doc/tutorial/ru/minimal-maxima.tex

   1 % v. 1.6
   2 % (c) 2005 Robert Dodier
   3 % (c) 2007 áÌÅËÓÅÊ âÅÛÅÎÏ× (al@beshenov.ru), ÒÕÓÓËÉÊ ÐÅÒÅ×ÏÄ
   4
   5 \documentclass[11pt,oneside]{article}
   6 %\documentclass[12pt]{article}
   7 \usepackage[russian]{babel}
   8
   9 \usepackage{cmap}
  10 \usepackage[koi8-r]{inputenc}
  11 \usepackage[T2A]{fontenc}
  12
  13 \usepackage[colorlinks]{hyperref}
  14
  15 % ó ÐÏÌÑÍÉ ÐÏ ÕÍÏÌÞÁÎÉÀ ÛÉÒÉÎÙ ÔÅËÓÔÁ ÎÅ È×ÁÔÁÅÔ, ÞÔÏÂÙ ×ÍÅÓÔÉÔØ ËÏÄ
  16 % ÐÒÉÍÅÒÏ× Ë ÐÏÓÌÅÄÎÅÍÕ ÒÁÚÄÅÌÕ. éÚ ÔÅÈ ÖÅ ÓÏÏÂÒÁÖÅÎÉÊ ÔÅËÓÔ ÎÁÂÒÁÎ
  17 % × 11 ÐÕÎËÔÏ× (× ÏÒÉÇÉÎÁÌÅ --- 12).
  18 \setlength{\textwidth}{18cm}
  19 \setlength{\textheight}{23cm}
  20 \setlength{\headheight}{0cm}
  21 \setlength{\headsep}{0cm}
  22 \setlength{\topskip}{0cm}
  23 \setlength{\voffset}{-1in}
  24 \setlength{\oddsidemargin}{-1in}
  25 \setlength{\evensidemargin}{-1in}
  26 \addtolength{\voffset}{1.5cm}
  27 \addtolength{\oddsidemargin}{2cm}
  28 \addtolength{\evensidemargin}{2cm}
  29
  30 \title{ëÏÒÏÔËÏ Ï Maxima}
  31 \author{òÏÂÅÒÔ äÏÄÉÅÒ}
  32 \date{}
  33
  34 \begin{document}
  35 \maketitle
  36
  37 \begin{figure}[b]
  38 {\flushleft\tiny
  39 \rule{50pt}{0.5pt}
  40
  41 \copyright~2005 Robert Dodier.\\
  42 \copyright~2007 áÌÅËÓÅÊ âÅÛÅÎÏ× (\href{mailto:al@beshenov.ru}{al@beshenov.ru}), ÒÕÓÓËÉÊ ÐÅÒÅ×ÏÄ.\\
  43 äÏÍÁÛÎÑÑ ÓÔÒÁÎÉÃÁ Maxima: \url{http://maxima.sourceforge.net/ru/}.\\
  44 }
  45 \end{figure}
  46
  47 \section{þÔÏ ÔÁËÏÅ Maxima?}
  48
  49 \noindent Maxima~--- ÓÉÓÔÅÍÁ ÄÌÑ ÒÁÂÏÔÙ Ó ×ÙÒÁÖÅÎÉÑÍÉ, ÔÁËÉÍÉ ËÁË $x + y$, $\sin (a + b \pi)$ É
  50 $u \cdot v - v \cdot u$.
  51
  52 Maxima ÎÅ ÏÓÏÂÏ ÚÁÂÏÔÉÔÓÑ Ï ÓÍÙÓÌÅ ×ÙÒÁÖÅÎÉÑ. ôÏÌØËÏ ÐÏÌØÚÏ×ÁÔÅÌØ ÒÅÛÁÅÔ, ËÁËÏÊ
  53 ÓÍÙÓÌ ÎÅÓÅÔ ×ÙÒÁÖÅÎÉÅ.
  54
  55 éÎÏÇÄÁ ÔÒÅÂÕÅÔÓÑ ÚÁÄÁÔØ ÚÎÁÞÅÎÉÑ ÎÅÉÚ×ÅÓÔÎÙÍ É ×ÙÞÉÓÌÉÔØ ×ÙÒÁÖÅÎÉÅ~--- Maxima
  56 Ó ÒÁÄÏÓÔØÀ ÓÄÅÌÁÅÔ ÜÔÏ. îÏ ÓÉÓÔÅÍÁ Ó ÔÏÊ ÖÅ ÒÁÄÏÓÔØÀ ÏÔÌÏÖÉÔ ÐÒÉÓ×ÁÉ×ÁÎÉÅ
  57 ËÏÎËÒÅÔÎÙÈ ÚÎÁÞÅÎÉÊ, ÔÁË ÞÔÏ ×Ù ÍÏÖÅÔÅ ÐÒÏ×ÅÓÔÉ Ó ×ÙÒÁÖÅÎÉÅÍ ÎÅËÏÔÏÒÙÅ ÐÒÅÏÂÒÁÚÏ×ÁÎÉÑ,
  58 ÐÏÓÌÅ ÞÅÇÏ ÕÖÅ ÏÐÒÅÄÅÌÉÔØ ÎÅÉÚ×ÅÓÔÎÙÅ (ÉÌÉ ÎÅ ÏÐÒÅÄÅÌÑÔØ ÉÈ ×Ï×ÓÅ).
  59
  60 òÁÓÓÍÏÔÒÉÍ ÎÅÓËÏÌØËÏ ÐÒÉÍÅÒÏ×.
  61
  62 \begin{enumerate}
  63
  64 \item îÕÖÎÏ ÎÁÊÔÉ ÏÂßÅÍ ÛÁÒÁ:
  65 % V: 4/3 * %pi * r^3;
  66 \begin{verbatim}
  67 (%i1) V: 4/3 * %pi * r^3;
  68                                    3
  69                             4 %pi r
  70 (%o1)                       --------
  71                                3
  72 \end{verbatim}
  73
  74 \item òÁÄÉÕÓ ÒÁ×ÅÎ 10:
  75 % r: 10;
  76 \begin{verbatim}
  77 (%i2) r: 10;
  78 (%o2)                          10
  79 \end{verbatim}
  80
  81 \item $V$~--- ÔÏ ÖÅ, ÞÔÏ É ÂÙÌÏ; Maxima ÎÅ ÐÏÍÅÎÑÅÔ $V$, ÅÓÌÉ ÜÔÏ ÎÅ ÕËÁÚÁÔØ:
  82 % V;
  83 \begin{verbatim}
  84 (%i3) V;
  85                                    3
  86                             4 %pi r
  87 (%o3)                       --------
  88                                3
  89 \end{verbatim}
  90
  91 \item <<Maxima, ÐÅÒÅÓÞÉÔÁÊ, ÐÏÖÁÌÕÊÓÔÁ, $V$>>:
  92 % ''V;
  93 \begin{verbatim}
  94 (%i4) ''V;
  95                             4000 %pi
  96 (%o4)                       --------
  97                                3
  98 \end{verbatim}
  99
 100 \item ÷ÍÅÓÔÏ ×ÙÒÁÖÅÎÉÑ ÈÏÔÅÌÏÓØ ÂÙ ×ÉÄÅÔØ ÞÉÓÌÅÎÎÏÅ ÚÎÁÞÅÎÉÅ:
 101 % ''V, numer;
 102 \begin{verbatim}
 103 (%i5) ''V, numer;
 104 (%o5)                   4188.79020478639
 105 \end{verbatim}
 106
 107 \end{enumerate}
 108
 109 \section{÷ÙÒÁÖÅÎÉÑ}
 110
 111 \noindent÷Ó£ × Maxima Ñ×ÌÑÅÔÓÑ ×ÙÒÁÖÅÎÉÑÍÉ, × ÔÏÍ ÞÉÓÌÅ ÍÁÔÅÍÁÔÉÞÅÓËÉÅ ×ÙÒÁÖÅÎÉÑ, ÏÂßÅËÔÙ
 112 É ÐÒÏÇÒÁÍÍÎÙÅ ÂÌÏËÉ. ÷ÙÒÁÖÅÎÉÅ~--- ÁÔÏÍ ÌÉÂÏ ÏÐÅÒÁÔÏÒ Ó ÁÒÇÕÍÅÎÔÁÍÉ.
 113
 114 áÔÏÍ~--- ÓÉÍ×ÏÌ (ÉÍÑ), ÓÔÒÏËÁ × ËÁ×ÙÞËÁÈ, ÌÉÂÏ ÞÉÓÌÏ (ÃÅÌÏÅ ÉÌÉ Ó ÐÌÁ×ÁÀÝÅÊ ÔÏÞËÏÊ).
 115
 116 ÷ÓÅ ×ÙÒÁÖÅÎÉÑ ÎÅ-ÁÔÏÍÙ ÐÒÅÄÓÔÁ×ÌÑÀÔÓÑ × ×ÉÄÅ $\mathit{op}(a_1, \ldots, a_n)$, ÇÄÅ
 117 $\mathit{op}$~--- ÉÍÑ ÏÐÅÒÁÔÏÒÁ, Á $a_1, \ldots, a_n$~--- ÅÇÏ ÁÒÇÕÍÅÎÔÙ.
 118 ÷ÙÒÁÖÅÎÉÑ ÍÏÇÕÔ ÏÔÏÂÒÁÖÁÔØÓÑ ÐÏ-ÒÁÚÎÏÍÕ, ÎÏ ×ÎÕÔÒÅÎÎÅÅ ÐÒÅÄÓÔÁ×ÌÅÎÉÅ ×ÓÅÇÄÁ ÏÄÉÎÁËÏ×Ï.
 119 áÒÇÕÍÅÎÔÙ ×ÙÒÁÖÅÎÉÑ ÍÏÇÕÔ ÂÙÔØ ÁÔÏÍÁÍÉ ÌÉÂÏ ×ÙÒÁÖÅÎÉÑÍÉ ÎÅ-ÁÔÏÍÁÍÉ.
 120
 121 íÁÔÅÍÁÔÉÞÅÓËÉÅ ×ÙÒÁÖÅÎÉÑ ×ËÌÀÞÁÀÔ ÍÁÔÅÍÁÔÉÞÅÓËÉÅ ÏÐÅÒÁÔÏÒÙ, ÔÁËÉÅ ËÁË
 122 \[
 123 + \; - \; * \; / \; < \; = \; >
 124 \]
 125 \noindentÌÉÂÏ ×ÙÞÉÓÌÅÎÉÅ ÆÕÎËÃÉÉ ×ÒÏÄÅ
 126 $\mathbf{sin}(x), \mathbf{bessel\_j}(n, x)$. ÷ ÔÁËÉÈ ÓÌÕÞÁÑÈ ÏÐÅÒÁÔÏÒÏÍ Ñ×ÌÑÅÔÓÑ ÆÕÎËÃÉÑ.
 127
 128 ïÂßÅËÔÙ × Maxima~--- ÔÏÖÅ ×ÙÒÁÖÅÎÉÑ.
 129 óÐÉÓÏË $[a_1, \ldots, a_n]$~--- ×ÙÒÁÖÅÎÉÅ $\mathbf{list}(a_1, \ldots, a_n)$.
 130 íÁÔÒÉÃÁ~--- ×ÙÒÁÖÅÎÉÅ
 131 \[
 132 \mathbf{matrix}(\mathbf{list}(a_{1,1}, \ldots, a_{1,n}), \ldots, \mathbf{list}(a_{m,1}, \ldots, a_{m,n}))
 133 \]
 134
 135 ðÒÏÇÒÁÍÍÎÙÍÉ ÂÌÏËÁÍÉ Ñ×ÌÑÀÔÓÑ ×ÙÒÁÖÅÎÉÑ.
 136 âÌÏË ËÏÄÁ $\mathbf{block} (a_1, \ldots, a_n)$~--- ×ÙÒÁÖÅÎÉÅ Ó ÏÐÅÒÁÔÏÒÏÍ $\mathbf{block}$
 137 É ÁÒÇÕÍÅÎÔÁÍÉ $a_1, \ldots, a_n$. õÓÌÏ×ÎÁÑ ËÏÎÓÔÒÕËÃÉÑ \mbox{$\mathbf{if\ } a \mathbf{\ then\ } b \mathbf{\ elseif\ } c \mathbf{\ then\ } d$}~--- ×ÙÒÁÖÅÎÉÅ $\mathbf{if}(a, b, c, d)$.
 138 ãÉËÌ $\mathbf{for\ } a \mathbf{\ in\ } L \mathbf{\ do\ } S$~--- ×ÙÒÁÖÅÎÉÅ, ÓÏÏÔ×ÅÔÓÔ×ÕÀÝÅÅ
 139 $\mathbf{do}(a, L, S)$.
 140
 141 æÕÎËÃÉÑ Maxima $\mathbf{op}$ ×ÏÚ×ÒÁÝÁÅÔ ÏÐÅÒÁÔÏÒ ×ÙÒÁÖÅÎÉÑ-ÎÅ-ÁÔÏÍÁ.
 142 æÕÎËÃÉÑ $\mathbf{args}$ ×ÒÚ×ÒÁÝÁÅÔ ÁÒÇÕÍÅÎÔÙ ×ÙÒÁÖÅÎÉÑ-ÎÅ-ÁÔÏÍÁ.
 143 æÕÎËÃÉÑ $\mathbf{atom}$ ÕËÁÚÙ×ÁÅÔ, Ñ×ÌÑÅÔÓÑ ÌÉ ×ÙÒÁÖÅÎÉÅ ÁÔÏÍÏÍ.
 144
 145 òÁÓÓÍÏÔÒÉÍ ÄÒÕÇÉÅ ÐÒÉÍÅÒÙ.
 146
 147 \begin{enumerate}
 148
 149 \item áÔÏÍÙ~--- ÓÉÍ×ÏÌÙ, ÓÔÒÏËÉ É ÞÉÓÌÁ. ÷ÏÔ ÓÐÉÓÏË Ó ÜÌÅÍÅÎÔÁÍÉ-ÁÔÏÍÁÍÉ:
 150 % [a, foo, foo_bar, "Hello, world!", 42, 17.29];
 151
 152 \begin{verbatim}
 153 (%i2) [a, foo, foo_bar, "Hello, world!", 42, 17.29];
 154 (%o2)      [a, foo, foo_bar, Hello, world!, 42, 17.29]
 155 \end{verbatim}
 156
 157 \item íÁÔÅÍÁÔÉÞÅÓËÉÅ ×ÙÒÁÖÅÎÉÑ:
 158 % [a + b + c, a * b * c, foo = bar, a*b < c*d];
 159
 160 \begin{verbatim}
 161 (%i1) [a + b + c, a * b * c, foo = bar, a*b < c*d];
 162 (%o1)       [c + b + a, a b c, foo = bar, a b < c d]
 163 \end{verbatim}
 164
 165 \item óÐÉÓËÉ É ÍÁÔÒÉÃÙ.
 166 üÌÅÍÅÎÔÁÍÉ ÓÐÉÓËÁ ÉÌÉ ÍÁÔÒÉÃÙ ÍÏÇÕÔ ÂÙÔØ ÌÀÂÙÅ ×ÙÒÁÖÅÎÉÑ, × ÔÏÍ ÞÉÓÌÅ ÓÐÉÓËÉ ÉÌÉ
 167 ÍÁÔÒÉÃÙ:
 168 % L: [a, b, c, %pi, %e, 1729, 1/(a*d - b*c)];
 169 % L2: [a, b, [c, %pi, [%e, 1729], 1/(a*d - b*c)]];
 170 % L [7];
 171 % L2 [3];
 172 % M: matrix ([%pi, 17], [29, %e]);
 173 % M2: matrix ([[%pi, 17], a*d - b*c], [matrix ([1, a], [b, 7]), %e]);
 174 % M [2][1];
 175 % M2 [2][1];
 176
 177 \begin{verbatim}
 178 (%i1) L: [a, b, c, %pi, %e, 1729, 1/(a*d - b*c)];
 179                                             1
 180 (%o1)          [a, b, c, %pi, %e, 1729, ---------]
 181                                         a d - b c
 182 \end{verbatim}
 183 % (éÎÁÞÅ ÄÒÏÂØ ÂÕÄÅÔ ÒÁÚÏÒ×ÁÎÁ ÎÁ Ä×Å ÓÔÒÁÎÉÃÙ)
 184 \begin{verbatim}
 185 (%i2) L2: [a, b, [c, %pi, [%e, 1729], 1/(a*d - b*c)]];
 186                                              1
 187 (%o2)        [a, b, [c, %pi, [%e, 1729], ---------]]
 188                                          a d - b c
 189 (%i3) L [7];
 190                                 1
 191 (%o3)                       ---------
 192                             a d - b c
 193 (%i4) L2 [3];
 194                                           1
 195 (%o4)            [c, %pi, [%e, 1729], ---------]
 196                                       a d - b c
 197 (%i5) M: matrix ([%pi, 17], [29, %e]);
 198                            [ %pi  17 ]
 199 (%o5)                      [         ]
 200                            [ 29   %e ]
 201 (%i6) M2: matrix ([[%pi, 17], a*d - b*c], [matrix ([1, a], [b, 7]), %e]);
 202                     [ [%pi, 17]  a d - b c ]
 203                     [                      ]
 204 (%o6)               [ [ 1  a ]             ]
 205                     [ [      ]      %e     ]
 206                     [ [ b  7 ]             ]
 207 (%i7) M [2][1];
 208 (%o7)                          29
 209 (%i8) M2 [2][1];
 210                             [ 1  a ]
 211 (%o8)                       [      ]
 212                             [ b  7 ]
 213 \end{verbatim}
 214
 215 \item ðÒÏÇÒÁÍÍÎÙÅ ÂÌÏËÉ~--- ×ÙÒÁÖÅÎÉÑ.
 216 $x : y$ ÏÚÎÁÞÁÅÔ ÐÒÉÓ×ÁÉ×ÁÎÉÅ $y$ Ë $x$; ÚÎÁÞÅÎÉÅ ×ÙÒÁÖÅÎÉÑ ÐÒÉÓ×ÁÉ×ÁÎÉÑ~---  $y$.
 217 $\mathbf{block}$ ÏÂßÅÄÉÎÑÅÔ ÎÅÓËÏÌØËÏ ×ÙÒÁÖÅÎÉÊ É ÐÏÓÌÅÄÏ×ÁÔÅÌØÎÏ ÉÈ ×ÙÞÉÓÌÑÅÔ;
 218 ÚÎÁÞÅÎÉÅ ÂÌÏËÁ ÓÏÏÔ×ÅÔÓÔ×ÕÅÔ ÚÎÁÞÅÎÉÀ ÅÇÏ ÐÏÓÌÅÄÎÅÇÏ ×ÙÒÁÖÅÎÉÑ.
 219 % (a: 42) - (b: 17);
 220 % [a, b];
 221 % block ([a], a: 42, a^2 - 1600) + block ([b], b: 5, %pi^b);
 222 % (if a > 1 then %pi else %e) + (if b < 0 then 1/2 else 1/7);
 223
 224 \begin{verbatim}
 225 (%i1) (a: 42) - (b: 17);
 226 (%o1)                          25
 227 (%i2) [a, b];
 228 (%o2)                       [42, 17]
 229 (%i3) block ([a], a: 42, a^2 - 1600) + block ([b], b: 5, %pi^b);
 230                               5
 231 (%o3)                      %pi  + 164
 232 (%i4) (if a > 1 then %pi else %e) + (if b < 0 then 1/2 else 1/7);
 233                                    1
 234 (%o4)                        %pi + -
 235                                    7
 236 \end{verbatim}
 237
 238 \item $\mathbf{op}$ ×ÏÚ×ÒÁÝÁÅÔ ÏÐÅÒÁÔÏÒ, $\mathbf{args}$ ×ÏÚ×ÒÁÝÁÅÔ ÁÒÇÕÍÅÎÔÙ,
 239 $\mathbf{atom}$ ÏÐÒÅÄÅÌÑÅÔ, Ñ×ÌÑÅÔÓÑ ÌÉ ×ÙÒÁÖÅÎÉÅ ÁÔÏÍÏÍ:
 240 % op (p + q);
 241 % op (p + q > p*q);
 242 % op (sin (p + q));
 243 % op (foo (p, q));
 244 % op (foo (p, q) := p - q);
 245 % args (p + q);
 246 % args (p + q > p*q);
 247 % args (sin (p + q));
 248 % args (foo (p, q));
 249 % args (foo (p, q) := p - q);
 250 % atom (p);
 251 % atom (p + q);
 252 % atom (sin (p + q));
 253
 254 \begin{verbatim}
 255 (%i1) op (p + q);
 256 (%o1)                           +
 257 (%i2) op (p + q > p*q);
 258 (%o2)                           >
 259 (%i3) op (sin (p + q));
 260 (%o3)                          sin
 261 (%i4) op (foo (p, q));
 262 (%o4)                          foo
 263 (%i5) op (foo (p, q) := p - q);
 264 (%o5)                          :=
 265 (%i6) args (p + q);
 266 (%o6)                        [q, p]
 267 (%i7) args (p + q > p*q);
 268 (%o7)                     [q + p, p q]
 269 (%i8) args (sin (p + q));
 270 (%o8)                        [q + p]
 271 (%i9) args (foo (p, q));
 272 (%o9)                       [p, - q]
 273 (%i10) args (foo (p, q) := p - q);
 274 (%o10)                 [foo(p, q), p - q]
 275 (%i11) atom (p);
 276 (%o11)                        true
 277 (%i12) atom (p + q);
 278 (%o12)                        false
 279 (%i13) atom (sin (p + q));
 280 (%o13)                        false
 281 \end{verbatim}
 282
 283 \item ïÐÅÒÁÔÏÒÙ É ÁÒÇÕÍÅÎÔÙ ÐÒÏÇÒÁÍÍÎÙÈ ÂÌÏËÏ×.
 284 ïÄÉÎÁÒÎÁÑ ËÁ×ÙÞËÁ ÕËÁÚÙ×ÁÅÔ Maxima ÓÏÚÄÁÔØ ×ÙÒÁÖÅÎÉÅ, ÎÏ ÏÔÌÏÖÉÔØ ÅÇÏ ×ÙÞÉÓÌÅÎÉÅ.
 285 íÙ ÅÝÅ ÒÁÓÓÍÏÔÒÉÍ ÜÔÏ ÐÏÚÖÅ.
 286 % op ('(block ([a], a: 42, a^2 - 1600)));
 287 % op ('(if p > q then p else q));
 288 % op ('(for x in L do print (x)));
 289 % args ('(block ([a], a: 42, a^2 - 1600)));
 290 % args ('(if p > q then p else q));
 291 % args ('(for x in L do print (x)));
 292
 293 \begin{verbatim}
 294 (%i1) op ('(block ([a], a: 42, a^2 - 1600)));
 295 (%o1)                         block
 296 (%i2) op ('(if p > q then p else q));
 297 (%o2)                          if
 298 (%i3) op ('(for x in L do print (x)));
 299 (%o3)                         mdoin
 300 (%i4) args ('(block ([a], a: 42, a^2 - 1600)));
 301                                    2
 302 (%o4)               [[a], a : 42, a  - 1600]
 303 (%i5) args ('(if p > q then p else q));
 304 (%o5)                  [p > q, p, true, q]
 305 (%i6) args ('(for x in L do print (x)));
 306 (%o6)     [x, L, false, false, false, false, print(x)]
 307 \end{verbatim}
 308
 309 \end{enumerate}
 310
 311 \section{÷ÙÞÉÓÌÅÎÉÅ}
 312
 313 \noindentúÎÁÞÅÎÉÅ ÓÉÍ×ÏÌÁ~--- ×ÙÒÁÖÅÎÉÅ, Ó×ÑÚÁÎÎÏÅ Ó ÜÔÉÍ ÓÉÍ×ÏÌÏÍ.
 314 ëÁÖÄÙÊ ÓÉÍ×ÏÌ ÉÍÅÅÔ ÚÎÁÞÅÎÉÅ; ÅÓÌÉ ÚÎÁÞÅÎÉÅ ÎÅ ÚÁÄÁ×ÁÌÏÓØ, ÓÉÍ×ÏÌ ×ÙÞÉÓÌÑÅÔÓÑ
 315 ÓÁÍ × ÓÅÂÑ. îÁÐÒÉÍÅÒ, $x$ ÉÍÅÅÔ ÚÎÁÞÅÎÉÅ $x$, ÅÓÌÉ ÓÉÍ×ÏÌÕ ÎÅ ÐÒÉÓ×ÁÉ×ÁÌÏÓØ
 316 ÚÎÁÞÅÎÉÅ.
 317
 318 þÉÓÌÁ É ÓÔÒÏËÉ ÓÏ×ÐÁÄÁÀÔ ÓÏ Ó×ÏÉÍÉ ÚÎÁÞÅÎÉÑÍÉ.
 319
 320 ÷ÙÒÁÖÅÎÉÅ-ÎÅ-ÁÔÏÍ ×ÙÞÉÓÌÑÅÔÓÑ ÐÒÉÂÌÉÚÉÔÅÌØÎÏ ÔÁËÉÍ ÏÂÒÁÚÏÍ:
 321
 322 \begin{enumerate}
 323 \item ÷ÙÞÉÓÌÑÅÔÓÑ ËÁÖÄÙÊ ÁÒÇÕÍÅÎÔ ÏÐÅÒÁÔÏÒÁ.
 324 \item åÓÌÉ ÏÐÅÒÁÔÏÒ Ó×ÑÚÁÎ Ó ×ÙÚÏ×ÏÍ ÆÕÎËÃÉÉ, ÔÏ ÚÎÁÞÅÎÉÅ, ×ÏÚ×ÒÁÝÅÎÎÏÅ ÆÕÎËÃÉÅÊ,
 325 Ñ×ÌÑÅÔÓÑ ÚÎÁÞÅÎÉÅÍ ×ÙÒÁÖÅÎÉÑ.
 326 \end{enumerate}
 327
 328 ÷ÙÞÉÓÌÅÎÉÅ ÍÏÖÅÔ ÐÒÏÈÏÄÉÔØ ÐÏ-ÒÁÚÎÏÍÕ. îÅËÏÔÏÒÙÅ ÉÚÍÅÎÅÎÉÑ ÕÍÅÎØÛÁÀÔ ÏÂßÅÍ
 329 ×ÙÞÉÓÌÅÎÉÊ:
 330
 331 \begin{enumerate}
 332 \item îÅËÏÔÏÒÙÅ ÆÕÎËÃÉÉ ÎÅ ×ÙÞÉÓÌÑÀÔ Ó×ÏÉ ÁÒÇÕÍÅÎÔÙ ÉÌÉ ÞÁÓÔØ ÉÚ ÎÉÈ, ÌÉÂÏ
 333 ÍÅÎÑÀÔ ÈÏÄ ×ÙÞÉÓÌÅÎÉÑ ÁÒÇÕÍÅÎÔÏ×.
 334     % Examples: $\mathbf{kill}$, $\mathbf{save}$, $\mathbf{sum}$, $\mathbf{:=}$ (function definition).
 335 \item ïÄÉÎÏÞÎÁÑ ËÁ×ÙÞËÁ $'$ ÐÒÅÄÏÔ×ÒÁÝÁÅÔ ×ÙÞÉÓÌÅÎÉÅ:
 336     \begin{enumerate}
 337     \item[---] $'a$ ×ÙÞÉÓÌÑÅÔÓÑ ËÁË $a$. ÷ÓÅ ÄÒÕÇÉÅ ÚÎÁÞÅÎÉÑ $a$ ÉÇÎÏÒÉÒÕÀÔÓÑ.
 338     \item[---] $'f(a_1, \ldots, a_n)$ ×ÙÞÉÓÌÑÅÔÓÑ ×
 339 $f(\mathbf{ev}(a_1), \ldots, \mathbf{ev}(a_n))$. ôÁËÉÍ ÏÂÒÁÚÏÍ, ×ÙÞÉÓÌÑÀÔÓÑ ÁÒÇÕÍÅÎÔÙ,
 340 ÎÏ $f$ ÎÅ ×ÙÚÙ×ÁÅÔÓÑ.
 341     \item[---] $'(\ldots)$ ÐÒÅÄÏÔ×ÒÁÝÁÅÔ ×ÙÞÉÓÌÅÎÉÅ ÌÀÂÙÈ ×ÙÒÁÖÅÎÉÊ ×ÎÕÔÒÉ $(\ldots)$.
 342     \end{enumerate}
 343 \end{enumerate}
 344
 345 îÅËÏÔÏÒÙÅ ÉÚÍÅÎÅÎÉÑ Õ×ÅÌÉÞÉ×ÁÀÔ ÏÂßÅÍ ×ÙÞÉÓÌÅÎÉÊ:
 346
 347 \begin{enumerate}
 348 \item ä×Å ÏÄÉÎÏÞÎÙÅ ËÁ×ÙÞËÉ $''a$ ×ÙÚÙ×ÁÀÔ ÄÏÐÏÌÎÉÔÅÌØÎÏÅ ×ÙÞÉÓÌÅÎÉÅ × ÍÏÍÅÎÔ ÏÂÒÁÂÏÔËÉ $a$.
 349 \item $\mathbf{ev}(a)$ ×ÙÚÙ×ÁÅÔ ÄÏÐÏÌÎÉÔÅÌØÎÏÅ ×ÙÞÉÓÌÅÎÉÅ $a$ ÐÒÉ ËÁÖÄÏÍ ×ÙÞÉÓÌÅÎÉÉ
 350     $\mathbf{ev}(a)$.
 351 \item úÁÐÉÓØ $\mathbf{apply}(f, [a_1, \ldots, a_n])$ ×ÙÚÙ×ÁÅÔ ×ÙÞÉÓÌÅÎÉÅ
 352     ÁÒÇÕÍÅÎÔÏ× $a_1, \ldots, a_n$, ÄÁÖÅ ÅÓÌÉ $f$ ÓÔÁ×ÉÔ ÐÅÒÅÄ ÎÉÍÉ ÏÄÉÎÏÞÎÙÅ
 353     ËÁ×ÙÞËÉ.
 354 \item $\mathbf{define}$ ÓÏÏÔ×ÅÔÓÔ×ÕÅÔ ÏÐÒÅÄÅÌÅÎÉÀ ÆÕÎËÃÉÉ ×ÒÏÄÅ $\mathbf{:=}$,
 355     ÎÏ ×ÙÞÉÓÌÑÅÔ ÔÅÌÏ ÆÕÎËÃÉÉ, × ÔÏ ×ÒÅÍÑ ËÁË $\mathbf{:=}$ ÏÔËÌÁÄÙ×ÁÅÔ
 356     ×ÙÞÉÓÌÅÎÉÅ.
 357 \end{enumerate}
 358
 359 òÁÓÓÍÏÔÒÉÍ, ËÁË ×ÙÞÉÓÌÑÀÔÓÑ ÎÅËÏÔÏÒÙÅ ×ÙÒÁÖÅÎÉÑ.
 360
 361 \begin{enumerate}
 362
 363 \item óÉÍ×ÏÌ ×ÙÞÉÓÌÑÅÔÓÑ ÓÁÍ × ÓÅÂÑ, ÅÓÌÉ ÅÍÕ ÎÅ ÐÒÉÓ×ÁÉ×ÁÌÏÓØ ÚÎÁÞÅÎÉÅ:
 364 % block (a: 1, b: 2, e: 5);
 365 % [a, b, c, d, e];
 366
 367 \begin{verbatim}
 368 (%i1) block (a: 1, b: 2, e: 5);
 369 (%o1)                           5
 370 (%i2) [a, b, c, d, e];
 371 (%o2)                    [1, 2, c, d, 5]
 372 \end{verbatim}
 373
 374 \item áÒÇÕÍÅÎÔÙ ÏÐÅÒÁÔÏÒÏ× ×ÙÞÉÓÌÑÀÔÓÑ ÏÂÙÞÎÙÍ ÐÕÔÅÍ (ÅÓÌÉ ×ÙÞÉÓÌÅÎÉÅ ÎÅ ÏÔÌÏÖÅÎÏ
 375 ÔÅÍ ÉÌÉ ÉÎÙÍ ÏÂÒÁÚÏÍ):
 376 % block (x: %pi, y: %e);
 377 % sin (x + y);
 378 % x > y;
 379 % x!;
 380
 381 \begin{verbatim}
 382 (%i1) block (x: %pi, y: %e);
 383 (%o1)                          %e
 384 (%i2) sin (x + y);
 385 (%o2)                       - sin(%e)
 386 (%i3) x > y;
 387 (%o3)                       %pi > %e
 388 (%i4) x!;
 389 (%o4)                         %pi!
 390 \end{verbatim}
 391
 392 \item åÓÌÉ ÏÐÅÒÁÔÏÒ Ó×ÑÚÁÎ Ó ×ÙÚÏ×ÏÍ ÆÕÎËÃÉÉ, ÚÎÁÞÅÎÉÅ, ×ÏÚ×ÒÁÝÅÎÎÏÅ ÆÕÎËÃÉÅÊ,
 393 Ñ×ÌÑÅÔÓÑ ÚÎÁÞÅÎÉÅÍ ×ÙÒÁÖÅÎÉÑ (ÅÓÌÉ ×ÙÞÉÓÌÅÎÉÅ ÎÅ ÏÔÌÏÖÅÎÏ); ÉÎÁÞÅ ×ÙÞÉÓÌÅÎÉÅ ÄÁÅÔ
 394 ÄÒÕÇÏÅ ×ÙÒÁÖÅÎÉÅ Ó ÔÅÍ ÖÅ ÏÐÅÒÁÔÏÒÏÍ:
 395 % foo (p, q) := p - q;
 396 % p: %phi;
 397 % foo (p, q);
 398 % bar (p, q);
 399
 400 \begin{verbatim}
 401 (%i1) foo (p, q) := p - q;
 402 (%o1)                  foo(p, q) := p - q
 403 (%i2) p: %phi;
 404 (%o2)                         %phi
 405 (%i3) foo (p, q);
 406 (%o3)                       %phi - q
 407 (%i4) bar (p, q);
 408 (%o4)                     bar(%phi, q)
 409 \end{verbatim}
 410
 411 \item îÅËÏÔÏÒÙÅ ÆÕÎËÃÉÉ ÏÔËÌÁÄÙ×ÁÀÔ ×ÙÞÉÓÌÅÎÉÅ ÁÒÇÕÍÅÎÔÏ×, ÎÁÐÒÉÍÅÒ,
 412 $\mathbf{save}$, $\mathbf{:=}$, $\mathbf{kill}$:
 413 % block (a: 1, b: %pi, c: x + y);
 414 % [a, b, c];
 415 % save ("tmp.save", a, b, c);
 416 % f (a) := a^b;
 417 % f (7);
 418 % kill (a, b, c);
 419 % [a, b, c];
 420
 421 \begin{verbatim}
 422 (%i1) block (a: 1, b: %pi, c: x + y);
 423 (%o1)                         y + x
 424 (%i2) [a, b, c];
 425 (%o2)                    [1, %pi, y + x]
 426 (%i3) save ("tmp.save", a, b, c);
 427 (%o3)                       tmp.save
 428 (%i4) f (a) := a^b;
 429                                     b
 430 (%o4)                      f(a) := a
 431 (%i5) f (7);
 432                                %pi
 433 (%o5)                         7
 434 (%i6) kill (a, b, c);
 435 (%o6)                         done
 436 (%i7) [a, b, c];
 437 (%o7)                       [a, b, c]
 438 \end{verbatim}
 439
 440 \item ïÄÉÎÏÞÎÁÑ ËÁ×ÙÞËÁ ÐÒÅÄÏÔ×ÒÁÝÁÅÔ ×ÙÞÉÓÌÅÎÉÅ, ÄÁÖÅ ÅÓÌÉ ÏÎÏ ÄÏÌÖÎÏ ÐÒÏÉÚ×ÏÄÉÔØÓÑ:
 441 % foo (x, y) := y - x;
 442 % block (a: %e, b: 17);
 443 % foo (a, b);
 444 % foo ('a, 'b);
 445 % 'foo (a, b);
 446 % '(foo (a, b));
 447
 448 \begin{verbatim}
 449 (%i1) foo (x, y) := y - x;
 450 (%o1)                  foo(x, y) := y - x
 451 (%i2) block (a: %e, b: 17);
 452 (%o2)                          17
 453 (%i3) foo (a, b);
 454 (%o3)                        17 - %e
 455 (%i4) foo ('a, 'b);
 456 (%o4)                         b - a
 457 (%i5) 'foo (a, b);
 458 (%o5)                      foo(%e, 17)
 459 (%i6) '(foo (a, b));
 460 (%o6)                       foo(a, b)
 461 \end{verbatim}
 462
 463 \item ä×Å ÏÄÉÎÏÞÎÙÅ ËÁ×ÙÞËÉ ×ÙÚÙ×ÁÀÔ ÄÏÐÏÌÎÉÔÅÌØÎÏÅ ×ÙÞÉÓÌÅÎÉÅ ×Ï ×ÒÅÍÑ ÏÂÒÁÂÏÔËÉ
 464 ×ÙÒÁÖÅÎÉÑ:
 465 % diff (sin (x), x);
 466 % foo (x) := diff (sin (x), x);
 467 % foo (x) := ''(diff (sin (x), x));
 468
 469 \begin{verbatim}
 470 (%i1) diff (sin (x), x);
 471 (%o1)                        cos(x)
 472 (%i2) foo (x) := diff (sin (x), x);
 473 (%o2)               foo(x) := diff(sin(x), x)
 474 (%i3) foo (x) := ''(diff (sin (x), x));
 475 (%o3)                   foo(x) := cos(x)
 476 \end{verbatim}
 477
 478 \item $\mathbf{ev}$ ×ÓÑËÉÊ ÒÁÚ ×ÙÚÙ×ÁÅÔ ÄÏÐÏÌÎÉÔÅÌØÎÏÅ ×ÙÞÉÓÌÅÎÉÅ (ÓÒÁ×ÎÉÔÅ
 479 ÜÔÏ Ó ÐÏ×ÅÄÅÎÉÅÍ ÄÌÑ Ä×ÕÈ ËÁ×ÙÞÅË):
 480 % block (xx: yy, yy: zz);
 481 % [xx, yy];
 482 % foo (x) := ''x;
 483 % foo (xx);
 484 % bar (x) := ev (x);
 485 % bar (xx);
 486
 487 \begin{verbatim}
 488 (%i1) block (xx: yy, yy: zz);
 489 (%o1)                          zz
 490 (%i2) [xx, yy];
 491 (%o2)                       [yy, zz]
 492 (%i3) foo (x) := ''x;
 493 (%o3)                      foo(x) := x
 494 (%i4) foo (xx);
 495 (%o4)                          yy
 496 (%i5) bar (x) := ev (x);
 497 (%o5)                    bar(x) := ev(x)
 498 (%i6) bar (xx);
 499 (%o6)                          zz
 500 \end{verbatim}
 501
 502 \item $\mathbf{apply}$ ×ÙÚÙ×ÁÅÔ ×ÙÞÉÓÌÅÎÉÅ ÁÒÇÕÍÅÎÔÏ×, ÄÁÖÅ ÅÓÌÉ ÐÅÒÅÄ ÎÉÍÉ ÓÔÏÑÔ ËÁ×ÙÞËÉ:
 503 % block (a: aa, b: bb, c: cc);
 504 % block (aa: 11, bb: 22, cc: 33);
 505 % [a, b, c, aa, bb, cc];
 506 % apply (kill, [a, b, c]);
 507 % [a, b, c, aa, bb, cc];
 508 % kill (a, b, c);
 509 % [a, b, c, aa, bb, cc];
 510
 511 \begin{verbatim}
 512 (%i1) block (a: aa, b: bb, c: cc);
 513 (%o1)                          cc
 514 (%i2) block (aa: 11, bb: 22, cc: 33);
 515 (%o2)                          33
 516 (%i3) [a, b, c, aa, bb, cc];
 517 (%o3)               [aa, bb, cc, 11, 22, 33]
 518 (%i4) apply (kill, [a, b, c]);
 519 (%o4)                         done
 520 (%i5) [a, b, c, aa, bb, cc];
 521 (%o5)               [aa, bb, cc, aa, bb, cc]
 522 (%i6) kill (a, b, c);
 523 (%o6)                         done
 524 (%i7) [a, b, c, aa, bb, cc];
 525 (%o7)                 [a, b, c, aa, bb, cc]
 526 \end{verbatim}
 527
 528 \item $\mathbf{define}$ ×ÙÞÉÓÌÑÅÔ ÔÅÌÏ ÏÐÒÅÄÅÌÅÎÉÑ ÆÕÎËÃÉÉ:
 529 % integrate (sin (a*x), x, 0, %pi);
 530 % foo (x) := integrate (sin (a*x), x, 0, %pi);
 531 % define (foo (x), integrate (sin (a*x), x, 0, %pi));
 532
 533 \begin{verbatim}
 534 (%i1) integrate (sin (a*x), x, 0, %pi);
 535                          1   cos(%pi a)
 536 (%o1)                    - - ----------
 537                          a       a
 538 (%i2) foo (x) := integrate (sin (a*x), x, 0, %pi);
 539 (%o2)       foo(x) := integrate(sin(a x), x, 0, %pi)
 540 (%i3) define (foo (x), integrate (sin (a*x), x, 0, %pi));
 541                               1   cos(%pi a)
 542 (%o3)               foo(x) := - - ----------
 543                               a       a
 544 \end{verbatim}
 545
 546 \end{enumerate}
 547
 548 \section{õÐÒÏÝÅÎÉÅ}
 549
 550 \noindentðÏÓÌÅ ×ÙÞÉÓÌÅÎÉÑ ×ÙÒÁÖÅÎÉÑ, Maxima ÐÙÔÁÅÔÓÑ ÎÁÊÔÉ ÜË×É×ÁÌÅÎÔÎÏÅ ÅÍÕ <<ÂÏÌÅÅ ÐÒÏÓÔÏÅ>>,
 551 ÄÌÑ ÞÅÇÏ ÐÒÉÍÅÎÑÅÔÓÑ ÒÑÄ ÐÒÁ×ÉÌ, Ó×ÑÚÁÎÎÙÈ Ó ÕÓÌÏ×ÎÙÍ ÐÏÎÑÔÉÅÍ ÐÒÏÓÔÏÔÙ.
 552 ôÁË, $1 + 1$ ÕÐÒÏÝÁÅÔÓÑ ÄÏ $2$, $x + x$~--- ÄÏ $2 x$, Á
 553 $\mathbf{sin}(\mathbf{\%pi})$~--- ÄÏ $0$.
 554
 555 ïÄÎÁËÏ ÍÎÏÇÉÅ ÉÚ×ÅÓÔÎÙÅ ÔÏÖÄÅÓÔ×Á ÎÅ ÐÒÉÍÅÎÑÀÔÓÑ Á×ÔÏÍÁÔÉÞÅÓËÉ. îÁÐÒÉÍÅÒ, ÎÅ
 556 ÉÓÐÏÌØÚÕÀÔÓÑ ÆÏÒÍÕÌÙ Ä×ÏÊÎÏÇÏ ÕÇÌÁ ÄÌÑ ÔÒÉÇÏÎÏÍÅÔÒÉÞÅÓËÉÈ ÆÕÎËÃÉÊ É ÎÅ ÐÒÏÉÚ×ÏÄÉÔÓÑ
 557 ÐÒÉ×ÅÄÅÎÉÅ ÄÒÏÂÅÊ ×ÉÄÁ $a/b + c/b \rightarrow (a + c)/b$. äÌÑ ÐÒÉÍÅÎÅÎÉÑ ÔÏÖÄÅÓÔ×
 558 ÓÕÝÅÓÔ×ÕÀÔ ÏÔÄÅÌØÎÙÅ ÆÕÎËÃÉÉ.
 559
 560 õÐÒÏÝÅÎÉÅ ×ÓÅÇÄÁ ÐÒÉÍÅÎÑÅÔÓÑ, ÅÓÌÉ ÎÅ ÂÙÌÏ Ñ×ÎÏ ÏÔÌÏÖÅÎÏ, ÄÁÖÅ × ÔÏÍ ÓÌÕÞÁÅ, ËÏÇÄÁ
 561 ×ÙÒÁÖÅÎÉÅ ÎÅ ×ÙÞÉÓÌÑÅÔÓÑ.
 562
 563 $\mathbf{tellsimpafter}$ ××ÏÄÉÔ ÐÏÌØÚÏ×ÁÔÅÌØÓËÉÅ ÐÒÁ×ÉÌÁ ÕÐÒÏÝÅÎÉÑ.
 564
 565 òÁÓÓÍÏÔÒÉÍ ÎÅÓËÏÌØËÏ ÐÒÉÍÅÒÏ×.
 566
 567 \begin{enumerate}
 568
 569 \item úÎÁË ËÁ×ÙÞËÉ ÏÔËÌÁÄÙ×ÁÅÔ ×ÙÞÉÓÌÅÎÉÅ, ÎÏ ÎÅ ÕÐÒÏÝÅÎÉÅ;
 570 åÓÌÉ ÄÌÑ ÇÌÏÂÁÌØÎÏÇÏ ÆÌÁÇÁ $\mathbf{simp}$ ÕÓÔÁÎÏ×ÌÅÎÏ $\mathbf{false}$,
 571 ÔÏ ÕÐÒÏÝÅÎÉÅ ÎÅ ÐÒÏÉÚ×ÏÄÉÔÓÑ, ÎÏ ÐÒÏÉÚ×ÏÄÉÔÓÑ ×ÙÞÉÓÌÅÎÉÅ:
 572
 573 % '[1 + 1, x + x, x * x, sin (%pi)];
 574 % simp: false$
 575 % block ([x: 1], x + x);
 576 % simp: true$
 577
 578 \begin{verbatim}
 579 (%i1) '[1 + 1, x + x, x * x, sin (%pi)];
 580                                    2
 581 (%o1)                    [2, 2 x, x , 0]
 582 (%i2) simp: false$
 583 (%i3) block ([x: 1], x + x);
 584 (%o3)                         1 + 1
 585 \end{verbatim}
 586
 587 \item îÅËÏÔÏÒÙÅ ÔÏÖÄÅÓÔ×Á ÎÅ ÐÒÉÍÅÎÑÀÔÓÑ Á×ÔÏÍÁÔÉÞÅÓËÉ.
 588 $\mathbf{expand}$, $\mathbf{ratsimp}$, $\mathbf{trigexpand}$, $\mathbf{demoivre}$~---
 589 ÐÒÉÍÅÒÙ ÆÕÎËÃÉÊ, ÐÒÉÍÅÎÑÀÝÉÈ ÔÏÖÄÅÓÔ×Á:
 590
 591 % (a + b)^2;
 592 % expand (%);
 593 % a/b + c/b;
 594 % ratsimp (%);
 595 % sin (2*x);
 596 % trigexpand (%);
 597 % a * exp (b * %i);
 598 % demoivre (%);
 599
 600 \begin{verbatim}
 601 (%i1) (a + b)^2;
 602                                    2
 603 (%o1)                       (b + a)
 604 (%i2) expand (%);
 605                           2            2
 606 (%o2)                    b  + 2 a b + a
 607 (%i3) a/b + c/b;
 608                               c   a
 609 (%o3)                         - + -
 610                               b   b
 611 (%i4) ratsimp (%);
 612                               c + a
 613 (%o4)                         -----
 614                                 b
 615 (%i5) sin (2*x);
 616 (%o5)                       sin(2 x)
 617 (%i6) trigexpand (%);
 618 (%o6)                    2 cos(x) sin(x)
 619 (%i7) a * exp (b * %i);
 620                                 %i b
 621 (%o7)                       a %e
 622 (%i8) demoivre (%);
 623 (%o8)                a (%i sin(b) + cos(b))
 624 \end{verbatim}
 625
 626 \end{enumerate}
 627
 628 \section{apply, map É lambda}
 629
 630 \begin{enumerate}
 631
 632 \item $\mathbf{apply}$ ÓÏÚÄÁÅÔ É ×ÙÞÉÓÌÑÅÔ ×ÙÒÁÖÅÎÉÅ. áÒÇÕÍÅÎÔÙ ×ÙÒÁÖÅÎÉÑ
 633 ×ÓÅÇÄÁ ×ÙÞÉÓÌÑÀÔÓÑ (ÄÁÖÅ, ÅÓÌÉ ÂÙ ÏÎÉ ÎÅ ×ÙÞÉÓÌÑÌÉÓØ ÐÒÉ ÄÒÕÇÉÈ ÏÂÓÔÏÑÔÅÌØÓÔ×ÁÈ):
 634
 635 % apply (sin, [x * %pi]);
 636 % L: [a, b, c, x, y, z];
 637 % apply ("+", L);
 638
 639 \begin{verbatim}
 640 (%i1) apply (sin, [x * %pi]);
 641 (%o1)                      sin(%pi x)
 642 (%i2) L: [a, b, c, x, y, z];
 643 (%o2)                  [a, b, c, x, y, z]
 644 (%i3) apply ("+", L);
 645 (%o3)                 z + y + x + c + b + a
 646 \end{verbatim}
 647
 648 \item $\mathbf{map}$ ÓÏÚÄÁÅÔ É ×ÙÞÉÓÌÑÅÔ ×ÙÒÁÖÅÎÉÅ ÄÌÑ ËÁÖÄÏÇÏ ÜÌÅÍÅÎÔÁ ÓÐÉÓËÁ
 649 ÁÒÇÕÍÅÎÔÏ×. áÒÇÕÍÅÎÔÙ ×ÙÒÁÖÅÎÉÑ ×ÓÅÇÄÁ ×ÙÞÉÓÌÑÀÔÓÑ (ÄÁÖÅ, ÅÓÌÉ ÂÙ ÏÎÉ ÎÅ ×ÙÞÉÓÌÑÌÉÓØ
 650 ÐÒÉ ÄÒÕÇÉÈ ÏÂÓÔÏÑÔÅÌØÓÔ×ÁÈ). ÷ ËÁÞÅÓÔ×Å ÒÅÚÕÌØÔÁÔÁ ×ÏÚ×ÒÁÝÁÅÔÓÑ ÓÐÉÓÏË:
 651
 652 % map (foo, [x, y, z]);
 653 % map ("+", [1, 2, 3], [a, b, c]);
 654 % map (atom, [a, b, c, a + b, a + b + c]);
 655
 656 \begin{verbatim}
 657 (%i1) map (foo, [x, y, z]);
 658 (%o1)               [foo(x), foo(y), foo(z)]
 659 (%i2) map ("+", [1, 2, 3], [a, b, c]);
 660 (%o2)                 [a + 1, b + 2, c + 3]
 661 (%i3) map (atom, [a, b, c, a + b, a + b + c]);
 662 (%o3)           [true, true, true, false, false]
 663 \end{verbatim}
 664
 665 \item $\mathbf{lambda}$ ÓÏÚÄÁÅÔ ÌÑÍÂÄÁ-×ÙÒÁÖÅÎÉÅ (ÂÅÚÙÍÑÎÎÕÀ ÆÕÎËÃÉÀ). ìÑÍÂÄÁ-×ÙÒÁÖÅÎÉÅ
 666 ÍÏÖÅÔ ÉÓÐÏÌØÚÏ×ÁÔØÓÑ × ÎÅËÏÔÏÒÙÈ ÓÌÕÞÁÑÈ ËÁË ÏÂÙÞÎÁÑ ÆÕÎËÃÉÑ. $\mathbf{lambda}$
 667 ÎÅ ×ÙÞÉÓÌÑÅÔ ÔÅÌÏ ÆÕÎËÃÉÉ:
 668
 669 % f: lambda ([x, y], (x + y)*(x - y));
 670 % f (a, b);
 671 % apply (f, [p, q]);
 672 % map (f, [1, 2, 3], [a, b, c]);
 673 %% apply (lambda ([x, y], (x + y)*(x - y)), [p, q]);
 674 %% map (lambda ([x, y], (x + y)*(x - y)), [1, 2, 3], [a, b, c]);
 675
 676 \begin{verbatim}
 677 (%i1) f: lambda ([x, y], (x + y)*(x - y));
 678 (%o1)            lambda([x, y], (x + y) (x - y))
 679 (%i2) f (a, b);
 680 (%o2)                    (a - b) (b + a)
 681 (%i3) apply (f, [p, q]);
 682 (%o3)                    (p - q) (q + p)
 683 (%i4) map (f, [1, 2, 3], [a, b, c]);
 684 (%o4)  [(1 - a) (a + 1), (2 - b) (b + 2), (3 - c) (c + 3)]
 685 \end{verbatim}
 686
 687 \end{enumerate}
 688
 689 \section{÷ÓÔÒÏÅÎÎÙÅ ÔÉÐÙ ÏÂßÅËÔÏ×}
 690
 691 \noindentïÂßÅËÔ ÐÒÅÄÓÔÁ×ÌÑÅÔÓÑ × ×ÉÄÅ ×ÙÒÁÖÅÎÉÑ. ëÁË É ÄÒÕÇÉÅ ×ÙÒÁÖÅÎÉÑ, ÏÂßÅËÔ ÓÏÄÅÒÖÉÔ ÏÐÅÒÁÔÏÒ
 692 É ÅÇÏ ÁÒÇÕÍÅÎÔÙ.
 693
 694 ïÓÎÏ×ÎÙÅ ×ÓÔÒÏÅÎÎÙÅ ÔÉÐÙ ÏÂßÅËÔÏ×~--- ÓÐÉÓËÉ, ÍÁÔÒÉÃÙ É ÍÎÏÖÅÓÔ×Á.
 695
 696 \subsection{óÐÉÓËÉ}
 697
 698 \begin{enumerate}
 699
 700 \item óÐÉÓÏË ÚÁÄÁÅÔÓÑ × ×ÉÄÅ $[a, b, c]$.
 701
 702 \item ÷ ÓÐÉÓËÅ $L$ $L[i]$~--- $i$-Ê ÜÌÅÍÅÎÔ. $L[1]$~--- ÐÅÒ×ÙÊ ÜÌÅÍÅÎÔ.
 703
 704 \item $\mathbf{map}(\mathit{f}, L)$ ÐÒÉÍÅÎÑÅÔ $\mathit{f}$ Ë ËÁÖÄÏÍÕ ÜÌÅÍÅÎÔÕ $L$.
 705
 706 \item $\mathbf{apply}(\mathbf{"+"}, L)$~--- ÓÕÍÍÁ ×ÓÅÈ ÜÌÅÍÅÎÔÏ× $L$.
 707
 708 \item $\mathbf{for\ } x \mathbf{\ in \ } L \mathbf{\ do \ } \mathit{expr}$ ×ÙÞÉÓÌÑÅÔ
 709 $\mathit{expr}$ ÄÌÑ ËÁÖÄÏÇÏ ÜÌÅÍÅÎÔÁ $L$.
 710
 711 \item $\mathbf{length}(L)$~--- ÞÉÓÌÏ ÜÌÅÍÅÎÔÏ× $L$.
 712
 713 \end{enumerate}
 714
 715 \subsection{íÁÔÒÉÃÙ}
 716
 717 \begin{enumerate}
 718
 719 \item íÁÔÒÉÃÁ ÚÁÄÁÅÔÓÑ × ×ÉÄÅ $\mathbf{matrix}(L_1, \ldots, L_n)$, ÇÄÅ
 720 $L_1, \ldots, L_n$~--- ÓÐÉÓËÉ ÜÌÅÍÅÎÔÏ× ÓÔÒÏË.
 721
 722 \item åÓÌÉ $M$~--- ÍÁÔÒÉÃÁ, ÔÏ $M[i, j]$ ÉÌÉ $M[i][j]$~--- ÅÅ $(i, j)$-Ê ÜÌÅÍÅÎÔ.
 723     $M[1,1]$~--- ÜÌÅÍÅÎÔ × ×ÅÒÈÎÅÍ ÌÅ×ÏÍ ÕÇÌÕ.
 724
 725 \item ïÐÅÒÁÔÏÒ $\mathbf{.}$ ÐÒÅÄÓÔÁ×ÌÑÅÔ ÎÅËÏÍÍÕÔÁÔÉ×ÎÏÅ ÕÍÎÏÖÅÎÉÅ. $M . L$, $L . M$ É
 726 $M . N$~--- ÎÅËÏÍÍÕÔÁÔÉ×ÎÙÅ ÐÒÏÉÚ×ÅÄÅÎÉÑ, ÇÄÅ $L$~--- ÓÐÉÓÏË, Á $M$ É $N$~--- ÍÁÔÒÉÃÙ.
 727
 728 % \item $M\mathbf{\hat{ }\hat{ }}n$ is the noncommutative exponent, i.e., $M . M . \ldots . M$.
 729
 730 \item $\mathbf{transpose}(M)$~--- ÔÒÁÎÓÐÏÎÉÒÏ×ÁÎÎÁÑ ÍÁÔÒÉÃÁ $M^T$.
 731
 732 \item $\mathbf{eigenvalues}(M)$ ×ÏÚ×ÒÁÝÁÅÔ ÓÏÂÓÔ×ÅÎÎÙÅ ÚÎÁÞÅÎÉÑ $M$.
 733
 734 \item $\mathbf{eigenvectors}(M)$ ×ÏÚ×ÒÁÝÁÅÔ ÓÏÂÓÔ×ÅÎÎÙÅ ×ÅËÔÏÒÙ $M$.
 735
 736 \item $\mathbf{length}(M)$ ×ÏÚ×ÒÁÝÁÅÔ ÞÉÓÌÏ ÓÔÒÏË $M$.
 737
 738 \item $\mathbf{length}(\mathbf{transpose}(M))$ ×ÏÚ×ÒÁÝÁÅÔ ÞÉÓÌÏ ÓÔÏÌÂÃÏ× $M$.
 739
 740 \end{enumerate}
 741
 742 \subsection{íÎÏÖÅÓÔ×Á}
 743
 744 \begin{enumerate}
 745
 746 \item Maxima ÒÁÂÏÔÁÅÔ Ó Ñ×ÎÏ ÚÁÄÁÎÎÙÍÉ ËÏÎÅÞÎÙÍÉ ÍÎÏÖÅÓÔ×ÁÍÉ. íÎÏÖÅÓÔ×Á~--- ÎÅ ÔÏ
 747 ÖÅ ÓÁÍÏÅ, ÞÔÏ É ÓÐÉÓËÉ, É ÐÒÅÏÂÒÁÚÏ×ÁÎÉÅ ÍÎÏÖÅÓÔ×Á × ÓÐÉÓÏË É ÎÁÏÂÏÒÏÔ ÄÏÌÖÎÏ
 748 ÐÒÏÉÚ×ÏÄÉÔØÓÑ × Ñ×ÎÏÍ ×ÉÄÅ.
 749
 750 \item íÎÏÖÅÓÔ×Ï ÚÁÄÁÅÔÓÑ × ×ÉÄÅ
 751     $\mathbf{set}(a, b, c, \ldots)$, ÇÄÅ $a, b, c, \ldots$~--- ÅÇÏ ÜÌÅÍÅÎÔÙ.
 752
 753 \item $\mathbf{union} (A, B)$~--- ÏÂßÅÄÉÎÅÎÉÅ ÍÎÏÖÅÓÔ× $A$ É $B$.
 754
 755 \item $\mathbf{intersection} (A, B)$~--- ÐÅÒÅÓÅÞÅÎÉÅ ÍÎÏÖÅÓÔ× $A$ É $B$.
 756
 757 \item $\mathbf{cardinality} (A)$~--- ÞÉÓÌÏ ÜÌÅÍÅÎÔÏ× ÍÎÏÖÅÓÔ×Á $A$.
 758
 759 \end{enumerate}
 760
 761 \section{ôÉÐÉÞÎÙÅ ÚÁÄÁÞÉ}
 762
 763 \subsection{ïÐÒÅÄÅÌÅÎÉÅ ÆÕÎËÃÉÉ}
 764
 765 \begin{enumerate}
 766
 767 \item æÕÎËÃÉÑ ÏÐÒÅÄÅÌÑÅÔÓÑ ÏÐÅÒÁÔÏÒÏÍ $\mathbf{:=}$, ÐÒÉ ÜÔÏÍ ×ÙÞÉÓÌÅÎÉÅ ÔÅÌÁ ÆÕÎËÃÉÉ
 768 ÏÔËÌÁÄÙ×ÁÅÔÓÑ.
 769
 770 \noindent÷ ÐÒÉÍÅÒÅ ÎÉÖÅ $\mathbf{diff}$ ÐÅÒÅÓÞÉÔÙ×ÁÅÔÓÑ ÐÒÉ ËÁÖÄÏÍ ×ÙÚÏ×Å ÆÕÎËÃÉÉ.
 771 áÒÇÕÍÅÎÔ ÐÏÄÓÔÁ×ÌÑÅÔÓÑ ×ÍÅÓÔÏ $x$, É ×ÙÞÉÓÌÑÅÔÓÑ ÒÅÚÕÌØÔÉÒÕÀÝÅÅ ×ÙÒÁÖÅÎÉÅ.
 772 ëÏÇÄÁ ÁÒÇÕÍÅÎÔ ÐÒÅÄÓÔÁ×ÌÑÅÔ ÓÏÂÏÊ ÎÅÞÔÏ ÏÔÌÉÞÎÏÅ ÏÔ ÓÉÍ×ÏÌÁ, ÐÒÏÉÓÈÏÄÉÔ ÏÛÉÂËÁ:
 773 ÄÌÑ $\mathbf{foo} (1)$ Maxima ÐÙÔÁÅÔÓÑ ×ÙÞÉÓÌÉÔØ $\mathbf{diff} (\mathbf{sin}(1)^2, 1)$.
 774 % foo (x) := diff (sin(x)^2, x);
 775 % foo (u);
 776 % foo (1);
 777
 778 \begin{verbatim}
 779 (%i1) foo (x) := diff (sin(x)^2, x);
 780                                      2
 781 (%o1)              foo(x) := diff(sin (x), x)
 782 (%i2) foo (u);
 783 (%o2)                    2 cos(u) sin(u)
 784 (%i3) foo (1);
 785 Non-variable 2nd argument to diff:
 786 1
 787 #0: foo(x=1)
 788  -- an error.
 789 \end{verbatim}
 790
 791 \item $\mathbf{define}$ ÏÐÒÅÄÅÌÑÅÔ ÆÕÎËÃÉÀ É ×ÙÞÉÓÌÑÅÔ ÅÅ ÔÅÌÏ.
 792
 793 \noindent÷ ÓÌÅÄÕÀÝÅÍ ÐÒÉÍÅÒÅ $\mathbf{diff}$ ×ÙÞÉÓÌÑÅÔÓÑ ÅÄÉÎÏÖÄÙ (ÐÒÉ ÏÐÒÅÄÅÌÅÎÉÉ), ÐÏÜÔÏÍÕ
 794 $\mathbf{foo} (1)$ ÎÅ ×ÙÚÙ×ÁÅÔ ÏÛÉÂËÉ:
 795 % define (foo (x), diff (sin(x)^2, x));
 796 % foo (u);
 797 % foo (1);
 798
 799 \begin{verbatim}
 800 (%i1) define (foo (x), diff (sin(x)^2, x));
 801 (%o1)               foo(x) := 2 cos(x) sin(x)
 802 (%i2) foo (u);
 803 (%o2)                    2 cos(u) sin(u)
 804 (%i3) foo (1);
 805 (%o3)                    2 cos(1) sin(1)
 806 \end{verbatim}
 807
 808 \end{enumerate}
 809
 810 \subsection{òÅÛÅÎÉÅ ÕÒÁ×ÎÅÎÉÊ}
 811 % eq_1: a * x + b * y + z = %pi;
 812 % eq_2: z - 5*y + x = 0;
 813 % s: solve ([eq_1, eq_2], [x, z]);
 814 % length (s);
 815 % [subst (s[1], eq_1), subst (s[1], eq_2)];
 816 % ratsimp (%);
 817
 818 \begin{verbatim}
 819 (%i1) eq_1: a * x + b * y + z = %pi;
 820 (%o1)                  z + b y + a x = %pi
 821 (%i2) eq_2: z - 5*y + x = 0;
 822 (%o2)                    z - 5 y + x = 0
 823 (%i3) s: solve ([eq_1, eq_2], [x, z]);
 824                 (b + 5) y - %pi      (b + 5 a) y - %pi
 825 (%o3)   [[x = - ---------------, z = -----------------]]
 826                      a - 1                 a - 1
 827 (%i4) length (s);
 828 (%o4)                           1
 829 (%i5) [subst (s[1], eq_1), subst (s[1], eq_2)];
 830        (b + 5 a) y - %pi   a ((b + 5) y - %pi)
 831 (%o5) [----------------- - ------------------- + b y = %pi,
 832              a - 1                a - 1
 833                    (b + 5 a) y - %pi   (b + 5) y - %pi
 834                    ----------------- - --------------- - 5 y = 0]
 835                          a - 1              a - 1
 836 (%i6) ratsimp (%);
 837 (%o6)                  [%pi = %pi, 0 = 0]
 838 \end{verbatim}
 839
 840 \subsection{éÎÔÅÇÒÉÒÏ×ÁÎÉÅ É ÄÉÆÆÅÒÅÎÃÉÒÏ×ÁÎÉÅ}
 841
 842 $\mathbf{integrate}$ ×ÙÞÉÓÌÑÅÔ ÏÐÒÅÄÅÌÅÎÎÙÅ É ÎÅÏÐÒÅÄÅÌÅÎÎÙÅ ÉÎÔÅÇÒÁÌÙ:
 843 % integrate (1/(1 + x), x, 0, 1);
 844 % integrate (exp(-u) * sin(u), u, 0, inf);
 845 % assume (a > 0);
 846 % integrate (1/(1 + x), x, 0, a);
 847 % integrate (exp(-a*u) * sin(a*u), u, 0, inf);
 848 % integrate (exp (sin (t)), t, 0, %pi);
 849 % 'integrate (exp(-u) * sin(u), u, 0, inf);
 850
 851 \begin{verbatim}
 852 (%i1) integrate (1/(1 + x), x, 0, 1);
 853 (%o1)                        log(2)
 854 (%i2) integrate (exp(-u) * sin(u), u, 0, inf);
 855                                 1
 856 (%o2)                           -
 857                                 2
 858 (%i3) assume (a > 0);
 859 (%o3)                        [a > 0]
 860 (%i4) integrate (1/(1 + x), x, 0, a);
 861 (%o4)                      log(a + 1)
 862 (%i5) integrate (exp(-a*u) * sin(a*u), u, 0, inf);
 863                                 1
 864 (%o5)                          ---
 865                                2 a
 866 (%i6) integrate (exp (sin (t)), t, 0, %pi);
 867                          %pi
 868                         /
 869                         [      sin(t)
 870 (%o6)                   I    %e       dt
 871                         ]
 872                         /
 873                          0
 874 (%i7) 'integrate (exp(-u) * sin(u), u, 0, inf);
 875                        inf
 876                       /
 877                       [      - u
 878 (%o7)                 I    %e    sin(u) du
 879                       ]
 880                       /
 881                        0
 882 \end{verbatim}
 883
 884 $\mathbf{diff}$ ×ÙÞÉÓÌÑÅÔ ÐÒÏÉÚ×ÏÄÎÙÅ É ÄÉÆÆÅÒÅÎÃÉÁÌÙ:
 885 % diff (sin (y*x));
 886 % diff (sin (y*x), x);
 887 % diff (sin (y*x), y);
 888 % diff (sin (y*x), x, 2);
 889 % 'diff (sin (y*x), x, 2);
 890
 891 \begin{verbatim}
 892 (%i1) diff (sin (y*x));
 893 (%o1)         x cos(x y) del(y) + y cos(x y) del(x)
 894 (%i2) diff (sin (y*x), x);
 895 (%o2)                      y cos(x y)
 896 (%i3) diff (sin (y*x), y);
 897 (%o3)                      x cos(x y)
 898 (%i4) diff (sin (y*x), x, 2);
 899                              2
 900 (%o4)                     - y  sin(x y)
 901 (%i5) 'diff (sin (y*x), x, 2);
 902                           2
 903                          d
 904 (%o5)                    --- (sin(x y))
 905                            2
 906                          dx
 907 \end{verbatim}
 908
 909 \subsection{ðÏÓÔÒÏÅÎÉÅ ÇÒÁÆÉËÏ×}
 910
 911 $\mathbf{plot2d}$ ÓÔÒÏÉÔ Ä×ÕÍÅÒÎÙÅ ÇÒÁÆÉËÉ:
 912 % plot2d (exp(-u) * sin(u), [u, 0, 2*%pi]);
 913 % plot2d ([exp(-u), exp(-u) * sin(u)], [u, 0, 2*%pi]);
 914 % xx: makelist (i/2.5, i, 1, 10);
 915 % yy: map (lambda ([x], exp(-x) * sin(x)), xx);
 916 % plot2d ([discrete, xx, yy]);
 917 % plot2d ([discrete, xx, yy], [gnuplot_curve_styles, ["with points"]]);
 918
 919 \begin{verbatim}
 920 (%i1) plot2d (exp(-u) * sin(u), [u, 0, 2*%pi]);
 921 (%o1)
 922 (%i2) plot2d ([exp(-u), exp(-u) * sin(u)], [u, 0, 2*%pi]);
 923 (%o2)
 924 (%i3) xx: makelist (i/2.5, i, 1, 10);
 925 (%o3)  [0.4, 0.8, 1.2, 1.6, 2.0, 2.4, 2.8, 3.2, 3.6, 4.0]
 926 (%i4) yy: map (lambda ([x], exp(-x) * sin(x)), xx);
 927 (%o4) [0.261034921143457, 0.322328869227062, .2807247779692679,
 928 .2018104299334517, .1230600248057767, .0612766372619573,
 929 .0203706503896865, - .0023794587414574, - .0120913057698414,
 930 - 0.013861321214153]
 931 (%i5) plot2d ([discrete, xx, yy]);
 932 (%o5)
 933 (%i6) plot2d ([discrete, xx, yy], [gnuplot_curve_styles, ["with points"]]);
 934 (%o6)
 935 \end{verbatim}
 936
 937 óÍ. ÔÁËÖÅ $\mathbf{plot3d}$.
 938
 939 \subsection{óÏÈÒÁÎÅÎÉÅ É ÚÁÇÒÕÚËÁ ÆÁÊÌÏ×}
 940
 941 $\mathbf{save}$ ÚÁÐÉÓÙ×ÁÅÔ ×ÙÒÁÖÅÎÉÑ × ÆÁÊÌ:
 942 % a: foo - bar;
 943 % b: foo^2 * bar;
 944 % save ("my.session", a, b);
 945 % save ("my.session", all);
 946
 947 \begin{verbatim}
 948 (%i1) a: foo - bar;
 949 (%o1)                       foo - bar
 950 (%i2) b: foo^2 * bar;
 951                                    2
 952 (%o2)                       bar foo
 953 (%i3) save ("my.session", a, b);
 954 (%o3)                      my.session
 955 (%i4) save ("my.session", all);
 956 (%o4)                      my.session
 957 \end{verbatim}
 958
 959 $\mathbf{load}$ ÞÉÔÁÅÔ ×ÙÒÁÖÅÎÉÑ ÉÚ ÆÁÊÌÁ.
 960 % load ("my.session");
 961 % a;
 962 % b;
 963
 964 \begin{verbatim}
 965 (%i1) load ("my.session");
 966 (%o4)                      my.session
 967 (%i5) a;
 968 (%o5)                       foo - bar
 969 (%i6) b;
 970                                    2
 971 (%o6)                       bar foo
 972 \end{verbatim}
 973
 974 óÍ. ÔÁËÖÅ $\mathbf{stringout}$ É $\mathbf{batch}$.
 975
 976 \section{ðÒÏÇÒÁÍÍÉÒÏ×ÁÎÉÅ ÐÏÄ Maxima}
 977
 978 % dynamic scope
 979 % argument-quoting and argument-evaluating functions
 980 % directory organization: src, tests, share, doc
 981
 982 óÕÝÅÓÔ×ÕÅÔ ÏÄÎÏ ÐÒÏÓÔÒÁÎÓÔ×Ï ÉÍÅÎ, ÓÏÄÅÒÖÁÝÅÅ ×ÓÅ ÓÉÍ×ÏÌÙ Maxima. äÒÕÇÏÅ
 983 ÐÒÏÓÔÒÁÎÓÔ×Ï ÉÍÅÎ ÓÏÚÄÁÔØ ÎÅÌØÚÑ.
 984
 985 ÷ÓÅ ÐÅÒÅÍÅÎÎÙÅ ÇÌÏÂÁÌØÎÙ, ÅÓÌÉ ÎÅ ÏÐÒÅÄÅÌÅÎÙ ÌÏËÁÌØÎÏ~--- × ÆÕÎËÃÉÑÈ, ÌÑÍÂÄÁ-×ÙÒÁÖÅÎÉÑÈ
 986 É ÂÌÏËÁÈ.
 987
 988 úÎÁÞÅÎÉÅÍ ÐÅÒÅÍÅÎÎÏÊ ÓÞÉÔÁÅÔÓÑ ÔÏ, ÞÔÏ ÂÙÌÏ ÐÒÉÓ×ÏÅÎÏ × ÐÏÓÌÅÄÎÉÊ ÒÁÚ, × Ñ×ÎÏÍ ×ÉÄÅ,
 989 ÌÉÂÏ ÞÅÒÅÚ ÐÒÉÓ×ÁÉ×ÁÎÉÅ ÚÎÁÞÅÎÉÑ ÌÏËÁÌØÎÏÊ ÐÅÒÅÍÅÎÎÏÊ × ÂÌÏËÅ, ÆÕÎËÃÉÉ ÉÌÉ ÌÑÍÂÄÁ-×ÙÒÁÖÅÎÉÉ.
 990 üÔÁ ËÏÎÃÅÐÃÉÑ ÉÚ×ÅÓÔÎÁ ËÁË {\it ÄÉÎÁÍÉÞÅÓËÁÑ ÏÂÌÁÓÔØ ×ÉÄÉÍÏÓÔÉ}.
 991
 992 åÓÌÉ ÐÅÒÅÍÅÎÎÁÑ Ñ×ÌÑÅÔÓÑ ÌÏËÁÌØÎÏÊ ×ÎÕÔÒÉ ÆÕÎËÃÉÉ, ÌÑÍÂÄÁ-×ÙÒÁÖÅÎÉÑ ÉÌÉ ÂÌÏËÁ, ÅÅ
 993 ÚÎÁÞÅÎÉÅ ÌÏËÁÌØÎÏ, ÎÏ ÏÓÔÁÌØÎÙÅ Ó×ÏÊÓÔ×Á (ÚÁÄÁÎÎÙÅ $\mathbf{declare}$) ÇÌÏÂÁÌØÎÙ.
 994 æÕÎËÃÉÑ $\mathbf{local}$ ÄÅÌÁÅÔ ÐÅÒÅÍÅÎÎÕÀ ÌÏËÁÌØÎÏÊ × ÏÔÎÏÛÅÎÉÉ ×ÓÅÈ Ó×ÏÊÓÔ×.
 995
 996 ðÏ ÕÍÏÌÞÁÎÉÀ, ÏÐÒÅÄÅÌÅÎÉÅ ÆÕÎËÃÉÉ ÇÌÏÂÁÌØÎÏ, ÄÁÖÅ ÅÓÌÉ ÏÎÏ ÓÏÄÅÒÖÉÔÓÑ ×ÎÕÔÒÉ ÆÕÎËÃÉÉ,
 997 ÌÑÍÂÄÁ-×ÙÒÁÖÅÎÉÑ ÉÌÉ ÂÌÏËÁ.
 998 $\mathbf{local}(f), f(x) \mathbf{\ :=\ } \ldots$ ÓÏÚÄÁÅÔ ÌÏËÁÌØÎÏÅ ÏÐÒÅÄÅÌÅÎÉÅ ÆÕÎËÃÉÉ.
 999
1000 $\mathbf{trace}(\mathit{foo})$ ÕËÁÚÙ×ÁÅÔ Maxima ÐÅÞÁÔÁÔØ ÓÏÏÂÝÅÎÉÅ ÐÒÉ ×ÈÏÄÅ × ÆÕÎËÃÉÀ
1001 $\mathit{foo}$ É ×ÙÈÏÄÅ ÉÚ ÎÅÅ.
1002
1003 òÁÓÓÍÏÔÒÉÍ ÎÅËÏÔÏÒÙÅ ÐÒÉÍÅÒÙ ÐÒÏÇÒÁÍÍÉÒÏ×ÁÎÉÑ ÐÏÄ Maxima.
1004
1005 \begin{enumerate}
1006
1007 \item ÷ÓÅ ÐÅÒÅÍÅÎÎÙÅ ÇÌÏÂÁÌØÎÙ, ÅÓÌÉ ÎÅ ÏÐÒÅÄÅÌÅÎÙ ÌÏËÁÌØÎÏ~--- × ÆÕÎËÃÉÑÈ,
1008 ÌÑÍÂÄÁ-×ÙÒÁÖÅÎÉÑÈ É ÂÌÏËÁÈ:
1009
1010 % (x: 42, y: 1729, z: foo*bar);
1011 % f (x, y) := x*y*z;
1012 % f (aa, bb);
1013 % lambda ([x, z], (x - z)/y);
1014 % apply (%, [uu, vv]);
1015 % block ([y, z], y: 65536, [x, y, z]);
1016
1017 \begin{verbatim}
1018 (%i1) (x: 42, y: 1729, z: foo*bar);
1019 (%o1)                        bar foo
1020 (%i2) f (x, y) := x*y*z;
1021 (%o2)                   f(x, y) := x y z
1022 (%i3) f (aa, bb);
1023 (%o3)                     aa bar bb foo
1024 (%i4) lambda ([x, z], (x - z)/y);
1025                                      x - z
1026 (%o4)                 lambda([x, z], -----)
1027                                        y
1028 (%i5) apply (%, [uu, vv]);
1029                              uu - vv
1030 (%o5)                        -------
1031                               1729
1032 (%i6) block ([y, z], y: 65536, [x, y, z]);
1033 (%o6)                    [42, 65536, z]
1034 \end{verbatim}
1035
1036 \item úÎÁÞÅÎÉÅÍ ÐÅÒÅÍÅÎÎÏÊ ÓÞÉÔÁÅÔÓÑ ÔÏ, ÞÔÏ ÂÙÌÏ ÐÒÉÓ×ÏÅÎÏ × ÐÏÓÌÅÄÎÉÊ ÒÁÚ, × Ñ×ÎÏÍ ×ÉÄÅ,
1037 ÌÉÂÏ ÞÅÒÅÚ ÐÒÉÓ×ÁÉ×ÁÎÉÅ ÚÎÁÞÅÎÉÑ ÌÏËÁÌØÎÏÊ ÐÅÒÅÍÅÎÎÏÊ:
1038
1039 % foo (y) := x - y;
1040 % x: 1729;
1041 % foo (%pi);
1042 % bar (x) := foo (%e);
1043 % bar (42);
1044
1045 \begin{verbatim}
1046 (%i1) foo (y) := x - y;
1047 (%o1)                    foo(y) := x - y
1048 (%i2) x: 1729;
1049 (%o2)                         1729
1050 (%i3) foo (%pi);
1051 (%o3)                      1729 - %pi
1052 (%i4) bar (x) := foo (%e);
1053 (%o4)                   bar(x) := foo(%e)
1054 (%i5) bar (42);
1055 (%o5)                        42 - %e
1056 \end{verbatim}
1057
1058 \end{enumerate}
1059
1060 \section{Lisp É Maxima}
1061
1062 % symbols, $ and ?
1063 % defining an argument-evaluating function in lisp
1064 % defining an argument-quoting function in lisp
1065 % calling a function defined in maxima from lisp
1066 % useful lisp fcns: meval, simplifya, displa
1067
1068 \noindentúÁÐÉÓØ {\bf :lisp} $\mathit{expr}$ ×ÙÞÉÓÌÑÅÔ $\mathit{expr}$ × ÉÎÔÅÒÐÒÅÔÁÔÏÒÅ Lisp.
1069 üÔÁ ÚÁÐÉÓØ ÒÁÓÐÏÚÎÁÅÔÓÑ × ÓÔÒÏËÅ ××ÏÄÁ É ÆÁÊÌÁÈ, ÏÂÒÁÂÁÔÙ×ÁÅÍÙÈ $\mathbf{batch}$,
1070 ÎÏ ÎÅ $\mathbf{load}$.
1071
1072 óÉÍ×ÏÌ $\mathbf{foo}$ × Maxima ÓÏÏÔ×ÅÔÓÔ×ÕÅÔ ÓÉÍ×ÏÌÕ \$foo × Lisp,
1073 Á ÓÉÍ×ÏÌ Lisp foo ÓÏÏÔ×ÅÔÓ×ÕÅÔ ÓÉÍ×ÏÌÕ Maxima $\mathbf{?foo}$.
1074
1075 {\bf :lisp} $\mathrm{(}\mathbf{defun\ } \mathrm{\$foo\ (a)\ (\ldots))}$
1076 ÚÁÄÁÅÔ ÆÕÎËÃÉÀ Lisp $\mathrm{foo}$, ×ÙÞÉÓÌÑÀÝÕÀ Ó×ÏÉ ÁÒÇÕÍÅÎÔÙ.
1077 éÚ Maxima ÆÕÎËÃÉÑ ×ÙÚÙ×ÁÅÔÓÑ ÚÁÐÉÓØÀ $\mathbf{foo}(a)$.
1078
1079 {\bf :lisp} $\mathrm{(}\mathbf{defmspec\ } \mathrm{\$foo\ (e)\ (\ldots))}$
1080 ÚÁÄÁÅÔ ÆÕÎËÃÉÀ Lisp $\mathbf{foo}$, ÏÔËÌÁÄÙ×ÁÀÝÕÀ ×ÙÞÉÓÌÅÎÉÅ ÁÒÇÕÍÅÎÔÏ×.
1081 éÚ Maxima ÆÕÎËÃÉÑ ×ÙÚÙ×ÁÅÔÓÑ ÚÁÐÉÓØÀ $\mathbf{foo}(a)$.
1082 áÒÇÕÍÅÎÔÁÍÉ $\mathrm{\$foo}$ Ñ×ÌÑÀÔÓÑ $(\mathbf{cdr\ } e)$, Á
1083 $(\mathbf{caar\ } e)$ ×ÓÅÇÄÁ ÓÏ×ÐÁÄÁÅÔ Ó $\mathrm{\$foo}$.
1084
1085 úÁÐÉÓØ $(\mathbf{mfuncall\ '\$}\mathrm{foo\ }a_1 \ldots a_n)$
1086 ×ÙÚÙ×ÁÅÔ ÉÚ Lisp ÆÕÎËÃÉÀ $\mathbf{foo}$, ÏÐÒÅÄÅÌÅÎÎÕÀ × Maxima.
1087
1088 ïÂÒÁÔÉÍÓÑ Ë Lisp ÉÚ Maxima É ÎÁÏÂÏÒÏÔ.
1089
1090 \begin{enumerate}
1091
1092 \item úÁÐÉÓØ {\bf :lisp} $\mathit{expr}$ ×ÙÞÉÓÌÑÅÔ $\mathit{expr}$ × ÉÎÔÅÒÐÒÅÔÁÔÏÒÅ Lisp:
1093
1094 % (aa + bb)^2;
1095 % :lisp $%
1096 \begin{verbatim}
1097 (%i1) (aa + bb)^2;
1098                                     2
1099 (%o1)                      (bb + aa)
1100 (%i2) :lisp $%
1101 ((MEXPT SIMP) ((MPLUS SIMP) $AA $BB) 2)
1102 \end{verbatim}
1103
1104 \item {\bf :lisp} $\mathrm{(}\mathbf{defun\ } \mathrm{\$foo\ (a)\ (\ldots))}$
1105 ÚÁÄÁÅÔ ÆÕÎËÃÉÀ Lisp $\mathrm{foo}$, ×ÙÞÉÓÌÑÀÝÕÀ Ó×ÏÉ ÁÒÇÕÍÅÎÔÙ:
1106
1107 % :lisp (defun $foo (a b) `((mplus) ((mtimes) ,a ,b) $%pi))
1108 % (p: x + y, q: x - y);
1109 % foo (p, q);
1110 \begin{verbatim}
1111 (%i1) :lisp (defun $foo (a b) `((mplus) ((mtimes) ,a ,b) $%pi))
1112 $FOO
1113 (%i1) (p: x + y, q: x - y);
1114 (%o1)                         x - y
1115 (%i2) foo (p, q);
1116 (%o2)                 (x - y) (y + x) + %pi
1117 \end{verbatim}
1118
1119 \item {\bf :lisp} $\mathrm{(}\mathbf{defmspec\ } \mathrm{\$foo\ (e)\ (\ldots))}$
1120 ÚÁÄÁÅÔ ÆÕÎËÃÉÀ Lisp $\mathbf{foo}$, ÏÔËÌÁÄÙ×ÁÀÝÕÀ ×ÙÞÉÓÌÅÎÉÅ ÁÒÇÕÍÅÎÔÏ×:
1121
1122 % :lisp (defmspec $bar (e) (let ((a (cdr e))) `((mplus) ((mtimes) ,@a) $%pi)))
1123 % bar (p, q);
1124 % bar (''p, ''q);
1125 \begin{verbatim}
1126 (%i1) :lisp (defmspec $bar (e) (let ((a (cdr e))) `((mplus) ((mtimes) ,@a) $%pi)))
1127 #<CLOSURE LAMBDA (E) (LET ((A (CDR E))) `((MPLUS) ((MTIMES) ,@A) $%PI))>
1128 (%i1) bar (p, q);
1129 (%o1)                       p q + %pi
1130 (%i2) bar (''p, ''q);
1131 (%o2)                       p q + %pi
1132 \end{verbatim}
1133
1134 \item úÁÐÉÓØ $(\mathbf{mfuncall\ '\$}\mathrm{foo\ }a_1 \ldots a_n)$
1135 ×ÙÚÙ×ÁÅÔ ÉÚ Lisp ÆÕÎËÃÉÀ $\mathbf{foo}$, ÏÐÒÅÄÅÌÅÎÎÕÀ × Maxima:
1136
1137 % blurf (x) := x^2;
1138 % :lisp (displa (mfuncall '$blurf '((mplus) $grotz $mumble)))
1139 \begin{verbatim}
1140 (%i1) blurf (x) := x^2;
1141                                       2
1142 (%o1)                    blurf(x) := x
1143 (%i2) :lisp (displa (mfuncall '$blurf '((mplus) $grotz $mumble)))
1144                 2
1145 (mumble + grotz)
1146 NIL
1147 \end{verbatim}
1148
1149 \end{enumerate}
1150
1151 \end{document}