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{SECT 0 {EXCHG {PARA 18 "" 0 "" {TEXT -1 41 "INTERNI DATOVA REPREZENTA
CE  A SUBSTITUCE" }}}{SECT 0 {PARA 3 "" 0 "" {TEXT -1 27 "Interni dato
va reprezentace" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "pol:=x^4+
x^3-x^2-x;\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$polG,**$)%\"xG\"\"%
\"\"\"F**$)F(\"\"$F*F**$)F(\"\"#F*!\"\"F(F1" }}}{EXCHG {PARA 0 "> " 0 
"" {MPLTEXT 1 0 16 "subs(1=7, pol);\n" }}{PARA 11 "" 1 "" {XPPMATH 20 
"6#,**&\"\"(\"\"\")%\"xG\"\"%F&F&*&F%F&)F(\"\"$F&F&*$)F(\"\"#F&!\"\"F(
F0" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "whattype(pol);\n" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#%\"+G" }}}{EXCHG {PARA 0 "" 0 "" 
{TEXT -1 0 "" }{TEXT 259 35 "Pomoci nops ziskame pocet scitancu." }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "nops(pol);\n" }}{PARA 11 "" 
1 "" {XPPMATH 20 "6#\"\"%" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }
{TEXT 261 55 "Posloupnost komponent (operandu) ziskame procedurou op.
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "op(pol);\n" }}{PARA 11 "
" 1 "" {XPPMATH 20 "6&*$)%\"xG\"\"%\"\"\"*$)F%\"\"$F',$*$)F%\"\"#F'!\"
\",$F%F/" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }{TEXT 263 38 "Nyni \+
si vsimneme kazdeho clenu zvlast." }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 25 "`prvni clen`:=op(1,pol);\n" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%+prvni~clenG*$)%\"xG\"\"%\"\"\"" }}}{EXCHG {PARA 0 "
" 0 "" {TEXT 262 43 "Na prvni operand se muzeme odkazat i pomoci" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "op(pol)[1];\n" }}{PARA 11 "
" 1 "" {XPPMATH 20 "6#*$)%\"xG\"\"%\"\"\"" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 13 "whattype(%);\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%
\"^G" }}}{EXCHG }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "dismantle(x
^4);\n" }}{PARA 6 "" 1 "" {TEXT -1 0 "" }}{PARA 6 "" 1 "" {TEXT -1 7 "
PROD(3)" }}{PARA 6 "" 1 "" {TEXT -1 13 "   NAME(4): x" }}{PARA 6 "" 1 
"" {TEXT -1 15 "   INTPOS(2): 4" }}{PARA 6 "" 1 "" {TEXT -1 0 "" }}}
{EXCHG {PARA 0 "" 0 "" {TEXT -1 144 "Symbol ^ predstavuje datovy typ p
ower (mocnina), pokud je exponent typu numeric, Maple provadi automati
cke zjednoduseni na typ product (soucin)." }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 16 "dismantle(x^a);\n" }}{PARA 6 "" 1 "" {TEXT -1 0 "" 
}}{PARA 6 "" 1 "" {TEXT -1 8 "POWER(3)" }}{PARA 6 "" 1 "" {TEXT -1 13 
"   NAME(4): x" }}{PARA 6 "" 1 "" {TEXT -1 13 "   NAME(4): a" }}{PARA 
6 "" 1 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "o
p(op(pol)[1]);\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$%\"xG\"\"%" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "op([1,1],pol),op([1,2],pol);
\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$%\"xG\"\"%" }}}{EXCHG {PARA 0 ">
 " 0 "" {MPLTEXT 1 0 25 "`treti clen`:=op(3,pol);\n" }}{PARA 11 "" 1 "
" {XPPMATH 20 "6#>%+treti~clenG,$*$)%\"xG\"\"#\"\"\"!\"\"" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "whattype(`treti clen`);\n" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#%\"*G" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 25 "dismantle(`treti clen`);\n" }}{PARA 6 "" 1 "" {TEXT -1 0 "" }}
{PARA 6 "" 1 "" {TEXT -1 6 "SUM(3)" }}{PARA 6 "" 1 "" {TEXT -1 10 "   \+
PROD(3)" }}{PARA 6 "" 1 "" {TEXT -1 16 "      NAME(4): x" }}{PARA 6 "
" 1 "" {TEXT -1 18 "      INTPOS(2): 2" }}{PARA 6 "" 1 "" {TEXT -1 16 
"   INTNEG(2): -1" }}{PARA 6 "" 1 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "
> " 0 "" {MPLTEXT 1 0 18 "op(`treti clen`);\n" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6$!\"\"*$)%\"xG\"\"#\"\"\"" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 26 "`ctvrty clen`:=op(4,pol);\n" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%,ctvrty~clenG,$%\"xG!\"\"" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 19 "op(`ctvrty clen`);\n" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6$!\"\"%\"xG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "op([4,2
],pol);\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%\"xG" }}}{EXCHG {PARA 0 
"> " 0 "" {MPLTEXT 1 0 13 "whattype(%);\n" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#%'symbolG" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 165 "Podo
bnym zpusobem muzeme v Maplu rozebrat jakykoliv vyraz, nejen polynomy.
\nMusime vsak neustale byt vedomi, ze identicke podvyrazy jsou interne
 ulozeny pouze jednou." }}}{EXCHG }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 16 "dismantle(pol);\n" }}{PARA 6 "" 1 "" {TEXT -1 0 "" }}{PARA 6 "
" 1 "" {TEXT -1 6 "SUM(9)" }}{PARA 6 "" 1 "" {TEXT -1 10 "   PROD(3)" 
}}{PARA 6 "" 1 "" {TEXT -1 16 "      NAME(4): x" }}{PARA 6 "" 1 "" 
{TEXT -1 18 "      INTPOS(2): 4" }}{PARA 6 "" 1 "" {TEXT -1 15 "   INT
POS(2): 1" }}{PARA 6 "" 1 "" {TEXT -1 10 "   PROD(3)" }}{PARA 6 "" 1 "
" {TEXT -1 16 "      NAME(4): x" }}{PARA 6 "" 1 "" {TEXT -1 18 "      \+
INTPOS(2): 3" }}{PARA 6 "" 1 "" {TEXT -1 15 "   INTPOS(2): 1" }}{PARA 
6 "" 1 "" {TEXT -1 10 "   PROD(3)" }}{PARA 6 "" 1 "" {TEXT -1 16 "    \+
  NAME(4): x" }}{PARA 6 "" 1 "" {TEXT -1 18 "      INTPOS(2): 2" }}
{PARA 6 "" 1 "" {TEXT -1 16 "   INTNEG(2): -1" }}{PARA 6 "" 1 "" 
{TEXT -1 13 "   NAME(4): x" }}{PARA 6 "" 1 "" {TEXT -1 16 "   INTNEG(2
): -1" }}{PARA 6 "" 1 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" 
{TEXT -1 167 "Vidime take, ze delka datoveho vektoru pro promennou je \+
4 - krome jmena promenne jeden ukazatel urcuje, ze promenna je nevyhod
nocenna a druhy, ze nema zadne attributy." }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 16 "dismantle(x-5);\n" }}{PARA 6 "" 1 "" {TEXT -1 0 "" 
}}{PARA 6 "" 1 "" {TEXT -1 6 "SUM(5)" }}{PARA 6 "" 1 "" {TEXT -1 13 " \+
  NAME(4): x" }}{PARA 6 "" 1 "" {TEXT -1 15 "   INTPOS(2): 1" }}{PARA 
6 "" 1 "" {TEXT -1 16 "   INTNEG(2): -5" }}{PARA 6 "" 1 "" {TEXT -1 
15 "   INTPOS(2): 1" }}{PARA 6 "" 1 "" {TEXT -1 0 "" }}}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 24 "dismantle(x^2*y^3*z^4);\n" }}{PARA 6 "" 
1 "" {TEXT -1 0 "" }}{PARA 6 "" 1 "" {TEXT -1 7 "PROD(7)" }}{PARA 6 "
" 1 "" {TEXT -1 13 "   NAME(4): x" }}{PARA 6 "" 1 "" {TEXT -1 15 "   I
NTPOS(2): 2" }}{PARA 6 "" 1 "" {TEXT -1 13 "   NAME(4): y" }}{PARA 6 "
" 1 "" {TEXT -1 15 "   INTPOS(2): 3" }}{PARA 6 "" 1 "" {TEXT -1 13 "  \+
 NAME(4): z" }}{PARA 6 "" 1 "" {TEXT -1 15 "   INTPOS(2): 4" }}{PARA 
6 "" 1 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 134 "Tento \+
priklad ukazuje, ze pouziti datoveho typu PROD je z pametoveho hledisk
a vyhodnejsi, nez kombinace datovych typu POWER a PRODUCT." }}}{EXCHG 
{PARA 0 "" 0 "" {TEXT -1 42 "Odhadnete vysledek nasledujici substituce
:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "pol2:=Pi*x+x+1;\n" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%pol2G,(*&%#PiG\"\"\"%\"xGF(F(F)F(F(
F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "dismantle(pol2);\n" }
}{PARA 6 "" 1 "" {TEXT -1 0 "" }}{PARA 6 "" 1 "" {TEXT -1 6 "SUM(7)" }
}{PARA 6 "" 1 "" {TEXT -1 10 "   PROD(5)" }}{PARA 6 "" 1 "" {TEXT -1 
30 "      NAME(4): Pi #[protected]" }}{PARA 6 "" 1 "" {TEXT -1 18 "   \+
   INTPOS(2): 1" }}{PARA 6 "" 1 "" {TEXT -1 16 "      NAME(4): x" }}
{PARA 6 "" 1 "" {TEXT -1 18 "      INTPOS(2): 1" }}{PARA 6 "" 1 "" 
{TEXT -1 15 "   INTPOS(2): 1" }}{PARA 6 "" 1 "" {TEXT -1 13 "   NAME(4
): x" }}{PARA 6 "" 1 "" {TEXT -1 15 "   INTPOS(2): 1" }}{PARA 6 "" 1 "
" {TEXT -1 15 "   INTPOS(2): 1" }}{PARA 6 "" 1 "" {TEXT -1 15 "   INTP
OS(2): 1" }}{PARA 6 "" 1 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 17 "subs(1=3, pol2);\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6
#,(*(\"\"$\"\"\")%#PiGF%F&)%\"xGF%F&F&*&F%F&F*F&F&\"\"*F&" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "nops(pol2);op(pol2);\n" }}{PARA 11 
"" 1 "" {XPPMATH 20 "6#\"\"$" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%*&%#Pi
G\"\"\"%\"xGF%F&F%" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "whatt
ype(op(1,pol2));\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%\"*G" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "op(op(1,pol2));\n" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6$%#PiG%\"xG" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 
-1 63 "Dale si vsimneme interni reprezentace racionalni lomene funkce.
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "r:=(y^2-1)/(y-1);\n" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"rG*&,&*$)%\"yG\"\"#\"\"\"F+F+!\"\"
F+,&F)F+F+F,F," }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "type(r, `
ratpoly`);\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%%trueG" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "whattype(r);\n" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#%\"*G" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "op(r
);\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$,&*$)%\"yG\"\"#\"\"\"F(F(!\"\"
*&F(F(,&F&F(F(F)F)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "op(2,r
);\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*&\"\"\"F$,&%\"yGF$F$!\"\"F'" 
}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "whattype(%);\n" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#%\"^G" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 8 "op(%%);\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$,&%\"yG\"\"\"F%!\"
\"F&" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "normal(r);\n" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#,&%\"yG\"\"\"F%F%" }}}{EXCHG {PARA 0 "
> " 0 "" {MPLTEXT 1 0 14 "dismantle(r);\n" }}{PARA 6 "" 1 "" {TEXT -1 
0 "" }}{PARA 6 "" 1 "" {TEXT -1 7 "PROD(5)" }}{PARA 6 "" 1 "" {TEXT 
-1 9 "   SUM(5)" }}{PARA 6 "" 1 "" {TEXT -1 13 "      PROD(3)" }}
{PARA 6 "" 1 "" {TEXT -1 19 "         NAME(4): y" }}{PARA 6 "" 1 "" 
{TEXT -1 21 "         INTPOS(2): 2" }}{PARA 6 "" 1 "" {TEXT -1 18 "   \+
   INTPOS(2): 1" }}{PARA 6 "" 1 "" {TEXT -1 19 "      INTNEG(2): -1" }
}{PARA 6 "" 1 "" {TEXT -1 18 "      INTPOS(2): 1" }}{PARA 6 "" 1 "" 
{TEXT -1 15 "   INTPOS(2): 1" }}{PARA 6 "" 1 "" {TEXT -1 9 "   SUM(5)
" }}{PARA 6 "" 1 "" {TEXT -1 16 "      NAME(4): y" }}{PARA 6 "" 1 "" 
{TEXT -1 18 "      INTPOS(2): 1" }}{PARA 6 "" 1 "" {TEXT -1 19 "      \+
INTNEG(2): -1" }}{PARA 6 "" 1 "" {TEXT -1 18 "      INTPOS(2): 1" }}
{PARA 6 "" 1 "" {TEXT -1 16 "   INTNEG(2): -1" }}{PARA 6 "" 1 "" 
{TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 155 "Opet vidime, ze \+
interni datova struktura se lisi od externi, zobrazene na obrazovce. R
acionalni funkce je soucinem citatele a jemnovatele umocneneho na -1.
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "r:=(sin(x)^2-1)/(sin(x)
-1);\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"rG*&,&*$)-%$sinG6#%\"xG
\"\"#\"\"\"F.F.!\"\"F.,&F)F.F.F/F/" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 20 "type(r, `ratpoly`);\n" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6#%&falseG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 39 "type(r, `
ratpoly`(`integer`, sin(x)));\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%%t
rueG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "dismantle(r);\n" }}
{PARA 6 "" 1 "" {TEXT -1 0 "" }}{PARA 6 "" 1 "" {TEXT -1 7 "PROD(5)" }
}{PARA 6 "" 1 "" {TEXT -1 9 "   SUM(5)" }}{PARA 6 "" 1 "" {TEXT -1 13 
"      PROD(3)" }}{PARA 6 "" 1 "" {TEXT -1 20 "         FUNCTION(3)" }
}{PARA 6 "" 1 "" {TEXT -1 46 "            NAME(4): sin #[protected, _s
yslib]" }}{PARA 6 "" 1 "" {TEXT -1 21 "            EXPSEQ(2)" }}{PARA 
6 "" 1 "" {TEXT -1 25 "               NAME(4): x" }}{PARA 6 "" 1 "" 
{TEXT -1 21 "         INTPOS(2): 2" }}{PARA 6 "" 1 "" {TEXT -1 18 "   \+
   INTPOS(2): 1" }}{PARA 6 "" 1 "" {TEXT -1 19 "      INTNEG(2): -1" }
}{PARA 6 "" 1 "" {TEXT -1 18 "      INTPOS(2): 1" }}{PARA 6 "" 1 "" 
{TEXT -1 15 "   INTPOS(2): 1" }}{PARA 6 "" 1 "" {TEXT -1 9 "   SUM(5)
" }}{PARA 6 "" 1 "" {TEXT -1 17 "      FUNCTION(3)" }}{PARA 6 "" 1 "" 
{TEXT -1 43 "         NAME(4): sin #[protected, _syslib]" }}{PARA 6 "
" 1 "" {TEXT -1 18 "         EXPSEQ(2)" }}{PARA 6 "" 1 "" {TEXT -1 22 
"            NAME(4): x" }}{PARA 6 "" 1 "" {TEXT -1 18 "      INTPOS(2
): 1" }}{PARA 6 "" 1 "" {TEXT -1 19 "      INTNEG(2): -1" }}{PARA 6 "
" 1 "" {TEXT -1 18 "      INTPOS(2): 1" }}{PARA 6 "" 1 "" {TEXT -1 16 
"   INTNEG(2): -1" }}{PARA 6 "" 1 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "
" 0 "" {TEXT -1 69 "R je racionalni funce v \"promenne\" sin(x) s raci
onalnimi koeficienty." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "no
rmal(r);\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&-%$sinG6#%\"xG\"\"\"F(
F(" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 205 "Maple povazuje r za zobecn
enou racionalni funkci.\nProcedura normal automaticky \"uzavira\" funk
ci sin(x) pouze do jmena, provede zjednoduseni\na opet fci sin(x) \"ot
evira\". Obdobne se chova i procedura factor." }}}}{SECT 0 {PARA 3 "" 
0 "" {TEXT -1 10 "Substituce" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 41 "Ne
jjednodussi formou substituce je prikaz" }}{PARA 0 "" 0 "" {TEXT -1 
30 "subs(promenna=hodnota, vyraz)." }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 34 "subs(x=0, cos(x)*(sin(x)+x^2+1));\n" }}{PARA 11 "" 1 
"" {XPPMATH 20 "6#*&-%$cosG6#\"\"!\"\"\",&-%$sinGF&F(F(F(F(" }}}
{EXCHG {PARA 0 "" 0 "" {TEXT -1 55 "Vysledek je zjednodusen, ale ne au
tomaticky vyhodnocen." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "eva
l(%);\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"\"" }}}{EXCHG {PARA 0 "
" 0 "" {TEXT -1 18 "Nasobne substituce" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 25 " expression:=1+tan(x)^2;\n" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%+expressionG,&\"\"\"F&*$)-%$tanG6#%\"xG\"\"#F&F&" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 61 "subs(tan(x)=sin(x)/cos(x), s
in(x)^2=1-cos(x)^2, expression);\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#
,&\"\"\"F$*&,&F$F$*$)-%$cosG6#%\"xG\"\"#F$!\"\"F$F)!\"#F$" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "normal(%);\n" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#*&\"\"\"F$*$)-%$cosG6#%\"xG\"\"#F$!\"\"" }}}{EXCHG 
{PARA 0 "" 0 "" {TEXT -1 148 "V tomto pripade se nejdrive provede prvn
i substituce a v ziskanem vyrazu nasledne substituce druha. Tomuto zpu
sobu se rikaz posloupnost substituci. " }}{PARA 0 "" 0 "" {TEXT -1 0 "
" }}{PARA 0 "" 0 "" {TEXT -1 116 "Druhym zpusobem je tzv. soucasna sub
stituce, substitucni rovnice v tomto pripade uzavreme do slozenych zav
orek (\{\})." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 46 "subs(\{x=y,
 y=z\}, x*y^2); #soucasna substituce\n" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6#*&%\"yG\"\"\")%\"zG\"\"#F%" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 47 "subs(x=y, y=z, x*y^2); #posloupnost substituci\n" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#*$)%\"zG\"\"$\"\"\"" }}}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 32 "subs(a=b, b=c, c=a, a+2*b+3*c);\n" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#,$*&\"\"'\"\"\"%\"aGF&F&" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "subs(\{a=b, b=c, c=a\}, a+2*b+3*c);
\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,(%\"bG\"\"\"*&\"\"#F%%\"cGF%F%*
&\"\"$F%%\"aGF%F%" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 139 "Muzeme prov
adet substituce i za casti vyrazu. Podminkou provedeni je to, za Maple
 internerne rozezna \"podvyraz\" (jako vystup procedury op)." }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 44 "expr1:=x*y+z; expr2:=x*y*z; \+
expr3:=(x*y)^2;\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%&expr1G,&*&%\"x
G\"\"\"%\"yGF(F(%\"zGF(" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%&expr2G*(
%\"xG\"\"\"%\"yGF'%\"zGF'" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%&expr3G
*&)%\"xG\"\"#\"\"\")%\"yGF(F)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 26 "subs(x*y=product, expr1);\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,
&%(productG\"\"\"%\"zGF%" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 
"subs(x*y=product, expr2);\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*(%\"x
G\"\"\"%\"yGF%%\"zGF%" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "su
bs(x*y=product, expr3);\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*&)%\"xG
\"\"#\"\"\")%\"yGF&F'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "op
(expr1);\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$*&%\"xG\"\"\"%\"yGF%%\"z
G" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "op(expr2);\n" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6%%\"xG%\"yG%\"zG" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 11 "op(expr3);\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$*$)
%\"xG\"\"#\"\"\"*$)%\"yGF&F'" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 32 "M
uzeme pouzit proceduru algsubs:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 29 "algsubs(x*y=product, expr2);\n" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6#*&%\"zG\"\"\"%(productGF%" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 29 "algsubs(x*y=product, expr3);\n" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6#*$)%(productG\"\"#\"\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 31 "applyrule(x*y=product, expr2);\n" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6#*&%\"zG\"\"\"%(productGF%" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 31 "applyrule(x*y=product, expr3);\n" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6#*&)%\"xG\"\"#\"\"\")%\"yGF&F'" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 
-1 122 "Substituce se  provadi za casti vyrazu \"algebraicky\", neni s
pjata s vystupy procedury op (s interni datovou reprezentaci)." }}
{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 62 "Dalsi moz
nosti je pouziti procedury powsubs z balicku student." }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "with(student):\n" }}}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 29 "powsubs(x*y=product, expr2);\n" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#*&%\"zG\"\"\"%(productGF%" }}}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 29 "powsubs(x*y=product, expr3);\n" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#*$)%(productG\"\"#\"\"\"" }}}{EXCHG {PARA 0 
"> " 0 "" {MPLTEXT 1 0 27 "powsubs(x*y^2=s, x^3*y^4);\n" }}{PARA 11 "
" 1 "" {XPPMATH 20 "6#*&)%\"sG\"\"#\"\"\"%\"xGF'" }}}{EXCHG {PARA 0 ">
 " 0 "" {MPLTEXT 1 0 24 "subs(x*y^2=s, x^3*y^4);\n" }}{PARA 11 "" 1 "
" {XPPMATH 20 "6#*&)%\"xG\"\"$\"\"\")%\"yG\"\"%F'" }}}{EXCHG {PARA 0 "
" 0 "" {TEXT -1 124 "Procedura algsubs (algebraic substitution) funguj
e i pro casti souctu a neni tak uzce spjata s interni strukturou jako \+
subs." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "vyraz:=a+b+c;\n" }
}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%&vyrazG,(%\"aG\"\"\"%\"bGF'%\"cGF'
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "subs(a+b=d, vyraz);\n" 
}}{PARA 11 "" 1 "" {XPPMATH 20 "6#,(%\"aG\"\"\"%\"bGF%%\"cGF%" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "algsubs(a+b=d, vyraz); \n" }
}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&%\"dG\"\"\"%\"cGF%" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "p:=a+2*b+3*c;\n" }}{PARA 11 "" 1 "
" {XPPMATH 20 "6#>%\"pG,(%\"aG\"\"\"*&\"\"#F'%\"bGF'F'*&\"\"$F'%\"cGF'
F'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "applyrule(a+b=d, p);
\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,(%\"aG\"\"\"*&\"\"#F%%\"bGF%F%*
&\"\"$F%%\"cGF%F%" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "algsub
s(a+b=d,p);\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,(%\"bG\"\"\"%\"dGF%*
&\"\"$F%%\"cGF%F%" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 45 "Prikaz elimi
noval a, chceme ale eliminovat b." }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 
69 "Jako dalsi argument procedury algsubs muzeme zadat poradi promenny
ch." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "algsubs(a+b=d,p,[b,a
]);\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,(%\"aG!\"\"*&\"\"#\"\"\"%\"d
GF(F(*&\"\"$F(%\"cGF(F(" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 41 "Dalsim
 volitelnym parametrem je 'exact': " }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 26 "algsubs(a+b=d,p,'exact');\n" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#,(%\"aG\"\"\"*&\"\"#F%%\"bGF%F%*&\"\"$F%%\"cGF%F%" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 36 "algsubs(a+b=d,2*a+2*b+3*c,'e
xact');\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&*&\"\"#\"\"\"%\"dGF&F&*
&\"\"$F&%\"cGF&F&" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 122 "Dalsi mozno
sti, jak provadet substituce, je nahrazovat primo operandy mapleovskeh
o vyrazu. K tomu slouzi procedura subsop:" }}{PARA 0 "" 0 "" {TEXT -1 
64 "subsob(cislo_operandu1=nahrada1, cislo_opearndu2=nahrada2,vyraz)" 
}}{PARA 0 "" 0 "" {TEXT -1 53 "Substituce se provadi pouze na dane uro
vni (hloubce)." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "vyraz:=x^
2+x+1/x;\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%&vyrazG,(*$)%\"xG\"\"#
\"\"\"F*F(F**&F*F*F(!\"\"F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
20 "subsop(3=y, vyraz);\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,(*$)%\"x
G\"\"#\"\"\"F(F&F(%\"yGF(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
24 "subsop(1=z, 2=y,vyraz);\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,(%\"
zG\"\"\"%\"yGF%*&F%F%%\"xG!\"\"F%" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 18 "subs(x=y, vyraz);\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "
6#,(*$)%\"yG\"\"#\"\"\"F(F&F(*&F(F(F&!\"\"F(" }}}{EXCHG {PARA 0 "" 0 "
" {TEXT -1 59 "Dalsi vyhodou procedury subsop je to, ze nemusime opiso
vat " }}{PARA 0 "" 0 "" {TEXT -1 45 "dlouhe casti vyrazu, ktere chceme
 nahrazovat." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 39 "soucin:=(x^
2+y^2+2*x*y) * ((x+y)^2+1);\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'so
ucinG*&,(*$)%\"xG\"\"#\"\"\"F+*$)%\"yGF*F+F+*(F*F+F)F+F.F+F+F+,&*$),&F
)F+F.F+F*F+F+F+F+F+" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "fact
or(soucin);\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*&),&%\"xG\"\"\"%\"yG
F'\"\"#F',**$)F&F)F'F'*$)F(F)F'F'*(F)F'F&F'F(F'F'F'F'F'" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 41 "subsop(1=factor(op(1, soucin)), sou
cin);\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*&),&%\"xG\"\"\"%\"yGF'\"\"
#F',&*$F$F'F'F'F'F'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "appl
yop(factor,1,soucin);\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*&),&%\"xG
\"\"\"%\"yGF'\"\"#F',&*$F$F'F'F'F'F'" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 
-1 45 "applyop(funkce,index, vyraz) je to same, jako" }}{PARA 0 "" 0 "
" {TEXT -1 45 "subsop(index=funkce(op(index,vyraz)), vyraz)." }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 36 "vyraz:=(x^2+2*x+1)^2+(x^2-2*
x+1)^2;\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%&vyrazG,&*$),(*$)%\"xG
\"\"#\"\"\"F-*&F,F-F+F-F-F-F-F,F-F-*$),(F)F-*&F,F-F+F-!\"\"F-F-F,F-F-
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "factor(vyraz);\n" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#,(*&\"\"#\"\"\")%\"xG\"\"%F&F&*&\"#7F&
)F(F%F&F&F%F&" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "op(vyraz);
\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$*$),(*$)%\"xG\"\"#\"\"\"F**&F)F*
F(F*F*F*F*F)F**$),(F&F**&F)F*F(F*!\"\"F*F*F)F*" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 61 "subsop(1=factor(op(1,vyraz)), 2=factor(op(2,vy
raz)), vyraz);\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&*$),&%\"xG\"\"\"
F(F(\"\"%F(F(*$),&F'F(F(!\"\"F)F(F(" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 
-1 59 "Tohoto zjednoduseni muzeme dosahnut s pomoci procedury map," }}
{PARA 0 "" 0 "" {TEXT -1 74 "ktera aplikuje prikaz na vsechny operandy
 daneho vyrazu (na kazdy zvlast)." }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 20 "map(factor, vyraz);\n" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6#,&*$),&%\"xG\"\"\"F(F(\"\"%F(F(*$),&F'F(F(!\"\"F)F(F(" }}}
{EXCHG {PARA 0 "" 0 "" {TEXT -1 75 "Zjednoduseni z prvniho prikladu je
 mozno dosahnout i nasledujicim postupem:" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 7 "soucin;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*&,(*$)%
\"xG\"\"#\"\"\"F)*$)%\"yGF(F)F)*(F(F)F'F)F,F)F)F),&*$),&F'F)F,F)F(F)F)
F)F)F)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "subs(x+y=z, souci
n);\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*&,(*$)%\"xG\"\"#\"\"\"F)*$)%
\"yGF(F)F)*(F(F)F'F)F,F)F)F),&*$)%\"zGF(F)F)F)F)F)" }}}{EXCHG {PARA 0 
"> " 0 "" {MPLTEXT 1 0 11 "factor(%);\n" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6#*&),&%\"xG\"\"\"%\"yGF'\"\"#F',&*$)%\"zGF)F'F'F'F'F'" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "subs(z=x+y, %);\n" }}{PARA 11 "" 1 
"" {XPPMATH 20 "6#*&),&%\"xG\"\"\"%\"yGF'\"\"#F',&*$F$F'F'F'F'F'" }}}
{EXCHG {PARA 0 "" 0 "" {TEXT -1 59 "Toto je velmi casto pouzivana tech
nika pri upravach vyrazu." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
26 "vyraz:=(x+y)^2+1/(x+y)^2;\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%&
vyrazG,&*$),&%\"xG\"\"\"%\"yGF*\"\"#F*F**&F*F**$F'F*!\"\"F*" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "normal(vyraz);\n" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#*&,.*$)%\"xG\"\"%\"\"\"F)*(\"\"'F))F'\"\"#F)
)%\"yGF-F)F)*(F(F))F'\"\"$F)F/F)F)*(F(F)F'F))F/F2F)F)*$)F/F(F)F)F)F)F)
,&F'F)F/F)!\"#" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "subs(x+y=
z, vyraz);\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&*$)%\"zG\"\"#\"\"\"F
(*&F(F(*$F%F(!\"\"F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "nor
mal(%);\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*&,&*$)%\"zG\"\"%\"\"\"F)
F)F)F)F'!\"#" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "subs(z=x+y,
 %);\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*&,&*$),&%\"xG\"\"\"%\"yGF)
\"\"%F)F)F)F)F)F'!\"#" }}}{EXCHG }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 30 "subs(x+y=freeze(x+y), vyraz);\n" }}{PARA 11 "" 1 "" {XPPMATH 20 
"6#,&*$)%*freeze/R0G\"\"#\"\"\"F(*&F(F(*$F%F(!\"\"F(" }}}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 11 "normal(%);\n" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#*&,&*$)%*freeze/R0G\"\"%\"\"\"F)F)F)F)F'!\"#" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "thaw(%);\n" }}{PARA 11 "" 1 "
" {XPPMATH 20 "6#*&,&*$),&%\"xG\"\"\"%\"yGF)\"\"%F)F)F)F)F)F'!\"#" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}}{MARK "2 78 0 0" 0 }
{VIEWOPTS 1 1 0 3 2 1804 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }