff9 fs6 fc0 sc0 lsd ws5b">n<span class="ffb ws5c">\u2212</span><span class="ls2e">k<span class="ff8 fs5 ls30 v4">´</span><span class="ffa ls37 vd">2</span><span class="ff8 fs5 ls30 v4">³</span></span><span class="ffa ws67 ve">2<span class="_0 blank"></span><span class="ff9">k</span></span></div><div class="t m0 x18 ha y7f ff9 fs6 fc0 sc0 ls38">k<span class="ff8 fs5 lsd ws5a v4">´</span><span class="ffa ls39 vd">2</span><span class="ff1 fs0 ls1b ws68 v6">.<span class="_2b blank"> </span>I didn\u2019t recognize any<span class="_2f blank"> </span>pattern in the \ufb01rst</span></div><div class="t m0 x12 h1 y80 ff1 fs0 fc0 sc0 ls52 ws69">v<span class="_2 blank"></span>alues 1, 8, 88, 1088, so<span class="_2f blank"> </span>I computed a<span class="_0 blank"></span>w<span class="_0 blank"></span>a<span class="_0 blank"></span>y with the G<span class="_0 blank"></span>osp<span class="_5 blank"> </span>er-Zeilberger algorithm.<span class="_1 blank"> </span>In</div><div class="t m0 x12 hb y81 ff1 fs0 fc0 sc0 ls53 ws6a">af<span class="_37 blank"></span>e<span class="_37 blank"></span>wm<span class="_37 blank"></span>i<span class="_37 blank"></span>n<span class="_37 blank"></span>u<span class="_37 blank"></span>t<span class="_37 blank"></span>e<span class="_37 blank"></span>sIl<span class="_37 blank"></span>e<span class="_37 blank"></span>a<span class="_37 blank"></span>r<span class="_37 blank"></span>n<span class="_37 blank"></span>e<span class="_37 blank"></span>dt<span class="_37 blank"></span>h<span class="_37 blank"></span>a<span class="_37 blank"></span>t<span class="ff6 lsd ws66">n<span class="ffa fs6 ls37 v8">3</span>S<span class="ff9 fs6 ls3a v9">n</span></span><span class="ls54 ws6b">=1<span class="_36 blank"></span>6<span class="_36 blank"></span>(<span class="_36 blank"></span><span class="ff6 ls3b">n<span class="ffc ls3c">\u2212<span class="ffa fs6 lsd vf">1</span></span></span></span></div><div class="t m0 x19 hc y82 ffa fs6 fc0 sc0 ls3d">2<span class="ff1 fs0 ls2 ws6c v6">)(2<span class="ff6 ls3e">n</span></span><span class="ls3f v10">2</span><span class="ffc fs0 ls40 v6">\u2212<span class="ff1 lsd ws6d">2<span class="ff6 ls3b">n</span><span class="ls55 ws6e">+1<span class="_1a blank"></span>)<span class="_10 blank"></span><span class="ff6 lsd ws66">S<span class="ff9 fs6 ws5b v9">n<span class="ffb ws5c">\u2212<span class="ffa ls41">1</span></span></span><span class="ffc ls40">\u2212<span class="ff1 ls46 ws6f">256(<span class="_0 blank"></span><span class="ff6 ls3b">n<span class="ffc ls42">\u2212<span class="ff1 ls46">1)</span></span></span></span></span></span></span></span></span></div><div class="t m0 x1a h8 y83 ffa fs6 fc0 sc0 ls39">3<span class="ff6 fs0 lsd ws66 v7">S</span><span class="ff9 lsd ws5b v5">n<span class="ffb ws5c">\u2212<span class="ffa ls43">2</span><span class="ff1 fs0 v11">.</span></span></span></div><div class="t m0 x13 h1 y84 ff1 fs0 fc0 sc0 ls56 ws70">Notice that the<span class="_1b blank"> </span>algorithm do<span class="_5 blank"> </span>es<span class="_5 blank"> </span>n\u2019t just verify a conjectured identit<span class="_2 blank"></span>y<span class="_1b blank"> </span>\u201c<span class="ff6 ls44">A</span><span class="ls34">=<span class="ff6 ls45">B</span><span class="ls21 ws71">\u201d. It</span></span></div><div class="t m0 x12 h1 y85 ff1 fs0 fc0 sc0 lsd ws72">also answ<span class="_0 blank"></span>ers the question \u201cWhat is <span class="ff6 ws66">A</span><span class="ls57 ws73">?\u201d,<span class="_3 blank"> </span>when w<span class="_0 blank"></span>e hav<span class="_0 blank"></span>en\u2019t b<span class="_5 blank"> </span>een able to formulate</span></div><div class="t m0 x12 h1 y86 ff1 fs0 fc0 sc0 ls57 ws74">a decent conjecture.<span class="_33 blank"> </span>The answer in the example just cons<span class="_5 blank"> </span>idered is a nonobvious</div><div class="t m0 x12 h1 y87 ff1 fs0 fc0 sc0 ls0 ws75">recurrence from whic<span class="_0 blank"></span>h it is p<span class="_5 blank"> </span>ossible to rule out an<span class="_0 blank"></span>y simple form for <span class="ff6 lsd ws66">S<span class="ff9 fs6 ls32 v9">n</span><span class="ff1">.</span></span></div><div class="t m0 x13 h1 y88 ff1 fs0 fc0 sc0 ls58 ws76">I\u2019m<span class="_34 blank"> </span>esp ecia lly<span class="_34 blank"> </span>pleased<span class="_34 blank"> </span>to<span class="_39 blank"> </span>see<span class="_34 blank"> </span>the<span class="_34 blank"> </span>app eara nce<span class="_34 blank"> </span>of<span class="_34 blank"> </span>this<span class="_34 blank"> </span>b o ok,<span class="_39 blank"> </span>b ecause<span class="_34 blank"> </span>its<span class="_39 blank"> </span>authors<span class="_34 blank"> </span>hav<span class="_0 blank"></span>e</div><div class="t m0 x12 h1 y89 ff1 fs0 fc0 sc0 ls29 ws77">not only play<span class="_0 blank"></span>ed k<span class="_0 blank"></span>ey roles in the new dev<span class="_0 blank"></span>elopments, they are a<span class="_5 blank"> </span>lso master exp<span class="_5 blank"> </span>ositors</div><div class="t m0 x12 h1 y8a ff1 fs0 fc0 sc0 ls3 ws78">of mathematic<span class="_0 blank"></span>s.<span class="_3 blank"> </span>It is alw<span class="_0 blank"></span>a<span class="_0 blank"></span>ys a treat to<span class="_2f blank"> </span>read their publicatio<span class="_0 blank"></span>ns, esp<span class="_5 blank"> </span>ecially when<span class="_2f blank"> </span>they</div><div class="t m0 x12 h1 y8b ff1 fs0 fc0 sc0 ls56 ws79">are<span class="_2f blank"> </span>discussing<span class="_1b blank"> </span>really<span class="_2f blank"> </span>imp ortan<span class="_0 blank"></span>t<span class="_2f blank"> </span>stu\ufb00.</div><div class="t m0 x13 h1 y8c ff1 fs0 fc0 sc0 ls59 ws7a">Science<span class="_34 blank"> </span>adv<span class="_2 blank"></span>a nces<span class="_34 blank"> </span>whenever<span class="_3a blank"> </span>an<span class="_34 blank"> </span>Art<span class="_3a blank"> </span>b ec om es<span class="_34 blank"> </span>a<span class="_3a blank"> </span>Sc ienc e.<span class="_28 blank"> </span>And<span class="_34 blank"> </span>the<span class="_3a blank"> </span>state<span class="_34 blank"> </span>of<span class="_3a blank"> </span>the<span class="_34 blank"> </span>Art<span class="_3a blank"> </span>ad -</div><div class="t m0 x12 h1 y8d ff1 fs0 fc0 sc0 ls56 ws7b">v<span class="_2 blank"></span>anc<span class="_5 blank"> </span>es to<span class="_5 blank"> </span>o, b<span class="_5 blank"> </span>ecause p<span class="_5 blank"> </span>eople a<span class="_5 blank"> </span>lw<span class="_0 blank"></span>a<span class="_0 blank"></span>ys leap in<span class="_0 blank"></span>to new territory once they ha<span class="_0 blank"></span>ve understoo<span class="_5 blank"> </span>d</div><div class="t m0 x12 h1 y8e ff1 fs0 fc0 sc0 ls1a ws7c">more<span class="_2f blank"> </span>ab out<span class="_2f blank"> </span>the<span class="_1b blank"> </span>old.<span class="_28 blank"> </span>This<span class="_2f blank"> </span>b o ok<span class="_1b blank"> </span>w<span class="_0 blank"></span>ill<span class="_2f blank"> </span>help<span class="_1b blank"> </span>y<span class="_0 blank"></span>ou<span class="_39 blank"> </span>r eac<span class="_0 blank"></span>h<span class="_2f blank"> </span>new<span class="_2f blank"> </span>frontiers.</div><div class="t m0 x1b h1 y8f ff1 fs0 fc0 sc0 ls12 ws7d">Donald<span class="_2f blank"> </span>E.<span class="_2f blank"> </span>Knuth</div><div class="t m0 x1b h1 y90 ff1 fs0 fc0 sc0 ls21 ws64">Stanford Univ<span class="_0 blank"></span>ersit<span class="_0 blank"></span>y</div><div class="t m0 x1c h1 y91 ff1 fs0 fc0 sc0 ls46 ws7e">20 Ma<span class="_0 blank"></span>y 1995</div></div><div class="pi" data-data='{"ctm":[1.000000,0.000000,0.000000,1.000000,0.000000,0.000000]}'></div></div> <div id="pfa" class="pf w0 h0" data-page-no="a"><div class="pc pca w0 h0"><img fetchpriority="low" loading="lazy" class="bi x0 y0 w1 h0" alt="" src="https://files.passeidireto.com/adb72897-ef92-4b54-a0dc-9a438317dc1a/bga.png"><div class="t m0 x11 h1 y11 ff4 fs0 fc0 sc0 ls50 ws7f">viii <span class="ls1e ws26">CONTENTS</span></div></div><div class="pi" data-data='{"ctm":[1.000000,0.000000,0.000000,1.000000,0.000000,0.000000]}'></div></div>
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