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{SECT 0 {EXCHG {PARA 18 "" 0 "" {TEXT -1 32 "Chyby a v\375hody Maplu V
 Release 4" }}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 5 "Chyby" }}{SECT 1 
{PARA 4 "" 0 "" {TEXT -1 22 "Vyhodnocov\341n\355 podm\355nek" }}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 80 "if 1 < Pi then true else fal
se fi;\nif sin(1) < ln(2.9) then true else false fi;\n" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 94 "if evalf(1 < Pi) then true else fal
se fi;\nif evalf(sin(1) < ln(2.9)) then true else false fi;\n" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 88 "if is(1 < Pi) then true else
 false fi;\nif is(sin(1) < ln(2.9)) then true else false fi;\n" }}}}
{SECT 1 {PARA 4 "" 0 "" {TEXT -1 22 "Hled\341n\355 extr\351mu funkc
\355" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 39 "maximize(abs(sin(x))
, x, \{x=-1..0.5\});\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 52 "p
lot(sin(x), x=-1..0.5, xtickmarks=3, ytickmarks=3);" }}}{PARA 4 "" 0 "
" {TEXT -1 0 "" }}}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 15 "Neurcit\351 v
\375razy" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 13 "argument(0);\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 19 "infinity-infinity;\n" }}}{EXCHG {PARA 0 "> " 0 "" {XPPEDIT 19 
1 "infinity+infinity;" "6#,&%)infinityG\"\"\"F$F%" }}}{EXCHG {PARA 0 "
> " 0 "" {MPLTEXT 1 0 12 "infinity/0;\n" }}}{EXCHG {PARA 0 "> " 0 "" 
{XPPEDIT 19 1 "0/infinity;" "6#*&\"\"!\"\"\"%)infinityG!\"\"" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "0^(-n);\n" }}}}{SECT 1 {PARA 
4 "" 0 "" {TEXT -1 18 "Chyby funkce  plot" }}{EXCHG {PARA 0 "" 0 "" 
{TEXT -1 68 "Jsou st\341l\375m zdrojem probl\351mu (i po odstranen\355
 mnoha chyb Release 3)." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "
plot(sin, 5..-5);\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "plot
(1e400*sin, -5..5);\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "1e
400*sin(-5.);\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "evalhf(1
e400*sin(-5.));\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "plot(t
an(x), x=-5..5, discont=true);\n" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 25 "f := x -> x-exp(x/1000);\n" }}}{EXCHG {PARA 0 "> " 0 
"" {MPLTEXT 1 0 48 "Limit(f(x), x=infinity)=limit(f(x), x=infinity);" 
}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "plot(f, -infinity..infini
ty);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "plot(f, -1e6..1e6);
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "plot(f, -1e5..1e5);" }}
}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 39 "plot(f(1000*x), x=-infinity
..infinity);" }}}}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 13 "Resen\355 rovni
c" }}{PARA 0 "" 0 "" {TEXT -1 25 "Nenach\341z\355 nekter\341 resen\355
:" }}{EXCHG {PARA 0 "> " 0 "" {XPPEDIT 19 1 "solve((sin^3)(x)*ln(x)=0,
 x);" "6#-%&solveG6$/*&-*$%$sinG\"\"$6#%\"xG\"\"\"-%#lnG6#F-F.\"\"!F-
" }}}{PARA 0 "" 0 "" {TEXT -1 22 "(chyb\355 resen\355 rovnice " }
{XPPEDIT 18 0 "sin(x)=0" "6#/-%$sinG6#%\"xG\"\"!" }{TEXT -1 1 ")" }}
{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {XPPEDIT 19 
1 "solve(sin(x)^3/x=0, x);" "6#-%&solveG6$/*&-%$sinG6#%\"xG\"\"$F+!\"
\"\"\"!F+" }}}{PARA 0 "" 0 "" {TEXT -1 24 "(nenach\341z\355 z\341dn
\351 resen\355)" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> \+
" 0 "" {XPPEDIT 19 1 "solve(sin(3*x)*cos(x)=0, x);" "6#-%&solveG6$/*&-
%$sinG6#*&\"\"$\"\"\"%\"xGF-F--%$cosG6#F.F-\"\"!F." }}}{PARA 0 "" 0 "
" {TEXT -1 31 "(chyb\355 nenulov\341 resen\355 rovnice " }{XPPEDIT 18 
0 "sin(3*x)=0" "6#/-%$sinG6#*&\"\"$\"\"\"%\"xGF)\"\"!" }{TEXT -1 1 ")
" }}}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 21 "Resen\355 soustav rovnic" }}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 90 "eq1:= x^2*y + 3*y*z - 4 = 0;
\neq2:= -3*x^2*z + 2*y^2 + 1 = 0;\neq3:= 2*y*z^2 - z^2 - 1 = 0;\n" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 40 "symb := [solve(\{eq||(1..3)
\}, \{x,y,z\})];\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 41 "simpl
ify(map(subs, symb, \{eq||(1..3)\}));\n" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 20 "num := evalf(symb);\n" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 0 "" }}}{PARA 0 "" 0 "" {TEXT -1 234 "(Samozrejme, ze v
\375sledek je zat\355zen numerick\375mi chybami.) \nNicm\351ne zmenou \+
znam\351nka u  x  v posledn\355ch dvou resen\355ch dost\341v\341me dal
s\355 dve resen\355, kter\341 nebyla nalezena!\nJeste pozoruhodnejs
\355 je, ze Maple V Release 3 tato resen\355 nach\341zel!" }}}{SECT 1 
{PARA 4 "" 0 "" {TEXT -1 29 "Resen\355 diferenci\341ln\355ch rovnic" }
}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 104 "assume(coef <> 0);\neq := \+
\{diff(y(x), x, x) + coef^2*y(x) = 0, y(0) = 0, D(y)(1) = 0\}:\ndsolve
(eq, y(x));\n" }}}}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 19 "Posloupnosti f
unkc\355" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 65 "Nap\355seme-li posloup
nost funkc\355, jsou zcela chybne interpretov\341ny:" }}}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 49 "f := t->sin(Pi*t): g := u->u^2: h := v->l
n(v^2):\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "eval(f); eval(
g); eval(h);\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "eval(f), \+
eval(g), eval(h);\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 40 "(t->
sin(Pi*t)), (u->u^2), (v->ln(v^2));\n" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 0 "" }}}}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 20 "Ukoncen\355
 bez ulozen\355" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}}
{SECT 1 {PARA 3 "" 0 "" {TEXT -1 25 "Uk\341zky efektivnosti Maplu" }}
{SECT 1 {PARA 4 "" 0 "" {TEXT -1 11 "Faktorizace" }}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 43 "fs := k -> sort(factor(sum(i^k, i=1..n))):\n" 
}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "fs(1), fs(2), fs(3);\n" }
}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "fs(30);\n" }}}{EXCHG {PARA 
0 "> " 0 "" {XPPEDIT 19 1 "fs(50);" "6#-%#fsG6#\"#]" }}}{PARA 259 "" 
0 "" {TEXT -1 37 "(v\375sledek pro \372sporu pap\355ru vynech\341n)" }
}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "pol:=x^4-3*x^2+1: pol=facto
r(pol);\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "alias(koren=Ro
otOf(z^2-z-1)):\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "pol=fa
ctor(pol,koren);\n" }}}}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 35 "Zjednodus
ov\341n\355 v\375razu s odmocninami" }}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 51 "sqrt(14+3*sqrt(3+2*sqrt(5-12*sqrt(3-2*sqrt(2)))));\n
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 148 "expr:=sqrt(6-2*sqrt(2)
-2*sqrt(3)+2*sqrt(6)):\n### WARNING: persistent store makes one-argume
nt readlib obsolete\nreadlib(radnormal): radnormal(expr);\n" }}}}
{SECT 1 {PARA 4 "" 0 "" {TEXT -1 37 "Nekonecn\351 soucty, derivace, in
tegr\341ly" }}{EXCHG {PARA 0 "> " 0 "" {XPPEDIT 19 1 "sum(1/n^4, n=1..
infinity);" "6#-%$sumG6$*&\"\"\"F'*$%\"nG\"\"%!\"\"/F);F'%)infinityG" 
}{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 59 "f := x
 -> x^10*cos(x^5*ln(x)):\nassume(x>0);\ndiff(f(x), x);\n" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "int(%, x);\n" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 10 "evalc(%);\n" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 8 "x:='x':\n" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 112 "Map
le dovede symbolicky vypoc\355tat i znacne slozit\351 integr\341ly, na
pr. n\341sleduj\355c\355 cvicen\355 na integraci per partes:" }}}
{EXCHG {PARA 0 "> " 0 "" {XPPEDIT 19 1 "int((sin(x))^256, x);" "6#-%$i
ntG6$*$-%$sinG6#%\"xG\"$c#F*" }}}{EXCHG {PARA 260 "" 0 "" {TEXT -1 37 
"(v\375sledek pro \372sporu pap\355ru vynech\341n)" }}}{EXCHG {PARA 0 
"> " 0 "" {MPLTEXT 1 0 9 "restart;\n" }}}}{SECT 1 {PARA 4 "" 0 "" 
{TEXT -1 31 "Integr\341l z\341visl\375 na parametrech" }}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 13 "assume(a<b);\n" }}}{EXCHG {PARA 0 "> " 0 
"" {MPLTEXT 1 0 45 "func := x -> 1/(a+b*cos(x)):\nint(func(x),x);\n" }
}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "diff(%,x);\n" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "simplify(func(x)-%);\n" }}}}{SECT 
1 {PARA 4 "" 0 "" {TEXT -1 19 "Nevlastn\355 integr\341ly" }}{EXCHG 
{PARA 0 "> " 0 "" {XPPEDIT 19 1 "int(1/x^2, x=-1..1);" "6#-%$intG6$*&
\"\"\"F'*$%\"xG\"\"#!\"\"/F);,$F'F+F'" }}}{EXCHG {PARA 0 "> " 0 "" 
{XPPEDIT 19 1 "int(1/sqrt(x), x=0..1);" "6#-%$intG6$*&\"\"\"F'-%%sqrtG
6#%\"xG!\"\"/F+;\"\"!F'" }}}{EXCHG {PARA 0 "> " 0 "" {XPPEDIT 19 1 "in
t(1/x, x=-1..1); " "6#-%$intG6$*&\"\"\"F'%\"xG!\"\"/F(;,$F'F)F'" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 42 "int(1/x, x=-1..1, CauchyPrin
cipalValue); \n" }}}}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 19 "Numerick\341
 integrace" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 47 "Int(exp(-x)/(1
+x^4), x=0..infinity):\nevalf(%);\n" }}}}{SECT 1 {PARA 4 "" 0 "" 
{TEXT -1 21 "Diferenci\341ln\355 rovnice" }}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 172 "diff(y(x), x, x) + y(x)*diff(y(x), x)^3 = 0:\n### WA
RNING: incomplete string;  use \" to end the string (note that the dit
to operator is now % instead of \")\ndsolve(\", y(x));\n" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 163 "x^2*diff(y(x),x)+2^x*y(x)-y(x)^3=0
:\n### WARNING: incomplete string;  use \" to end the string (note tha
t the ditto operator is now % instead of \")\ndsolve(\", y(x));\n" }}}
}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 31 "Soustavy diferenci\341ln\355ch r
ovnic" }}{EXCHG {PARA 0 "> " 0 "" {XPPEDIT 19 1 "System:= [diff(x(t), \+
t) = x(t) - y(t), diff(y(t), t) = x(t) + y(t)]:" "6#>%'SystemG7$/-%%di
ffG6$-%\"xG6#%\"tGF-,&-F+6#F-\"\"\"-%\"yG6#F-!\"\"/-F(6$-F36#F-F-,&-F+
6#F-F1-F36#F-F1" }}}{EXCHG {PARA 0 "> " 0 "" {XPPEDIT 19 1 "dsolve(Sys
tem, \{x(t), y(t)\});" "6#-%'dsolveG6$%'SystemG<$-%\"xG6#%\"tG-%\"yG6#
F+" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "eval(subs(\", System)
); map(evalb,\");\n" }}}}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 9 "Oper\341t
ory" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "Delta := D[1,1] + D[2
,2] + D[3,3]:\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 41 "field :=
 (x,y,z) -> 1/sqrt(x^2+y^2+z^2):\n" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 21 "Delta(field)(x,y,z);\n" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 123 "### WARNING: incomplete string;  use \" to end the s
tring (note that the ditto operator is now % instead of \")\nsimplify(
\");\n" }}}}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 20 "Kombinatorick\351 \+
\372lohy" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 83 "Maple dovoluje resit i
 kombinatoricky n\341rocn\351 \372lohy pri minim\341ln\355m \372sil
\355 uzivatele." }}}{EXCHG {PARA 0 "" 0 "" {TEXT 265 15 "Probl\351m ba
tohu:" }{TEXT -1 1 " " }{TEXT 266 56 "K dan\351mu seznamu c\355sel naj
dete podseznam s dan\375m souctem" }{TEXT -1 1 "." }}}{EXCHG {PARA 0 "
" 0 "" {TEXT -1 23 "Resen\355 Petra Savick\351ho:" }}}{EXCHG {PARA 0 "
> " 0 "" {MPLTEXT 1 0 253 "with(combinat, choose):\n\nknapsack := proc
(List, TheSum) local p;\n### WARNING: combinat[choose] with numeric fi
rst parameter now returns a sorted list rather than a set\n     for p \+
in choose(List) do if convert(p,`+`)=TheSum then print(p) fi od\n     \+
end:\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "s:=[binomial(14,i
) $i=0..14];\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "knapsack(
s,8192);\n" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 53 " Resen\355 \"metodo
u kanadsk\375ch drevorubcu\" vedlo k c\355li!" }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 7 "# KONEC" }}}}}{SECT 1 {PARA 5 "" 0 "" {TEXT -1 
18 "Pouzit\341 literatura" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 17 "J. Bu
char & all, " }{TEXT 258 48 "Introduction to Maple V Programming Tool \+
(Czech)" }{TEXT -1 41 " (University of Agriculture, Brno, 1994)." }}}
{EXCHG {PARA 0 "" 0 "" {TEXT -1 29 "M.R. Garey and D.S. Johnson, " }
{TEXT 261 70 "Computers and Intractability: A Guide to the Theory of N
P-Completeness" }{TEXT -1 32 " (Freeman, San Francisco, 1979)." }}}
{EXCHG {PARA 0 "" 0 "" {TEXT -1 41 "K.M. Heal, M.L. Hansen and K.M. Ri
ckard, " }{TEXT 256 22 "Maple V Learning Guide" }{TEXT -1 18 " (Spring
er, 1996)." }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 68 "M.B. Monagan, K.O. \+
Geddes, K.M. Heal, G.Labahn and S.M. Vorkoetter, " }{TEXT 257 25 "Mapl
e V Programming Guide" }{TEXT -1 18 " (Springer, 1996)." }}}{EXCHG 
{PARA 0 "" 0 "" {TEXT -1 9 "L. Vrba, " }{TEXT 259 69 "Comparison of Co
mplex Arithmetics in Computer Algebra Systems (Czech)" }{TEXT -1 56 ",
 Bac. Thesis (Czech Technical University, Praha, 1997)." }}}{EXCHG 
{PARA 0 "" 0 "" {TEXT -1 11 "M. Wester, " }{TEXT 260 41 "A Review of C
AS Mathematical Capabilities" }{TEXT -1 57 ", preprint (University of \+
New Mexico, Albuquerque, 1994)." }}}}}{MARK "0 0 0" 0 }{VIEWOPTS 1 1 
0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }