{VERSION 6 0 "IBM INTEL LINUX" "6.0" } {USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 1 0 0 0 0 1 }{CSTYLE "2D Math" -1 2 "Times" 0 1 0 0 0 0 0 0 2 0 0 0 0 0 0 1 }{CSTYLE "2D Output" 2 20 "" 0 1 0 0 255 1 0 0 0 0 0 0 0 0 0 1 } {CSTYLE "" -1 256 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 257 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 258 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 259 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 263 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 1 } {PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "Times" 1 24 0 0 0 0 2 2 2 0 0 0 0 0 0 1 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Text Output" -1 2 1 {CSTYLE "" -1 -1 "Courier" 1 10 0 0 255 1 0 0 0 0 0 1 3 0 3 1 } 1 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Heading 1" 0 3 1 {CSTYLE "" -1 -1 "" 1 18 0 0 0 0 0 1 0 0 0 0 0 0 0 1 }1 0 0 0 8 4 0 0 0 0 0 0 -1 0 }{PSTYLE "Warning" 2 7 1 {CSTYLE "" -1 -1 "" 0 1 0 0 255 1 0 0 0 0 0 0 1 0 0 1 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Error" 7 8 1 {CSTYLE "" -1 -1 "" 0 1 255 0 255 1 0 0 0 0 0 0 0 0 0 1 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Maple Output" 0 11 1 {CSTYLE "" -1 -1 " " 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }3 3 0 -1 -1 -1 0 0 0 0 0 0 -1 0 } {PSTYLE "" 11 12 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }1 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Maple Plot" 0 13 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }3 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Title" 0 18 1 {CSTYLE "" -1 -1 "" 1 18 0 0 0 0 0 1 1 0 0 0 0 0 0 1 }3 0 0 -1 12 12 0 0 0 0 0 0 19 0 }{PSTYLE "R3 Fo nt 0" -1 256 1 {CSTYLE "" -1 -1 "Helvetica" 1 24 0 0 0 0 2 1 2 0 0 0 0 0 0 1 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "R3 Font 2" -1 257 1 {CSTYLE "" -1 -1 "Courier" 1 14 0 0 0 0 2 2 2 0 0 0 0 0 0 1 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }} {SECT 0 {EXCHG {PARA 18 "" 0 "" {TEXT -1 11 "DATOVE TYPY" }}}{SECT 0 {PARA 3 "" 0 "" {TEXT -1 11 "Posloupnost" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "#typ posloupnost (sequence)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "polynomial:=x^3-6*x^2+11*x-6;\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%+polynomialG,**$)%\"xG\"\"$\"\"\"F**&\"\"'F*)F( \"\"#F*!\"\"*&\"#6F*F(F*F*F,F/" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "sequence:=op(polynomial);\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6 #>%)sequenceG6&*$)%\"xG\"\"$\"\"\",$*&\"\"'F*)F(\"\"#F*!\"\",$*&\"#6F* F(F*F*!\"'" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 75 "Jednotlive objekty \+ jsou oddeleny carkami, objekty nemusi byt stejneho typu." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "whattype(sequence);\n" }}{PARA 11 " " 1 "" {XPPMATH 20 "6#%(exprseqG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "s:=1,4,9,16,25;\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6# >%\"sG6'\"\"\"\"\"%\"\"*\"#;\"#D" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "t:=sin, cos, tan;\n" }}{PARA 11 "" 1 "" {XPPMATH 20 " 6#>%\"tG6%%$sinG%$cosG%$tanG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "s,s;\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6,\"\"\"\"\"%\"\"*\"#;\"# DF#F$F%F&F'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "empty:=NULL; #prazdna posloupnost\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%&emptyG6 \"" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 8 "Prikazy " }{TEXT 257 2 "op" }{TEXT -1 3 " a " }{TEXT 258 5 "nops " }{TEXT -1 35 "nemuzeme aplikova t na posloupnosti." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "op(s); \n" }}{PARA 8 "" 1 "" {TEXT -1 66 "Error, invalid input: op expects 1 \+ or 2 arguments, but received 5\n" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 69 "Posloupnosti muzeme vytvaret (generovat) pomoci funkce seq:\nSynta xe: " }{TEXT 259 3 "seq" }{TEXT -1 60 "(f(i), i=m..n); generuje poslou pnost f(m), f(m+1), .., f(n)." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "seq(i^2, i=1..5);\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6'\"\"\"\" \"%\"\"*\"#;\"#D" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "seq(ith prime(i), i=1..9);\n" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 30 "(generuje prvnich 9 prvocisel)" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 55 "Alternat ivne muzeme pouzit posloupnostniho operatoru $:" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 5 "x$4;\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6&%\"xG F#F#F#" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 33 "seq(seq([i,j], i= 1..2), j=3..4);\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6&7$\"\"\"\"\"$7$\" \"#F%7$F$\"\"%7$F'F)" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 89 "Volani se q(f(i), i=vyraz) generuje posloupnost aplikaci funkce f na kazdy opera nd vyrazu." }}{PARA 0 "" 0 "" {TEXT -1 29 "Prikaz je ekvivalentni vola ni" }}{PARA 0 "" 0 "" {TEXT -1 30 "seq(f(op(i,a)), i=1..nops(a))." }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "seq(i^2, i=x+y+z);\n" }} {PARA 11 "" 1 "" {XPPMATH 20 "6%*$)%\"xG\"\"#\"\"\"*$)%\"yGF&F'*$)%\"z GF&F'" }}}{PARA 0 "" 0 "" {TEXT -1 65 "Jednotlive cleny posloupnosti m uzeme vybirat pomoci operatoru []." }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "%[2];\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*$)%\"yG\" \"#\"\"\"" }}}{PARA 0 "" 0 "" {TEXT -1 39 "Odkaz na vice clenu posloup nosti naraz:" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "sequence:=v, w,x,y,z: sequence[2..4];\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%%\"wG%\" xG%\"yG" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 19 "Druhy prvek zprava." } }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "sequence[-2];\n" }}}{PARA 0 "" 0 "" {TEXT -1 52 "Jiny priklad pouziti: (generovani posloupnosti \+ jmen)" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "p||(1..5);\n" }} {PARA 11 "" 1 "" {XPPMATH 20 "6'%#p1G%#p2G%#p3G%#p4G%#p5G" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "seq(p||i, i=1..5);\n" }}{PARA 11 " " 1 "" {XPPMATH 20 "6'%#p1G%#p2G%#p3G%#p4G%#p5G" }}}{PARA 0 "" 0 "" {TEXT -1 26 "Vyraz 1..5 je typu rozsah." }}}{SECT 0 {PARA 3 "" 0 "" {TEXT -1 7 "Mnozina" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restar t;" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 36 "\"Posloupnost ve slozenych \+ zavorkach\"" }}{PARA 0 "" 0 "" {TEXT -1 156 "Zadna data se nesmi vysky tovat vic nez jednou, system pouziva vnitrni system usporadani, ktere \+ uzivatel nemuze ovlivnit (zavisi na adrese objektu v pameti)." }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 33 "#typ mnozina (set)\ns:=\{1, \+ 5, 3\};\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"sG<%\"\"\"\"\"$\"\"& " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "whattype(s);\n" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#%$setG" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 67 "Jednotlive prvky muzeme vybirat pomoci funkce op nebo ope ratoru []." }}{PARA 0 "" 0 "" {TEXT -1 64 "Pouziti op je mene efektivn i, protoze vyhodnocuje celou mnozinu." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "op(1,s);\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "s[1];\n" }}{PARA 11 "" 1 " " {XPPMATH 20 "6#\"\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 " op(1..3,s);\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"\"\"\"\"$\"\"&" }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 26 "Zakladni mnozinove operace" }} {PARA 0 "" 0 "" {TEXT -1 11 "Sjednoceni:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "\{0,1,2,3\} union \{0,2,4,6\};\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#<(\"\"!\"\"\"\"\"#\"\"$\"\"%\"\"'" }}}{EXCHG {PARA 0 " " 0 "" {TEXT -1 7 "Rozdil:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "\{0,1,2,3\} minus \{0,2,4,6\};\n" }}{PARA 11 "" 1 "" {XPPMATH 20 " 6#<$\"\"\"\"\"$" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 7 "Prunik:" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "\{0,1,2,3\} intersect \{0,2, 4,6\};\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#<$\"\"!\"\"#" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 25 "Pridani prvku do mnoziny:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "s union \{x\};\n" }}{PARA 11 "" 1 " " {XPPMATH 20 "6#<&\"\"\"\"\"$\"\"&%\"xG" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 27 "Odstraneni prvku z mnoziny:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "s minus \{1\};\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#< $\"\"$\"\"&" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 24 "Nahrazeni prvku mn oziny:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "subsop(1=x,s);\n " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#<%\"\"$\"\"&%\"xG" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 42 "Zjisteni, zda dany prvek patri do mnoziny ." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "member(2, \{0,1,2,3\}, 'pos');\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%%trueG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "pos;\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"$" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 86 "Funkce powerset z \+ baliku combinat generuje vsechny podmonoziny dane mnoziny (\{1,2,3\}). " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "collection:=combinat[po werset](3);\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%+collectionG<*<$\" \"\"\"\"$<#F'<\"<%F'\"\"#F(<$F,F(<#F(<#F,<$F'F," }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 18 "nops(collection);\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\")" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "col lection[4];\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#<%\"\"\"\"\"#\"\"$" } }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "collection[6..8];\n" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#<%<#\"\"$<#\"\"#<$\"\"\"F'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "op(8, collection);\n" }}{PARA 11 " " 1 "" {XPPMATH 20 "6#<$\"\"\"\"\"#" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 62 "K vybirani prvku podle nejakeho kriteria slouzi funkce select. " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 77 "die:=rand(-10..10): #ge neruje nahodne zvolena cela cisla z intervalu -10..10\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "numberset:=\{seq(die(), i=1..10)\}; \n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%*numbersetG<*!\")!\"'!\"&!\"% \"\"'\"\"(\"\")\"#5" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 56 "Syntaxe: s elect(kriterium, mnozina, zvlastni_argumenty);" }}{PARA 0 "" 0 "" {TEXT -1 47 "kde kriterium musi vzdy vracet true nebo false." }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 46 "select(isprime, numberset); \+ #vybira prvocisla\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#<#\"\"(" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 38 "select(type, numberset, 'non negint');\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#<&\"\"'\"\"(\"\")\"#5" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "select(x->x>-5, numberset );\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#<'!\"%\"\"'\"\"(\"\")\"#5" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "remove(x->x>-5, numberset); \n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#<%!\")!\"'!\"&" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 7 "Prikaz " }{TEXT 256 4 "map " }{TEXT -1 48 "aplik uje zadanou funkci na vsechny prvky mnoziny" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "numbers:=\{0,Pi/3,Pi/2,Pi\};\n" }}{PARA 11 "" 1 " " {XPPMATH 20 "6#>%(numbersG<&\"\"!%#PiG,$*&\"\"$!\"\"F'\"\"\"F,,$*&\" \"#F+F'F,F," }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "map(g, numbe rs);\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#<&-%\"gG6#\"\"!-F%6#%#PiG-F% 6#,$*&\"\"$!\"\"F*\"\"\"F1-F%6#,$*&\"\"#F0F*F1F1" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "map(sin, numbers);\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#<%\"\"!\"\"\",$*&\"\"#!\"\"\"\"$#F%F(F%" }}}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 6 "Seznam" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart;" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" } {MPLTEXT 1 0 19 "#typ SEZNAM (list)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "s:=[x, x, x*y, x*(x-1)];\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"sG7&%\"xGF&*&F&\"\"\"%\"yGF(*&F&F(,&F&F(F(!\"\"F(" }}}{PARA 0 "" 0 "" {TEXT -1 160 "Rozdily oproti typu mnozina: stejne o bjekty se mohou vyskytovat vice nez jednou, zachovava se zadane\nuspor adani. Tedy [a,b,c], a [b,c,a] jsou dva ruzne seznamy." }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "whattype(s);\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%%listG" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 22 "Prevod \+ na typ mnozina." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "m:=conve rt(s, 'set');\n" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 39 "a zpet na sezn am (odstraneni duplicit)." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "convert(m, 'list');\n" }}}{PARA 0 "" 0 "" {TEXT -1 26 "Prevod na t yp posloupnost:" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "op(s);\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "[x$5];\n" }}}{PARA 0 "" 0 "" {TEXT -1 17 "Prace se seznamy:" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 46 "cl:=[black, red, green, yellow, blue, white];\n" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%#clG7(%&blackG%$redG%&greenG%'yellow G%%blueG%&whiteG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "nops(cl );\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"'" }}}{PARA 0 "" 0 "" {TEXT -1 40 "Test, zda dany element patri do seznamu:" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "member(indigo, cl);\n" }}{PARA 11 "" 1 " " {XPPMATH 20 "6#%&falseG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "member(blue, cl, 'position');" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#% %trueG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "position;" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"&" }}}{PARA 0 "" 0 "" {TEXT -1 36 "Vyber jednotlivych elementu seznamu:" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "cl[5];\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%%blueG" } }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "op(5, cl);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%%blueG" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 25 "je mene efektivni zpusob." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 " cl[3..6];\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7&%&greenG%'yellowG%%bl ueG%&whiteG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "cl[-1];cl[-2 ];\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%&whiteG" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%%blueG" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 30 "Posledn i a predposledni prvek." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 32 " L := [1,[2,3],[4,[5,6],7],8,9];\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#> %\"LG7'\"\"\"7$\"\"#\"\"$7%\"\"%7$\"\"&\"\"'\"\"(\"\")\"\"*" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "L[3,2,1];\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"&" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "L[3][2][1];\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"&" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 25 "Pridani prvku do seznamu:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "cl:=[op(cl),pink];\n" }}{PARA 11 " " 1 "" {XPPMATH 20 "6#>%#clG7)%&blackG%$redG%&greenG%'yellowG%%blueG%& whiteG%%pinkG" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 28 "Odstraneni prvku ze seznamu:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "cl:=subsop( 7=NULL,cl);\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#clG7(%&blackG%$red G%&greenG%'yellowG%%blueG%&whiteG" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 32 "Nahrazeni prvku v seznamu jinym:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "cl[5]:=purple;cl;\n" }}{PARA 11 "" 1 "" {XPPMATH 20 " 6#>&%#clG6#\"\"&%'purpleG" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7(%&black G%$redG%&greenG%'yellowG%'purpleG%&whiteG" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 68 "Tento zpusob prirazeni hodnoty prvku v seznamu je efektiv nejsi, nez:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "cl:=subsop(5 =indigo, cl);\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#clG7(%&blackG%$r edG%&greenG%'yellowG%'indigoG%&whiteG" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 90 "ale prime prirazeni hodnot prvkum seznamu je omezeno na s eznamy o maximalne 100 polozkach." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 10 "Setrideni:" } }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "sort(cl, lexorder);\n" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#7(%&blackG%&greenG%'indigoG%$redG%&whi teG%'yellowG" }}}{EXCHG {PARA 11 "" 1 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 22 "Secteni prvku seznamu:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "x:=[1,2,3,4,5,5];\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"xG7(\"\"\"\"\"#\"\"$\"\"%\"\"&F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "add(i, i=x);\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"#?" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 29 "(add secte posloupnost prvku)" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 22 "Slouceni d vou seznamu:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "X:=[seq(ith prime(i), i=1..6)];\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"XG7(\"\"# \"\"$\"\"&\"\"(\"#6\"#8" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 " Y:=[seq(i^2, i=1..6)];\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"YG7(\" \"\"\"\"%\"\"*\"#;\"#D\"#O" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "pair:=(x,y)->[x,y];\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%pairGj +6$%\"xG%\"yG6\"6$%)operatorG%&arrowGF)7$9$9%F)F)F)6$\"\"!F1" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "P:=zip(pair, X,Y);\n" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"PG7(7$\"\"#\"\"\"7$\"\"$\"\"%7$\" \"&\"\"*7$\"\"(\"#;7$\"#6\"#D7$\"#8\"#O" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 43 "Pokud maji seznamy rozdilnou delku, prikaz " }{TEXT 263 4 "zip " }{TEXT -1 54 "vytvori seznam delky odpovidajici kratsimu ze s eznamu." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 45 "zip(igcd, [7567, 342,876], [34,756,213,346]);\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7%\" \"\"\"#=\"\"$" }}}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 19 "Pole (array, A rray)" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "squares:=array(1..3 );\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%(squaresG-%&arrayG6$;\"\"\" \"\"$7\"" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 51 "Ve verzi 9 je k dispo zici a datova struktura Array." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "sq:=Array(1..3);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#sqG-%'R TABLEG6%\"*%G$)o8-%'VECTORG6#7%\"\"!F-F-%&ArrayG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 47 "squares[1]:=1; squares[2]:=2.0; squares[3]:=c ;\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%(squaresG6#\"\"\"F'" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>&%(squaresG6#\"\"#$\"#?!\"\"" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>&%(squaresG6#\"\"$%\"cG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "squares;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%(squaresG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "eval(squares);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#K%'vectorG6#7%\" \"\"$\"#?!\"\"%\"cGQ)pprint386\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "sq[1]:=1;sq[2]:=2.0;sq[3]:=c;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%#sqG6#\"\"\"F'" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>& %#sqG6#\"\"#$\"#?!\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%#sqG6#\" \"$%\"cG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 3 "sq;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'RTABLEG6%\"*%G$)o8-%'VECTORG6#7%\"\"\"$\"#?! \"\"%\"cG%&ArrayG" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 60 "Pro array pl ati pravidlo Last name evaluation, pro Array ne." }}}{EXCHG {PARA 0 " " 0 "" {TEXT -1 96 "Proc ma Maple dve datove struktury pro pole? Hlavn im duvodem je to, ze balicek linalg je zalozen" }}{PARA 0 "" 0 "" {TEXT -1 17 "na pouziti array." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "cubes:=array(1..3, [1,8,27]);\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%&cubesGK%'vectorG6#7%\"\"\"\"\")\"#FQ(pprint06\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "squares[2];\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"#?!\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "squares;\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%(squaresG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "eval(squares);\n" }}{PARA 11 "" 1 " " {XPPMATH 20 "6#K%'vectorG6#7%\"\"\"$\"#?!\"\"%\"cGQ(pprint16\"" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "whattype(eval(squares));\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%&arrayG" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 42 "Definice dvojdimenzionalniho pole (3 x 3)." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "pwrs:=array(1..3,1..3,[]);\n" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%%pwrsG-%&arrayG6%;\"\"\"\"\"$F(7\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 41 "pwrs[1,1]:=1; pwrs[1,2]:= 1;pwrs[1,3]:=1;\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%%pwrsG6$\"\"\" F'F'" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%%pwrsG6$\"\"\"\"\"#F'" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>&%%pwrsG6$\"\"\"\"\"$F'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 98 "pwrs[2,1]:=2: pwrs[2,2]:=4: pwrs[2, 3]:=8:\npwrs[3,1]:=3: pwrs[3,2]:=9: pwrs[3,3]:=27:\nprint(pwrs);\n" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#K%'matrixG6#7%7%\"\"\"F(F(7%\"\"#\"\"% \"\")7%\"\"$\"\"*\"#FQ(pprint26\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "pwrs[2,3];\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\") " }}}{PARA 0 "" 0 "" {TEXT -1 106 "Nejdrive specifikujeme rozsah dvoud imenzionalniho pole, pote jeho prvky (neni nutno specifikovat vsechny) ." }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 57 "array(1..3, 1..2, [(1,1 )=a, (1,2)=b, (2,1)=c, (2,2)=d]);\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6 #K%'matrixG6#7%7$%\"aG%\"bG7$%\"cG%\"dG7$&%\"?G6$\"\"$\"\"\"&F/6$F1\" \"#Q(pprint36\"" }}}{PARA 0 "" 0 "" {TEXT -1 39 "\nPole muze byt konst ruovano ze seznamu:" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restar t;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 36 "M:=array([[1-p, 2-q], [1-r, 2-s]]);\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"MGK%'matrixG6# 7$7$,&\"\"\"F+%\"pG!\"\",&\"\"#F+%\"qGF-7$,&F+F+%\"rGF-,&F/F+%\"sGF-Q( pprint46\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "whattype(eval (M));\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%&arrayG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 56 "pwrs2:=array(1..3, 1..3, [[1,1,1], [2,4,8 ], [3,9,27]]);\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%&pwrs2GK%'matrix G6#7%7%\"\"\"F*F*7%\"\"#\"\"%\"\")7%\"\"$\"\"*\"#FQ(pprint56\"" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "obr:=array(1..2);\n" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%$obrG-%&arrayG6$;\"\"\"\"\"#7\"" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "obr[1]:=plot(sin(x), x=-3..3 ):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "obr[2]:=plot(cos(x), \+ x=-3..3):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "with(plots):di splay(obr);\n" }}{PARA 7 "" 1 "" {TEXT -1 50 "Warning, the name change coords has been redefined\n" }}{PARA 13 "" 1 "" {GLPLOT2D 314 314 314 {PLOTDATA 2 "6J-%'CURVESG6$7Y7$$!+++++5!\")$!+\\`369!\"*7$$!+>p0k&*F-$ !+Tt8!p#F-7$$!+s^u%=*F-$!+\"e,kw$F-7$$!+X%p\"e()F-$!+!p+z\"\\F-7$$!+#4 m(G$)F-$!+&ydd*fF-7$$!+AOS,zF-$!++:')ppF-7$$!+0R=0vF-$!+qy3rxF-7$$!+Q8 #\\4(F-$!+!)Q,&[)F-7$$!+0siqmF-$!+[%4#)3*F-7$$!+)y$pZiF-$!+9=8V&*F-7$$ !+%yaE\"eF-$!+\\O%4&)*F-7$$!+)[j5i&F-$!++fcL**F-7$$!+\">s%HaF-$!+'fzL) **F-7$$!+rdy8_F-$!+**********F-7$$!+^$*4)*\\F-$!+Pdwu**F-7$$!+,t_\"y%F -$!+K;U2**F-7$$!+^_&\\c%F-$!+9#p#)z*F-7$$!+^1aZTF-$!+?')zr%*F-7$$!+/#) [oPF-$!+PljY!*F-7$$!+%=exJ$F-$!+H4`*Q)F-7$$!+M2$f$HF-$!+VM[7xF-7$$!+QY x\"\\#F-$!+:!3%)z'F-7$$!+M7i)4#F-$!+Jb;))eF-7$$!+Q'psm\"F-$!+x1'ez%F-7 $$!+84_c7F-$!+dd*3o$F-7$$!+&3x%z#)!#5$!+w!3$eCF-7$$!+3s$QM%Fcs$!+CoM*H \"F-7$$!+p;zr)*!#7$!+chkWH!#67$$\"+ezw5VFcs$\"+1#\\)*G\"F-7$$\"+v$Q#\\ \")Fcs$\"+Yav?CF-7$$\"+f\"*[H7F-$\"+T6r0OF-7$$\"++dxd;F-$\"+pw=rZF-7$$ \"+D0xw?F-$\"+%\\$RNeF-7$$\"+j&p@[#F-$\"+qoexnF-7$$\"+wgHKHF-$\"+?x(eq (F-7$$\"+nZvOLF-$\"+E7v?%)F-7$$\"+^2goPF-$\"+*[?r/*F-7$$\"+(R<*fTF-$\" +1Q)R[*F-7$$\"+^)Hxe%F-$\"+QD/7)*F-7$$\"+T*)**)y%F-$\"+qMy5**F-7$$\"+J !o-*\\F-$\"+YHSt**F-7$$\"+@Al+_F-$\"+++++5F*7$$\"+9k.6aF-$\"+0cx')**F- 7$$\"+9as;cF-$\"+/xRN**F-7$$\"+=WTAeF-$\"+r7?Y)*F-7$$\"+l!*3`iF-$\"+w; 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Rozdi l" }}{PARA 0 "" 0 "" {TEXT -1 51 "je v tom, ze indexem muze byt cokoli v (u pole pouze" }}{PARA 0 "" 0 "" {TEXT -1 12 "cela cisla)." }} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 49 "translate:=table([one=jedna, two=dve,three=tri]);\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%*translate GK%&TABLEG6#7%/%&threeG%$triG/%$twoG%$dveG/%$oneG%&jednaGQ(pprint66\" " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "whattype(eval(translate ));\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%&tableG" }}}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 16 "translate[two];\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%$dveG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "ba rva[cervena]:=red,rot;\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%&barvaG 6#%(cervenaG6$%$redG%$rotG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "barva[modra]:=blue,blau;\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%& barvaG6#%&modraG6$%%blueG%%blauG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "barva[zluta]:=yellow,gelb;\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%&barvaG6#%&zlutaG6$%'yellowG%%gelbG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "whattype(eval(barva));\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%&tableG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "indices(barva);\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6% 7#%&modraG7#%(cervenaG7#%&zlutaG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "entries(barva);\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6% 7$%%blueG%%blauG7$%$redG%$rotG7$%'yellowG%%gelbG" }}}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 7 "Retezec" }}{PARA 0 "" 0 "" {TEXT -1 8 "(string)" } }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "\"Toto je retezec.\";\n" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#Q1Toto~je~retezec.6\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "r:=\"Toto je retezec.\";\n" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"rGQ1Toto~je~retezec.6\"" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "r[6..-2];\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#Q+je~retezec6\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "length(r);\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"#; " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "whattype(r);\n" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#%'stringG" }}}}{SECT 1 {PARA 3 "" 0 " " {TEXT -1 16 "Linearni algebra" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "with(lin alg);\n" }}{PARA 7 "" 1 "" {TEXT -1 80 "Warning, the protected names n orm and trace have been redefined and unprotected\n" }}{PARA 12 "" 1 " " {XPPMATH 20 "6#7^r%.BlockDiagonalG%,GramSchmidtG%,JordanBlockG%)LUde compG%)QRdecompG%*WronskianG%'addcolG%'addrowG%$adjG%(adjointG%&angleG %(augmentG%(backsubG%%bandG%&basisG%'bezoutG%,blockmatrixG%(charmatG%) charpolyG%)choleskyG%$colG%'coldimG%)colspaceG%(colspanG%*companionG%' concatG%%condG%)copyintoG%*crossprodG%%curlG%)definiteG%(delcolsG%(del rowsG%$detG%%diagG%(divergeG%(dotprodG%*eigenvalsG%,eigenvaluesG%-eige nvectorsG%+eigenvectsG%,entermatrixG%&equalG%,exponentialG%'extendG%,f fgausselimG%*fibonacciG%+forwardsubG%*frobeniusG%*gausselimG%*gaussjor dG%(geneqnsG%*genmatrixG%%gradG%)hadamardG%(hermiteG%(hessianG%(hilber tG%+htransposeG%)ihermiteG%*indexfuncG%*innerprodG%)intbasisG%(inverse G%'ismithG%*issimilarG%'iszeroG%)jacobianG%'jordanG%'kernelG%*laplacia nG%*leastsqrsG%)linsolveG%'mataddG%'matrixG%&minorG%(minpolyG%'mulcolG %'mulrowG%)multiplyG%%normG%*normalizeG%*nullspaceG%'orthogG%*permanen tG%&pivotG%*potentialG%+randmatrixG%+randvectorG%%rankG%(ratformG%$row G%'rowdimG%)rowspaceG%(rowspanG%%rrefG%*scalarmulG%-singularvalsG%&smi thG%,stackmatrixG%*submatrixG%*subvectorG%)sumbasisG%(swapcolG%(swapro wG%*sylvesterG%)toeplitzG%&traceG%*transposeG%,vandermondeG%*vecpotent G%(vectdimG%'vectorG%*wronskianG" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 199 "Matice muzeme zadavat bud primo jako dvou dimenzionalni pole nebo pomoci prikazu matrix z baliku linalag. V Maplu verze 9.5 je k dispoz ici i modernejsi balicek LinearAlgebra (definuje prikaz Matrix)." }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "with(LinearAlgebra);" }} {PARA 7 "" 1 "" {TEXT -1 47 "Warning, the name GramSchmidt has been re bound\n" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#7br%#&xG%$AddG%(AdjointG%3B ackwardSubstituteG%+BandMatrixG%&BasisG%-BezoutMatrixG%/BidiagonalForm G%-BilinearFormG%5CharacteristicMatrixG%9CharacteristicPolynomialG%'Co lumnG%0ColumnDimensionG%0ColumnOperationG%,ColumnSpaceG%0CompanionMatr ixG%0ConditionNumberG%/ConstantMatrixG%/ConstantVectorG%%CopyG%2Create PermutationG%-CrossProductG%-DeleteColumnG%*DeleteRowG%,DeterminantG%) DiagonalG%/DiagonalMatrixG%*DimensionG%+DimensionsG%+DotProductG%6Eige nConditionNumbersG%,EigenvaluesG%-EigenvectorsG%&EqualG%2ForwardSubsti tuteG%.FrobeniusFormG%4GaussianEliminationG%2GenerateEquationsG%/Gener ateMatrixG%2GetResultDataTypeG%/GetResultShapeG%5GivensRotationMatrixG %,GramSchmidtG%-HankelMatrixG%,HermiteFormG%3HermitianTransposeG%/Hess enbergFormG%.HilbertMatrixG%2HouseholderMatrixG%/IdentityMatrixG%2Inte rsectionBasisG%+IsDefiniteG%-IsOrthogonalG%*IsSimilarG%*IsUnitaryG%2Jo rdanBlockMatrixG%+JordanFormG%(LA_MainG%0LUDecompositionG%-LeastSquare sG%,LinearSolveG%$MapG%%Map2G%*MatrixAddG%2MatrixExponentialG%/MatrixF unctionG%.MatrixInverseG%5MatrixMatrixMultiplyG%+MatrixNormG%,MatrixPo werG%5MatrixScalarMultiplyG%5MatrixVectorMultiplyG%2MinimalPolynomialG %&MinorG%(ModularG%)MultiplyG%,NoUserValueG%%NormG%*NormalizeG%*NullSp aceG%3OuterProductMatrixG%*PermanentG%&PivotG%*PopovFormG%0QRDecomposi tionG%-RandomMatrixG%-RandomVectorG%%RankG%6RationalCanonicalFormG%6Re ducedRowEchelonFormG%$RowG%-RowDimensionG%-RowOperationG%)RowSpaceG%-S calarMatrixG%/ScalarMultiplyG%-ScalarVectorG%*SchurFormG%/SingularValu esG%*SmithFormG%*SubMatrixG%*SubVectorG%)SumBasisG%0SylvesterMatrixG%/ ToeplitzMatrixG%&TraceG%*TransposeG%0TridiagonalFormG%+UnitVectorG%2Va ndermondeMatrixG%*VectorAddG%,VectorAngleG%5VectorMatrixMultiplyG%+Vec torNormG%5VectorScalarMultiplyG%+ZeroMatrixG%+ZeroVectorG%$ZipG" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 36 "M:=array([[1-p, 2-q], [1-r, \+ 2-s]]);\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"MGK%'matrixG6#7$7$,& \"\"\"F+%\"pG!\"\",&\"\"#F+%\"qGF-7$,&F+F+%\"rGF-,&F/F+%\"sGF-Q(pprint 76\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "M:=matrix([[1-p, 2- q], [1-r, 2-s]]);\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"MGK%'matrix G6#7$7$,&\"\"\"F+%\"pG!\"\",&\"\"#F+%\"qGF-7$,&F+F+%\"rGF-,&F/F+%\"sGF -Q(pprint86\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 38 "MM:=Matrix ([[1-p, 2-q], [1-r, 2-s]]);\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#MM G-%'RTABLEG6%\"*g&ek8-%'MATRIXG6#7$7$,&\"\"\"F/%\"pG!\"\",&\"\"#F/%\"q GF17$,&F/F/%\"rGF1,&F3F/%\"sGF1%'MatrixG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "v:=vector([1+a, 2+b, 3+c]);\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"vGK%'vectorG6#7%,&\"\"\"F*%\"aGF*,&\"\"#F*%\"bGF*,& \"\"$F*%\"cGF*Q(pprint96\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "VV:=vector([1+a, 2+b, 3+c]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>% #VVGK%'vectorG6#7%,&\"\"\"F*%\"aGF*,&\"\"#F*%\"bGF*,&\"\"$F*%\"cGF*Q)p print396\"" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 27 "Definovani indexacn i funkce" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "h:=(i,j)->1/(i+ j-x);\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"hGj+6$%\"iG%\"jG6\"6$%) operatorG%&arrowGF)*&\"\"\"F.,(9$F.9%F.%\"xG!\"\"F3F)F)F)6$\"\"!F5" }} }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "matrix(4,4,h);\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#K%'matrixG6#7&7&*&\"\"\"F),&\"\"#F)%\"xG!\" \"F-*&F)F),&\"\"$F)F,F-F-*&F)F),&\"\"%F)F,F-F-*&F)F),&\"\"&F)F,F-F-7&F .F1F4*&F)F),&\"\"'F)F,F-F-7&F1F4F8*&F)F),&\"\"(F)F,F-F-7&F4F8F<*&F)F), &\"\")F)F,F-F-Q)pprint106\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "matrix(3,3,0);\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#K%'matrixG6#7% 7%\"\"!F(F(F'F'Q)pprint116\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 3 "v;\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%\"vG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "eval(v);\n" }}{PARA 11 "" 1 "" {XPPMATH 20 " 6#K%'vectorG6#7%,&\"\"\"F(%\"aGF(,&\"\"#F(%\"bGF(,&\"\"$F(%\"cGF(Q)ppr int126\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "op(eval(v));\n " }}{PARA 11 "" 1 "" {XPPMATH 20 "6$;\"\"\"\"\"$7%/F$,&F$F$%\"aGF$/\" \"#,&F+F$%\"bGF$/F%,&F%F$%\"cGF$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "A:=matrix(2,2, [[a,b],[c,d]]);\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"AGK%'matrixG6#7$7$%\"aG%\"bG7$%\"cG%\"dGQ)pprint436 \"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "AA:=Matrix(2,2, [[a,b ],[c,d]]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#AAG-%'RTABLEG6%\"*)y% >Q\"-%'MATRIXG6#7$7$%\"aG%\"bG7$%\"cG%\"dG%'MatrixG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "B:=toeplitz([alpha, beta]); \n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"BGK%'matrixG6#7$7$%&alphaG%%betaG7$F+F*Q )pprint446\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 45 "BB:=Toeplit zMatrix([alpha, beta], symmetric);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6# >%#BBG-%'RTABLEG6%\"*GS@Q\"-%'MATRIXG6#7$7$%&alphaG%%betaG7$F/F.%'Matr ixG" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 84 "Pro aritmetiku s maticemi \+ pouzivame funkci evalm (evaluate using matrix arithmetic)." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "evalm(A+B);\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#K%'matrixG6#7$7$,&%\"aG\"\"\"%&alphaGF*,&%\"bGF*%%betaG F*7$,&%\"cGF*F.F*,&%\"dGF*F+F*Q)pprint456\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "AA+BB;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'RTABLE G6%\"*ol3Q\"-%'MATRIXG6#7$7$,&%\"aG\"\"\"%&alphaGF.,&%\"bGF.%%betaGF.7 $,&%\"cGF.F2F.,&%\"dGF.F/F.%'MatrixG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "evalm(3*A-2/7*B);\n" }}{PARA 11 "" 1 "" {XPPMATH 20 " 6#K%'matrixG6#7$7$,&*&\"\"$\"\"\"%\"aGF+F+*(\"\"#F+\"\"(!\"\"%&alphaGF +F0,&*&F*F+%\"bGF+F+*(F.F+F/F0%%betaGF+F07$,&*&F*F+%\"cGF+F+*(F.F+F/F0 F6F+F0,&*&F*F+%\"dGF+F+*(F.F+F/F0F1F+F0Q)pprint466\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "3*AA-2/7*BB;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'RTABLEG6%\"*S5oQ\"-%'MATRIXG6#7$7$,&*&\"\"$\"\"\"%\" aGF/F/*(\"\"#F/\"\"(!\"\"%&alphaGF/F4,&*&F.F/%\"bGF/F/*(F2F/F3F4%%beta GF/F47$,&*&F.F/%\"cGF/F/*(F2F/F3F4F:F/F4,&*&F.F/%\"dGF/F/*(F2F/F3F4F5F /F4%'MatrixG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "evalm(A-1); \n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#K%'matrixG6#7$7$,&%\"aG\"\"\"F*! \"\"%\"bG7$%\"cG,&%\"dGF*F*F+Q)pprint476\"" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 5 "AA-1;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'RTABLEG6 %\"*+oIN\"-%'MATRIXG6#7$7$,&%\"aG\"\"\"F.!\"\"%\"bG7$%\"cG,&%\"dGF.F.F /%'MatrixG" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 79 "Pro nasobeni matic \+ se pouziva operator &*. Za operatorem je nutno zadat mezeru." }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "evalm(B &* A);\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#K%'matrixG6#7$7$,&*&%&alphaG\"\"\"%\"aGF+F+* &%%betaGF+%\"cGF+F+,&*&F*F+%\"bGF+F+*&F.F+%\"dGF+F+7$,&*&F.F+F,F+F+*&F *F+F/F+F+,&*&F.F+F2F+F+*&F*F+F4F+F+Q)pprint486\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "BB.AA;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'R TABLEG6%\"*'Rlq8-%'MATRIXG6#7$7$,&*&%&alphaG\"\"\"%\"aGF/F/*&%%betaGF/ %\"cGF/F/,&*&F.F/%\"bGF/F/*&F2F/%\"dGF/F/7$,&*&F2F/F0F/F/*&F.F/F3F/F/, &*&F2F/F6F/F/*&F.F/F8F/F/%'MatrixG" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 8 "Mocniny:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "evalm(B^3 );\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#K%'matrixG6#7$7$,&*&,&*$)%&alp haG\"\"#\"\"\"F/*$)%%betaGF.F/F/F/F-F/F/*(F.F/F-F/F1F/F/,&*&F*F/F2F/F/ *(F.F/F,F/F2F/F/7$F4F(Q)pprint196\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "BB^3;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'RTABLEG6% 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