{VERSION 6 0 "IBM INTEL NT" "6.0" } {USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 1 12 255 0 0 1 0 1 0 2 1 2 0 0 0 1 }{CSTYLE "2D Output" -1 20 "Times" 1 12 0 0 255 1 0 0 0 2 2 1 0 0 0 1 }{CSTYLE "" -1 256 "" 1 18 0 0 0 0 0 1 0 0 0 0 0 0 0 0 } {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 2 0 2 0 2 2 0 1 }{PSTYLE "Heading 1" -1 3 1 {CSTYLE "" -1 -1 "Times" 1 18 0 0 0 1 2 1 2 2 2 2 1 1 1 1 }1 1 0 0 8 4 2 0 2 0 2 2 0 1 }{PSTYLE "Maple Output" -1 11 1 {CSTYLE "" -1 -1 "Ti mes" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }3 3 0 0 0 0 1 0 1 0 2 2 0 1 } {PSTYLE "Normal" -1 256 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }3 1 0 0 0 0 2 0 2 0 2 2 0 1 }} {SECT 0 {EXCHG {PARA 256 "" 0 "" {TEXT 256 30 "Esame Algebra I del 01. 07.2004" }{TEXT -1 0 "" }}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 30 "Calcol o dei numeri di Lagrange" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 " L1:=chrem([1,0,0],[3,5,11]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#L1G \"#b" }}}{EXCHG }{EXCHG }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "L2: =chrem([0,1,0],[3,5,11]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#L2G\"# m" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "L3:=chrem([0,0,1],[3,5 ,11]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#L3G\"#X" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "11*L1+2*L2+6*L3 mod 3*5*11;" }{TEXT -1 41 "soluzione finale come combinazione intera" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"#<" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "chre m([11,2,6],[3,5,11]);" }{TEXT -1 33 "uso diretto del comando di maple " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"#<" }}}}{EXCHG }{EXCHG }{EXCHG } {EXCHG }{SECT 1 {PARA 3 "" 0 "" {TEXT -1 16 "Sviluppo p-adico" }} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "with(padic):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "p:=3;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"pG\"\"$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "ord:=4; " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$ordG\"\"%" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "f:=y->y^2-7;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"fGf*6#%\"yG6\"6$%)operatorG%&arrowGF(,&*$)9$\"\"#\"\"\"F1\"\"(! \"\"F(F(F(" }}}{EXCHG }{EXCHG }{EXCHG }{EXCHG }{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 61 "for x from 0 to p-1 do if f(x) mod p=0 then e:=x;br eak;fi;od;" }{TEXT -1 57 "determino valore iniziale soluzione (prima c ifra 3-adica)" }}}{EXCHG }{EXCHG }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 75 "for i to ord do c:=-iquo(f(e),p^i)*(1/D(f)(1) mod p) mod p;c;e:= e+c*p^i:od;" }{TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 61 "applico met odo Newton-Hensel per ottenere le cifre successive" }}{PARA 11 "" 1 " " {XPPMATH 20 "6#>%\"cG\"\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\" \"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"eG\"\"%" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"cG\"\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"\" " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"eG\"#8" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"cG\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"!" } }{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"eG\"#8" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"cG\"\"#" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"#" } }{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"eG\"$v\"" }}}{EXCHG }{EXCHG } {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "b:= evalp (RootOf (f(y)),p,5 );" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"bG6$,,\"\"#\"\"\"-%!G6#\"\"$ F(*$)F)F'F(F(*&F'F()F)F,F(F(-%\"OG6#*$)F)\"\"&F(F(,,F(F(F)F(F-F(*&F'F( )F)\"\"%F(F(F1F(" }}}{EXCHG }}{EXCHG }{EXCHG }{SECT 0 {PARA 3 "" 0 "" {TEXT -1 24 "Fattorizzazione modulare" }}{EXCHG }{EXCHG }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "with(LinearAlgebra):x:='x';" }}{PARA 11 " " 1 "" {XPPMATH 20 "6#>%\"xGF$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "p:=5;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"pG\"\"&" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "f:=x->x^4+3*x^3+x+1;" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"fGf*6#%\"xG6\"6$%)operatorG%&arrow GF(,**$)9$\"\"%\"\"\"F1*&\"\"$F1)F/F3F1F1F/F1F1F1F(F(F(" }}}{EXCHG } {EXCHG }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "d:=degree(f(x),x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"dG\"\"%" }}}{EXCHG }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 53 "u:=(i,j)->coeff(rem(x^(p*(i-1)),f(x ),x) mod p,x,j-1);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"uGf*6$%\"iG% \"jG6\"6$%)operatorG%&arrowGF)-%&coeffG6%-%$modG6$-%$remG6%)%\"xG*&%\" pG\"\"\",&9$F:F:!\"\"F:-%\"fG6#F7F7F9F7,&9%F:F:F=F)F)F)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "Q:=Matrix(d,u);" }}{PARA 11 "" 1 " " {XPPMATH 20 "6#>%\"QG-%'RTABLEG6%\")k " 0 "" {MPLTEXT 1 0 29 "ee:=Matrix(d,shape=identity) ;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#eeG-%'RTABLEG6%\")7*fS$-%'MATR IXG6#7&7&\"\"\"\"\"!F/F/7&F/F.F/F/7&F/F/F.F/7&F/F/F/F.%'MatrixG" }}} {EXCHG }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 33 "Nullspace(Transpose( Q-ee)) mod p;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#<$-%'RTABLEG6%\")wKFM -%'MATRIXG6#7&7#\"\"!7#\"\"#7#\"\"\"F0&%'VectorG6#%'columnG-F%6%\")'Rt U$-F)6#7&F0F,F,F,F2" }}}{EXCHG }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 44 "seq(Gcd(f(x),2*x+x^2+x^3-s) mod p,s=0..p-1);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6'\"\"\",(*$)%\"xG\"\"#F#F#*&\"\"$F#F'F#F#F*F#F#,&F%F#F(F #F#" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 33 "Berlekamp(x^4+3*x^3+ x+1,x) mod 5;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#<$,(*$)%\"xG\"\"#\"\" \"F)*&\"\"$F)F'F)F)F+F),&F%F)F(F)" }}}{EXCHG }}{EXCHG }{EXCHG }{EXCHG }{EXCHG }{EXCHG }{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{MARK "9" 0 } {VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 } {RTABLE_HANDLES 32281764 34059912 34273276 34273396 }{RTABLE M7R0 I5RTABLE_SAVE/32281764X,%)anythingG6"6"[gl!"%!!!#1"%"%"""""$""%""!F*""#F(F*F*F) F(F*F*F)F)F)F& } {RTABLE M7R0 I5RTABLE_SAVE/34059912X,%)anythingG6#%)identityG6"[gl!""!!!#!"%"%F' } {RTABLE M7R0 I5RTABLE_SAVE/34273276X*%)anythingG6"6"[gl!#%!!!"%"%""!""#"""F)F& } {RTABLE M7R0 I5RTABLE_SAVE/34273396X*%)anythingG6"6"[gl!#%!!!"%"%"""""!F(F(F& }