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{SECT 0 {EXCHG {PARA 265 "" 0 "" {TEXT 272 35 "Matematick\351 v\375po
\350ty se syst\351m Maple" }}}{EXCHG {PARA 266 "" 0 "" {TEXT -1 77 "au
tor:  Ing. Vladim\355r \216\341k\n  email:  zakyn@centrum.cz\n        \+
         web:   " }{URLLINK 17 "www.vladimirzak.com/maple" 4 "www.vlad
imirzak.com/maple" "" }}{PARA 265 "" 0 "" {TEXT -1 0 "" }}{PARA 265 "
" 0 "" {TEXT -1 12 "            " }{TEXT 270 9 "recenzent" }{TEXT -1 
3 ":  " }{TEXT 269 31 "Prof. RNDr. Ji\370\355 H\370eb\355\350ek, CSc.
" }}{PARA 265 "" 0 "" {TEXT -1 48 "CENTRUM BIOSTATISTIKY A ANAL\335Z (
CBA LF a P\370F MU)" }}{PARA 265 "" 0 "" {TEXT -1 43 "L\351ka\370sk
\341 a P\370\355rodov\354deck\341 fakulta MU v Brn\354" }}{PARA 265 "
" 0 "" {TEXT -1 20 "hrebicek@cba.muni.cz" }}{PARA 265 "" 0 "" {TEXT 
-1 0 "" }}}{EXCHG {PARA 265 "" 0 "" {TEXT -1 478 "Tento dokument je ur
\350en jen pro v\375ukov\351 \372\350ely a pro pou\236it\355 jen osoba
mi, kter\375m byl tento dokument poskytnut p\370\355mo autorem, pop
\370. si ho st\341hli z webov\351ho s\355dla autora. Jak\351koliv \350
\341sti dokumentu nen\355 mo\236n\351 pou\236\355t bez citace zdoje, t
edy n\341zvu dokumentu a jm\351na autora s kontaktn\355mi informacemi \+
(jak je zobrazeno v hlavi\350ce), kter\341 mus\355 b\375t autorovi sd
\354lena. Pro jin\351 pou\236it\355 ne\236 pro osobn\355 pot\370eby os
ob, tedy pro distribuci \350i kop\355rov\341n\355, je nutn\351 obdr
\236et p\355semn\375 souhlas autora. " }}{PARA 265 "" 0 "" {TEXT -1 0 
"" }}{PARA 265 "" 0 "" {TEXT -1 0 "" }{TEXT 271 59 "Soubor vznikl s po
dporou grantov\351ho projektu FRV\212 3323/2006" }{TEXT -1 0 "" }}}
{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 4 "" 0 "" {TEXT -1 38 "Funkce za
dan\351 parametrick\375mi rovnicemi" }}{EXCHG {PARA 0 "" 0 "" {TEXT 
-1 158 "Tento odstavec uk\341\236e mo\236nost vytvo\370en\355 vlastn
\355 procedury. P\371jde o p\370\355kaz, pomoc\355 kter\351ho spo\350t
eme derivaci funkc\355 dan\375ch parametricky a\236 do \370\341du \350
ty\370i v\350etn\354." }}{PARA 0 "" 0 "" {TEXT -1 72 "Nejprve uve\357m
e n\354kolik vztah\371, pomoc\355 kter\375ch se tyto derivace po\350
\355taj\355." }}{PARA 0 "" 0 "" {TEXT -1 53 "Z v\354ty o derivaci funk
ce dan\351 parametricky m\341 funkce " }{TEXT 256 4 "f(x)" }{TEXT -1 
33 " v p\370\355slu\232n\351m intervalu prom\354nn\351 " }{TEXT 257 1 
"x" }{TEXT -1 45 " derivaci a v odpov\355daj\355c\355ch si bodech plat
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{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 63 "Nyn\355 p
\370istupme k vytvo\370en\355 ji\236 zmi\362ovan\351 procedury. Nazvem
e ji " }{TEXT 258 7 "diffpar" }{TEXT -1 1 "." }}{PARA 0 "" 0 "" {TEXT 
263 30 "diffpar( [rce1,rce2], prom)   " }{TEXT -1 49 "                \+
                     - 1.derivace" }}{PARA 0 "" 0 "" {TEXT 262 44 "dif
fpar( [rce1,rce2], prom, prom)           " }{TEXT -1 32 "             \+
      - 2. derivace" }}{PARA 0 "" 0 "" {TEXT 261 40 "diffpar( [rce1,rc
e2], prom, prom, prom) " }{TEXT -1 31 "                  - 3. derivace
" }}{PARA 0 "" 0 "" {TEXT 260 45 "diffpar( [rce1,rce2], prom, prom, pr
om, prom)" }{TEXT -1 21 "         - 4.derivace" }}{PARA 0 "" 0 "" 
{TEXT -1 0 "" }}}{SECT 0 {PARA 5 "" 0 "" {TEXT -1 17 "Procedura diffpa
r" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 263 "Tato procedura byla z d\371v
odu p\370ehlednosti naps\341na pomoc\355 z\341kladn\355ch p\370\355kaz
\371 programov\341n\355 v syst\351mu Maple. Lze ji upravit tak, aby se
 chovala jako procedura, kter\341 je sou\350\341st\355 programu. Jde p
\370edev\232\355m o typovou kontrolu. Pro pochopen\355 je v\232ak nutn
\351 p\370e\350\355st p\370\355lohu " }{TEXT 259 24 "Programov\341n
\355 - jazyk MPJ" }{TEXT -1 1 "." }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 1227 "diffpar:=proc(rce,prom)\n local vysl,x,y,dx,dy,dxx,
dyy,dxxx,dyyy,dxxxx,dyyyy;\n\n if is(type(rce,'list')) and (nops(rce)=
2) then \n    # spravny parametr\n  else\n    return  `Chyba - nesprav
ny pocet rovnic`;\n end if; \n\n x:=rce[1];             # z\355sk\341n
\355 zadan\375ch rovnic \n y:=rce[2];\n dx:=diff(x,prom);      # v\375
po\350et derivace\n dy:=diff(y,prom);\n \n if nargs=2 then\n    lprint
(`1.derivace`);\n    vysl:=dy/dx ;\n\n elif nargs=3 then\n    lprint(`
2.derivace`);\n    dxx:=diff(dx,prom);\n    dyy:=diff(dy,prom);\n    v
ysl:=simplify((dyy*dx-dxx*dy)/(dx)^3);    \n\n elif nargs=4 then \n   \+
 lprint(`3.derivace`);\n    dxx:=diff(dx,prom);\n    dyy:=diff(dy,prom
);\n    dxxx:=diff(dxx,prom);\n    dyyy:=diff(dyy,prom);\n    vysl:=si
mplify((dx^2*dyyy-dx*dy*dxxx-3*dx*dxx*dyy+3*dxx^2*dy)/(dx^5));\n\n eli
f nargs=5 then \n    lprint(`4.derivace`);\n    dxx:=diff(dx,prom);\n \+
   dyy:=diff(dy,prom);\n    dxxx:=diff(dxx,prom);\n    dyyy:=diff(dyy,
prom);\n    dxxxx:=diff(dxxx,prom);\n    dyyyy:=diff(dyyy,prom);\n    \+
vysl:=simplify(1/dx^5*(-6*dx^2*dxx*dyyy+dx^3*dyyyy-4*dx^2*dyy*dxxx\n  \+
        -dx^2*dy*dxxxx+10*dx*dxx*dxxx*dy+15*dx*dxx^2*dyy-15*dxx^3*dy))
;\n\n elif nargs>5 then\n     return `Tato procedura pocita maximalne \+
4.derivaci`;\n end if;   \n\nreturn vysl;\nend proc:" }}}}{EXCHG 
{PARA 0 "" 0 "" {TEXT -1 14 "Uk\341zka pou\236it\355" }}}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 27 "diffpar([ln(t),1/(1-t)],t);" }}{PARA 6 "
" 1 "" {TEXT -1 12 "`1.derivace`" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*&
,&\"\"\"F%%\"tG!\"\"!\"#F&F%" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 29 "diffpar([ln(t),1/(1-t),0],t);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6
#%?Chyba~-~nespravny~pocet~rovnicG" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 29 "diffpar([ln(t),1/(1-t)],t,t);" }}{PARA 6 "" 1 "" 
{TEXT -1 12 "`2.derivace`" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$*(,&%\"
tG\"\"\"F'F'F'F&F',&F'!\"\"F&F'!\"$F)" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 31 "diffpar([ln(t),1/(1-t)],t,t,t);" }}{PARA 6 "" 1 "" 
{TEXT -1 12 "`3.derivace`" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*(,(*$)%
\"tG\"\"#\"\"\"F)F)F)*&\"\"%F)F'F)F)F)F'F),&F)!\"\"F'F)!\"%" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 78 "diffpar([ln(t),1/(1-t)],t$4)
;       # je mo\236n\351 u\236\355t oper\341toru $ jako opakova\350e" 
}}{PARA 6 "" 1 "" {TEXT -1 12 "`4.derivace`" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#,$*(%\"tG!\"\",**&\"#6\"\"\")F%\"\"#F*F**$)F%\"\"$F*F**
&F)F*F%F*F*F*F*F*,&F*F&F%F*!\"&F&" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 35 "diffpar([ln(t),1/(1-t)],t,t,t,t,t);" }}{PARA 11 "" 1 
"" {XPPMATH 20 "6#%KTato~procedura~pocita~maximalne~4.derivaciG" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}
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