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1DE69AD42C3C4BFED70A3D70A3D62BFE77318FC504808BFE1C432CA57A774BFD8C7E28 240B758BFCD495182A992B4BFB47AE147AE13C43FAE4F765FD8AF303FC82A9930BE0E5 03FD3C36113404ED53FDAD42C3C9EECEE3FE0A3D70A3D70BB3FE38EF34D6A16353FE62 B6AE7D566E53FE8793DD97F62CC3FEA786C226809EA3FEC28F5C28F5C3E3FED8ADAB9F 559C83FEE9E1B089A02893FEF62B6AE7D56803FEFD8ADAB9F55AE3FF00000000000093 FEFD8ADAB9F55AC3FEF62B6AE7D567D3FEE9E1B089A02853FED8ADAB9F559C23FEC28F 5C28F5C363FEA786C226809E13FE8793DD97F62C23FE62B6AE7D566DA3FE38EF34D6A1 6283FE0A3D70A3D70AD3FDAD42C3C9EECCF3FD3C36113404EB23FC82A9930BE0E083FA E4F765FD8ADE0BFB47AE147AE146CBFCD495182A99314BFD8C7E28240B788BFE1C432C A57A78FBFE77318FC504823BFED70A3D70A3D80BFF1DE69AD42C3D3BFF52BD3C361134 CBFF8A0902DE00D2ABFFC3C9EECBFB16CC000000000000009-%*AXESSTYLEG6#%&FRAM EG-%&STYLEG6#%-PATCHCONTOURG" 3 340 340 340 4 0 1 0 2 1 0 3 2 1.000000 45.000000 45.000000 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 257 257 0 0 0 0 0 0 }}}{EXCHG {PARA 278 "" 0 "" {TEXT -1 36 "Defin ovani po castech spojite funkce" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 301 15 "Pomoci vetveni." }}}{EXCHG {PARA 452 "" 0 "" {TEXT -1 8 "Syntaxe: " }{TEXT 304 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }{TEXT 305 9 "parame tr " }{TEXT -1 5 "-> if" }{TEXT 312 12 " podminka 1 " }{TEXT -1 4 "the n" }{TEXT 313 10 " hodnota 1" }}{PARA 0 "" 0 "" {TEXT -1 25 " \+ elif " }{TEXT 306 11 "podminka 2 " }{TEXT -1 4 "then" } {TEXT 314 10 " hodnota 2" }}{PARA 0 "" 0 "" {TEXT -1 20 " \+ " }{TEXT 309 8 "........" }}{PARA 0 "" 0 "" {TEXT -1 25 " \+ elif " }{TEXT 307 11 "podminka n " }{TEXT -1 4 "then" } {TEXT 315 31 " hodnota n\n " }{TEXT -1 5 "else " } {TEXT 310 18 "implicitni hodnota" }}{PARA 0 "" 0 "" {TEXT -1 37 " \+ fi " }}}{EXCHG {PARA 453 "" 0 "" {TEXT -1 9 "Definujme" }{TEXT 311 92 " nyni funkci, ktera ma hodnotu -1 pro \+ realna cisla mensi jak 1, 0 pro hodnotu x=1 a 1 jinak." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 51 "step:=x-> if x<1 then -1 elif x=1 t hen 0 else 1 fi;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%stepGR6#%\"xG6 \"6$%)operatorG%&arrowGF(@'29$\"\"\"!\"\"/F.F/\"\"!F/F(F(F(" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "step(3/2), step(1), step(1/2 );" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"\"\"\"\"!!\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 67 "plot(step, -1..Pi, discont=true, co lor=black, scaling=constrained);" }}{PARA 13 "" 1 "" {INLPLOT "6'-%'CU RVESG6$7S7$$!\"\"\"\"!F(7$$!1,2Axj3k&*!#;F(7$$!14z&[E+[=*F.F(7$$!1&y4K O`#e()F.F(7$$!1Ne\"=.z)G$)F.F(7$$!1#=o;WX:!zF.F(7$$!1ET4,DN0vF.F(7$$!1 D/_fw6&4(F.F(7$$!1**y^*>_3n'F.F(7$$!1/jAkt%zC'F.F(7$$!1'*p^fx$H\"eF.F( 7$$!1t$3H1\"yHaF.F(7$$!1OQ%HPP%)*\\F.F(7$$!1ccMWDKlXF.F(7$$!1n^w_h$z9% F.F(7$$!1m\"zGK4*oPF.F(7$$!1Q[)=w4#=LF.F(7$$!1**QO:\"3k$HF.F(7$$!1]46N ?G#\\#F.F(7$$!1o)=)*>b\"*4#F.F(7$$!1%*=DaF$ym\"F.F(7$$!11*)>(y6rD\"F.F (7$$!1g%z`XvcG)!#9)FhoF(7$$\"1_%3=GI(G7F.F(7$$\"1Z%[g*eTF.F(7$$\"1TKEFSu'e%F.F(7$$\"1[DM .]D*)\\F.F(7$$\"1$Q6;&\\**4aF.F(7$$\"1U]Ib^M@eF.F(7$$\"1a&>mp!*>D'F.F( 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1*Gh,*f2iDFbuFcu7$$\"1I9'[gx^g#FbuFcu7$$\"1R))Q67B]EFbuFcu7$$\"1.*=oMz Up#FbuFcu7$$\"1`aWiORSFFbuFcu7$$\"1S-@Hs![y#FbuFcu7$$\"1<3-;lAIGFbuFcu 7$$\"1+\\?3(p_(GFbuFcu7$$\"1+r\"Qsfm\"HFbuFcu7$$\"1Z&pDN(4kHFbuFcu7$$ \"17QBLh_1IFbuFcu7$$\"1Ag)G1k<0$FbuFcu7$$\"1ZHzLD1&4$FbuFcu7$$\"1+++aE fTJFbuFcuFht-%(SCALINGG6#%,CONSTRAINEDG-%+AXESLABELSG6$%!GF\\_l-%%VIEW G6$;F($\"0z*e`EfTJ!#9%(DEFAULTG" 2 472 472 472 2 0 1 0 2 9 0 4 1 1.000000 45.000000 45.000000 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 16368 -17735 0 0 0 0 0 0 }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "step(Pi);" }}{PARA 8 "" 1 "" {TEXT -1 40 "Error, (in step) cannot e valuate boolean" }}}{EXCHG {PARA 454 "" 0 "" {TEXT -1 85 "Problem je v tom, ze Maple umi porovnavat pouze cisla typu integer, fraction a flo at." }}{PARA 455 "> " 0 "" {MPLTEXT 1 0 10 "step(1.1);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"\"" }}}{EXCHG {PARA 360 "> " 0 "" {MPLTEXT 1 0 39 "STEP:=x->piecewise(x<1, -1, x=1, 0, 1);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%STEPGR6#%\"xG6\"6$%)operatorG%&arrowGF(-%*piecewiseG 6'29$\"\"\"!\"\"/F0F1\"\"!F1F(F(F(" }}}{EXCHG {PARA 361 "> " 0 "" {MPLTEXT 1 0 41 "STEP(3/2), STEP(1), STEP(1/2), STEP(Pi); " }}{PARA 11 "" 1 "" {XPPMATH 20 "6&\"\"\"\"\"!!\"\"F#" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "STEP(u);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%*PI ECEWISEG6%7$!\"\"2%\"uG\"\"\"7$\"\"!/F)F*7$F*%*otherwiseG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "f:=x->piecewise(x<=1, x^2, sin(x)); " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"fGR6#%\"xG6\"6$%)operatorG%&ar rowGF(-%*piecewiseG6%19$\"\"\"*$)F0\"\"#\"\"\"-%$sinG6#F0F(F(F(" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "D(f);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#R6#%\"xG6\"6$%)operatorG%&arrowGF&-%*piecewiseG6%19$\" \"\",$F.\"\"#-%$cosG6#F.F&F&F&" }}}{EXCHG {PARA 289 "" 0 "" {TEXT 281 43 "Definice funkce pomoci Maplovske procedury:" }}{PARA 290 "> " 0 " " {MPLTEXT 1 0 33 "sgn:=proc(n::integer) (-1)^n end:" }}}{EXCHG {PARA 291 "> " 0 "" {MPLTEXT 1 0 8 "sgn(Pi);" }}{PARA 8 "" 1 "" {TEXT -1 78 "Error, sgn expects its 1st argument, n, to be of type integer, but re ceived Pi" }}}{EXCHG {PARA 292 "> " 0 "" {MPLTEXT 1 0 7 "sgn(4);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"\"" }}}{EXCHG {PARA 293 "" 0 "" {TEXT -1 42 "Definice procedury ma obecne tuto syntaxi:" }}{PARA 294 " " 0 "" {TEXT 287 4 "proc" }{TEXT -1 23 "(posloupnost_parametru)" }} {PARA 295 "" 0 "" {TEXT -1 10 " [" }{TEXT 289 5 "local" } {TEXT -1 20 " posloupnost_jmen;] " }}{PARA 438 "" 0 "" {TEXT -1 10 " \+ [" }{TEXT 290 6 "global" }{TEXT -1 19 " posloupnost_jmen;]" }} {PARA 296 "" 0 "" {TEXT -1 10 " [" }{TEXT 291 7 "options" } {TEXT -1 20 " posloupnost_jmen;] " }}{PARA 439 "" 0 "" {TEXT -1 10 " \+ [" }{TEXT 292 11 "description" }{TEXT -1 10 " retezec;]" }} {PARA 297 "" 0 "" {TEXT -1 16 " prikazy" }}{PARA 298 "" 0 "" {TEXT 288 3 "end" }}{PARA 299 "" 0 "" {TEXT -1 104 "U kazdeho parametr u muze byt uvedeno, jakeho je typu.\nObecne procedura vraci posledni p ocitanou hodnotu." }}{PARA 300 "> " 0 "" {MPLTEXT 1 0 19 "y:=proc(x) x ^2 end:" }}}{EXCHG {PARA 301 "> " 0 "" {MPLTEXT 1 0 17 "y(x), y(0), y( 2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%*$)%\"xG\"\"#\"\"\"\"\"!\"\"%" }}}{EXCHG {PARA 302 "> " 0 "" {MPLTEXT 1 0 13 "whattype(%%);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%*procedureG" }}}{EXCHG {PARA 377 "> " 0 "" {MPLTEXT 1 0 8 "restart;" }}}{EXCHG {PARA 303 "" 0 "" {TEXT -1 8 "Reku rse:" }}{PARA 304 "" 0 "" {TEXT -1 0 "" }}{PARA 305 "" 0 "" {TEXT -1 70 "Rekursivni definici funkce nebo procedury budeme ilustrovat na vyp octu" }}{PARA 306 "" 0 "" {TEXT -1 74 "tzv. Lucasovych cisel Ln, ktere jsou definovany pomoci linerani rekurence:" }}{PARA 307 "" 0 "" {TEXT -1 42 "L(1)=1, L(2)=3, L(n)=L(n-1)+L(n-2) pro n>2" }}{PARA 308 " > " 0 "" {MPLTEXT 1 0 18 "L:=proc(n::posint)" }}{PARA 309 "> " 0 "" {MPLTEXT 1 0 13 "if n=1 then 1" }}{PARA 310 "> " 0 "" {MPLTEXT 1 0 15 "elif n=2 then 3" }}{PARA 311 "> " 0 "" {MPLTEXT 1 0 18 "else L(n-1)+L (n-2)" }}{PARA 312 "> " 0 "" {MPLTEXT 1 0 2 "fi" }}{PARA 313 "> " 0 " " {MPLTEXT 1 0 4 "end:" }}}{EXCHG {PARA 441 "> " 0 "" {MPLTEXT 1 0 6 " L(-6);" }}{PARA 8 "" 1 "" {TEXT -1 75 "Error, L expects its 1st argume nt, n, to be of type posint, but received -6" }}}{EXCHG {PARA 378 "> \+ " 0 "" {MPLTEXT 1 0 12 "time(L(20));" }}{PARA 11 "" 1 "" {XPPMATH 20 " 6#$\"#\")!\"$" }}}{EXCHG {PARA 368 "> " 0 "" {MPLTEXT 1 0 17 "readlib( profile):" }}}{EXCHG {PARA 369 "> " 0 "" {MPLTEXT 1 0 11 "profile(L): " }}}{EXCHG {PARA 370 "> " 0 "" {MPLTEXT 1 0 5 "L(6);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"#=" }}}{EXCHG {PARA 371 "> " 0 "" {MPLTEXT 1 0 14 "showprofile();" }}{PARA 6 "" 1 "" {TEXT -1 74 "function \+ depth calls time time% bytes bytes%" }}{PARA 6 "" 1 "" {TEXT -1 75 "---------------------------------------------------- -----------------------" }}{PARA 6 "" 1 "" {TEXT -1 74 "L \+ 5 15 0.000 0.00 14236 100.00" }}{PARA 6 "" 1 "" {TEXT -1 75 "----------------------------------------------- ----------------------------" }}{PARA 6 "" 1 "" {TEXT -1 74 "total: \+ 5 15 0.000 0.00 14236 100.00" }} {PARA 6 "" 1 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart;" }}}{EXCHG {PARA 315 "" 0 "" {TEXT -1 79 "Pro zefektivne ni procedury pouzijeme option remeber, ktera zpusobi zapamatovani" }} {PARA 316 "" 0 "" {TEXT -1 40 "funkcnich hodnot tak, jak jsou pocitany ." }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 317 "> " 0 "" {MPLTEXT 1 0 36 "L L:=proc(n::nonnegint) Lucas(n) end:" }}}{EXCHG {PARA 318 "" 0 "" {TEXT -1 45 " pri zavolani L je kontrolovan typ argumentu," }}{PARA 319 "" 0 "" {TEXT -1 101 "pokud je v poradku, vola se rekursivni defin ice Lukas (timto zamezime opetovnemu testovani argumentu)" }}{PARA 320 "> " 0 "" {MPLTEXT 1 0 15 "Lucas:=proc(n) " }}{PARA 321 "> " 0 "" {MPLTEXT 1 0 16 "option remember;" }}{PARA 322 "" 0 "" {TEXT -1 101 " \+ kazda Maplovska procedura je spojena s pametovou tabulkou, ktera se ak tivuje pomoci option remember." }}{PARA 323 "" 0 "" {TEXT -1 96 "Poloz ky tabulky jsou funkcni hodnoty, indexovane pomoci argumentu, odpovida jicimu volani funkce." }}{PARA 324 "" 0 "" {TEXT -1 86 "Pokud zavolame Lucas(n), Maple se podiva do tabulky, zda tam neni ulozena odpovidaji ci" }}{PARA 325 "" 0 "" {TEXT -1 173 "funkcni hodnota. Pokud ne, vyvol a se telo procedury a dvojice (n, Lucas(n)) se automaticky ulozi do pa metove tabulky. Tim dosahneme, ze kazde cislo je pocitano pouze jednou ." }}{PARA 326 "> " 0 "" {MPLTEXT 1 0 13 "if n=1 then 1" }}{PARA 327 " > " 0 "" {MPLTEXT 1 0 15 "elif n=2 then 3" }}{PARA 328 "> " 0 "" {MPLTEXT 1 0 26 "else Lucas(n-1)+Lucas(n-2)" }}{PARA 329 "> " 0 "" {MPLTEXT 1 0 2 "fi" }}{PARA 330 "> " 0 "" {MPLTEXT 1 0 4 "end:" }}} {EXCHG {PARA 380 "> " 0 "" {MPLTEXT 1 0 6 "LL(6);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"#=" }}}{EXCHG {PARA 372 "" 0 "" {TEXT -1 60 "Pametova tabulka je pristupna jako ctvrty operand procedury." }}{PARA 373 "> \+ " 0 "" {MPLTEXT 1 0 19 "op(4, eval(Lucas));" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#-%&TABLEG6#7(/\"\"#\"\"$/F)\"\"%/F+\"\"(/\"\"&\"#6/\"\" '\"#=/\"\"\"F5" }}}{EXCHG {PARA 374 "" 0 "" {TEXT -1 28 "Odstraneni pa metove tabulky:" }}{PARA 375 "> " 0 "" {MPLTEXT 1 0 28 "subsop(4=NULL, eval(Lucas)):" }}}{EXCHG {PARA 376 "> " 0 "" {MPLTEXT 1 0 19 "op(4, e val(Lucas));" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "readlib(pro file):" }}}{EXCHG {PARA 366 "> " 0 "" {MPLTEXT 1 0 15 "profile(Lucas): " }}}{EXCHG {PARA 331 "> " 0 "" {MPLTEXT 1 0 6 "LL(6);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"#=" }}}{EXCHG {PARA 367 "> " 0 "" {MPLTEXT 1 0 14 "showprofile();" }}{PARA 6 "" 1 "" {TEXT -1 74 "function \+ depth calls time time% bytes bytes%" }}{PARA 6 "" 1 "" {TEXT -1 75 "---------------------------------------------------- -----------------------" }}{PARA 6 "" 1 "" {TEXT -1 74 "Lucas \+ 5 9 0.000 0.00 8452 100.00" }}{PARA 6 "" 1 "" {TEXT -1 75 "----------------------------------------------- ----------------------------" }}{PARA 6 "" 1 "" {TEXT -1 74 "total: \+ 5 9 0.000 0.00 8452 100.00" }} {PARA 6 "" 1 "" {TEXT -1 0 "" }}}{EXCHG {PARA 381 "> " 0 "" {MPLTEXT 1 0 17 "time(Lucas(300));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"#%*!\" $" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "Lucas:=proc(n)" }}{PARA 0 "> " 0 " " {MPLTEXT 1 0 31 "Lucas(n):=Lucas(n-1)+Lucas(n-2)" }}{PARA 0 "> " 0 " " {MPLTEXT 1 0 4 "end:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "L ucas(1):=1: Lucas(2):=3:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "op(4, eval(Lucas));" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#-%&TABLEG6#7$/ \"\"\"F(/\"\"#\"\"$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "Luca s(5): op(4, eval(Lucas));" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#-%&TABLEG 6#7'/\"\"$\"\"%/F)\"\"(/\"\"&\"#6/\"\"\"F0/\"\"#F(" }}}{EXCHG {PARA 332 "" 0 "" {TEXT -1 8 "UNAPPLY\n" }}{PARA 333 "" 0 "" {TEXT -1 63 "Te nto zpusob definovani funkce je vyhodny zejmena tehdy, pokud " }} {PARA 359 "" 0 "" {TEXT -1 49 "z nejakeho vyrazu ci formule chceme ude lat funkci" }{MPLTEXT 1 0 0 "" }}{PARA 334 "> " 0 "" {MPLTEXT 1 0 62 " vzorec:=(b^2*x^2*sin(b*x)-2*sin(b*x)+2*b*x*cos(b*x)*a*t)/b^3; " }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%'vzorecG*&,(*()%\"bG\"\"#\"\"\")%\"x GF*F+-%$sinG6#*&F)\"\"\"F-F2F2F2F.!\"#*,F)F+F-F+-%$cosGF0F2%\"aGF2%\"t GF2F*F+*$)F)\"\"$F+!\"\"" }}}{EXCHG {PARA 335 "> " 0 "" {MPLTEXT 1 0 25 "F:=unapply(vzorec, x, t);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"F GR6$%\"xG%\"tG6\"6$%)operatorG%&arrowGF)*&,(*()%\"bG\"\"#\"\"\")9$F2F3 -%$sinG6#*&F1\"\"\"F5F:F:F:F6!\"#*,F1F3F5F3-%$cosGF8F:%\"aGF:9%F:F2F3* $)F1\"\"$F3!\"\"F)F)F)" }}}{EXCHG {PARA 336 "> " 0 "" {MPLTEXT 1 0 17 "F(0,1),F(Pi/b,5);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$\"\"!,$*&*&%#PiG \"\"\"%\"aGF(\"\"\"*$)%\"bG\"\"$F*!\"\"!#5" }}}{EXCHG {PARA 337 "" 0 " " {TEXT -1 22 "Jine pokusy selhavaji." }}{PARA 338 "> " 0 "" {MPLTEXT 1 0 7 "vzorec;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*&,(*()%\"bG\"\"#\" \"\")%\"xGF(F)-%$sinG6#*&F'\"\"\"F+F0F0F0F,!\"#*,F'F)F+F)-%$cosGF.F0% \"aGF0%\"tGF0F(F)*$)F'\"\"$F)!\"\"" }}}{EXCHG {PARA 339 "> " 0 "" {MPLTEXT 1 0 12 "F:=(x,t)->%;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"F GR6$%\"xG%\"tG6\"6$%)operatorG%&arrowGF)%\"%GF)F)F)" }}}{EXCHG {PARA 340 "> " 0 "" {MPLTEXT 1 0 7 "F(0,1);" }}}{EXCHG {PARA 341 "> " 0 "" {MPLTEXT 1 0 17 "G:=(x,t)->vzorec;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6# >%\"GGR6$%\"xG%\"tG6\"6$%)operatorG%&arrowGF)%'vzorecGF)F)F)" }}} {EXCHG {PARA 342 "> " 0 "" {MPLTEXT 1 0 14 "F(u,v),G(u,v);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*&,(*()%\"bG\"\"#\"\"\")%\"xGF(F)-%$sinG6#*& F'\"\"\"F+F0F0F0F,!\"#*,F'F)F+F)-%$cosGF.F0%\"aGF0%\"tGF0F(F)*$)F'\"\" $F)!\"\"" }}}{EXCHG {PARA 343 "" 0 "" {TEXT -1 25 "Jinou moznosti je j edine:" }}{PARA 344 "> " 0 "" {MPLTEXT 1 0 34 "H:=subs(telo=vzorec, (x ,t)->telo);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"HGR6$%\"xG%\"tG6\"6 $%)operatorG%&arrowGF)*&,(*()%\"bG\"\"#\"\"\")9$F2F3-%$sinG6#*&F1\"\" \"F5F:F:F:F6!\"#*,F1F3F5F3-%$cosGF8F:%\"aGF:9%F:F2F3*$)F1\"\"$F3!\"\"F )F)F)" }}}{EXCHG {PARA 345 "> " 0 "" {MPLTEXT 1 0 7 "H(u,v);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*&,(*()%\"bG\"\"#\"\"\")%\"uGF(F)-%$sinG6#*& F'\"\"\"F+F0F0F0F,!\"#*,F'F)F+F)-%$cosGF.F0%\"aGF0%\"vGF0F(F)*$)F'\"\" $F)!\"\"" }}}{EXCHG {PARA 346 "" 0 "" {TEXT -1 19 "Operace s funkcemi. " }}{PARA 347 "> " 0 "" {MPLTEXT 1 0 30 "f:=x->ln(x)+1; g:=y->exp(y)-1 ;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"fGR6#%\"xG6\"6$%)operatorG%&a rrowGF(,&-%#lnG6#9$\"\"\"F1F1F(F(F(" }}{PARA 11 "" 1 "" {XPPMATH 20 "6 #>%\"gGR6#%\"yG6\"6$%)operatorG%&arrowGF(,&-%$expG6#9$\"\"\"!\"\"F1F(F (F(" }}}{EXCHG {PARA 348 "> " 0 "" {MPLTEXT 1 0 13 "h:=f+g: h(z);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#,&-%#lnG6#%\"zG\"\"\"-%$expGF&F(" }}} {EXCHG {PARA 349 "> " 0 "" {MPLTEXT 1 0 13 "h:=f*g: h(z);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*&,&-%#lnG6#%\"zG\"\"\"F)F)F),&-%$expGF'F)!\"\" F)F)" }}}{EXCHG {PARA 350 "> " 0 "" {MPLTEXT 1 0 13 "h:=f@g: h(z);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#,&-%#lnG6#,&-%$expG6#%\"zG\"\"\"!\"\"F ,F,F,F," }}}{EXCHG {PARA 351 "> " 0 "" {MPLTEXT 1 0 13 "h:=g@f: h(z); " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&-%$expG6#,&-%#lnG6#%\"zG\"\"\"F, F,F,!\"\"F," }}}{EXCHG {PARA 352 "> " 0 "" {MPLTEXT 1 0 12 "simplify(% );" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&*&%\"zG\"\"\"-%$expG6#F&F&F&! \"\"F&" }}}{EXCHG {PARA 353 "> " 0 "" {MPLTEXT 1 0 38 "(f@@4)(z); #ekv ivalent k f(f(f(f(z))))" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&-%#lnG6#, &-F%6#,&-F%6#,&-F%6#%\"zG\"\"\"F1F1F1F1F1F1F1F1F1F1F1" }}}{EXCHG {PARA 354 "> " 0 "" {MPLTEXT 1 0 19 "map(x->x^2, a+b+c);" }}{PARA 11 " " 1 "" {XPPMATH 20 "6#,(*$)%\"aG\"\"#\"\"\"\"\"\"*$)%\"bGF'F(F)*$)%\"c GF'F(F)" }}}{EXCHG {PARA 445 "> " 0 "" {MPLTEXT 1 0 21 "map(x->x+2, [1 ,2,3]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7%\"\"$\"\"%\"\"&" }}}} {PARA 398 "" 0 "" {TEXT -1 0 "" }}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 13 "Reseni rovnic" }}{EXCHG {PARA 382 "> " 0 "" {MPLTEXT 1 0 21 "eqn:=(x- 1)*(x^2+x+1);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$eqnG*&,&%\"xG\"\" \"!\"\"F(F(,(*$)F'\"\"#\"\"\"F(F'F(F(F(F(" }}}{EXCHG {PARA 383 "> " 0 "" {MPLTEXT 1 0 18 "sol:=solve(eqn,x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$solG6%\"\"\",&#!\"\"\"\"#F&*&%\"IGF&-%%sqrtG6#\"\"$\"\"\"#F&F *,&F(F&F+F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "subs(x=sol[2 ], eqn);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*&,&#!\"$\"\"#\"\"\"*&%\"I GF(-%%sqrtG6#\"\"$\"\"\"#F(F'F(,(*$),&#!\"\"F'F(F)F0F'F/F(F0F(F)F0F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "expand(%);" }}{PARA 11 " " 1 "" {XPPMATH 20 "6#\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "eval(eqn, x=sol[3]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*&,&#!\"$ \"\"#\"\"\"*&%\"IGF(-%%sqrtG6#\"\"$\"\"\"#!\"\"F'F(,(*$),&F0F(F)F0F'F/ F(#F(F'F(F)F0F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "expand(% );" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "eqn:=x^3+2*a*x^2+a*x=1;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$eqnG/,(*$)%\"xG\"\"$\"\"\"\"\"\"*&%\"aGF,)F)\"\"#F+F 0*&F.F+F)F,F,F," }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "solve(eq n, x);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6%,(*$),**$)%\"aG\"\"#\"\"\"\" #s\"$3\"\"\"\"*$)F)\"\"$F+!#k*$-%%sqrtG6#,*F/!#%)*$)F)\"\"%F+!#7F'F-\" #\")F.F+\"#7#F.F1F+#F.\"\"'*&,&F)F?F'#!\"%\"\"*F+*$)F&#\"\"\"F1F+!\"\" !\"'F)#!\"#F1,*F$#!\"\"F>FBF1F)FM*(%\"IGF.-F56#F1F+,&F$F@FBFAF.#F.F*,* F$FPFBF1F)FMFR#FQF*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "expr :=%2/ %1^(1/3);" }}{PARA 8 "" 1 "" {TEXT -1 15 "undefined label" }}} {EXCHG {PARA 384 "> " 0 "" {MPLTEXT 1 0 33 "solve(\{x+2*y=3, y+1/x=1\} , \{x,y\});" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$<$/%\"xG!\"\"/%\"yG\"\" #<$/F%F)/F(#\"\"\"F)" }}}{EXCHG {PARA 385 "> " 0 "" {MPLTEXT 1 0 25 "e qns:=\{x+2*y=3, y+1/x=1\};" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%eqnsG <$/,&%\"xG\"\"\"%\"yG\"\"#\"\"$/,&F*F)*&\"\"\"F0F(!\"\"F)F)" }}} {EXCHG {PARA 386 "> " 0 "" {MPLTEXT 1 0 25 "soln:=solve(eqns, \{x,y\}) ;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%solnG6$<$/%\"xG!\"\"/%\"yG\"\" #<$/F(F,/F+#\"\"\"F," }}}{EXCHG {PARA 387 "> " 0 "" {MPLTEXT 1 0 8 "so ln[1];" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#<$/%\"xG!\"\"/%\"yG\"\"#" }} }{EXCHG {PARA 388 "> " 0 "" {MPLTEXT 1 0 8 "soln[2];" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#<$/%\"xG\"\"#/%\"yG#\"\"\"F&" }}}{EXCHG {PARA 389 "> " 0 "" {MPLTEXT 1 0 20 "eval(eqns, soln[1]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#<$/\"\"\"F%/\"\"$F'" }}}{EXCHG {PARA 390 "> " 0 "" {MPLTEXT 1 0 24 "solve(\{x^2=y^2\}, \{x,y\});" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$<$/%\"yGF%/%\"xGF%<$/F',$F%!\"\"F$" }}}{EXCHG {PARA 391 "> " 0 "" {MPLTEXT 1 0 30 "solve(\{x^2=y^2, x<>y\},\{x,y\}); " }} {PARA 11 "" 1 "" {XPPMATH 20 "6#<$/%\"xG,$%\"yG!\"\"/F'F'" }}}{EXCHG {PARA 448 "> " 0 "" {MPLTEXT 1 0 30 "solve(\{y^2+1=x, x+2=y\},\{x,y\}) ;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#<$/%\"xG,&!\"#\"\"\"-%'RootOfG6#, (*$)%#_ZG\"\"#\"\"\"F(\"\"$F(F/!\"\"F(/%\"yGF)" }}}{EXCHG {PARA 449 "> " 0 "" {MPLTEXT 1 0 13 "allvalues(%);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$<$/%\"xG,&#!\"$\"\"#\"\"\"*&%\"IGF*-%%sqrtG6#\"#6\"\"\"#F*F)/%\" yG,&F2F*F+F2<$/F%,&F'F*F+#!\"\"F)/F4,&F2F*F+F9" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 10 "Nerovnosti" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "solve(x^3+4*x^2+2*x-1>0, x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$ -%*RealRangeG6$-%%OpenG6#,&#!\"$\"\"#\"\"\"*$-%%sqrtG6#\"#8\"\"\"#!\" \"F,-F'6#F5-F$6$-F'6#,&F*F-F.#F-F,%)infinityG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "solve(x^3+4*x^2+2*x-1>0, \{x\});" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$<$2,&#!\"$\"\"#\"\"\"*$-%%sqrtG6#\"#8\"\"\"#!\"\"F (%\"xG2F2F1<#2,&F&F)F*#F)F(F2" }}}{EXCHG {PARA 11 "" 1 "" {TEXT -1 0 " " }}}{EXCHG {PARA 427 "" 0 "" {TEXT -1 9 "Problemy:" }}}{EXCHG {PARA 392 "> " 0 "" {MPLTEXT 1 0 8 "restart;" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 293 29 "Maple nevraci vsechna reseni:" }}}{EXCHG {PARA 393 "> " 0 "" {MPLTEXT 1 0 20 "solve(sin(x)=1/2,x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$%#PiG#\"\"\"\"\"'" }}}{EXCHG {PARA 394 "> " 0 "" {MPLTEXT 1 0 25 "_EnvAllSolutions := true:" }}}{EXCHG {PARA 395 "> " 0 "" {MPLTEXT 1 0 21 "solve(sin(x)=1/2, x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,(%#PiG#\"\"\"\"\"'*&F$F&%%_B1|irGF&#\"\"#\"\"$*&F$\"\" \"%%_Z1|irGF&F+" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "map(abou t,indets(%, name)):" }}{PARA 6 "" 1 "" {TEXT -1 29 "Originally _B1, re named _B1~:" }}{PARA 6 "" 1 "" {TEXT -1 31 " is assumed to be: OrProp (0,1)" }}{PARA 6 "" 1 "" {TEXT -1 0 "" }}{PARA 6 "" 1 "" {TEXT -1 3 "P i:" }}{PARA 6 "" 1 "" {TEXT -1 22 " is assumed to be: Pi" }}{PARA 6 " " 1 "" {TEXT -1 0 "" }}{PARA 6 "" 1 "" {TEXT -1 29 "Originally _Z1, re named _Z1~:" }}{PARA 6 "" 1 "" {TEXT -1 27 " is assumed to be: intege r" }}{PARA 6 "" 1 "" {TEXT -1 0 "" }}}{EXCHG {PARA 412 "> " 0 "" {MPLTEXT 1 0 11 "indets(%%);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#<$%%_B 1|irG%%_Z1|irG" }}}{EXCHG {PARA 428 "> " 0 "" {MPLTEXT 1 0 29 "eqn := \+ product(x-k,k=1..110);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%$eqnG*hx,& %\"xG\"\"\"!\"\"F(F(,&F'F(!\"#F(F(,&F'F(!\"$F(F(,&F'F(!\"%F(F(,&F'F(! \"&F(F(,&F'F(!\"'F(F(,&F'F(!\"(F(F(,&F'F(!\")F(F(,&F'F(!\"*F(F(,&F'F(! #5F(F(,&F'F(!#6F(F(,&F'F(!#7F(F(,&F'F(!#8F(F(,&F'F(!#9F(F(,&F'F(!#:F(F (,&F'F(!#;F(F(,&F'F(!#F(F(,&F'F(!#?F(F(,&F' F(!#@F(F(,&F'F(!#AF(F(,&F'F(!#BF(F(,&F'F(!#CF(F(,&F'F(!#DF(F(,&F'F(!#E F(F(,&F'F(!#FF(F(,&F'F(!#GF(F(,&F'F(!#HF(F(,&F'F(!#IF(F(,&F'F(!#JF(F(, &F'F(!#KF(F(,&F'F(!#LF(F(,&F'F(!#MF(F(,&F'F(!#NF(F(,&F'F(!#OF(F(,&F'F( !#PF(F(,&F'F(!#QF(F(,&F'F(!#RF(F(,&F'F(!#SF(F(,&F'F(!#TF(F(,&F'F(!#UF( F(,&F'F(!#VF(F(,&F'F(!#WF(F(,&F'F(!#XF(F(,&F'F(!#YF(F(,&F'F(!#ZF(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(!#aF(F(,&F'F(!#bF(F(,&F'F(!#cF(F(,&F'F(!#dF(F(,&F'F(!#eF(F (,&F'F(!#fF(F(,&F'F(!#gF(F(,&F'F(!#hF(F(,&F'F(!#iF(F(,&F'F(!#jF(F(,&F' F(!#kF(F(,&F'F(!#lF(F(,&F'F(!#mF(F(,&F'F(!#nF(F(,&F'F(!#oF(F(,&F'F(!#p F(F(,&F'F(!#qF(F(,&F'F(!#rF(F(,&F'F(!#sF(F(,&F'F(!#tF(F(,&F'F(!#uF(F(, &F'F(!#vF(F(,&F'F(!#wF(F(,&F'F(!#xF(F(,&F'F(!#yF(F(,&F'F(!#zF(F(,&F'F( !#!)F(F(,&F'F(!#\")F(F(,&F'F(!##)F(F(,&F'F(!#$)F(F(,&F'F(!#%)F(F(,&F'F (!#&)F(F(,&F'F(!#')F(F(,&F'F(!#()F(F(,&F'F(!#))F(F(,&F'F(!#*)F(F(,&F'F (!#!*F(F(,&F'F(!#\"*F(F(,&F'F(!##*F(F(,&F'F(!#$*F(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(!$+\"F(F(,&F'F(!$,\"F(F(,&F'F(!$-\"F(F(,&F'F(!$.\"F(F(,&F'F(!$/\"F(F (,&F'F(!$0\"F(F(,&F'F(!$1\"F(F(,&F'F(!$2\"F(F(,&F'F(!$3\"F(F(,&F'F(!$4 \"F(F(,&F'F(!$5\"F(F(" }}}{EXCHG {PARA 429 "> " 0 "" {MPLTEXT 1 0 22 " nops(\{solve(eqn,x)\}); " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"$+\"" }} }{EXCHG {PARA 430 "> " 0 "" {MPLTEXT 1 0 14 "_MaxSols:=200;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%)_MaxSolsG\"$+#" }}}{EXCHG {PARA 431 "> " 0 "" {MPLTEXT 1 0 21 "nops(\{solve(eqn,x)\});" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"$5\"" }}}{EXCHG {PARA 432 "> " 0 "" {MPLTEXT 1 0 14 " _MaxSols:=100;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%)_MaxSolsG\"$+\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "eqn:=x+x^(1/3)=-2;" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%$eqnG/,&%\"xG\"\"\"*$)F'#F(\"\"$\"\" \"F(!\"#" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "solve(eqn, x); " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "infolevel[solve]:=2;" } }{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%*infolevelG6#%&solveG\"\"#" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "solve(eqn, x);" }}{PARA 6 " " 1 "" {TEXT -1 36 "solve: Warning: no solutions found" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "eq:=convert(eqn, RootOf);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#eqG/,&%\"xG\"\"\"-%'RootOfG6#,&*$)%#_ZG\" \"$\"\"\"F(F'!\"\"F(!\"#" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "sol:=solve(eq,\{x\});" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$solG6%<#/ %\"xG!\"\"<#/F(,&#!\"&\"\"#\"\"\"*&%\"IGF0-%%sqrtG6#\"\"(\"\"\"#F0F/<# /F(,&F-F0F1#F)F/" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 54 "Tj. byly nale zeny komplexni koreny polynomu (x+2)^3+x." }}}{EXCHG {PARA 433 "" 0 " " {TEXT -1 20 "Prilis mnoho reseni:" }}}{EXCHG {PARA 434 "> " 0 "" {MPLTEXT 1 0 49 " eqn := sin(x)^3 -13/2*sin(x)^2 + 11*sin(x) = 4; " }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%$eqnG/,(*$)-%$sinG6#%\"xG\"\"$\"\"\" \"\"\"*$)F)\"\"#F.#!#8F2F)\"#6\"\"%" }}}{EXCHG {PARA 435 "> " 0 "" {MPLTEXT 1 0 17 "solve(\{eqn\},\{x\});" }}{PARA 12 "" 1 "" {XPPMATH 20 "6%<#/%\"xG,*-%'arcsinG6#\"\"#\"\"\"*&F'F+%%_B1|irGF+!\"#*&%#PiGF+% %_Z1|irGF+F**&F0\"\"\"F-F3F+<#/F%,(F0#F+\"\"'*&F0F3F-F3#F*\"\"$*&F0F3F 1F3F*<#/F%,*-F(6#\"\"%F+*&F@F+F-F3F.*&F0F3F1F3F**&F0F3F-F3F+" }}} {EXCHG {PARA 436 "> " 0 "" {MPLTEXT 1 0 18 "solve(eqn,sin(x));" }} {PARA 11 "" 1 "" {XPPMATH 20 "6%\"\"##\"\"\"F#\"\"%" }}}{EXCHG {PARA 437 "> " 0 "" {MPLTEXT 1 0 20 "solve(sin(x)=1/2,x);" }}{PARA 11 "" 1 " " {XPPMATH 20 "6#,(%#PiG#\"\"\"\"\"'*&F$F&%%_B1|irGF&#\"\"#\"\"$*&F$\" \"\"%%_Z1|irGF&F+" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "rl:=(x -1)^2/(x^2-1)=0;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#rlG/*&*$),&%\"x G\"\"\"!\"\"F+\"\"#\"\"\"F.,&*$)F*F-F.F+F,F+!\"\"\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "solve(rl);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "su bs(x=1, rl);" }}{PARA 8 "" 1 "" {TEXT -1 23 "Error, division by zero" }}}{EXCHG {PARA 397 "" 0 "" {TEXT -1 47 "K hledani numerickeho reseni \+ pouzivame prikazu " }{TEXT 261 6 "fsolve" }{TEXT -1 1 "." }}}{EXCHG {PARA 402 "> " 0 "" {MPLTEXT 1 0 33 "r:=x^7-2*x^6-4*x^5-x^3+x^2+6*x+4; " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"rG,0*$)%\"xG\"\"(\"\"\"\"\"\"* $)F(\"\"'F*!\"#*$)F(\"\"&F*!\"%*$)F(\"\"$F*!\"\"*$)F(\"\"#F*F+F(F.\"\" %F+" }}}{EXCHG {PARA 403 "> " 0 "" {MPLTEXT 1 0 10 "fsolve(r);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6%$!+xz1O7!\"*$\"+yRIn6F%$\"+xz1OKF%" }} }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "fsolve(r, x, complex);" }} {PARA 12 "" 1 "" {XPPMATH 20 "6)$!+xz1O7!\"*,&$!+OV%)[w!#5\"\"\"%\"IG$ !+garCNF),&F'F*F+$\"+garCNF),&$\"+XWK7=F)F*F+$!+,T&R3\"F%,&F2F*F+$\"+, T&R3\"F%$\"+yRIn6F%$\"+xz1OKF%" }}}{EXCHG {PARA 404 "> " 0 "" {MPLTEXT 1 0 31 "fsolve(r, x, 0..2, fulldigits);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+yRIn6!\"*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "readlib(realroot);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#R6$%%polyG %*widthgoalG6'%\"xG%\"LG%&poly1G%+widthgoal1G%-powerremoverG6#%aoCopyr ight~(c)~1991~by~the~University~of~Waterloo.~All~rights~reserved.G6\"C ,@$-%%typeG6$9$.%(numericG@%0F5\"\"!-%'RETURNG6#7\"F;>8$-%'indetsG6#F5 @$550-%%nopsG6#F@\"\"\"4-F36$-%#opGFJ%%nameG4-F36$F5-.%(polynomG6$%)an ythingGFO-%&ERRORG6#%Ofirst~argument~must~be~a~univariate~polynomialG@ $-%(hastypeG6$F5.%&floatG-Fen6#%Urequires~exact,~non-floating~polynomi al~coefficientsG>F@FO@'/9#FK>8'%%NULLG3-F36$9%F72F:F[p>FfoF[p-Fen6#%G2 nd~argument~must~be~a~positive~numberG>8&-%(convertG6$F5.%(sqrfreeG@&- F36$Fbp%\"*GC$>8(R6#F(F/F-F/@'-F36$F5.%(integerGFK-F36$F5%\"^G-FP6$FKF 5F5F/F/F/>Fbp-%'expandG6#-%$mapG6$F^qFbp-F36$FbpFhq>Fbp-FP6$FKFbp>8%-% )uspenskyG6%-F]r6#FbpF@Ffo-F<6#FhrF/F/F/" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "realroot(r);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7%7$ \"\"!\"\"#7$F&\"\"%7$!\"#!\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "realroot(r, 1/100);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7%7$#\" $\\\"\"$G\"#\"#v\"#k7$#\"$2#F*#\"$:%F'7$#!$f\"F'#!#zF*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "readlib(sturm);" }}{PARA 11 "" 1 " " {XPPMATH 20 "6#R6$%#ssG%#xxG60%#a1G%#a2G%#c1G%#c2G%#s1G%#s2G%\"tG%\" iG%#n1G%#n2G%\"xG%\"aG%\"bG%\"sG6#%aoCopyright~(c)~1991~by~the~Univers ity~of~Waterloo.~All~rights~reserved.G6\"C1@'3/9#\"\"#-%%typeG6$9%/%%n ameG%&rangeGC%>8.-%#opG6$\"\"\"FB>8/-FJ6$7$F>FLFB>80-FJ6$7$F>F>FB/F=\" \"%C%>FHFB>FN&9\"6#\"\"$>FS&Fgn6#FX-%&ERRORG6#%>incorrect~number~of~ar gumentsG>819$@$-F@6$Fbo-%(polynomG6$%(numericGFH>Fbo-%)sturmseqG6$FboF H@$4-F@6$Fbo-%%listG6#Fgo-F^o6#%Zfirst~argument~should~be~a~Sturm~sequ ence~or~a~polynomialG@%/FN,$%)infinityG!\"\">8$-%$mapG6%R6$%\"pGF2F86$ %)operatorG%&arrowGF8*&-%'lcoeffG6$FcoFBFL)F]q-%'degreeGF\\rFLF8F8F8Fb oFH>F_q-%%subsG6$/FHFNFbo@%/FSF\\q>8%-Faq6%F[rFboFH>Fhr-Fbr6$/FHFSFbo> F_q-Fbr6$/\"\"!%%NULLGF_q>Fhr-Fbr6$FbsFhr>8&Fcs>8,-%%nopsG6#F_q@$2FcsF [tC$>8(&F_q6#FL?(8+F>FLF[t%%trueGC%>8*&F_q6#Fgt@$0-%%signG6#Fct-Fau6#F [u>Fis,&FisFLFLFL>FctF[u>8'Fcs>8--F]t6#Fhr@$2FcsF[vC$>8)&FhrFet?(FgtF> FLF[vFhtC%>F[u&FhrF]u@$0-Fau6#FbvFcu>Fiu,&FiuFLFLFL>FbvF[u,&FisFLFiuF] qF8F8F8" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 32 "sturm(r,x, -infi nity, infinity);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "sturm(r, x, 2,4);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"\"" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 294 10 "Proc edura " }{TEXT -1 19 "realroot(p, sirka) " }{TEXT 297 77 "najde otevre ne intervaly pro realne koreny celociselneho polynomu, procedura " } {TEXT -1 5 "sturm" }{TEXT 299 60 " vraci pocet realnych korenu polynom u na zadanem intervalu. " }}}{EXCHG {PARA 405 "" 0 "" {TEXT -1 0 "" } {TEXT 264 0 "" }{TEXT 265 31 "Pro polynomialni rovnice vraci " }{TEXT 266 6 "fsolve" }{TEXT 267 42 " vetsinou vsechna realna reseni, s volbo u " }{TEXT 268 8 "complex " }{TEXT 269 94 "vsechna komplexni reseni. P ro vsechny ostatni rovnice fsolve vetsinou vraci jen jedno reseni. " } }}{EXCHG {PARA 406 "" 0 "" {TEXT -1 0 "" }{TEXT 270 0 "" }{TEXT 271 11 "Standardne " }{TEXT 272 6 "fsolve" }{TEXT 273 67 " uziva pro vypoc ty mensi pocet cislic, nez je predepsano promennou " }{TEXT 274 6 "Dig its" }{TEXT 275 45 " (vzhledem k uspore casu a pameti). Parametr " } {TEXT 276 10 "fulldigits" }{TEXT 277 74 " zpusobi dodrzeni pozadovaneh o poctu platnych cislic uvedeneho v promenne " }{TEXT 278 6 "Digits" } {TEXT 279 51 ". Parametr maxsols=n urcuje maximalni pocet reseni." }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "eqn:=sin(x)=x/2;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$eqnG/-%$sinG6#%\"xG,$F)#\"\"\"\"\"#" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "fsolve(eqn, x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "fsolve(eqn, x, avoid=\{x=0\});" }}{PARA 11 "" 1 "" {XPPMATH 20 " 6#$!+nU\\&*=!\"*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 33 "fsolve( eqn, x, avoid=\{x=0, x=%\});" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+nU \\&*=!\"*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 39 "fsolve(eqn, x, avoid=\{x=0, x=%%, x=%\});" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'fsol veG6%/-%$sinG6#%\"xG,$F*#\"\"\"\"\"#F*/%&avoidG<%/F*\"\"!/F*$!+nU\\&*= !\"*/F*$\"+nU\\&*=F7" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "fso lve(eqn, x, 0.1..infinity);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+nU \\&*=!\"*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "fsolve(eqn, x, -0.1..0.1);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 32 "fsolve(eqn, x, -infinity..-0.1);" } }{PARA 11 "" 1 "" {XPPMATH 20 "6#$!+nU\\&*=!\"*" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }{TEXT 320 7 "Prikaz " }{TEXT -1 7 "fsolve " } {TEXT 321 148 "je zalozen na (vicedimensionalni) Newtonove metode a (p okud tato selze) na (vicedimensionalni) metode secen. Muzeme tedy urci t pocatecni aproximaci." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 " fsolve(sin(x), x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"!" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "fsolve(sin(x), x=3);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+aEfTJ!\"*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}}{MARK "1" 0 }{VIEWOPTS 1 1 0 3 2 1804 }