{VERSION 5 0 "IBM INTEL NT" "5.0" } {USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 1 12 255 0 0 1 2 1 2 2 1 2 0 0 0 1 }{CSTYLE "Text" -1 200 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 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 0 0 1 }1 1 0 0 0 0 2 0 2 0 2 2 -1 1 }} {SECT 0 {EXCHG {PARA 0 "" 0 "" {TEXT 200 3 "01." }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 14 "c:=1:d:=x^3+x:" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 200 3 "02." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "res:=re sultant(c-z*diff(d,x),d,x);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 200 3 "03 ." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 38 "sol:=convert(\{solve(r es=0,\{z\})\},list);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 200 7 "04./05." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 38 "zlist:=convert(\{solve(re s=0,z)\},list);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 200 11 "06./07./08." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 62 "vlist:=convert(map(y->gcd (subs(y,c-z*diff(d,x)),d),sol),list);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 200 3 "09." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 50 "ListToo ls[DotProduct](zlist,map(y->log(y),vlist));" }}}{EXCHG {PARA 0 "" 0 " " {TEXT 200 3 "10." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 48 "integ ral:=1/2*log(x^3+x-1)-2/3*log(x^5+2*x^2-3);" }}}{EXCHG {PARA 0 "" 0 " " {TEXT 200 3 "11." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "r:=no rmal(diff(integral,x));" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 200 3 "12." } }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "c:=numer(r)/6:\n" } {MPLTEXT 1 0 14 "d:=denom(r)/6:" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 200 3 "13." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "res:=resultant(c- z*diff(d,x),d,x);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 200 3 "14." }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 38 "sol:=convert(\{solve(res=0, \{z\})\},list);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 200 3 "15." }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 43 "zlist:=convert(map(y->subs(y ,z),sol),list);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 200 7 "16./17." }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 62 "vlist:=convert(map(y->gcd(su bs(y,c-z*diff(d,x)),d),sol),list);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 200 3 "18." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 50 "ListTools[Dot Product](zlist,map(y->log(y),vlist));" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 200 3 "19." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "int(r,x );\n" }{MPLTEXT 1 0 34 "expand((x-1)*(x^4+x^3+x^2+3*x+3));" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 200 3 "20." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "c:=x:d:=1+x+x^7:" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 200 3 "21." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "res:=resultan t(c-z*diff(d,x),d,x);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 200 3 "22." }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "factor(res);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 200 3 "23." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "RothsteinTrager:=proc(r,x)\n" }{MPLTEXT 1 0 33 "local c,d,z,res,sol,zlist,vlist;\n" }{MPLTEXT 1 0 13 "c:=numer(r);\n" } {MPLTEXT 1 0 13 "d:=denom(r);\n" }{MPLTEXT 1 0 35 "res:=resultant(c-z* diff(d,x),d,x);\n" }{MPLTEXT 1 0 39 "sol:=convert(\{solve(res=0,\{z\}) \},list);\n" }{MPLTEXT 1 0 44 "zlist:=convert(map(y->subs(y,z),sol),li st);\n" }{MPLTEXT 1 0 63 "vlist:=convert(map(y->gcd(subs(y,c-z*diff(d, x)),d),sol),list);\n" }{MPLTEXT 1 0 51 "ListTools[DotProduct](zlist,ma p(y->log(y),vlist));\n" }{MPLTEXT 1 0 9 "end proc:" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 200 3 "24." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "RothsteinTrager(1/(x^3+x),x);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 200 3 "25." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "RothsteinTrager(r,x );" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 200 3 "26." }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 29 "RothsteinTrager(1/(x^2-2),x);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 200 3 "27." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "int(1/(x^2-2),x);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 200 3 "28." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 55 "RT:=Rothstein Trager((-x^2-9*x+1)/(18*(x^4-x^3+x-1)),x);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 200 3 "29." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 49 "integra l:=int((-x^2-9*x+1)/(18*(x^4-x^3+x-1)),x);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 200 3 "30." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "plot(in tegral,x=1..3);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 200 3 "31." }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "plot(RT-integral,x=1..3);" } }}{EXCHG {PARA 0 "" 0 "" {TEXT 200 3 "32." }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 28 "normal(diff(RT-integral,x));" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 200 3 "33." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "co nst:=subs(x=0,RT-integral);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 200 3 "34 ." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "const:=evalc(const);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 200 3 "35." }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 13 "evalf(const);" }}}}{MARK "1 0 0" 0 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }