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{SECT 0 {PARA 18 "" 0 "" {TEXT -1 17 "Maple V Release 4" }}{PARA 0 "" 
0 "" {TEXT -1 0 "" }}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 33 "Pokracov\341
n\355 z\341kladn\355ch dovednost\355" }}{SECT 1 {PARA 4 "" 0 "" {TEXT 
-1 42 "Dals\355 datov\351 struktury, operace a konverze" }}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 147 "posl:= a,2,3,a,2,3;\ns1 := [posl];
    \ns2 := [2*x, x^4-5, (x-1)^2, x+1];\ns3 := [modra, bila, cervena];
\nmnoz1:=\{posl\}; mnoz2:=\{a,c,d\};\nb:=sqrt(x+2);\n" }}}{SECT 1 
{PARA 5 "" 0 "" {TEXT -1 4 "Pole" }}{PARA 0 "" 0 "" {TEXT -1 114 "Polo
ha kazd\351 polozky je urcena c\355seln\375mi souradnicemi (uspor\341d
anou n-tic\355 prirozen\375ch c\355sel), kter\351 se kontroluj\355." }
}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 62 "mocniny:=array(1..3,[]);\ns
eq(assign(mocniny[i],i^2),i=1..3);\n\n" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 11 "mocniny[3];" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 56 "mocniny;\neval(mocniny), value(mocniny), print(mocniny);\n" }}}
{SECT 1 {PARA 20 "" 0 "" {TEXT 256 17 "V\355cerozmern\341 pole" }}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 110 "A := array(symmetric, 1..2,
1..2);\nA[1,1]:=11: A[1,2]:=12: A[2,2]:=22:\nC:= array(1..2,1..2,[[11,
12],[21,22]]);\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "eval(A)
, C;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "B := copy(A);\n" }}
}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "B[2,1]:=w:" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "eval(A),`    `, eval(B);" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "B:=C;\n" }}}{EXCHG {PARA 0 ">
 " 0 "" {MPLTEXT 1 0 35 "B[2,1]:=w:\neval(B),`    `, eval(C);" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 62 "pole3d:= array(1..2,1..2,1..
2,[[[1,2],[3,4]],[[5,6],[7,8]]]);\n" }}}{PARA 0 "" 0 "" {TEXT -1 76 "S
tandardn\355 maticov\351 operace jsou definov\341ny, ale dostaneme se \+
k nim pozdeji." }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}}
{SECT 1 {PARA 5 "" 0 "" {TEXT -1 7 "Tabulky" }}{PARA 0 "" 0 "" {TEXT 
-1 50 "Na rozd\355l od pol\355 jsou polozky oznaceny libovolne." }}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 45 "barva:=table([nebe=`modra`, \+
trava=`zelena`]);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "barva[
nebe], barva[mraku];" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "bar
va[mraku]:=`seda`; \n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "ev
al(barva);" }}}{PARA 258 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 28 "barva[nebe]:='barva[nebe]';\n" }}}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 13 "value(barva);" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 0 "" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{SECT 1 {PARA 
5 "" 0 "" {TEXT -1 18 "Operace a konverze" }}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 10 "nops(s1);\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 24 "seq(nops(s||i),i=1..3);\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 18 "b||posl;\nposl||b;\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 35 "member(ruda, s3);\nmember(a,mnoz1);\n" }}}{EXCHG {PARA 0 "> " 0 
"" {MPLTEXT 1 0 61 "mnoz1 union mnoz2;\nmnoz1 intersect mnoz2;\nmnoz1 \+
minus mnoz2;\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "op(s1);\n
op(mnoz1);\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 61 "convert(mno
z1, list);\nconvert(C, listlist);\nconvert(%, set);\n" }}}}}{SECT 1 
{PARA 4 "" 0 "" {TEXT -1 25 "Automatick\351 vyhodnocov\341n\355" }}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "0*x + z*4*3 + (3/4)^2;     \+
\n" }}}{PARA 11 "" 1 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 56 "35/115;\n((x - 1) * (x^3 - 4)) / ((y + 6) * (x -1)); \+
   \n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "   x + x + x + y*y
;\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "3/4 * (x + 2*y); \n
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 71 "sin(Pi/4),  sin(-x),  c
os(x+Pi/2),  exp(1),  ln(1), sqrt(Pi^2 * x^2); \n" }}}{EXCHG {PARA 0 "
> " 0 "" {MPLTEXT 1 0 56 "sin(arcsin(x)), arcsin(sin(x));\nln(exp(x)),
 exp(ln(x));\n" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{SECT 1 {PARA 4 "
" 0 "" {TEXT -1 19 "Manipulace s v\375razy" }}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 30 "unassign('x','y','z','a','b'):" }}}{SECT 1 {PARA 5 
"" 0 "" {TEXT -1 6 "expand" }}{PARA 15 "" 0 "" {TEXT -1 19 "Mocniny a \+
odmocniny" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "x^(y+z): % = ex
pand(%);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "(x*y)^z: % = ex
pand(%); " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "(x^(1/2))^(y/2
): % = expand(%);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "vyr:= \+
(x + y)*(x + 8*y);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "evyr:
=expand(vyr);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 40 "expand(vyr
, x + 8*y);\nexpand(vyr, x+y);\n" }}}{PARA 15 "" 0 "" {TEXT -1 37 "Tri
gonometrick\351 a hyperbolick\351 funkce" }}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 24 "cos(2*x): % = expand(%);" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 25 "tanh(3*x): % = expand(%);" }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 24 "sin(x+y): % = expand(%);" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 26 "sin(x+2*y): % = expand(%);" }}}{PARA 15 "" 0 "
" {TEXT -1 7 "exp, ln" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "exp
(x+ln(y)): % = expand(%);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
23 "ln(x*y): % = expand(%);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
23 "ln(x^y): % = expand(%);" }}}{PARA 15 "" 0 "" {TEXT -1 7 "Ostatn
\355" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "(n+1)!: % = expand(%
);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 70 "M:=array(1..3,1..3):
\ndet(M^3): % = expand(%);\ndet(3*M): % = expand(%);" }}}}{SECT 1 
{PARA 5 "" 0 "" {TEXT -1 8 "simplify" }}{PARA 15 "" 0 "" {TEXT -1 19 "
Mocniny a odmocniny" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "simpl
ify(\{vyr, evyr\});\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "si
mplify((x^y)^z);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 36 "% = sim
plify(%, 'power','symbolic');" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 75 "(1 + 5*x -x^2 + y^3)/(x + 2) - (x^2 + 3*x + 1)/(x^2 - 4):\n% = s
implify(%);\n" }}}{PARA 15 "" 0 "" {TEXT -1 37 "Trigonometrick\351 a h
yperbolick\351 funkce" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 39 "cos
h(x)^2 - sinh(x)^2: % = simplify(%);" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 40 "4^(1/2) - sin(x)^2 - 1: % = simplify(%);" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "%% = simplify(%%, trig);" }}}{PARA 
15 "" 0 "" {TEXT -1 7 "exp, ln" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 41 "exp(ln(5*a) + 3*log(x)): % = simplify(%);" }}}{PARA 15 "" 0 "" 
{TEXT -1 7 "Ostatn\355" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 62 "w:
= 1 - (sin(x))^2  + exp(x)^(3/2) * sqrt((1 + 2*x +x^2) * y);" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 58 "simplify(w, power);\nsimplif
y(w, trig);\nsimplify(w, sqrt);\n" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}
}{SECT 1 {PARA 5 "" 0 "" {TEXT -1 6 "factor" }}{PARA 15 "" 0 "" {TEXT 
-1 19 "Mocniny a odmocniny" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
42 "factor(x^4 - 10*x^3 + 35*x^2 - 50*x + 24);" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 17 "factor(x^2 + 16);" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 21 "factor(x^2 + 16, I );" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 23 "factor(x^3+5, 5^(1/3));" }}}{PARA 15 "" 0 "" {TEXT 
-1 37 "Trigonometrick\351 a hyperbolick\351 funkce" }}{EXCHG {PARA 0 "
> " 0 "" {MPLTEXT 1 0 32 "sin(x)+sin(2*x): % = factor(%);\n" }}}{PARA 
15 "" 0 "" {TEXT -1 7 "exp, ln" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 33 "exp(x+y) + exp(x): % = factor(%);" }}}{PARA 15 "" 0 "" {TEXT -1 
7 "Ostatn\355" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 39 "(x^3 - y^3)
/(x^5 - y^5): % = factor(%);" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}
{SECT 1 {PARA 5 "" 0 "" {TEXT -1 6 "normal" }}{PARA 15 "" 0 "" {TEXT 
-1 19 "Mocniny a odmocniny" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
35 "v1:= 1/x + x^2 -1: % = normal(%); \n" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 18 "v1 = simplify(v1);" }}}{PARA 15 "" 0 "" {TEXT -1 37 "
Trigonometrick\351 a hyperbolick\351 funkce" }}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 41 " v2:= sin(x) + 1/sin(x)^2: % = normal(%);" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 " v2 = simplify(v2);" }}}
{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{SECT 1 {PARA 5 "" 0 "" {TEXT -1 7 "c
ombine" }}{PARA 15 "" 0 "" {TEXT -1 19 "Mocniny a odmocniny" }}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 33 "x^(1/4)* y^(1/4): % = combine(%);" 
}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 39 "(1/2)^m*(1/2)^n: % = comb
ine(%, power);" }}}{PARA 15 "" 0 "" {TEXT -1 37 "Trigonometrick\351 a \+
hyperbolick\351 funkce" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 32 "2*
sin(x)*sin(y): % = combine(%);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 26 "cosh(x)^5: % = combine(%);" }}}{PARA 15 "" 0 "" {TEXT -1 7 "ex
p, ln" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 45 "f:= exp( sin(a)*cos
(b)) * exp(cos(a)*sin(b)):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
21 "f = combine( f, exp);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
27 "f = combine(f, [trig,exp]);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 56 "ln(x) + 1/2*ln(y) - ln(z): % = combine( %, ln,symbolic);" }}}
{EXCHG {PARA 0 "" 0 "" {TEXT -1 84 "Do predchoz\355ho pr\355kazu je mo
zn\351 doplnit dals\355 parametry napr. integer, positive, ..." }}}
{PARA 15 "" 0 "" {TEXT -1 7 "Ostatn\355" }}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 26 "-(-x+1)/x: % = combine(%);" }}}{EXCHG {PARA 0 "> " 0 
"" {MPLTEXT 1 0 51 "Limit(exp(x),x=a)*Limit(x^2,x=a)+c: % = combine(%)
;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 76 "Sum(1/(2*k), k=1..infi
nity) - Sum(1/(2*k-1), k=1..infinity):\n% = combine(%);" }}}{PARA 0 "
" 0 "" {TEXT -1 0 "" }}}{SECT 1 {PARA 5 "" 0 "" {TEXT -1 7 "convert" }
}{PARA 0 "" 0 "" {TEXT -1 167 "Druh\375 paramatr ud\341v\341 typ v\375
sledku (exp, ln, expln, expsincos, factorial, sincos, tan, trig, parcf
rac, polynom, ...). K pr\355kazu se budeme postupne podle potreby vrac
et." }}{PARA 15 "" 0 "" {TEXT -1 16 "C\355sla a objekty." }}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "3.14: % = convert(%, fraction);" }}
}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "convert(7, binary);" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "convert( [i $i=1..100], `+` \+
);" }}}{PARA 15 "" 0 "" {TEXT -1 19 "Mocniny a odmocniny" }}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 48 "x^4+4*x^3-2*x^2-6*x +10: % = conver
t(%, horner);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 93 "racfce:= (
x^2 + 3*x - 2) / (x^4 + 5*x^3 +8*x^2 + 20*x + 16):\nracfce = convert(%
, parfrac, x);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "racfce = \+
convert(racfce, confrac, x);" }}}{PARA 15 "" 0 "" {TEXT -1 37 "Trigono
metrick\351 a hyperbolick\351 funkce" }}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 33 "tan(x): % = convert(%, sincos);  " }}}{PARA 258 "" 0 
"" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "s:=conver
t(sin(x), exp):\nsin(x)=s;\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 10 "evalb(%);\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "simpli
fy(sin(x) - s);\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "exp(I*
y): %=convert(%, trig);" }}}{PARA 15 "" 0 "" {TEXT -1 7 "exp, ln" }}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "arcsinh(x): % = convert(%, l
n);" }}}{PARA 15 "" 0 "" {TEXT -1 7 "Ostatn\355" }}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 64 "GAMMA(x):  % = convert(%,factorial);\nn!: % = \+
convert(%, GAMMA);\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 45 "bin
omial(n, k):   %  = convert(%, factorial);" }}}}{SECT 1 {PARA 5 "" 0 "
" {TEXT -1 4 "sort" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "sort([
4, 5, 3, 2, 1]);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 61 "v:= 3*x
 + 4*x^4 - 3*y^2 + 5*x*y + x^3 + 2 + x^2*y^2 - x^2;   " }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 145 "sort(v);                    # podl
e mocniny\nsort(v, [x,y], plex);       # lexikografick\351 uspor\341d
\341n\355\nsort(v, y);                 # podle promenn\351\n" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 106 "v:=(cos(x) - sin(x)) / (sin
(x) + cos(x));\nsort(v, [cos(x),sin(x)], plex);\nsort(v, [sin(x),cos(x
)], plex);\n" }}}}{SECT 1 {PARA 5 "" 0 "" {TEXT -1 7 "collect" }}
{PARA 0 "" 0 "" {TEXT -1 25 "vytknut\355 promenn\351, v\375razu" }}
{PARA 15 "" 0 "" {TEXT -1 19 "Mocniny a odmocniny" }}{EXCHG {PARA 0 ">
 " 0 "" {MPLTEXT 1 0 46 "f:= (a + 1)*x + a^2 * x + a + (a + 1)^2 * x^2
;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "poly:=collect(f, x);" 
}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "collect(f, a);" }}}{PARA 
15 "" 0 "" {TEXT -1 37 "Trigonometrick\351 a hyperbolick\351 funkce" }
}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "y:= 'y':" }}}{EXCHG {PARA 0 
"> " 0 "" {MPLTEXT 1 0 23 "v:=y*(sin(x)+1)+sin(x):" }}}{EXCHG {PARA 0 
"> " 0 "" {MPLTEXT 1 0 23 "v = collect(v, sin(x));" }}}{PARA 15 "" 0 "
" {TEXT -1 7 "exp, ln" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 83 "v:=
a*ln(x)-ln(x)*x-x*exp(x)+x^2*exp(x):\nv = collect(v, ln);\nv = collect
(v, exp(x));" }}}{PARA 15 "" 0 "" {TEXT -1 7 "ostatn\355" }}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 97 "DE := diff(y(x),x,x)*sin(x)-diff(y(
x),x)*sin(y(x))+sin(x)*diff(y(x),x)+\nsin(y(x))*diff(y(x),x,x);" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "collect(DE,diff);" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "collect(DE,sin);" }}}{PARA 
0 "" 0 "" {TEXT -1 0 "" }}}{SECT 1 {PARA 5 "" 0 "" {TEXT -1 5 "coeff" 
}}{PARA 0 "" 0 "" {TEXT -1 32 "koeficient polynomu v promenn\351 x" }}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "poly;" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 36 "coeff(poly, x^2), coeff(poly, x, 2);" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 " coeff(poly, x, 0);" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "coeffs(poly,x);\n" }}}{PARA 
0 "" 0 "" {TEXT -1 0 "" }}}{SECT 1 {PARA 5 "" 0 "" {TEXT -1 12 "numer,
 denom" }}{PARA 0 "" 0 "" {TEXT -1 28 "citatel  a jmenovatel v\375razu
" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "f:=x*y / (1+x*y);" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 42 "citatel = numer(f);\njmenova
tel = denom(f);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "g:= 1/x \+
+ 1;\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "numer(g), denom(g
);" }}}}}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 26 "Relace a logick\351 oper
\341tory" }}{PARA 5 "" 0 "" {TEXT -1 35 "Relace     =   >   <   <=   >
=   <>" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 4 "2=3;" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 4 "2<3;" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 8 "is(2>3);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 73 
"x:= 5;\nevalb(x < 3);\nevalb(x + y = y + x);\nevalb((x + y)*z = z*x +
 y*z);\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 4 "x=6;" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "evalb(%), is(%);" }}}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 19 "1 < 3  and  5 < 2;\n" }}}{EXCHG {PARA 0 "
> " 0 "" {MPLTEXT 1 0 32 "7 = 7  or   5 < 2   or   a > b ;" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "a, b;" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 52 "evalb(x = 13);\nevalb(not x = 13);\nevalb(not x = 5);
\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 2 "x;" }}}{EXCHG {PARA 0 
"> " 0 "" {MPLTEXT 1 0 11 "is(x <> 3);" }}}{PARA 0 "" 0 "" {TEXT -1 0 
"" }}}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 26 "Pouzit\355 pr\355kazu z kni
hoven" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 50 "x:='x': y:='y':\nvy
r:= x^2 + 5*x + y^2 + 2*y + 10;\n" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 48 "completesquare(vyr,x);      #doplnen\355 na ctverec" 
}}}{PARA 0 "" 0 "" {TEXT -1 35 "Pr\355kaz nen\355 ve standardn\355 kni
hovne." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 89 "### WARNING: persistent store makes one-argument read
lib obsolete\nreadlib(comletesquare);" }}}{PARA 0 "" 0 "" {TEXT -1 88 
"Takhle to tak\351 nepujde, pr\355kaz nen\355 ani ve sm\355sen\351 kni
hovne, ale na readlib jest\351 dojde." }}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 49 "student[completesquare](vyr,x);   #pouze pouzije\n" }
}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 52 "with(student,completesquar
e);     #prenese do pameti" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
57 "with(student);                    #prenese celou knihovnu" }}}
{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 29 "
Z\341kladn\355 pr\355kazy pro calculus" }}{SECT 1 {PARA 5 "" 0 "" 
{TEXT -1 6 "Limita" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "x:='x'
:\nf:= sin(x)/x;\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "limit
( f, x=0);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "Limit( f, x=0
);\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "value(%);\n" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 40 "Limit(log(x), x=0) = limit(l
og(x), x=0);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 48 "limit(Heavi
side(x), x=0);\nlimit(sin(1/x), x=0);\n" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 24 "plot(Heaviside, -3.. 3);" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 25 "plot(sin(1/x), x= -3..3);" }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 132 "Limit(Heaviside(x), x=0,left): % = value(%);\nL
imit(Heaviside(x), x=0,right): % = value(%);\nLimit(sin(1/x),x=0, left
): % = value(%);\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 86 "Limit
(exp(x), x= - infinity): % = value(%);\nLimit(exp(x), x= infinity): % \+
= value(%);\n" }}}}{SECT 1 {PARA 5 "" 0 "" {TEXT -1 9 "Derivace " }}
{PARA 20 "" 0 "" {TEXT -1 15 "Derivace v\375razu" }}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 59 "Diff((ln(1 + sin(x)))^3, x) = diff((ln(1 + sin
(x)))^3, x);\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 46 "Diff((ln(
1 + sin(x)))^3, x, x): % = value(%);\n" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 45 "Diff((ln(1 + sin(x)))^3, x$3): % = value(%);\n" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 43 "Diff(sin(x*y + 3), x$2, y ):
 % = value(%);\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "f:= x -
> exp(x)/(1 + exp(x));\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 
"derf:=D(f);          \n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 
"evalf(derf(2));" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 75 "f:= (x,
 y, z) -> sin(x) * sin(y) * sin(z);\nfz := D[3](f);\nfyx:= D[1,2](f);
\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "fx:=diff(y(x),x$2);\n
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 32 "convert(fx,D);\nconvert
(%,diff);\n" }}}}{SECT 1 {PARA 5 "" 0 "" {TEXT -1 9 "Integrace" }}
{PARA 20 "" 0 "" {TEXT -1 17 "Neurcit\375 integr\341l" }}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 7 "x:='x':" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 21 "Int(1, x) = int(1,x);" }}}{PARA 0 "" 0 "" {TEXT -1 
39 "Konstantu si mus\355te ovsem doplnit sami." }}{PARA 0 "" 0 "" 
{TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 42 "Int((x^2)/sq
rt(1 - x^2), x): % = value(%);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 51 "with(student, in
tparts);\na:= Int(x^2 * exp(x) ,x);\n" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 21 "b:= intparts(a, x^2);" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 21 "c:= intparts(b, 2*x);" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 18 "value(c);         " }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 62 "start:=time():\nint(x^100 * exp(x) ,x):\n(time()-star
t)*sekund;\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 32 "Int(x/(x^5+
1),x): % = value(%);\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 62 "a
:='a':\nInt(x^3 * sqrt(x^2 - a^2), x = a..2*a): % = value(%);\n" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "a:=3;\n%%;\n" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 84 "Int( Int( 1 / ((1 + x^2)*(1 + y^2))
 , x=0..infinity), y=0..infinity): % = value(%);\n" }}}{EXCHG {PARA 0 
"> " 0 "" {MPLTEXT 1 0 31 "prim:=unapply(int(1/x^2,x),x);\n" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "prim(1) - prim(-1);\n" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "int(1/x^2,x=-1..1);\n" }}}
{PARA 0 "" 0 "" {TEXT -1 13 "Kde je chyba?" }}{PARA 0 "" 0 "" {TEXT 
-1 0 "" }}}{SECT 1 {PARA 5 "" 0 "" {TEXT -1 24 "Soucty, souciny, rozvo
je" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "sum(i, i=1..50);\n" }}
}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 47 "Sum(1/i, i=1..infinity): % \+
= value(%);         " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 52 "Sum
(1/((2*n+1)*(n+2)), n=1..infinity): % = value(%);" }}}{EXCHG {PARA 0 "
> " 0 "" {MPLTEXT 1 0 43 "Product(i/(i+1), i= 5..100): % = value(%);\n
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "t1:=taylor(sin(x), x=0,
 4);\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "t2:=taylor(sin(x)
, x=Pi/2, 5);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "poly:= con
vert(t1, polynom);\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 50 "a:=
2:\nplot(\{sin(x), poly\}, x=-a*Pi..a*Pi, -2..2);\n" }}}}}}}{MARK "0 0
" 0 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }