{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 35 "rem(sum(a[k]*x^k,k=0..10),x^2-2,x);" }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 3 "02." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 267 "reducepol:=proc(p,x,redp)\nlocal n,m,rules,pol;\npol :=p;\nn:=degree(redp,x);\nm:=degree(p,x);\nrules:=seq(map(y->y*x^i,x^n =-redp+lcoeff(redp)*x^n),i=0..m-n);\nwhile degree(pol,x)>=n do\n pol: =subs(rules,pol);\nend do;\npol\nend proc:\n\nreducepol(sum(a[k]*x^k,k =0..10),x,x^2-2);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 3 "03." }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "rem(sum(a[k]*x^k,k=0..10),x^ 2-2,x);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 3 "04." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "sum(a[k]*(sqrt(2))^k,k=0..10);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 3 "05." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "rem(x^9,x^2-2,x) mod 5;" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 3 "06." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "rem(sum(a[k]*x^k,k= 0..10),x^2+1,x);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 3 "07." }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 41 "reducepol(sum(a[k]*x^k,k=0.. 10),x,x^2+1);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 3 "08." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "rem(sum(a[k]*x^k,k=0..10),x^2+1,x); " }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 3 "09." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "sum(a[k]*I^k,k=0..10);" }}}}{MARK "1 0 0" 0 } {VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }