{VERSION 5 0 "IBM INTEL NT" "5.0" } {USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 1 0 0 0 0 1 }{PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }1 1 0 0 0 0 1 0 1 0 2 2 0 1 }} {SECT 0 {EXCHG {PARA 0 "" 0 "" {TEXT -1 3 "01." }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 512 "extendedgcd:=proc(m,n,var)\nlocal x,k,rule,r, q,X,bezout;\nglobal gcdmatrix;\nx[0]:=m;\nx[1]:=n;\nk:=0;\nrule:=[];\n gcdmatrix:=[];\nwhile not x[k+1]=0 do\n k:=k+1;\n r[k]:=rem(x[k-1],x [k],var);\n q[k]:=quo(x[k-1],x[k],var);\n x[k+1]:=r[k];\n rule:=[op (rule),collect(subs(rule,X[k+1]=X[k-1]-q[k]*X[k]),[X[0],X[1]],\n expa nd)];\n gcdmatrix:=[op(gcdmatrix),[k,x[k-1],q[k],x[k],r[k]]];\nend do ;\ngcdmatrix:=Matrix(k,5,gcdmatrix);\nbezout:=subs(rule,X[k-2]-q[k-1]* X[k-1]);\n[x[k],[coeff(bezout,X[0]),coeff(bezout,X[1])]]\nend proc:" } }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 3 "02." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 122 "a:=6*x^3+19*x^2+19*x+6:\nb:=6*x^5+13*x^4+12*x^3+13*x ^2+6*x:\ngst:=extendedgcd(a,b,x);\ng:=gst[1]: s:=gst[2][1]: t:=gst[2][ 2]:" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 3 "03." }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 18 "expand(s*a+t*b-g);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 3 "04." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "gcdmatri x;" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 3 "05." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 124 "rnd:=rand(1..10):\na:=convert([seq(rnd()*x^k,k= 0..5)],`+`);\nb:=convert([seq(rnd()*x^k,k=1..6)],`+`);\nres:=extendedg cd(a,b,x);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 7 "06./07." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "[gcdex(a,b,x,'s','t'),[s,t]];" }}}} {MARK "1 0 0" 0 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }