{VERSION 7 1 "Linux" "7.1" } {USTYLETAB {PSTYLE "Ordered List 5" -1 200 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 3 3 2 144 2 0 2 2 -1 1 } {PSTYLE "Heading 4" -1 20 1 {CSTYLE "" -1 -1 "MS Serif" 1 12 0 0 0 1 1 2 2 2 2 2 1 0 0 1 }1 1 0 0 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "Text Output " -1 2 1 {CSTYLE "" -1 -1 "Courier" 1 12 0 0 255 1 2 2 2 2 2 1 3 0 0 1 }1 1 0 0 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "Ordered List 1" -1 201 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 3 3 2 0 2 0 2 2 -1 1 }{PSTYLE "Bullet Item" -1 15 1 {CSTYLE "" -1 -1 "Tim es" 1 12 0 0 0 1 2 2 2 2 2 2 1 0 0 1 }1 1 0 0 3 3 2 0 2 0 2 2 -1 1 } {PSTYLE "Author" -1 19 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 0 0 1 }3 1 0 0 8 8 2 0 2 0 2 2 -1 1 }{PSTYLE "Dash Item" -1 16 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 3 3 2 0 2 0 2 2 -1 1 }{PSTYLE "Heading 3" -1 5 1 {CSTYLE "" -1 -1 "MS S erif" 1 14 0 0 0 1 1 1 2 2 2 2 1 0 0 1 }1 1 0 0 0 0 2 0 2 0 2 2 -1 1 } {PSTYLE "Diagnostic" -1 9 1 {CSTYLE "" -1 -1 "Courier" 1 12 40 120 40 1 2 2 2 2 2 1 2 0 0 1 }1 1 0 0 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "Ordered \+ List 4" -1 202 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 3 3 2 108 2 0 2 2 -1 1 }{PSTYLE "Maple Output" -1 11 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 0 0 1 }3 1 0 0 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "List Item" -1 14 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 3 3 2 0 2 0 2 2 -1 1 } {PSTYLE "Line Printed Output" -1 6 1 {CSTYLE "" -1 -1 "Courier" 1 12 0 0 255 1 2 2 2 2 2 1 2 0 0 1 }1 1 0 0 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "H eading 2" -1 4 1 {CSTYLE "" -1 -1 "MS Serif" 1 16 0 0 0 1 2 1 2 2 2 2 1 0 0 1 }1 1 0 0 8 2 2 0 2 0 2 2 -1 1 }{PSTYLE "Ordered List 3" -1 203 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 3 3 2 72 2 0 2 2 -1 1 }{PSTYLE "Error" -1 8 1 {CSTYLE "" -1 -1 "Courie r" 1 12 255 0 255 1 2 2 2 2 2 1 1 0 0 1 }1 1 0 0 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "Maple Plot" -1 13 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 0 0 1 }3 1 0 0 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "Warning" -1 7 1 {CSTYLE "" -1 -1 "Courier" 1 12 0 0 255 1 2 2 2 2 2 1 1 0 0 1 }1 1 0 0 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "Heading 1" -1 3 1 {CSTYLE "" -1 -1 "MS Serif" 1 18 0 0 0 1 2 1 2 2 2 2 1 0 0 1 }1 1 0 0 8 4 2 0 2 0 2 2 -1 1 }{PSTYLE "Title" -1 18 1 {CSTYLE "" -1 -1 "Times" 1 18 0 0 0 1 2 1 2 2 2 2 1 0 0 1 }3 1 0 0 12 12 2 0 2 0 2 2 -1 1 }{PSTYLE "Ordered Li st 2" -1 204 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 3 3 2 36 2 0 2 2 -1 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 }{CSTYLE "Equation Label" -1 200 "Courier" 1 12 0 0 0 1 2 1 2 2 2 2 0 0 0 1 }{CSTYLE "Text" -1 201 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 0 0 0 1 }{CSTYLE "Page Number" -1 33 "Times" 1 10 0 0 0 1 2 2 2 2 2 2 0 0 0 1 }{CSTYLE "Maple Input" -1 0 "Courier" 1 12 255 0 0 1 2 1 2 2 1 2 0 0 0 1 }{CSTYLE "2D Output" -1 20 "Times" 1 12 0 0 255 1 2 2 2 2 2 1 0 0 0 1 }{CSTYLE "Dictionary Hyperlink" -1 45 "MS Serif" 1 12 147 0 15 1 2 2 1 2 2 2 0 0 0 1 }{CSTYLE "2D Input" -1 19 "Times" 1 12 0 0 0 1 2 2 2 2 1 2 0 0 0 1 }{CSTYLE "Maple Input Placeholder" -1 202 "Couri er" 1 12 200 0 200 1 2 1 2 2 1 2 0 0 0 1 }{CSTYLE "2D Math" -1 2 "Time s" 1 12 0 0 0 1 2 2 2 2 2 2 0 0 0 1 }{CSTYLE "Hyperlink" -1 17 "MS Ser if" 1 12 0 128 128 1 2 2 1 2 2 2 0 0 0 1 }} {SECT 0 {EXCHG {PARA 18 "" 0 "" {TEXT 201 11 "Kalkulus I." }}}{EXCHG {PARA 19 "" 0 "" {TEXT 203 18 "J\303\241rai Antal" }}}{EXCHG {PARA 19 "" 0 "" {TEXT 203 68 "Ezek a programok csak szeml\303\251ltet\303\251s re szolg\303\241lnak" }}}{SECT 1 {PARA 3 "" 0 "" {TEXT 204 11 "1. Halm azok" }}{PARA 0 "" 0 "" {TEXT 201 0 "" }}}{SECT 0 {PARA 3 "" 0 "" {TEXT 204 16 "2. Sz\303\241mok" }}{PARA 0 "" 0 "" {TEXT 201 0 "" }} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart;" }}}{SECT 0 {PARA 4 "" 0 "" {TEXT 205 31 "2.1. Val\303\263s sz\303\241mok" }}{PARA 0 "" 0 "" {TEXT 201 0 "" }}{SECT 0 {PARA 5 "" 0 "" {TEXT 206 12 "2.1.1. Test. " }}{EXCHG {PARA 0 "" 0 "" {XPPEDIT 2 0 "" "%#%?G" }}}}{SECT 0 {PARA 5 "" 0 "" {TEXT 206 20 "2.1.2. P\303\251lda." }}{PARA 0 "" 0 "" {TEXT 201 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 49 "&+(0,0):=0; &+(0, 1):=1; &+(1,0):=1; &+(1,1):=0;\n" }{MPLTEXT 1 0 2 "\n" }{MPLTEXT 1 0 49 "&*(0,0):=0; &*(0,1):=0; &*(1,0):=0; &*(1,1):=1;\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"\"" }} {PARA 11 "" 1 "" {XPPMATH 20 "\"\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 " \"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"\"" }}}{EXCHG {PARA 0 "" 0 "" {XPPEDIT 2 0 "" "%#%?G" }}}}{SECT 0 {PARA 5 "" 0 "" {TEXT 206 28 "2.1.3. P\303\251ld \303\241k." }}{PARA 0 "" 0 "" {TEXT 201 0 "" }}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 63 "`&+`:=(x,y)->irem(x+y,5); `&*`:=(x,y)->irem(x*y,5); 3&+4; 3&*4;" }}{PARA 11 "" 1 "" {XPPMATH 20 "f*6$I\"xG6\"I\"yGF%F%6$I )operatorGF%I&arrowGF%F%-I%iremG%*protectedG6$,&F$\"\"\"F&F/\"\"&F%F%F %" }}{PARA 11 "" 1 "" {XPPMATH 20 "f*6$I\"xG6\"I\"yGF%F%6$I)operatorGF %I&arrowGF%F%-I%iremG%*protectedG6$*&F$\"\"\"F&F/\"\"&F%F%F%" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"#" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"#" }}}{EXCHG {PARA 0 "" 0 "" {XPPEDIT 2 0 "" "%#%?G" }}}}{SECT 0 {PARA 5 "" 0 "" {TEXT 206 43 "* 2.1.4. Algebrai strukt\303\272r\303\241k." }} {PARA 0 "" 0 "" {TEXT 201 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 49 "isgrupoid:=proc(G::set,f::procedure) local x,y;\n" }{MPLTEXT 1 0 70 "for x in G do for y in G do if not f(x,y) in G then return false fi;\n" }{MPLTEXT 1 0 20 "od; od; true; end;\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "f*6$'I\"GG6\"I$setG%*protectedG'I\"fGF&I*procedureGF(6$I \"xGF&I\"yGF&F&F&C$?&F-F%I%trueGF(?&F.F%F1@$4-I#inGF(6$-F*F,F%OI&false GF(F1F&F&F&" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 51 "neutral:=pro c(G::set,f::procedure) local x,y,s,S;\n" }{MPLTEXT 1 0 44 "if not isgr upoid(G,f) then return NULL fi;\n" }{MPLTEXT 1 0 38 "for x in G do s:= true; for y in G do\n" }{MPLTEXT 1 0 55 " if f(x,y)<>y or f(y,x)<>y t hen s:=false; break; fi;\n" }{MPLTEXT 1 0 42 "od; if s then return x f i; od; NULL end;\n" }{MPLTEXT 1 0 2 "\n" }{MPLTEXT 1 0 55 "G:=\{a,b,c \};neutral(G,(x,y)->y);neutral(G,(x,y)->y);\n" }{MPLTEXT 1 0 2 "\n" } {MPLTEXT 1 0 40 "neutral(\{0,1,2\},(x,y)->irem(x+y,3));\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "f*6$'I\"GG6\"I$setG%*protectedG'I\"fGF&I*procedur eGF(6&I\"xGF&I\"yGF&I\"sGF&I\"SGF&F&F&C%@$4-I*isgrupoidGF&6$F%F*OI%NUL LGF(?&F-F%I%trueGF(C%>F/F:?&F.F%F:@$50-F*6$F-F.F.0-F*6$F.F-F.C$>F/I&fa lseGF([@$F/OF-F8F&F&F&" }}{PARA 11 "" 1 "" {XPPMATH 20 "<%I\"aG6\"I\"b GF$I\"cGF$" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 53 "issemigroup:=proc(G::set,f::procedure) local x,y,z;\n" }{MPLTEXT 1 0 45 "if not isgrupoid(G,f) then return false f i;\n" }{MPLTEXT 1 0 43 "for x in G do for y in G do for z in G do\n" } {MPLTEXT 1 0 53 " if f(x,f(y,z))<>f(f(x,y),z) then return false fi;\n " }{MPLTEXT 1 0 23 "od; od; od; true end;\n" }{MPLTEXT 1 0 2 "\n" } {MPLTEXT 1 0 34 "issemigroup(\{a,b,c\},(x,y)->x);\n" }{MPLTEXT 1 0 2 " \n" }{MPLTEXT 1 0 50 "issemigroup(\{true,false\},(x,y)-> x implies y); \n" }}{PARA 11 "" 1 "" {XPPMATH 20 "f*6$'I\"GG6\"I$setG%*protectedG'I \"fGF&I*procedureGF(6%I\"xGF&I\"yGF&I\"zGF&F&F&C%@$4-I*isgrupoidGF&6$F %F*OI&falseGF(?&F-F%I%trueGF(?&F.F%F9?&F/F%F9@$0-F*6$F--F*6$F.F/-F*6$- F*6$F-F.F/F6F9F&F&F&" }}{PARA 11 "" 1 "" {XPPMATH 20 "I%trueG%*protect edG" }}{PARA 11 "" 1 "" {XPPMATH 20 "I&falseG%*protectedG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 51 "isgroup:=proc(G::set,f::procedure) \+ local x,y,n,i;\n" }{MPLTEXT 1 0 45 "if not isgrupoid(G,f) then return \+ false fi;\n" }{MPLTEXT 1 0 47 "if not issemigroup(G,f) then return fal se fi;\n" }{MPLTEXT 1 0 50 "n:=neutral(G,f); if n=NULL then return fal se fi;\n" }{MPLTEXT 1 0 39 "for x in G do i:=false; for y in G do\n" } {MPLTEXT 1 0 52 " if f(x,y)=n and f(y,x)=n then i:=true; break fi;\n" }{MPLTEXT 1 0 53 "od; if i=false then return false fi; od; true; end; \n" }{MPLTEXT 1 0 2 "\n" }{MPLTEXT 1 0 40 "isgroup(\{0,1,2\},(x,y)->ir em(x+y,3));\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "f*6$'I\"GG6\"I$setG%*pr otectedG'I\"fGF&I*procedureGF(6&I\"xGF&I\"yGF&I\"nGF&I\"iGF&F&F&C(@$4- I*isgrupoidGF&6$F%F*OI&falseGF(@$4-I,issemigroupGF&F6F7>F/-I(neutralGF &F6@$/F/I%NULLGF(F7?&F-F%I%trueGF(C%>F0F8?&F.F%FD@$3/-F*6$F-F.F//-F*6$ F.F-F/C$>F0FD[@$/F0F8F7FDF&F&F&" }}{PARA 11 "" 1 "" {XPPMATH 20 "I%tru eG%*protectedG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 53 "iscommuta tive:=proc(G::set,f::procedure) local x,y;\n" }{MPLTEXT 1 0 45 "if not isgrupoid(G,f) then return false fi;\n" }{MPLTEXT 1 0 29 "for x in G \+ do for y in G do\n" }{MPLTEXT 1 0 43 " if f(x,y)<>f(y,x) then return \+ false fi;\n" }{MPLTEXT 1 0 20 "od; od; true; end;\n" }{MPLTEXT 1 0 2 " \n" }{MPLTEXT 1 0 46 "iscommutative(\{0,1,2\},(x,y)->irem(x+y,3));\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "f*6$'I\"GG6\"I$setG%*protectedG'I\"fGF &I*procedureGF(6$I\"xGF&I\"yGF&F&F&C%@$4-I*isgrupoidGF&6$F%F*OI&falseG F(?&F-F%I%trueGF(?&F.F%F8@$0-F*F,-F*6$F.F-F5F8F&F&F&" }}{PARA 11 "" 1 "" {XPPMATH 20 "I%trueG%*protectedG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 43 "isabeliangroup:=proc(G::set,f::procedure)\n" } {MPLTEXT 1 0 42 "isgroup(G,f) and iscommutative(G,f) end;\n" }{MPLTEXT 1 0 2 "\n" }{MPLTEXT 1 0 46 "iscommutative(\{0,1,2\},(x,y)->irem(x+y, 3));\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "f*6$'I\"GG6\"I$setG%*protected G'I\"fGF&I*procedureGF(F&F&F&3-I(isgroupGF&6$F%F*-I.iscommutativeGF&F/ F&F&F&" }}{PARA 11 "" 1 "" {XPPMATH 20 "I%trueG%*protectedG" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 73 "isleftdistributive:=proc(R:: set,f::procedure,g::procedure) local x,y,z;\n" }{MPLTEXT 1 0 45 "if no t isgrupoid(R,f) then return false fi;\n" }{MPLTEXT 1 0 45 "if not isg rupoid(R,g) then return false fi;\n" }{MPLTEXT 1 0 43 "for x in R do f or y in R do for z in R do\n" }{MPLTEXT 1 0 58 " if g(x,f(y,z))<>f(g( x,y),g(x,z)) then return false fi;\n" }{MPLTEXT 1 0 21 "od; od; od; tr ue end;" }}{PARA 11 "" 1 "" {XPPMATH 20 "f*6%'I\"RG6\"I$setG%*protecte dG'I\"fGF&I*procedureGF('I\"gGF&F+6%I\"xGF&I\"yGF&I\"zGF&F&F&C&@$4-I*i sgrupoidGF&6$F%F*OI&falseGF(@$4-F66$F%F-F8?&F/F%I%trueGF(?&F0F%F??&F1F %F?@$0-F-6$F/-F*6$F0F1-F*6$-F-6$F/F0-F-6$F/F1F8F?F&F&F&" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 74 "isrightdistributive:=proc(R::set,f: :procedure,g::procedure) local x,y,z;\n" }{MPLTEXT 1 0 45 "if not isgr upoid(R,f) then return false fi;\n" }{MPLTEXT 1 0 45 "if not isgrupoid (R,g) then return false fi;\n" }{MPLTEXT 1 0 43 "for x in R do for y i n R do for z in R do\n" }{MPLTEXT 1 0 58 " if g(f(y,z),x)<>f(g(y,x),g (z,x)) then return false fi;\n" }{MPLTEXT 1 0 21 "od; od; od; true end ;" }}{PARA 11 "" 1 "" {XPPMATH 20 "f*6%'I\"RG6\"I$setG%*protectedG'I\" fGF&I*procedureGF('I\"gGF&F+6%I\"xGF&I\"yGF&I\"zGF&F&F&C&@$4-I*isgrupo idGF&6$F%F*OI&falseGF(@$4-F66$F%F-F8?&F/F%I%trueGF(?&F0F%F??&F1F%F?@$0 -F-6$-F*6$F0F1F/-F*6$-F-6$F0F/-F-6$F1F/F8F?F&F&F&" }}}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 48 "isring:=proc(R::set,f::procedure,g::procedur e)\n" }{MPLTEXT 1 0 42 "isabeliangroup(R,f) and issemigroup(R,g)\n" } {MPLTEXT 1 0 65 "and isleftdistributive(R,f,g) and isrightdistributive (R,f,g) end;" }}{PARA 11 "" 1 "" {XPPMATH 20 "f*6%'I\"RG6\"I$setG%*pro tectedG'I\"fGF&I*procedureGF('I\"gGF&F+F&F&F&333-I/isabeliangroupGF&6$ F%F*-I,issemigroupGF&6$F%F--I3isleftdistributiveGF&6%F%F*F--I4isrightd istributiveGF&F9F&F&F&" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 59 "i scommutativering:=proc(R::set,f::procedure,g::procedure)\n" }{MPLTEXT 1 0 41 "isring(R,f,g) and iscommutative(R,g) end;" }}{PARA 11 "" 1 "" {XPPMATH 20 "f*6%'I\"RG6\"I$setG%*protectedG'I\"fGF&I*procedureGF('I\" gGF&F+F&F&F&3-I'isringGF&6%F%F*F--I.iscommutativeGF&6$F%F-F&F&F&" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 57 "isringwithunity:=proc(R::set ,f::procedure,g::procedure)\n" }{MPLTEXT 1 0 41 "isring(R,f,g) and neu tral(R,g)<>NULL end;" }}{PARA 11 "" 1 "" {XPPMATH 20 "f*6%'I\"RG6\"I$s etG%*protectedG'I\"fGF&I*procedureGF('I\"gGF&F+F&F&F&3-I'isringGF&6%F% F*F-0-I(neutralGF&6$F%F-I%NULLGF(F&F&F&" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 62 "isskewfield:=proc(R::set,f::procedure,g::procedure) l ocal n;\n" }{MPLTEXT 1 0 50 "n:=neutral(R,f); if n=NULL then return fa lse fi;\n" }{MPLTEXT 1 0 47 "isring(R,f,g) and isgroup(R minus \{n\},g ) end;" }}{PARA 11 "" 1 "" {XPPMATH 20 "f*6%'I\"RG6\"I$setG%*protected G'I\"fGF&I*procedureGF('I\"gGF&F+6#I\"nGF&F&F&C%>F/-I(neutralGF&6$F%F* @$/F/I%NULLGF(OI&falseGF(3-I'isringGF&6%F%F*F--I(isgroupGF&6$-I&minusG F(6$F%<#F/F-F&F&F&" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 58 "isfie ld:=proc(R::set,f::procedure,g::procedure) local n;\n" }{MPLTEXT 1 0 50 "n:=neutral(R,f); if n=NULL then return false fi;\n" }{MPLTEXT 1 0 54 "isring(R,f,g) and isabeliangroup(R minus \{n\},g) end;" }}{PARA 11 "" 1 "" {XPPMATH 20 "f*6%'I\"RG6\"I$setG%*protectedG'I\"fGF&I*procedu reGF('I\"gGF&F+6#I\"nGF&F&F&C%>F/-I(neutralGF&6$F%F*@$/F/I%NULLGF(OI&f alseGF(3-I'isringGF&6%F%F*F--I/isabeliangroupGF&6$-I&minusGF(6$F%<#F/F -F&F&F&" }}}{EXCHG {PARA 0 "" 0 "" {XPPEDIT 2 0 "" "%#%?G" }}}}{SECT 0 {PARA 5 "" 0 "" {TEXT 206 30 "* 2.1.5. P\303\251ld\303\241k." }} {PARA 0 "" 0 "" {TEXT 201 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 53 "iff:=(x,y)->evalb((x implies y) and (y implies x));\n" }{MPLTEXT 1 0 2 "\n" }{MPLTEXT 1 0 55 "X:=\{true,false\}; isabeliangroup(X,(x,y )->iff(x,y));\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "f*6$I\"xG6\"I\"yGF%F% 6$I)operatorGF%I&arrowGF%F%-I&evalbG%*protectedG6#3hF$F&hF&F$F%F%F%" } }{PARA 11 "" 1 "" {XPPMATH 20 "<$I&falseG%*protectedGI%trueGF$" }} {PARA 11 "" 1 "" {XPPMATH 20 "I%trueG%*protectedG" }}}{EXCHG {PARA 0 " " 0 "" {XPPEDIT 2 0 "" "%#%?G" }}}}{SECT 0 {PARA 5 "" 0 "" {TEXT 206 30 "* 2.1.6. P\303\251ld\303\241k." }}{PARA 0 "" 0 "" {TEXT 201 0 "" } }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 86 "X:=\{a,b,c\};with(combinat, powerset);P:=powerset(X);isgroup(P,(x,y)->symmdiff(x,y));\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "<%I\"aG6\"I\"bGF$I\"cGF$" }}{PARA 11 "" 1 "" {XPPMATH 20 "7#I)powersetG6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "<*<\"<% I\"aG6\"I\"bGF&I\"cGF&<$F'F(<#F(<$F%F(<#F%<#F'<$F%F'" }}{PARA 11 "" 1 "" {XPPMATH 20 "I%trueG%*protectedG" }}}{EXCHG {PARA 0 "" 0 "" {XPPEDIT 2 0 "" "%#%?G" }}}}{SECT 0 {PARA 5 "" 0 "" {TEXT 206 30 "* 2. 1.7. P\303\251ld\303\241k." }}{PARA 0 "" 0 "" {TEXT 201 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 32 "isring(\{0\},(x,y)->0,(x,y)->0);" } }{PARA 11 "" 1 "" {XPPMATH 20 "I%trueG%*protectedG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 43 "isring(P,(x,y)->symmdiff(x,y),(x,y)->\{\}); " }}{PARA 11 "" 1 "" {XPPMATH 20 "I%trueG%*protectedG" }}}{EXCHG {PARA 0 "" 0 "" {XPPEDIT 2 0 "" "%#%?G" }}}}{SECT 0 {PARA 5 "" 0 "" {TEXT 206 30 "* 2.1.8. P\303\251ld\303\241k." }}{PARA 0 "" 0 "" {TEXT 201 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 65 "iscommutativering (P,(x,y)->symmdiff(x,y),(x,y)->x intersect y);\n" }{MPLTEXT 1 0 2 "\n" }{MPLTEXT 1 0 63 "isringwithunity(P,(x,y)->symmdiff(x,y),(x,y)->x int ersect y);\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "I%trueG%*protectedG" }} {PARA 11 "" 1 "" {XPPMATH 20 "I%trueG%*protectedG" }}}{EXCHG {PARA 0 " " 0 "" {XPPEDIT 2 0 "" "%#%?G" }}}}{SECT 1 {PARA 5 "" 0 "" {TEXT 206 30 "* 2.1.9. P\303\251ld\303\241k." }}{EXCHG {PARA 0 "" 0 "" {XPPEDIT 2 0 "" "%#%?G" }}}}{SECT 0 {PARA 5 "" 0 "" {TEXT 206 23 "2.1.10. Rende zett test." }}{PARA 0 "" 0 "" {TEXT 201 0 "" }}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 62 "abs(7.4); abs(-3); abs(0); signum(7.4); signum(-3); signum(0);" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"#u!\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"$" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }} {PARA 11 "" 1 "" {XPPMATH 20 "\"\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 " !\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}}{EXCHG {PARA 0 "" 0 " " {XPPEDIT 2 0 "" "%#%?G" }}}}{SECT 1 {PARA 5 "" 0 "" {TEXT 206 21 "2. 1.11. T\303\251tel." }}{EXCHG {PARA 0 "" 0 "" {XPPEDIT 2 0 "" "%#%?G" }}}}{SECT 1 {PARA 5 "" 0 "" {TEXT 206 29 "2.1.12. P\303\251ld\303\241k ." }}{EXCHG {PARA 0 "" 0 "" {XPPEDIT 2 0 "" "%#%?G" }}}}{SECT 1 {PARA 5 "" 0 "" {TEXT 206 21 "2.1.13. T\303\251tel." }}{EXCHG {PARA 0 "" 0 " " {XPPEDIT 2 0 "" "%#%?G" }}}}{SECT 1 {PARA 5 "" 0 "" {TEXT 206 35 "2. 1.14. Val\303\263s sz\303\241mok." }}{EXCHG {PARA 0 "" 0 "" {XPPEDIT 2 0 "" "%#%?G" }}}}{SECT 0 {PARA 5 "" 0 "" {TEXT 206 41 "2.1.15. Term\3 03\251szetes sz\303\241mok." }}{PARA 0 "" 0 "" {TEXT 201 0 "" }} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 44 "inc:=x->x+1;0;inc(%);inc(%); inc(%);inc(%);\n" }{MPLTEXT 1 0 37 "dec:=x->x-1;4;dec(%);dec(%);dec(%) ;\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "f*6#I\"xG6\"F%6$I)operatorGF%I&ar rowGF%F%,&F$\"\"\"F*F*F%F%F%" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" } }{PARA 11 "" 1 "" {XPPMATH 20 "\"\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"#" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"$" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"%" }}{PARA 11 "" 1 "" {XPPMATH 20 "f*6#I\"xG6\"F%6$I) operatorGF%I&arrowGF%F%,&F$\"\"\"F*!\"\"F%F%F%" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"%" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"$" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"#" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"\"" }} }{EXCHG {PARA 0 "" 0 "" {XPPEDIT 2 0 "" "%#%?G" }}}}{SECT 0 {PARA 5 "" 0 "" {TEXT 206 36 "2.1.16. Rekurzi\303\263t\303\251tel." }}{PARA 0 "" 0 "" {TEXT 201 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 57 "n:=16 ;twopower:=1;for i to n do twopower:=twopower*2; od;" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"#;" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"#" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"%" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\")" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"#;" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"#K" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"#k" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"$G\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"$c#" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"$7&" }} {PARA 11 "" 1 "" {XPPMATH 20 "\"%C5" }}{PARA 11 "" 1 "" {XPPMATH 20 " \"%[?" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"%'4%" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"%#>)" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"&%Q;" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"&oF$" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"&Ob' " }}}{EXCHG {PARA 0 "" 0 "" {XPPEDIT 2 0 "" "%#%?G" }}}}{SECT 1 {PARA 5 "" 0 "" {TEXT 206 21 "2.1.17. T\303\251tel." }}{EXCHG {PARA 0 "" 0 " " {XPPEDIT 2 0 "" "%#%?G" }}}}{SECT 0 {PARA 5 "" 0 "" {TEXT 206 18 "2. 1.18. Sorozatok." }}{PARA 0 "" 0 "" {TEXT 201 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 70 "i:='i';j:='j';$3..9;i^2$i=2/3..10/3;x[i]$i=3. .8;\{j^i$j=i..8\}$i=2..4;" }}{PARA 11 "" 1 "" {XPPMATH 20 "I\"iG6\"" } }{PARA 11 "" 1 "" {XPPMATH 20 "I\"jG6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6)\"\"$\"\"%\"\"&\"\"'\"\"(\"\")\"\"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%#\"\"%\"\"*#\"#DF%#\"#kF%" }}{PARA 11 "" 1 "" {XPPMATH 20 "6(&I\"xG6\"6#\"\"$&F$6#\"\"%&F$6#\"\"&&F$6#\"\"'&F$6#\"\"(&F$6#\" \")" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%<)\"\"%\"\"*\"#;\"#D\"#O\"#\\\" #k<(\"#FF*\"$D\"\"$;#\"$V$\"$7&<'\"$c#\"$D'\"%'H\"\"%,C\"%'4%" }}} {EXCHG {PARA 0 "" 0 "" {XPPEDIT 2 0 "" "%#%?G" }}}}{SECT 0 {PARA 5 "" 0 "" {TEXT 206 21 "2.1.19. P\303\251lda." }}{PARA 0 "" 0 "" {TEXT 201 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 68 "cat(\"ab\",\"bcc\");c at(\"bcc\",\"ab\");evalb(%=%%);\"ab\"||\"bcc\";" }}{PARA 11 "" 1 "" {XPPMATH 20 "Q&abbcc6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "Q&bccab6\"" } }{PARA 11 "" 1 "" {XPPMATH 20 "I&falseG%*protectedG" }}{PARA 11 "" 1 " " {XPPMATH 20 "Q&abbcc6\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 47 "with(StringTools,Generate):Generate(4,\"abc\");" }}{PARA 11 "" 1 " " {XPPMATH 20 "7]pQ%aaaa6\"Q%aaabF$Q%aaacF$Q%aabaF$Q%aabbF$Q%aabcF$Q%a acaF$Q%aacbF$Q%aaccF$Q%abaaF$Q%ababF$Q%abacF$Q%abbaF$Q%abbbF$Q%abbcF$Q %abcaF$Q%abcbF$Q%abccF$Q%acaaF$Q%acabF$Q%acacF$Q%acbaF$Q%acbbF$Q%acbcF $Q%accaF$Q%accbF$Q%acccF$Q%baaaF$Q%baabF$Q%baacF$Q%babaF$Q%babbF$Q%bab cF$Q%bacaF$Q%bacbF$Q%baccF$Q%bbaaF$Q%bbabF$Q%bbacF$Q%bbbaF$Q%bbbbF$Q%b bbcF$Q%bbcaF$Q%bbcbF$Q%bbccF$Q%bcaaF$Q%bcabF$Q%bcacF$Q%bcbaF$Q%bcbbF$Q %bcbcF$Q%bccaF$Q%bccbF$Q%bcccF$Q%caaaF$Q%caabF$Q%caacF$Q%cabaF$Q%cabbF $Q%cabcF$Q%cacaF$Q%cacbF$Q%caccF$Q%cbaaF$Q%cbabF$Q%cbacF$Q%cbbaF$Q%cbb bF$Q%cbbcF$Q%cbcaF$Q%cbcbF$Q%cbccF$Q%ccaaF$Q%ccabF$Q%ccacF$Q%ccbaF$Q%c cbbF$Q%ccbcF$Q%cccaF$Q%cccbF$Q%ccccF$" }}}{EXCHG {PARA 0 "" 0 "" {XPPEDIT 2 0 "" "%#%?G" }}}}{SECT 1 {PARA 5 "" 0 "" {TEXT 206 89 "2.1. 20. Motiv\303\241ci\303\263: tov\303\241bbi rekurz\303\255v defin\303 \255ci\303\263k." }}{EXCHG {PARA 0 "" 0 "" {XPPEDIT 2 0 "" "%#%?G" }}} }{SECT 1 {PARA 5 "" 0 "" {TEXT 206 61 "2.1.21. \303\201ltal\303\241nos rekurzi\303\263 t\303\251tel." }}{EXCHG {PARA 0 "" 0 "" {XPPEDIT 2 0 "" "%#%?G" }}}}{SECT 0 {PARA 5 "" 0 "" {TEXT 206 32 "2.1.22. Fibonacci -sz\303\241mok." }}{PARA 0 "" 0 "" {TEXT 201 0 "" }}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 123 "Fib:=proc(n::nonnegint) option remember; if n <2 then n else Fib(dec(n))+Fib(dec(dec(n))) fi end;interface(verbosepr oc=3):\n" }{MPLTEXT 1 0 2 "\n" }{MPLTEXT 1 0 13 "print(Fib);\n" } {MPLTEXT 1 0 2 "\n" }{MPLTEXT 1 0 20 "Fib(3);print(Fib);\n" }{MPLTEXT 1 0 2 "\n" }{MPLTEXT 1 0 18 "Fib(7);print(Fib);" }}{PARA 11 "" 1 "" {XPPMATH 20 "f*6#'I\"nG6\"I*nonnegintG%*protectedGF&6#I)rememberGF&F&@ %2F%\"\"#F%,&-I$FibGF&6#-I$decGF&6#F%\"\"\"-F06#-F3F1F5F&F&F&" }} {PARA 11 "" 1 "" {XPPMATH 20 "f*6#'I\"nG6\"I*nonnegintG%*protectedGF&6 #I)rememberGF&F&@%2F%\"\"#F%,&-I$FibGF&6#-I$decGF&6#F%\"\"\"-F06#-F3F1 F5F&F&F&" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"#" }}{PARA 11 "" 1 "" {XPPMATH 20 "f*6#'I\"nG6\"I*nonnegintG%*protectedGF&6#I)rememberGF&E \\s%\"\"!F,\"\"\"F-\"\"#F-\"\"$F.@%2F%F.F%,&-I$FibGF&6#-I$decGF&6#F%F- -F46#-F7F5F-F&F&F&" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"#8" }}{PARA 11 " " 1 "" {XPPMATH 20 "f*6#'I\"nG6\"I*nonnegintG%*protectedGF&6#I)remembe rGF&E\\s)\"\"!F,\"\"\"F-\"\"#F-\"\"$F.\"\"&F0\"\"%F/\"\"(\"#8\"\"'\"\" )@%2F%F.F%,&-I$FibGF&6#-I$decGF&6#F%F--F:6#-F=F;F-F&F&F&" }}}{EXCHG {PARA 0 "" 0 "" {XPPEDIT 2 0 "" "%#%?G" }}}}{SECT 0 {PARA 5 "" 0 "" {TEXT 206 44 "2.1.23. Szorzatok \303\251s \303\266sszegek." }}{PARA 0 "" 0 "" {TEXT 201 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 93 "pro dfrom1:=proc(x,n) if n<1 then 1 elif n=1 then x[1] else prodfrom1(x,de c(n))*x[n] fi end;\n" }{MPLTEXT 1 0 2 "\n" }{MPLTEXT 1 0 17 "prodfrom1 (y,5);\n" }{MPLTEXT 1 0 2 "\n" }{MPLTEXT 1 0 23 "product(y[i],i=0..7); \n" }{MPLTEXT 1 0 2 "\n" }{MPLTEXT 1 0 23 "sum(x[j],j=4.5..8.7);\n" }} {PARA 11 "" 1 "" {XPPMATH 20 "f*6$I\"xG6\"I\"nGF%F%F%F%@'2F&\"\"\"F)/F &F)&F$6#F)*&-I*prodfrom1GF%6$F$-I$decGF%6#F&F)&F$F3F)F%F%F%" }}{PARA 11 "" 1 "" {XPPMATH 20 "*,&I\"yG6\"6#\"\"\"F'&F$6#\"\"#F'&F$6#\"\"$F'& F$6#\"\"%F'&F$6#\"\"&F'" }}{PARA 11 "" 1 "" {XPPMATH 20 "*2&I\"yG6\"6# \"\"!\"\"\"&F$6#F(F(&F$6#\"\"#F(&F$6#\"\"$F(&F$6#\"\"%F(&F$6#\"\"&F(&F $6#\"\"'F(&F$6#\"\"(F(" }}{PARA 11 "" 1 "" {XPPMATH 20 ",*&I\"xG6\"6# \"\"&\"\"\"&F$6#\"\"'F(&F$6#\"\"(F(&F$6#\"\")F(" }}}{EXCHG {PARA 0 "" 0 "" {XPPEDIT 2 0 "" "%#%?G" }}}}{SECT 0 {PARA 5 "" 0 "" {TEXT 206 73 "2.1.24. Az \303\241ltal\303\241nos disztributivit\303\241s t\303\251t ele." }}{PARA 0 "" 0 "" {TEXT 201 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 54 "A:=sum(a[i],i=1..4);B:=sum(b[j],j=1..5);A*B;expand(%) ;" }}{PARA 11 "" 1 "" {XPPMATH 20 ",*&I\"aG6\"6#\"\"\"F'&F$6#\"\"#F'&F $6#\"\"$F'&F$6#\"\"%F'" }}{PARA 11 "" 1 "" {XPPMATH 20 ",,&I\"bG6\"6# \"\"\"F'&F$6#\"\"#F'&F$6#\"\"$F'&F$6#\"\"%F'&F$6#\"\"&F'" }}{PARA 11 " " 1 "" {XPPMATH 20 "*&,*&I\"aG6\"6#\"\"\"F(&F%6#\"\"#F(&F%6#\"\"$F(&F% 6#\"\"%F(F(,,&I\"bGF&F'F(&F4F*F(&F4F-F(&F4F0F(&F46#\"\"&F(F(" }}{PARA 11 "" 1 "" {XPPMATH 20 ",J*&&I\"aG6\"6#\"\"\"F(&I\"bGF&F'F(F(*&F$F(&F* 6#\"\"#F(F(*&F$F(&F*6#\"\"$F(F(*&F$F(&F*6#\"\"%F(F(*&F$F(&F*6#\"\"&F(F (*&&F%F-F(F)F(F(*&F " 0 "" {MPLTEXT 1 0 27 "0!; 1!; 2!; 3!; 4!; 5!; 6!;" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"#" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"'" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"#C" }}{PARA 11 "" 1 "" {XPPMATH 20 " \"$?\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"$?(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 72 "binomial(6,0);binomial(6,1);binomial(6,2);binomi al(6,3);binomial(6,4);\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"\"" }} {PARA 11 "" 1 "" {XPPMATH 20 "\"\"'" }}{PARA 11 "" 1 "" {XPPMATH 20 " \"#:" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"#?" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"#:" }}}{EXCHG {PARA 0 "" 0 "" {XPPEDIT 2 0 "" "%#%?G" } }}}{SECT 0 {PARA 5 "" 0 "" {TEXT 206 39 "2.1.26. Binomi\303\241lis t\3 03\251tel." }}{PARA 0 "" 0 "" {TEXT 201 0 "" }}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 18 "(x+y)^6;expand(%);" }}{PARA 11 "" 1 "" {XPPMATH 20 "*$),&I\"xG6\"\"\"\"I\"yGF&F'\"\"'F'" }}{PARA 11 "" 1 "" {XPPMATH 20 " ,0*$)I\"xG6\"\"\"'\"\"\"F(*(F'F()F%\"\"&F(I\"yGF&F(F(*(\"#:F()F%\"\"%F ()F,\"\"#F(F(*(\"#?F()F%\"\"$F()F,F6F(F(*(F.F()F%F2F()F,F0F(F(*(F'F(F% F()F,F+F(F(*$)F,F'F(F(" }}}{EXCHG {PARA 0 "" 0 "" {XPPEDIT 2 0 "" "%#% ?G" }}}}{SECT 0 {PARA 5 "" 0 "" {TEXT 206 37 "* 2.1.27. K\303\266vetke zm\303\251ny." }}{PARA 0 "" 0 "" {TEXT 201 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 61 "sum(binomial(n,k),k=0..n);sum(binomial(n,k)*(-1) ^k,k=0..n);\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"&Ob'" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}}{EXCHG {PARA 0 "" 0 "" {XPPEDIT 2 0 "" "%#% ?G" }}}}{SECT 0 {PARA 5 "" 0 "" {TEXT 206 35 "2.1.28. Eg\303\251sz sz \303\241mok." }}{PARA 0 "" 0 "" {TEXT 201 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 73 "type(5,integer); type(-3,integer); type(0,integer ); type(3.14,integer);\n" }{MPLTEXT 1 0 2 "\n" }{MPLTEXT 1 0 86 "type( 5,posint); type(-3,negint); type(0,posint); type(0,nonnegint); type(0, nonposint);" }}{PARA 11 "" 1 "" {XPPMATH 20 "I%trueG%*protectedG" }} {PARA 11 "" 1 "" {XPPMATH 20 "I%trueG%*protectedG" }}{PARA 11 "" 1 "" {XPPMATH 20 "I%trueG%*protectedG" }}{PARA 11 "" 1 "" {XPPMATH 20 "I&fa lseG%*protectedG" }}{PARA 11 "" 1 "" {XPPMATH 20 "I%trueG%*protectedG" }}{PARA 11 "" 1 "" {XPPMATH 20 "I%trueG%*protectedG" }}{PARA 11 "" 1 "" {XPPMATH 20 "I&falseG%*protectedG" }}{PARA 11 "" 1 "" {XPPMATH 20 " I%trueG%*protectedG" }}{PARA 11 "" 1 "" {XPPMATH 20 "I%trueG%*protecte dG" }}}{EXCHG {PARA 0 "" 0 "" {XPPEDIT 2 0 "" "%#%?G" }}}}{SECT 0 {PARA 5 "" 0 "" {TEXT 206 64 "2.1.29. Hatv\303\241nyoz\303\241s eg\303 \251sz kitev\305\221vel." }}{PARA 0 "" 0 "" {TEXT 201 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 48 "x^(-5); x^(n+m); expand(%); (x^4)^( -5); (x*y)^5;" }}{PARA 11 "" 1 "" {XPPMATH 20 "*$)I\"xG6\"\"\"&!\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 ")I\"xG6\",&\"#;\"\"\"I\"mGF$F'" }} {PARA 11 "" 1 "" {XPPMATH 20 "*&)I\"xG6\"\"#;\"\"\")F$I\"mGF%F'" }} {PARA 11 "" 1 "" {XPPMATH 20 "*$)I\"xG6\"\"#?!\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "*&)I\"xG6\"\"\"&\"\"\")I\"yGF%F&F'" }}}{EXCHG {PARA 0 "" 0 "" {XPPEDIT 2 0 "" "%#%?G" }}}}{SECT 0 {PARA 5 "" 0 "" {TEXT 206 40 "2.1.30. Racion\303\241lis sz\303\241mok." }}{PARA 0 "" 0 "" {TEXT 201 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "type(5/7,rational ); type(0,rational);" }}{PARA 11 "" 1 "" {XPPMATH 20 "I%trueG%*protect edG" }}{PARA 11 "" 1 "" {XPPMATH 20 "I%trueG%*protectedG" }}}{EXCHG {PARA 0 "" 0 "" {XPPEDIT 2 0 "" "%#%?G" }}}}{SECT 1 {PARA 5 "" 0 "" {TEXT 206 54 "2.1.31. Archim\303\251d\303\251szi tulajdons\303\241g." }}{EXCHG {PARA 0 "" 0 "" {XPPEDIT 2 0 "" "%#%?G" }}}}{SECT 1 {PARA 5 " " 0 "" {TEXT 206 37 "2.1.32. \303\201ll\303\255t\303\241s." }}{EXCHG {PARA 0 "" 0 "" {XPPEDIT 2 0 "" "%#%?G" }}}}{SECT 0 {PARA 5 "" 0 "" {TEXT 206 49 "2.1.33. Eg\303\251sz r\303\251sz, marad\303\251k." }} {PARA 0 "" 0 "" {TEXT 201 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 38 "floor(3.14); ceil(3.14); ceil(-3.14); " }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"$" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"%" }}{PARA 11 "" 1 "" {XPPMATH 20 "!\"$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 80 "Rmod:=proc(x::realcons,y::realcons) if y=0 then x else x-floor(x/y )*y fi; end;\n" }{MPLTEXT 1 0 2 "\n" }{MPLTEXT 1 0 31 "Rmod(5,0); Rmod (3.1415,2.78);\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "f*6$'I\"xG6\"I)realc onsG%*protectedG'I\"yGF&F'F&F&F&@%/F*\"\"!F%,&F%\"\"\"*&-I&floorG6$F(I (_syslibGF&6#*&F%F/F*!\"\"F/F*F/F7F&F&F&" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"&" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"%:O!\"%" }}}{EXCHG {PARA 0 "" 0 "" {XPPEDIT 2 0 "" "%#%?G" }}}}{SECT 1 {PARA 5 "" 0 "" {TEXT 206 21 "2.1.34. T\303\251tel." }}{EXCHG {PARA 0 "" 0 "" {XPPEDIT 2 0 "" "%#%?G" }}}}{SECT 0 {PARA 5 "" 0 "" {TEXT 206 46 "2.1. 35. T\303\251tel: gy\303\266kvon\303\241s." }}{PARA 0 "" 0 "" {TEXT 201 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 53 "root[2](2); evalf (%); sqrt(2); root[12](2); evalf(%);" }}{PARA 11 "" 1 "" {XPPMATH 20 " *$)\"\"##\"\"\"F$F&" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+iN@99!\"*" }} {PARA 11 "" 1 "" {XPPMATH 20 "*$)\"\"##\"\"\"F$F&" }}{PARA 11 "" 1 "" {XPPMATH 20 "*$)\"\"##\"\"\"\"#7F&" }}{PARA 11 "" 1 "" {XPPMATH 20 "$ \"+%4j%f5!\"*" }}}{EXCHG {PARA 0 "" 0 "" {XPPEDIT 2 0 "" "%#%?G" }}}} {SECT 1 {PARA 5 "" 0 "" {TEXT 206 35 "2.1.36. K\303\266vetkezm\303\251 ny." }}{PARA 0 "" 0 "" {TEXT 201 0 "" }}}{SECT 1 {PARA 5 "" 0 "" {TEXT 206 39 "* 2.1.37. \303\201ll\303\255t\303\241s." }}{EXCHG {PARA 0 "" 0 "" {XPPEDIT 2 0 "" "%#%?G" }}}}{SECT 1 {PARA 5 "" 0 "" {TEXT 206 39 "* 2.1.38. \303\201ll\303\255t\303\241s." }}{EXCHG {PARA 0 "" 0 "" {XPPEDIT 2 0 "" "%#%?G" }}}}{SECT 0 {PARA 5 "" 0 "" {TEXT 206 58 "2.1. 39. B\305\221v\303\255tett val\303\263s sz\303\241mok." }}{PARA 0 "" 0 "" {TEXT 201 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 59 "infinit y; -infinity; evalb(5 " 0 " " {MPLTEXT 1 0 8 "restart;" }}}{PARA 0 "" 0 "" {TEXT 201 0 "" }}{SECT 1 {PARA 5 "" 0 "" {TEXT 206 38 "2.2.1. Halmazok ekvivalenci\303\241ja. " }}{EXCHG {PARA 0 "" 0 "" {XPPEDIT 2 0 "" "%#%?G" }}}}{SECT 1 {PARA 5 "" 0 "" {TEXT 206 36 "2.2.2. \303\201ll\303\255t\303\241s." }}{EXCHG {PARA 0 "" 0 "" {XPPEDIT 2 0 "" "%#%?G" }}}}{SECT 1 {PARA 5 "" 0 "" {TEXT 206 25 "2.2.3. Megjegyz\303\251s." }}{EXCHG {PARA 0 "" 0 "" {XPPEDIT 2 0 "" "%#%?G" }}}}{SECT 1 {PARA 5 "" 0 "" {TEXT 206 20 "2.2. 4. T\303\251tel." }}{EXCHG {PARA 0 "" 0 "" {XPPEDIT 2 0 "" "%#%?G" }}} }{SECT 1 {PARA 5 "" 0 "" {TEXT 206 20 "2.2.5. T\303\251tel." }}{EXCHG {PARA 0 "" 0 "" {XPPEDIT 2 0 "" "%#%?G" }}}}{SECT 1 {PARA 5 "" 0 "" {TEXT 206 55 "2.2.6. V\303\251ges \303\251s v\303\251gtelen halmazok." }}{EXCHG {PARA 0 "" 0 "" {XPPEDIT 2 0 "" "%#%?G" }}}}{SECT 0 {PARA 5 "" 0 "" {TEXT 206 49 "2.2.7. Karakterisztikus f\303\274ggv\303\251nyek ." }}{PARA 0 "" 0 "" {TEXT 201 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 113 "X:=\{a,b,c,d,e\}; Y:=\{a,c,e\}; chi:=x-> if x in Y t hen 1 elif x in X then 0 else FAIL fi;chi(a);chi(b);chi(1);\n" }} {PARA 11 "" 1 "" {XPPMATH 20 "<'I\"aG6\"I\"bGF$I\"cGF$I\"eGF$I\"dGF$" }}{PARA 11 "" 1 "" {XPPMATH 20 "<%I\"aG6\"I\"cGF$I\"eGF$" }}{PARA 11 " " 1 "" {XPPMATH 20 "f*6#I\"xG6\"F%6$I)operatorGF%I&arrowGF%F%@'-I#inG% *protectedG6$F$I\"YGF%\"\"\"-F+6$F$I\"XGF%\"\"!I%FAILGF,F%F%F%" }} {PARA 11 "" 1 "" {XPPMATH 20 "\"\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 " \"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "I%FAILG%*protectedG" }}}{EXCHG {PARA 0 "" 0 "" {XPPEDIT 2 0 "" "%#%?G" }}}}{SECT 1 {PARA 5 "" 0 "" {TEXT 206 20 "2.2.8. T\303\251tel." }}{EXCHG {PARA 0 "" 0 "" {XPPEDIT 2 0 "" "%#%?G" }}}}{SECT 1 {PARA 5 "" 0 "" {TEXT 206 19 "2.2.9 Skatuly a elv." }}{EXCHG {PARA 0 "" 0 "" {XPPEDIT 2 0 "" "%#%?G" }}}}{SECT 1 {PARA 5 "" 0 "" {TEXT 206 21 "2.2.10. T\303\251tel." }}{EXCHG {PARA 0 "" 0 "" {XPPEDIT 2 0 "" "%#%?G" }}}}{SECT 1 {PARA 5 "" 0 "" {TEXT 206 53 "2.2.11. Megsz\303\241ml\303\241lhat\303\263 halmazok." }}{EXCHG {PARA 0 "" 0 "" {XPPEDIT 2 0 "" "%#%?G" }}}}{SECT 1 {PARA 5 "" 0 "" {TEXT 206 21 "2.2.12. T\303\251tel." }}{EXCHG {PARA 0 "" 0 "" {XPPEDIT 2 0 "" "%#%?G" }}}}{SECT 1 {PARA 5 "" 0 "" {TEXT 206 21 "2.2. 13. T\303\251tel." }}{EXCHG {PARA 0 "" 0 "" {XPPEDIT 2 0 "" "%#%?G" }} }}{SECT 1 {PARA 5 "" 0 "" {TEXT 206 21 "2.2.14. T\303\251tel." }} {EXCHG {PARA 0 "" 0 "" {XPPEDIT 2 0 "" "%#%?G" }}}}{SECT 0 {PARA 5 "" 0 "" {TEXT 206 21 "2.2.15. T\303\251tel." }}{PARA 0 "" 0 "" {TEXT 201 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 115 "for k from 0 do for \+ m from 0 to k do n:=k-m: T:=time(); while time() " 0 "" {MPLTEXT 1 0 8 "restart;" }}}{PARA 0 "" 0 "" {TEXT 201 0 "" }}{SECT 0 {PARA 5 "" 0 "" {TEXT 206 29 "2.3.1. Komplex sz\303 \241mok." }}{PARA 0 "" 0 "" {TEXT 201 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 44 "`&+`:=proc(z,w) [z[1]+w[1],z[2]+w[2]] end;\n" } {MPLTEXT 1 0 64 "`&*`:=proc(z,w) [z[1]*w[1]-z[2]*w[2],z[1]*w[2]+z[2]*w [1]] end;\n" }{MPLTEXT 1 0 2 "\n" }{MPLTEXT 1 0 45 "[x,y]&+[0,0]; [x,y ]&+[-x,-y]; [x,y]&*[1,0];\n" }{MPLTEXT 1 0 2 "\n" }{MPLTEXT 1 0 49 "[x ,y]&*[x/(x^2+y^2),-y/(x^2+y^2)]; simplify(%);\n" }{MPLTEXT 1 0 2 "\n" }{MPLTEXT 1 0 15 "[0,1]&*[0,1];\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "f*6 $I\"zG6\"I\"wGF%F%F%F%7$,&&F$6#\"\"\"F+&F&F*F+,&&F$6#\"\"#F+&F&F/F+F%F %F%" }}{PARA 11 "" 1 "" {XPPMATH 20 "f*6$I\"zG6\"I\"wGF%F%F%F%7$,&*&&F $6#\"\"\"F,&F&F+F,F,*&&F$6#\"\"#F,&F&F0F,!\"\",&*&F*F,F2F,F,*&F/F,F-F, F,F%F%F%" }}{PARA 11 "" 1 "" {XPPMATH 20 "7$I\"xG6\"I\"yGF$" }}{PARA 11 "" 1 "" {XPPMATH 20 "7$\"\"!F#" }}{PARA 11 "" 1 "" {XPPMATH 20 "7$I \"xG6\"I\"yGF$" }}{PARA 11 "" 1 "" {XPPMATH 20 "7$,&*&)I\"xG6\"\"\"#\" \"\",&*$F%F)F)*$)I\"yGF'F(F)F)!\"\"F)*&F-F)F*F/F)\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "7$\"\"\"\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "7$!\" \"\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 69 "Complex(3,5); z: =3+5*I; w:=-2-6*I; z*w; Re(z); Im(z); conjugate(z);\n" }}{PARA 11 "" 1 "" {XPPMATH 20 ",&\"\"$\"\"\"*&\"\"&F$^#F$F$F$" }}{PARA 11 "" 1 "" {XPPMATH 20 ",&\"\"$\"\"\"*&\"\"&F$^#F$F$F$" }}{PARA 11 "" 1 "" {XPPMATH 20 ",&\"\"#!\"\"*&\"\"'\"\"\"^#F'F'F$" }}{PARA 11 "" 1 "" {XPPMATH 20 ",&\"#C\"\"\"*&\"#GF$^#F$F$!\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"$" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"&" }}{PARA 11 "" 1 "" {XPPMATH 20 ",&\"\"$\"\"\"*&\"\"&F$^#F$F$!\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "z:='z';w:='w'; conjugate(z);\n" } {MPLTEXT 1 0 2 "\n" }{MPLTEXT 1 0 56 "conjugate(conjugate(z));conjugat e(z+w);conjugate(1/z);\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "I\"zG6\"" }} {PARA 11 "" 1 "" {XPPMATH 20 "I\"wG6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "-I*conjugateG%*protectedG6#I\"zG6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "I\"zG6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "-I*conjugateG%*protectedG6# ,&I\"zG6\"\"\"\"I\"wGF(F)" }}{PARA 11 "" 1 "" {XPPMATH 20 "*$-I*conjug ateG%*protectedG6#I\"zG6\"!\"\"" }}}{EXCHG {PARA 0 "" 0 "" {XPPEDIT 2 0 "" "%#%?G" }}}}{SECT 0 {PARA 5 "" 0 "" {TEXT 206 20 "2.3.2. P\303\25 1lda." }}{PARA 0 "" 0 "" {TEXT 201 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "64/(3^(1/2)+I); evalc(%);" }}{PARA 11 "" 1 "" {XPPMATH 20 ",$*&\"#k\"\"\",&*$)\"\"$#F%\"\"#F%F%^#F%F%!\"\"F%" }} {PARA 11 "" 1 "" {XPPMATH 20 ",&*&\"#;\"\"\")\"\"$#F%\"\"#F%F%*&F$F%^# F%F%!\"\"" }}}{EXCHG {PARA 0 "" 0 "" {XPPEDIT 2 0 "" "%#%?G" }}}} {SECT 0 {PARA 5 "" 0 "" {TEXT 206 66 "2.3.3. Komplex sz\303\241mok abs zol\303\272t \303\251rt\303\251ke." }}{PARA 0 "" 0 "" {TEXT 201 0 "" } }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 71 "z:=x+I*y;abs(z);evalc(%);ev alc(1/(x+I*y));evalc(conjugate(z)/abs(z)^2);" }}{PARA 11 "" 1 "" {XPPMATH 20 ",&I\"xG6\"\"\"\"*&^#F%F%I\"yGF$F%F%" }}{PARA 11 "" 1 "" {XPPMATH 20 "-I$absG%*protectedG6#,&I\"xG6\"\"\"\"*&^#F)F)I\"yGF(F)F)" }}{PARA 11 "" 1 "" {XPPMATH 20 "*$),&*$)I\"xG6\"\"\"#\"\"\"F**$)I\"yG F(F)F*F*#F*F)F*" }}{PARA 11 "" 1 "" {XPPMATH 20 ",&*&I\"xG6\"\"\"\",&* $)F$\"\"#F&F&*$)I\"yGF%F*F&F&!\"\"F&*(,$^#F&F&F&F-F&F'F.F." }}{PARA 11 "" 1 "" {XPPMATH 20 ",&*&I\"xG6\"\"\"\",&*$)F$\"\"#F&F&*$)I\"yGF%F*F& F&!\"\"F&*(,$^#F&F&F&F-F&F'F.F." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "signum(3+4*I); signum(-5); signum(0);" }}{PARA 11 "" 1 "" {XPPMATH 20 ",&#\"\"$\"\"&\"\"\"*&#\"\"%F%F&^#F&F&F&" }}{PARA 11 "" 1 "" {XPPMATH 20 "!\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}} {EXCHG {PARA 0 "" 0 "" {XPPEDIT 2 0 "" "%#%?G" }}}}{SECT 0 {PARA 5 "" 0 "" {TEXT 206 74 "2.3.4. Komplex sz\303\241mok argumentuma \303\251s \+ trigonometrikus alakja." }}{PARA 0 "" 0 "" {TEXT 201 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 73 "polar(x+I*y); op(1,%); op(2,%%); po lar(3+4*I); evalc(%); argument(3+I*4);" }}{PARA 11 "" 1 "" {XPPMATH 20 "-I&polarGI(_syslibG6\"6$-I$absG%*protectedG6#,&I\"xGF%\"\"\"*&^#F-F- I\"yGF%F-F--I)argumentG6$F)F$F*" }}{PARA 11 "" 1 "" {XPPMATH 20 "-I$ab sG%*protectedG6#,&I\"xG6\"\"\"\"*&^#F)F)I\"yGF(F)F)" }}{PARA 11 "" 1 " " {XPPMATH 20 "-I)argumentG6$%*protectedGI(_syslibG6\"6#,&I\"xGF'\"\" \"*&^#F+F+I\"yGF'F+F+" }}{PARA 11 "" 1 "" {XPPMATH 20 "-I&polarGI(_sys libG6\"6$\"\"&-I'arctanG6$%*protectedGF$6##\"\"%\"\"$" }}{PARA 11 "" 1 "" {XPPMATH 20 ",&\"\"$\"\"\"*&\"\"%F$^#F$F$F$" }}{PARA 11 "" 1 "" {XPPMATH 20 "-I'arctanG6$%*protectedGI(_syslibG6\"6##\"\"%\"\"$" }}} {EXCHG {PARA 0 "" 0 "" {XPPEDIT 2 0 "" "%#%?G" }}}}{SECT 0 {PARA 5 "" 0 "" {TEXT 206 20 "2.3.5. P\303\251lda." }}{PARA 0 "" 0 "" {TEXT 201 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "z:=16*sqrt(3)-I*16; p olar(z);" }}{PARA 11 "" 1 "" {XPPMATH 20 ",&*&\"#;\"\"\")\"\"$#F%\"\"# F%F%*&F$F%^#F%F%!\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "-I&polarGI(_sys libG6\"6$\"#K,$*&#\"\"\"\"\"'F+I#PiG%*protectedGF+!\"\"" }}}{EXCHG {PARA 0 "" 0 "" {XPPEDIT 2 0 "" "%#%?G" }}}}{SECT 1 {PARA 5 "" 0 "" {TEXT 206 61 "2.3.6. Gy\303\266kvon\303\241s komplex sz\303\241mb\303 \263l." }}{EXCHG {PARA 0 "" 0 "" {XPPEDIT 2 0 "" "%#%?G" }}}}{SECT 0 {PARA 5 "" 0 "" {TEXT 206 20 "2.3.7. P\303\251lda." }}{PARA 0 "" 0 "" {TEXT 201 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 66 "z:='z'; i:= 'i'; w:=16*sqrt(3)-I*16; solve(z^5=w,z); z1:=w^(1/5);\n" }{MPLTEXT 1 0 2 "\n" }{MPLTEXT 1 0 30 "r:=abs(w); phi:=argument(w);\n" }{MPLTEXT 1 0 2 "\n" }{MPLTEXT 1 0 71 "r^(1/5)*(cos(phi/5+i*2*Pi/5)+I*sin(phi/5+ i*2*Pi/5))$i=0..4; evalf(%);\n" }{MPLTEXT 1 0 2 "\n" }{MPLTEXT 1 0 40 "solve(z^5=1); map(z->evalf(z*z1),[%]);\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "I\"zG6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "I\"iG6\"" }} {PARA 11 "" 1 "" {XPPMATH 20 ",&*&\"#;\"\"\")\"\"$#F%\"\"#F%F%*&F$F%^# F%F%!\"\"" }}{PARA 7 "" 1 "" {TEXT 207 37 "Warning, solutions may have been lost" }}{PARA 11 "" 1 "" {XPPMATH 20 "*$),&*&\"#;\"\"\")\"\"$#F' \"\"#F'F'*&F&F'^#F'F'!\"\"#F'\"\"&F'" }}{PARA 11 "" 1 "" {XPPMATH 20 " \"#K" }}{PARA 11 "" 1 "" {XPPMATH 20 ",$*&#\"\"\"\"\"'F%I#PiG%*protect edGF%!\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6'*&)\"#K#\"\"\"\"\"&F',&- I$sinG6$%*protectedGI(_syslibG6\"6#,$*&#\"\"(\"#:F'I#PiGF-F'F'F'*&,$^# F'F'F'-I$cosGF,F0F'!\"\"F'*&F$F',&-F+6#,$*&#\"\"#F5F'F6F'F'F'*&F9F'-F; F@F'F'F'*&F$F',&-F+6#,$*&#\"\"%F5F'F6F'F'F<*&F9F'-F;FJF'F'F'*&F$F',&*& #F'FDF')\"\"$FTF'F<*&FTF'F9F'F!\"*\" \"\"*&$\"+e#p04#!#5F'^#F'F'!\"\",&$\"+gGtM\")F+F'*&$\"+:44F=F&F'F,F'F' ,&$\"+^'*G'[\"F&F-*&$\"+77EQ8F&F'F,F'F',&$\"+330KF&F'F,F'F-" }}{PARA 7 "" 1 "" {TEXT 207 37 "Warning, solutions may have been lost" }}{PARA 11 "" 1 "" {XPPMATH 20 "6'\"\"\",(#F#\"\"%!\"\"*&F%F#)\"\"&#F#\"\"#F#F#*(*&F%F#^# F#F#F#)F,F+F#),&F*F#*$F)F#F#F+F#F#,(F%F'F(F'*(F.F#F0F#),&F*F#F3F'F+F#F #,(F%F'F(F'*(,$F.F#F#F0F#F6F#F',(F%F'F(F#*(F:F#F0F#F1F#F'" }}{PARA 11 "" 1 "" {XPPMATH 20 "7',&$\"+\"zV!*)>!\"*\"\"\"*&$\"+l#p04#!#5F'^#F'F' !\"\",&$\"+eGtM\")F+F'*&$\"+:44F=F&F'F,F'F',&$\"+^'*G'[\"F&F-*&$\"+77E Q8F&F'F,F'F',&$\"+230KF&F'F,F'F-" }}}{EXCHG {PARA 0 "" 0 "" {XPPEDIT 2 0 "" "%#%?G" }}}}{SECT 0 {PARA 5 "" 0 "" {TEXT 206 52 "2.3.8. B\305\221v\303\255te tt komplex sz\303\241mok." }}{PARA 0 "" 0 "" {TEXT 201 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 61 "z:=infinity+I*infinity; w:=infinity -I*infinity; evalb(z=w);\n" }}{PARA 11 "" 1 "" {XPPMATH 20 ",&I)infini tyG%*protectedG\"\"\"*&F#F%^#F%F%F%" }}{PARA 11 "" 1 "" {XPPMATH 20 ", &I)infinityG%*protectedG\"\"\"*&,$F#F%F%^#F%F%!\"\"" }}{PARA 11 "" 1 " " {XPPMATH 20 "I%trueG%*protectedG" }}}{EXCHG {PARA 0 "" 0 "" {XPPEDIT 2 0 "" "%#%?G" }}}}{SECT 0 {PARA 5 "" 0 "" {TEXT 206 25 "2.3. 9. Kvaterni\303\263k." }}{PARA 0 "" 0 "" {TEXT 201 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "`&+`:=(p,q)->[p[1]+q[1],p[2]+q[2]]; \n" }{MPLTEXT 1 0 77 "`&*`:=(p,q)->[p[1]*q[1]-conjugate(q[2])*p[2],q[2 ]*p[1]+p[2]*conjugate(q[1])];" }}{PARA 11 "" 1 "" {XPPMATH 20 "f*6$I\" pG6\"I\"qGF%F%6$I)operatorGF%I&arrowGF%F%7$,&&F$6#\"\"\"F.&F&F-F.,&&F$ 6#\"\"#F.&F&F2F.F%F%F%" }}{PARA 11 "" 1 "" {XPPMATH 20 "f*6$I\"pG6\"I \"qGF%F%6$I)operatorGF%I&arrowGF%F%7$,&*&&F$6#\"\"\"F/&F&F.F/F/*&-I*co njugateG%*protectedG6#&F&6#\"\"#F/&F$F7F/!\"\",&*&F-F/F6F/F/*&F9F/-F36 #F0F/F/F%F%F%" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 49 "p:=[a+I*b, c+I*d]; p&+[0,0]; p&+[-a-I*b,-c-I*d];\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "7$,&I\"aG6\"\"\"\"*&^#F&F&I\"bGF%F&F&,&I\"cGF%F&*&F(F&I\"dGF%F&F&" }}{PARA 11 "" 1 "" {XPPMATH 20 "7$,&I\"aG6\"\"\"\"*&^#F&F&I\"bGF%F&F& ,&I\"cGF%F&*&F(F&I\"dGF%F&F&" }}{PARA 11 "" 1 "" {XPPMATH 20 "7$\"\"!F #" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "p&*[1,0]; [1,0]&*p;\n" }{MPLTEXT 1 0 2 "\n" }{MPLTEXT 1 0 60 "q:=[(a-I*b)/(a^2+b^2+c^2+d^2), (-c-I*d)/(a^2+b^2+c^2+d^2)];\n" }{MPLTEXT 1 0 55 "p&*q;evalc(%);simpli fy(%); q&*p;evalc(%);simplify(%);\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "7 $,&I\"aG6\"\"\"\"*&^#F&F&I\"bGF%F&F&,&I\"cGF%F&*&F(F&I\"dGF%F&F&" }} {PARA 11 "" 1 "" {XPPMATH 20 "7$,&I\"aG6\"\"\"\"*&^#F&F&I\"bGF%F&F&,&I \"cGF%F&*&F(F&I\"dGF%F&F&" }}{PARA 11 "" 1 "" {XPPMATH 20 "7$*&,&I\"aG 6\"\"\"\"*&,$^#F'F'F'I\"bGF&F'!\"\"F',**$)F%\"\"#F'F'*$)F+F0F'F'*$)I\" cGF&F0F'F'*$)I\"dGF&F0F'F'F,*&,&F5F,*&F)F'F8F'F,F'F-F," }}{PARA 11 "" 1 "" {XPPMATH 20 "7$,&*(,&I\"aG6\"\"\"\"*&^#F(F(I\"bGF'F(F(F(,&F&F(*&, $F*F(F(F+F(!\"\"F(,**$)F&\"\"#F(F(*$)F+F3F(F(*$)I\"cGF'F3F(F(*$)I\"dGF 'F3F(F(F/F(*&-I*conjugateG%*protectedG6#*&,&F8F/*&F.F(F;F(F/F(F0F/F(,& F8F(*&F*F(F;F(F(F(F/,&*(F%F(FBF(F0F/F(*&FDF(-F>6#*&F,F(F0F/F(F(" }} {PARA 11 "" 1 "" {XPPMATH 20 "7$,(*&,&*$)I\"aG6\"\"\"#\"\"\"F+*$)I\"bG F)F*F+F+F+,*F&F+F,F+*$)I\"cGF)F*F+F+*$)I\"dGF)F*F+F+!\"\"F+*&F1F+F/F6F +*&F4F+F/F6F+,**&,&*&F(F+F2F+F6*&F.F+F5F+F+F+F/F6F+*(F2F+F(F+F/F6F+*(F 5F+F.F+F/F6F6*&^#F+F+,(*&,&*&F.F+F2F+F6*&F(F+F5F+F6F+F/F6F+*(F5F+F(F+F /F6F+*(F2F+F.F+F/F6F+F+F+" }}{PARA 11 "" 1 "" {XPPMATH 20 "7$\"\"\"\" \"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "7$,&*(,&I\"aG6\"\"\"\"*&^#F(F(I\" bGF'F(F(F(,&F&F(*&,$F*F(F(F+F(!\"\"F(,**$)F&\"\"#F(F(*$)F+F3F(F(*$)I\" cGF'F3F(F(*$)I\"dGF'F3F(F(F/F(*(-I*conjugateG%*protectedG6#,&F8F(*&F*F (F;F(F(F(,&F8F/*&F.F(F;F(F/F(F0F/F/,&*(F,F(F0F/FAF(F(*(FCF(F0F/-F>6#F% F(F(" }}{PARA 11 "" 1 "" {XPPMATH 20 "7$,&*&,&*$)I\"aG6\"\"\"#\"\"\"F+ *$)I\"bGF)F*F+F+F+,*F&F+F,F+*$)I\"cGF)F*F+F+*$)I\"dGF)F*F+F+!\"\"F+*&, &F0F+F3F+F+F/F6F+\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "7$\"\"\"\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 58 "z:='z';w:='w';z1:='z1';p :=[z,w];p1:=[z1,w1];p2:=[z2,w2];\n" }{MPLTEXT 1 0 2 "\n" }{MPLTEXT 1 0 46 "p&*(p1&*p2);expand(%);(p&*p1)&*p2;expand(%);\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "I\"zG6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "I\"wG6\"" }} {PARA 11 "" 1 "" {XPPMATH 20 "I#z1G6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "7$I\"zG6\"I\"wGF$" }}{PARA 11 "" 1 "" {XPPMATH 20 "7$I#z1G6\"I#w1GF$ " }}{PARA 11 "" 1 "" {XPPMATH 20 "7$I#z2G6\"I#w2GF$" }}{PARA 11 "" 1 " " {XPPMATH 20 "7$,&*&I\"zG6\"\"\"\",&*&I#z1GF&F'I#z2GF&F'F'*&-I*conjug ateG%*protectedG6#I#w2GF&F'I#w1GF&F'!\"\"F'F'*&-F.6#,&*&F*F'F1F'F'*&F2 F'-F.6#F+F'F'F'I\"wGF&F'F3,&*&F%F'F7F'F'*&F " 0 "" {MPLTEXT 1 0 41 "p&*(p1 &+p2);expand(%);(p&*p1)&+(p&*p2);\n" }{MPLTEXT 1 0 41 "(p1&+p2)&*p;exp and(%);(p1&*p)&+(p2&*p);\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "7$,&*&I\"z G6\"\"\"\",&I#z1GF&F'I#z2GF&F'F'F'*&-I*conjugateG%*protectedG6#,&I#w1G F&F'I#w2GF&F'F'I\"wGF&F'!\"\",&*&F%F'F0F'F'*&F3F'-F-6#F(F'F'" }}{PARA 11 "" 1 "" {XPPMATH 20 "7$,**&I\"zG6\"\"\"\"I#z1GF&F'F'*&F%F'I#z2GF&F' F'*&-I*conjugateG%*protectedG6#I#w1GF&F'I\"wGF&F'!\"\"*&F1F'-F-6#I#w2G F&F'F2,**&F%F'F0F'F'*&F%F'F6F'F'*&F1F'-F-6#F(F'F'*&F1F'-F-6#F*F'F'" }} {PARA 11 "" 1 "" {XPPMATH 20 "7$,**&I\"zG6\"\"\"\"I#z1GF&F'F'*&F%F'I#z 2GF&F'F'*&-I*conjugateG%*protectedG6#I#w1GF&F'I\"wGF&F'!\"\"*&F1F'-F-6 #I#w2GF&F'F2,**&F%F'F0F'F'*&F%F'F6F'F'*&F1F'-F-6#F(F'F'*&F1F'-F-6#F*F' F'" }}{PARA 11 "" 1 "" {XPPMATH 20 "7$,&*&I\"zG6\"\"\"\",&I#z1GF&F'I#z 2GF&F'F'F'*&-I*conjugateG%*protectedG6#I\"wGF&F',&I#w1GF&F'I#w2GF&F'F' !\"\",&*&F(F'F0F'F'*&F1F'-F-6#F%F'F'" }}{PARA 11 "" 1 "" {XPPMATH 20 " 7$,**&I\"zG6\"\"\"\"I#z1GF&F'F'*&F%F'I#z2GF&F'F'*&-I*conjugateG%*prote ctedG6#I\"wGF&F'I#w1GF&F'!\"\"*&F,F'I#w2GF&F'F2,**&F0F'F(F'F'*&F0F'F*F 'F'*&-F-6#F%F'F1F'F'*&F9F'F4F'F'" }}{PARA 11 "" 1 "" {XPPMATH 20 "7$,* *&I\"zG6\"\"\"\"I#z1GF&F'F'*&F%F'I#z2GF&F'F'*&-I*conjugateG%*protected G6#I\"wGF&F'I#w1GF&F'!\"\"*&F,F'I#w2GF&F'F2,**&F0F'F(F'F'*&F0F'F*F'F'* &-F-6#F%F'F1F'F'*&F9F'F4F'F'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "j:=[0,1]; j&*j; [z,0]&+([w,0]&*j);" }}{PARA 11 "" 1 "" {XPPMATH 20 "7$\"\"!\"\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "7$!\"\"\"\"!" }} {PARA 11 "" 1 "" {XPPMATH 20 "7$I\"zG6\"I\"wGF$" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 76 "k:=[0,I]; k&*k; i:=[I,0]; i&*i; [a,0]&+([b,0]& *i)&+([c,0]&*j)&+([d,0]&*k);\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "7$\"\" !^#\"\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "7$!\"\"\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "7$^#\"\"\"\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "7$ !\"\"\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "7$,&I\"aG6\"\"\"\"*&^#F&F& I\"bGF%F&F&,&I\"cGF%F&*&F(F&I\"dGF%F&F&" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 53 "p:=[a+I*b,c+I*d]; evalc([x,0]&*p); evalc(p&*[x,0]);\n " }}{PARA 11 "" 1 "" {XPPMATH 20 "7$,&I\"aG6\"\"\"\"*&^#F&F&I\"bGF%F&F &,&I\"cGF%F&*&F(F&I\"dGF%F&F&" }}{PARA 11 "" 1 "" {XPPMATH 20 "7$,&*&I \"xG6\"\"\"\"I\"aGF&F'F'*(^#F'F'F%F'I\"bGF&F'F',&*&F%F'I\"cGF&F'F'*(F* F'F%F'I\"dGF&F'F'" }}{PARA 11 "" 1 "" {XPPMATH 20 "7$,&*&I\"xG6\"\"\" \"I\"aGF&F'F'*(^#F'F'F%F'I\"bGF&F'F',&*&F%F'I\"cGF&F'F'*(F*F'F%F'I\"dG F&F'F'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "j&*[z,0]; [z,0]&* j;" }}{PARA 11 "" 1 "" {XPPMATH 20 "7$\"\"!-I*conjugateG%*protectedG6# I\"zG6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "7$\"\"!I\"zG6\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "i&*j; j&*k; k&*i; j&*i; k&*j; i&*k; \n" }}{PARA 11 "" 1 "" {XPPMATH 20 "7$\"\"!^#\"\"\"" }}{PARA 11 "" 1 " " {XPPMATH 20 "7$^#\"\"\"\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "7$\"\" !\"\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "7$\"\"!,$^#\"\"\"!\"\"" }} {PARA 11 "" 1 "" {XPPMATH 20 "7$,$^#\"\"\"!\"\"\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "7$\"\"!!\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 72 "C2toR4:=q->evalc([Re(q[1]),Im(q[1]),Re(q[2]),Im(q[2])]); q:=C2to R4(p);\n" }{MPLTEXT 1 0 2 "\n" }{MPLTEXT 1 0 53 "R4toC2:=q->[q[1]+I*q[ 2],q[3]+I*q[4]]; p:=R4toC2(q);\n" }{MPLTEXT 1 0 1 " " }}{PARA 11 "" 1 "" {XPPMATH 20 "f*6#I\"qG6\"F%6$I)operatorGF%I&arrowGF%F%-I&evalcG6$%* protectedGI(_syslibGF%6#7&-I#ReGF,6#&F$6#\"\"\"-I#ImGF,F2-F16#&F$6#\" \"#-F7F9F%F%F%" }}{PARA 11 "" 1 "" {XPPMATH 20 "7&I\"aG6\"I\"bGF$I\"cG F$I\"dGF$" }}{PARA 11 "" 1 "" {XPPMATH 20 "f*6#I\"qG6\"F%6$I)operatorG F%I&arrowGF%F%7$,&&F$6#\"\"\"F-*&^#F-F-&F$6#\"\"#F-F-,&&F$6#\"\"$F-*&F /F-&F$6#\"\"%F-F-F%F%F%" }}{PARA 11 "" 1 "" {XPPMATH 20 "7$,&I\"aG6\" \"\"\"*&^#F&F&I\"bGF%F&F&,&I\"cGF%F&*&F(F&I\"dGF%F&F&" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "i:='i'; j:='j'; k:='k';\n" } {MPLTEXT 1 0 2 "\n" }{MPLTEXT 1 0 74 "C2toH:=q->evalc(Re(q[1])+Im(q[1] )*i+Re(q[2])*j+Im(q[2])*k); q:=C2toH(p);\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "I\"iG6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "I\"jG6\"" }} {PARA 11 "" 1 "" {XPPMATH 20 "I\"kG6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "f*6#I\"qG6\"F%6$I)operatorGF%I&arrowGF%F%-I&evalcG6$%*protectedGI(_s yslibGF%6#,*-I#ReGF,6#&F$6#\"\"\"F5*&-I#ImGF,F2F5I\"iGF%F5F5*&-F16#&F$ 6#\"\"#F5I\"jGF%F5F5*&-F8F " 0 "" {MPLTEXT 1 0 102 "HtoC2:=q->[q-coeff(q,i)*i-coeff(q,j)*j-coeff(q,k)*k+I*coeff(q,i), coeff(q,j)+I*coeff(q,k)]; HtoC2(q);\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "f*6#I\"qG6\"F%6$I)operatorGF%I&arrowGF%F%7$,,F$\"\"\"*&-I&coeffG%*pro tectedG6$F$I\"iGF%F+F1F+!\"\"*&-F.6$F$I\"jGF%F+F6F+F2*&-F.6$F$I\"kGF%F +F:F+F2*&^#F+F+F-F+F+,&F4F+*&F " 0 "" {MPLTEXT 1 0 82 "qIm:=q->coeff(q ,i)*i+coeff(q,j)*j+coeff(q,k)*k;qRe:=q->q-qIm(q); qRe(q); qIm(q);\n" } }{PARA 11 "" 1 "" {XPPMATH 20 "f*6#I\"qG6\"F%6$I)operatorGF%I&arrowGF% F%,(*&-I&coeffG%*protectedG6$F$I\"iGF%\"\"\"F/F0F0*&-F,6$F$I\"jGF%F0F4 F0F0*&-F,6$F$I\"kGF%F0F8F0F0F%F%F%" }}{PARA 11 "" 1 "" {XPPMATH 20 "f* 6#I\"qG6\"F%6$I)operatorGF%I&arrowGF%F%,&F$\"\"\"-I$qImGF%F#!\"\"F%F%F %" }}{PARA 11 "" 1 "" {XPPMATH 20 "I\"aG6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 ",(*&I\"bG6\"\"\"\"I\"iGF%F&F&*&I\"cGF%F&I\"jGF%F&F&*&I\"d GF%F&I\"kGF%F&F&" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 46 "qconjug ate:=q->qRe(q)-qIm(q); qconjugate(q);\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "f*6#I\"qG6\"F%6$I)operatorGF%I&arrowGF%F%,&-I$qReGF%F#\"\"\"-I$qIm GF%F#!\"\"F%F%F%" }}{PARA 11 "" 1 "" {XPPMATH 20 ",*I\"aG6\"\"\"\"*&I \"bGF$F%I\"iGF$F%!\"\"*&I\"cGF$F%I\"jGF$F%F)*&I\"dGF$F%I\"kGF$F%F)" }} }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 66 "q; qconjugate(q); qconjugat e(%); q+qconjugate(q); q-qconjugate(q);" }}{PARA 11 "" 1 "" {XPPMATH 20 ",*I\"aG6\"\"\"\"*&I\"bGF$F%I\"iGF$F%F%*&I\"cGF$F%I\"jGF$F%F%*&I\"d GF$F%I\"kGF$F%F%" }}{PARA 11 "" 1 "" {XPPMATH 20 ",*I\"aG6\"\"\"\"*&I \"bGF$F%I\"iGF$F%!\"\"*&I\"cGF$F%I\"jGF$F%F)*&I\"dGF$F%I\"kGF$F%F)" }} {PARA 11 "" 1 "" {XPPMATH 20 ",*I\"aG6\"\"\"\"*&I\"bGF$F%I\"iGF$F%F%*& I\"cGF$F%I\"jGF$F%F%*&I\"dGF$F%I\"kGF$F%F%" }}{PARA 11 "" 1 "" {XPPMATH 20 ",$*&\"\"#\"\"\"I\"aG6\"F%F%" }}{PARA 11 "" 1 "" {XPPMATH 20 ",(*(\"\"#\"\"\"I\"bG6\"F%I\"iGF'F%F%*(F$F%I\"cGF'F%I\"jGF'F%F%*(F$ F%I\"dGF'F%I\"kGF'F%F%" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 47 "q 1:=a1+b1*i+c1*j+d1*k; q2:=a2+b2*i+c2*j+d2*k;\n" }{MPLTEXT 1 0 2 "\n" } {MPLTEXT 1 0 75 "q1+q2; collect(%,[i,j,k]); `&+`:=(q1,q2)->collect(q1+ q2,[i,j,k]); q1&+q2;\n" }{MPLTEXT 1 0 2 "\n" }{MPLTEXT 1 0 50 "`&*`:=p roc(q1,q2) local a1,a2,b1,b2,c1,c2,d1,d2;\n" }{MPLTEXT 1 0 58 "a1:=qRe (q1);a2:=qRe(q2);b1:=coeff(q1,i);b2:=coeff(q2,i);\n" }{MPLTEXT 1 0 66 "c1:=coeff(q1,j);c2:=coeff(q2,j);d1:=coeff(q1,k);d2:=coeff(q2,k);\n" } {MPLTEXT 1 0 56 "(a1*a2-b1*b2-c1*c2-d1*d2)+(a1*b2+a2*b1+c1*d2-d1*c2)*i +\n" }{MPLTEXT 1 0 62 "(a1*c2+c1*a2+d1*b2-b1*d2)*j+(a1*d2+d1*a2+b1*c2- c1*b2)*k;end;\n" }{MPLTEXT 1 0 2 "\n" }{MPLTEXT 1 0 9 "q1&*q2;\n" } {MPLTEXT 1 0 2 "\n" }{MPLTEXT 1 0 53 "qconjugate(q1&+q2); qconjugate(q 1)&+qconjugate(q2);\n" }{MPLTEXT 1 0 2 "\n" }{MPLTEXT 1 0 66 "qconjuga te(q1&*q2);qconjugate(q2)&*qconjugate(q1); expand(%%-%);\n" }}{PARA 11 "" 1 "" {XPPMATH 20 ",*I#a1G6\"\"\"\"*&I#b1GF$F%I\"iGF$F%F%*&I#c1GF$F %I\"jGF$F%F%*&I#d1GF$F%I\"kGF$F%F%" }}{PARA 11 "" 1 "" {XPPMATH 20 ",* I#a2G6\"\"\"\"*&I#b2GF$F%I\"iGF$F%F%*&I#c2GF$F%I\"jGF$F%F%*&I#d2GF$F%I \"kGF$F%F%" }}{PARA 11 "" 1 "" {XPPMATH 20 ",2I#a1G6\"\"\"\"*&I#b1GF$F %I\"iGF$F%F%*&I#c1GF$F%I\"jGF$F%F%*&I#d1GF$F%I\"kGF$F%F%I#a2GF$F%*&I#b 2GF$F%F(F%F%*&I#c2GF$F%F+F%F%*&I#d2GF$F%F.F%F%" }}{PARA 11 "" 1 "" {XPPMATH 20 ",,*&,&I#b1G6\"\"\"\"I#b2GF&F'F'I\"iGF&F'F'*&,&I#c2GF&F'I# c1GF&F'F'I\"jGF&F'F'*&,&I#d2GF&F'I#d1GF&F'F'I\"kGF&F'F'I#a1GF&F'I#a2GF &F'" }}{PARA 11 "" 1 "" {XPPMATH 20 "f*6$I#q1G6\"I#q2GF%F%6$I)operator GF%I&arrowGF%F%-I(collectG6$%*protectedGI(_syslibGF%6$,&F$\"\"\"F&F17% I\"iGF%I\"jGF%I\"kGF%F%F%F%" }}{PARA 11 "" 1 "" {XPPMATH 20 ",,*&,&I#b 1G6\"\"\"\"I#b2GF&F'F'I\"iGF&F'F'*&,&I#c2GF&F'I#c1GF&F'F'I\"jGF&F'F'*& ,&I#d2GF&F'I#d1GF&F'F'I\"kGF&F'F'I#a1GF&F'I#a2GF&F'" }}{PARA 11 "" 1 " " {XPPMATH 20 "f*6$I#q1G6\"I#q2GF%6*I#a1GF%I#a2GF%I#b1GF%I#b2GF%I#c1GF %I#c2GF%I#d1GF%I#d2GF%F%F%C+>F(-I$qReGF%6#F$>F)-F36#F&>F*-I&coeffG%*pr otectedG6$F$I\"iGF%>F+-F:6$F&F=>F,-F:6$F$I\"jGF%>F--F:6$F&FD>F.-F:6$F$ I\"kGF%>F/-F:6$F&FK,0*&F(\"\"\"F)FQFQ*&F*FQF+FQ!\"\"*&F,FQF-FQFS*&F.FQ F/FQFS*&,**&F(FQF+FQFQ*&F)FQF*FQFQ*&F,FQF/FQFQ*&F.FQF-FQFSFQF=FQFQ*&,* *&F(FQF-FQFQ*&F,FQF)FQFQ*&F.FQF+FQFQ*&F*FQF/FQFSFQFDFQFQ*&,**&F(FQF/FQ FQ*&F.FQF)FQFQ*&F*FQF-FQFQ*&F,FQF+FQFSFQFKFQFQF%F%F%" }}{PARA 11 "" 1 "" {XPPMATH 20 ",0*&I#a1G6\"\"\"\"I#a2GF%F&F&*&I#b1GF%F&I#b2GF%F&!\"\" *&I#c1GF%F&I#c2GF%F&F+*&I#d1GF%F&I#d2GF%F&F+*&,**&F$F&F*F&F&*&F'F&F)F& F&*&F-F&F1F&F&*&F0F&F.F&F+F&I\"iGF%F&F&*&,**&F$F&F.F&F&*&F-F&F'F&F&*&F 0F&F*F&F&*&F)F&F1F&F+F&I\"jGF%F&F&*&,**&F$F&F1F&F&*&F0F&F'F&F&*&F)F&F. F&F&*&F-F&F*F&F+F&I\"kGF%F&F&" }}{PARA 11 "" 1 "" {XPPMATH 20 ",,I#a1G 6\"\"\"\"I#a2GF$F%*&,&I#b1GF$F%I#b2GF$F%F%I\"iGF$F%!\"\"*&,&I#c2GF$F%I #c1GF$F%F%I\"jGF$F%F,*&,&I#d2GF$F%I#d1GF$F%F%I\"kGF$F%F," }}{PARA 11 " " 1 "" {XPPMATH 20 ",,*&,&I#b1G6\"!\"\"I#b2GF&F'\"\"\"I\"iGF&F)F)*&,&I #c2GF&F'I#c1GF&F'F)I\"jGF&F)F)*&,&I#d2GF&F'I#d1GF&F'F)I\"kGF&F)F)I#a1G F&F)I#a2GF&F)" }}{PARA 11 "" 1 "" {XPPMATH 20 ",0*&I#a1G6\"\"\"\"I#a2G F%F&F&*&I#b1GF%F&I#b2GF%F&!\"\"*&I#c1GF%F&I#c2GF%F&F+*&I#d1GF%F&I#d2GF %F&F+*&,**&F$F&F*F&F&*&F'F&F)F&F&*&F-F&F1F&F&*&F0F&F.F&F+F&I\"iGF%F&F+ *&,**&F$F&F.F&F&*&F-F&F'F&F&*&F0F&F*F&F&*&F)F&F1F&F+F&I\"jGF%F&F+*&,** &F$F&F1F&F&*&F0F&F'F&F&*&F)F&F.F&F&*&F-F&F*F&F+F&I\"kGF%F&F+" }}{PARA 11 "" 1 "" {XPPMATH 20 ",0*&I#a1G6\"\"\"\"I#a2GF%F&F&*&I#b1GF%F&I#b2GF %F&!\"\"*&I#c1GF%F&I#c2GF%F&F+*&I#d1GF%F&I#d2GF%F&F+*&,**&F'F&F)F&F+*& F$F&F*F&F+*&F0F&F.F&F&*&F-F&F1F&F+F&I\"iGF%F&F&*&,**&F-F&F'F&F+*&F$F&F .F&F+*&F)F&F1F&F&*&F0F&F*F&F+F&I\"jGF%F&F&*&,**&F0F&F'F&F+*&F$F&F1F&F+ *&F-F&F*F&F&*&F)F&F.F&F+F&I\"kGF%F&F&" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}}{EXCHG {PARA 0 "" 0 "" {XPPEDIT 2 0 "" "%#%?G" }}}}{SECT 0 {PARA 5 "" 0 "" {TEXT 206 98 "2.3.10. Kvaterni\303\263k \303\251s a h \303\241rom dimenzi\303\263s euklid\303\251szi t\303\251r." }}{PARA 0 "" 0 "" {TEXT 201 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 61 "q1 :=b1*i+c1*j+d1*k; q2:=b2*i+c2*j+d2*k; q3:=b3*i+c3*j+d3*k;\n" }{MPLTEXT 1 0 2 "\n" }{MPLTEXT 1 0 55 "scalarprod:=(q1,q2)->-qRe(q1&*q2); scala rprod(q1,q2);\n" }{MPLTEXT 1 0 2 "\n" }{MPLTEXT 1 0 35 "vectorprod:=(q 1,q2)->qIm(q1&*q2);\n" }{MPLTEXT 1 0 2 "\n" }{MPLTEXT 1 0 39 "vectorpr od(q1,q2); vectorprod(q2,q1);\n" }{MPLTEXT 1 0 2 "\n" }{MPLTEXT 1 0 35 "vectorprod(q1,vectorprod(q2,q3));\n" }{MPLTEXT 1 0 2 "\n" } {MPLTEXT 1 0 58 "scalarprod(q1,q3)*q2-scalarprod(q1,q2)*q3; expand(%%- %);\n" }{MPLTEXT 1 0 2 "\n" }{MPLTEXT 1 0 58 "mixedprod:=(q1,q2,q3)->s calarprod(q1,vectorprod(q2,q3));\n" }{MPLTEXT 1 0 22 "mixedprod(q1,q2, q3);\n" }}{PARA 11 "" 1 "" {XPPMATH 20 ",(*&I#b1G6\"\"\"\"I\"iGF%F&F&* &I#c1GF%F&I\"jGF%F&F&*&I#d1GF%F&I\"kGF%F&F&" }}{PARA 11 "" 1 "" {XPPMATH 20 ",(*&I#b2G6\"\"\"\"I\"iGF%F&F&*&I#c2GF%F&I\"jGF%F&F&*&I#d2 GF%F&I\"kGF%F&F&" }}{PARA 11 "" 1 "" {XPPMATH 20 ",(*&I#b3G6\"\"\"\"I \"iGF%F&F&*&I#c3GF%F&I\"jGF%F&F&*&I#d3GF%F&I\"kGF%F&F&" }}{PARA 11 "" 1 "" {XPPMATH 20 "f*6$I#q1G6\"I#q2GF%F%6$I)operatorGF%I&arrowGF%F%,$-I $qReGF%6#-I#&*GF%F#!\"\"F%F%F%" }}{PARA 11 "" 1 "" {XPPMATH 20 ",(*&I# b1G6\"\"\"\"I#b2GF%F&F&*&I#c1GF%F&I#c2GF%F&F&*&I#d1GF%F&I#d2GF%F&F&" } }{PARA 11 "" 1 "" {XPPMATH 20 "f*6$I#q1G6\"I#q2GF%F%6$I)operatorGF%I&a rrowGF%F%-I$qImGF%6#-I#&*GF%F#F%F%F%" }}{PARA 11 "" 1 "" {XPPMATH 20 " ,(*&,&*&I#c1G6\"\"\"\"I#d2GF'F(F(*&I#d1GF'F(I#c2GF'F(!\"\"F(I\"iGF'F(F (*&,&*&F+F(I#b2GF'F(F(*&I#b1GF'F(F)F(F-F(I\"jGF'F(F(*&,&*&F4F(F,F(F(*& F&F(F2F(F-F(I\"kGF'F(F(" }}{PARA 11 "" 1 "" {XPPMATH 20 ",(*&,&*&I#d1G 6\"\"\"\"I#c2GF'F(F(*&I#c1GF'F(I#d2GF'F(!\"\"F(I\"iGF'F(F(*&,&*&I#b1GF 'F(F,F(F(*&F&F(I#b2GF'F(F-F(I\"jGF'F(F(*&,&*&F+F(F4F(F(*&F2F(F)F(F-F(I \"kGF'F(F(" }}{PARA 11 "" 1 "" {XPPMATH 20 ",(*&,&*&I#c1G6\"\"\"\",&*& I#b2GF'F(I#c3GF'F(F(*&I#c2GF'F(I#b3GF'F(!\"\"F(F(*&I#d1GF'F(,&*&I#d2GF 'F(F/F(F(*&F+F(I#d3GF'F(F0F(F0F(I\"iGF'F(F(*&,&*&F2F(,&*&F.F(F7F(F(*&F 5F(F,F(F0F(F(*&I#b1GF'F(F)F(F0F(I\"jGF'F(F(*&,&*&F@F(F3F(F(*&F&F(F " 0 "" {MPLTEXT 1 0 65 "qa bs:=q->sqrt(qRe(q)^2+coeff(q,i)^2+coeff(q,j)^2+coeff(q,k)^2);\n" } {MPLTEXT 1 0 2 "\n" }{MPLTEXT 1 0 28 "qabs(q); q&*qconjugate(q);\n" }} {PARA 11 "" 1 "" {XPPMATH 20 "f*6#I\"qG6\"F%6$I)operatorGF%I&arrowGF%F %-I%sqrtG6$%*protectedGI(_syslibGF%6#,**$)-I$qReGF%F#\"\"#\"\"\"F5*$)- I&coeffGF,6$F$I\"iGF%F4F5F5*$)-F96$F$I\"jGF%F4F5F5*$)-F96$F$I\"kGF%F4F 5F5F%F%F%" }}{PARA 11 "" 1 "" {XPPMATH 20 "*$),**$)I\"aG6\"\"\"#\"\"\" F**$)I\"bGF(F)F*F**$)I\"cGF(F)F*F**$)I\"dGF(F)F*F*#F*F)F*" }}{PARA 11 "" 1 "" {XPPMATH 20 ",**$)I\"aG6\"\"\"#\"\"\"F(*$)I\"bGF&F'F(F(*$)I\"c GF&F'F(F(*$)I\"dGF&F'F(F(" }}}{EXCHG {PARA 0 "" 0 "" {XPPEDIT 2 0 "" " %#%?G" }}}}{SECT 0 {PARA 5 "" 0 "" {TEXT 206 86 "2.3.12. A skal\303\24 1r- vektor- \303\251s vegyes szorzat geometriai jelent\303\251se." }} {PARA 0 "" 0 "" {TEXT 201 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "qabs(q1&+q2)^2-qabs(q1-q2)^2;" }}{PARA 11 "" 1 "" {XPPMATH 20 ", (*(\"\"%\"\"\"I#b1G6\"F%I#b2GF'F%F%*(F$F%I#c1GF'F%I#c2GF'F%F%*(F$F%I#d 1GF'F%I#d2GF'F%F%" }}}{EXCHG {PARA 0 "" 0 "" {XPPEDIT 2 0 "" "%#%?G" } }}}{SECT 1 {PARA 5 "" 0 "" {TEXT 206 27 "2.3.13. Geometriai alkalmaz" }{TEXT 206 12 "\303\241sok." }}{EXCHG {PARA 0 "" 0 "" {XPPEDIT 2 0 "" "%#%?G" }}}}{EXCHG {PARA 0 "" 0 "" {XPPEDIT 2 0 "" "%#%?G" }}}}{SECT 0 {PARA 4 "" 0 "" {TEXT 205 14 "2.4. Polinomok" }}{PARA 0 "" 0 "" {TEXT 201 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart;" }}} {PARA 0 "" 0 "" {TEXT 201 0 "" }}{SECT 1 {PARA 5 "" 0 "" {TEXT 206 29 "2.4.1. Jel\303\266l\303\251s." }}{EXCHG {PARA 0 "" 0 "" {XPPEDIT 2 0 "" "%#%?G" }}}}{SECT 1 {PARA 5 "" 0 "" {TEXT 206 81 "2.4.2. Polinomok \+ \303\251s racion\303\241lis t\303\266rtf\303\274ggv\303\251nyek." }} {EXCHG {PARA 0 "" 0 "" {XPPEDIT 2 0 "" "%#%?G" }}}}{SECT 0 {PARA 5 "" 0 "" {TEXT 206 66 "2.4.3. A marad\303\251kos oszt\303\241s t\303\251te le polinomokra." }}{PARA 0 "" 0 "" {TEXT 201 0 "" }}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 67 "f:=3*x^3+6*x^2+7*x-8; g:=x^2+8*x-2; q:=quo(f,g ,x); r:=rem(f,g,x);\n" }{MPLTEXT 1 0 17 "g*q+r; expand(%);" }}{PARA 11 "" 1 "" {XPPMATH 20 ",**&\"\"$\"\"\")I\"xG6\"F$F%F%*&\"\"'F%)F'\"\"#F %F%*&\"\"(F%F'F%F%\"\")!\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 ",(*$)I\" xG6\"\"\"#\"\"\"F(*&\"\")F(F%F(F(F'!\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 ",&*&\"\"$\"\"\"I\"xG6\"F%F%\"#=!\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 ",&\"#W!\"\"*&\"$d\"\"\"\"I\"xG6\"F'F'" }}{PARA 11 "" 1 "" {XPPMATH 20 ",(*&,(*$)I\"xG6\"\"\"#\"\"\"F**&\"\")F*F'F*F*F)!\"\"F*,&* &\"\"$F*F'F*F*\"#=F-F*F*\"#WF-*&\"$d\"F*F'F*F*" }}{PARA 11 "" 1 "" {XPPMATH 20 ",**&\"\"$\"\"\")I\"xG6\"F$F%F%*&\"\"'F%)F'\"\"#F%F%*&\"\" (F%F'F%F%\"\")!\"\"" }}}{EXCHG {PARA 0 "" 0 "" {XPPEDIT 2 0 "" "%#%?G" }}}}{SECT 0 {PARA 5 "" 0 "" {TEXT 206 60 "2.4.4. K\303\266vetkezm\303 \251ny: Horner-elrendez\303\251s." }}{PARA 0 "" 0 "" {TEXT 201 0 "" }} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "rem(f,x-5,x); subs(x=5,f);" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"$_&" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"$_&" }}}{EXCHG {PARA 0 "" 0 "" {XPPEDIT 2 0 "" "%#%?G" }}}}{SECT 0 {PARA 5 "" 0 "" {TEXT 206 95 "2.4.5. K\303\266vetkezm\303\251ny: gy\30 3\266kt\303\251nyez\305\221 lev\303\241laszt\303\241sa." }}{PARA 0 "" 0 "" {TEXT 201 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 45 "f:=(x- 1)^2*(x-2); f:=expand(f); quo(f,x-2,x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "*&),&I\"xG6\"\"\"\"F'!\"\"\"\"#F',&F%F'F)F(F'" }}{PARA 11 "" 1 "" {XPPMATH 20 ",**$)I\"xG6\"\"\"$\"\"\"F(*&\"\"%F()F%\"\"#F(!\"\"*&\"\"& F(F%F(F(F,F-" }}{PARA 11 "" 1 "" {XPPMATH 20 ",(*$)I\"xG6\"\"\"#\"\"\" F(*&F'F(F%F(!\"\"F(F(" }}}{EXCHG {PARA 0 "" 0 "" {XPPEDIT 2 0 "" "%#%? G" }}}}{SECT 0 {PARA 5 "" 0 "" {TEXT 206 34 "2.4.6. K\303\266vetkezm\3 03\251ny." }}{EXCHG {PARA 0 "" 0 "" {XPPEDIT 2 0 "" "%#%?G" }}}}{SECT 0 {PARA 5 "" 0 "" {TEXT 206 34 "2.4.7. K\303\266vetkezm\303\251ny." }} {EXCHG {PARA 0 "" 0 "" {XPPEDIT 2 0 "" "%#%?G" }}}}{SECT 0 {PARA 5 "" 0 "" {TEXT 206 65 "2.4.8. Polinomok egy\303\251rtelm\305\261 fel\303\2 55r\303\241sa." }}{PARA 0 "" 0 "" {TEXT 201 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 95 "coeff(f,x,0); coeff(f,x,1); coeff(f,x,2); coeff (f,x,3); coeff(f,x,4); lcoeff(f,x); lcoeff(0,x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "!\"#" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"&" }}{PARA 11 " " 1 "" {XPPMATH 20 "!\"%" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"\"" }} {PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 " \"\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "degree(f); degree(0);" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"$" }}{PARA 11 "" 1 "" {XPPMATH 20 ",$I)infinityG%*pro tectedG!\"\"" }}}{EXCHG {PARA 0 "" 0 "" {XPPEDIT 2 0 "" "%#%?G" }}}} {SECT 0 {PARA 5 "" 0 "" {TEXT 206 76 "2.4.9. A marad\303\251kos oszt\3 03\241s egy\303\251rtelm\305\261s\303\251ge." }}{EXCHG {PARA 0 "" 0 "" {XPPEDIT 2 0 "" "%#%?G" }}}}{SECT 0 {PARA 5 "" 0 "" {TEXT 206 61 "2.4 .10. T\303\266bbsz\303\266r\303\266s gy\303\266k\303\266k." }}{PARA 0 "" 0 "" {TEXT 201 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 57 "sub s(x=1,f); quo(f,x-1,x); subs(x=1,f); quo(f,(x-1)^2,x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 ",(*$)I\"xG6\" \"\"#\"\"\"F(*&\"\"$F(F%F(!\"\"F'F(" }}{PARA 11 "" 1 "" {XPPMATH 20 " \"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 ",&I\"xG6\"\"\"\"\"\"#!\"\"" }}} {EXCHG {PARA 0 "" 0 "" {XPPEDIT 2 0 "" "%#%?G" }}}}{SECT 0 {PARA 5 "" 0 "" {TEXT 206 37 "2.4.11. Az algebra alapt\303\251tele." }}{PARA 0 "" 0 "" {TEXT 201 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "solve (f,x); solve(x^3=1,x); r:=[%];\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\" \"#\"\"\"F$" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"\"\",&#F#\"\"#!\"\"*& *&F%F#^#F#F#F#)\"\"$F%F#F#,&F%F'*&,$F)F#F#F+F#F'" }}{PARA 11 "" 1 "" {XPPMATH 20 "7%\"\"\",&#F#\"\"#!\"\"*&*&F%F#^#F#F#F#)\"\"$F%F#F#,&F%F' *&,$F)F#F#F+F#F'" }}}{EXCHG {PARA 0 "" 0 "" {XPPEDIT 2 0 "" "%#%?G" }} }}{SECT 0 {PARA 5 "" 0 "" {TEXT 206 81 "2.4.12. Gy\303\266kt\303\251ny ez\305\221s el\305\221\303\241ll\303\255t\303\241s." }}{PARA 0 "" 0 "" {TEXT 201 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 42 "map(y->x-y ,r); convert(%,`*`); evalc(%);\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "7%,& I\"xG6\"\"\"\"F&!\"\",(F$F&#F&\"\"#F&*&,$*&F)F&^#F&F&F&F&)\"\"$F)F&F', (F$F&F)F&*&F-F&F/F&F&" }}{PARA 11 "" 1 "" {XPPMATH 20 "*(,&I\"xG6\"\" \"\"F&!\"\"F&,(F$F&#F&\"\"#F&*&,$*&F)F&^#F&F&F&F&)\"\"$F)F&F'F&,(F$F&F )F&*&F-F&F/F&F&F&" }}{PARA 11 "" 1 "" {XPPMATH 20 ",&*$)I\"xG6\"\"\"$ \"\"\"F(F(!\"\"" }}}{EXCHG {PARA 0 "" 0 "" {XPPEDIT 2 0 "" "%#%?G" }}} }{SECT 0 {PARA 5 "" 0 "" {TEXT 206 46 "* 2.4.13. Lagrange-interpol\303 \241ci\303\263." }}{PARA 0 "" 0 "" {TEXT 201 0 "" }}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 63 "CurveFitting[PolynomialInterpolation]([0,1,2,3 ],[0,3,1,3],x);\n" }{MPLTEXT 1 0 2 "\n" }{MPLTEXT 1 0 77 "CurveFitting [PolynomialInterpolation]([0,1,2,3],[0,3,1,3],x,form=Lagrange);\n" }} {PARA 11 "" 1 "" {XPPMATH 20 ",(*&#\"\"$\"\"#\"\"\")I\"xG6\"F%F'F'*&\" \"(F')F)F&F'!\"\"*&#\"# " 0 "" {MPLTEXT 1 0 59 "f:=5*x^2*y; type( f,monomial); type(f,polynom); degree(f);\n" }{MPLTEXT 1 0 2 "\n" } {MPLTEXT 1 0 59 "f:=f+x*y^3; type(f,monomial); type(f,polynom); degree (f);\n" }}{PARA 11 "" 1 "" {XPPMATH 20 ",$*(\"\"&\"\"\")I\"xG6\"\"\"#F %I\"yGF(F%F%" }}{PARA 11 "" 1 "" {XPPMATH 20 "I%trueG%*protectedG" }} {PARA 11 "" 1 "" {XPPMATH 20 "I%trueG%*protectedG" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"$" }}{PARA 11 "" 1 "" {XPPMATH 20 ",&*(\"\"&\"\"\")I \"xG6\"\"\"#F%I\"yGF(F%F%*&F'F%)F*\"\"$F%F%" }}{PARA 11 "" 1 "" {XPPMATH 20 "I&falseG%*protectedG" }}{PARA 11 "" 1 "" {XPPMATH 20 "I%t rueG%*protectedG" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"%" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 39 "f/(2*x*y-5*x^2*y^2); type(f,ratpoly );\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "*&,&*(\"\"&\"\"\")I\"xG6\"\"\"#F &I\"yGF)F&F&*&F(F&)F+\"\"$F&F&F&,&*(F*F&F(F&F+F&F&*(F%F&F'F&)F+F*F&!\" \"F3" }}{PARA 11 "" 1 "" {XPPMATH 20 "I%trueG%*protectedG" }}}{EXCHG {PARA 0 "" 0 "" {XPPEDIT 2 0 "" "%#%?G" }}}}{EXCHG {PARA 0 "" 0 "" {XPPEDIT 2 0 "" "%#%?G" }}}}{PARA 0 "" 0 "" {TEXT 201 0 "" }}}{SECT 1 {PARA 3 "" 0 "" {TEXT 204 34 "3. Hat\303\241r\303\251rt\303\251k" }} {EXCHG {PARA 0 "" 0 "" {XPPEDIT 2 0 "" "%#%?G" }}}}{SECT 1 {PARA 3 "" 0 "" {TEXT 204 51 "4. Differenci\303\241lsz\303\241m\303\255t\303\241s " }}{EXCHG {PARA 0 "" 0 "" {XPPEDIT 2 0 "" "%#%?G" }}}}{SECT 1 {PARA 3 "" 0 "" {TEXT 204 47 "5. Integr\303\241lsz\303\241m\303\255t\303\241s " }}{EXCHG {PARA 0 "" 0 "" {XPPEDIT 2 0 "" "%#%?G" }}}}{EXCHG {PARA 0 "" 0 "" {XPPEDIT 2 0 "" "%#%?G" }}}} {MARK "0 0 0" 0 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }