Maxima - руководство на русском языке

A numeral-число may be (может быть) the first-первым character-символом of an

identifier-идентификатора if it is preceded-предшествует by a backslash. Numerals which are

the second or later characters need not be preceded by a backslash-обратный_слэш.

Characters may be declared alphabetic by the declare function. If so declared, they need

not be preceded-предшествовать by a backslash-обратный_слэш in an identifier. The

alphabetic characters are initially A through Z, a through-через z, %, and _.

Maxima is case-sensitive-РЕГИСТРОЗАВИСИМАЯ!!!. The identifiers foo, FOO, and Foo

are distinct-разные. See Lisp and Maxima for more on this point.

A Maxima identifier is a Lisp symbol which begins with a dollar sign $. Any other Lisp

symbol is preceded-предшествуют by a question mark ? when it appears in Maxima. See Lisp

and Maxima for more on this point.

Примеры:

(%i1) %an_ordinary_identifier42;

(%o1) %an_ordinary_identifier42

(%i2) embedded\ spaces\ in\ an\ identifier;

(%o2) embedded spaces in an identifier

(%i3) symbolp (%);

(%o3) true

(%i4) [foo+bar, foo\+bar];

(%o4) [foo+bar,foo+bar]

(%i5) [1729, \1729];

(%o5) [1729,1729]

(%i6) [symbolp (foo\+bar), symbolp (\1729)];

(%o6) [true,true]

(%i7) [is (foo\+bar = foo+bar), is (\1729 = 1729)];

(%o7) [false,false]

(%i8) baz\~quux;

(%o8) baz~quux

(%i9) declare ("~", alphabetic);

(%o9) done

(%i10) baz~quux;

(%o10) baz~quux

(%i11) [is (foo = FOO), is (FOO = Foo), is (Foo = foo)];

(%o11) [false,false,false]

(%i12) :lisp (defvar *my-lisp-variable* '$foo);

*MY-LISP-VARIABLE*

(%i12) ?\*my\-lisp\-variable\*;

(%o12) foo

8.6 Strings - Строки

Strings (quoted-закавыченные character-символьные sequences-последовательности)

are enclosed-заключённые in double-двойные quote-кавычки marks-маркеры " for input, and

displayed-дисплеятся with or without the quote marks, depending-в_зависимости on the

global variable stringdisp.

Strings may contain-содержать any characters, including embedded tab, newline, and

carriage return characters. The sequence \" is recognized-понимается as a literal double

quote, and \\ as a literal backslash (то есть когда надо изобразить в тексте двойную кавычку

или обратный слэш – экранирование символа). When backslash appears at the end of a

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line-строки, то the backslash and the line-строки termination-завершение (either newline or

carriage return and newline) are ignored-игнорировать, so that the string-строка continues-

продолжается with the next line-линии. No other special combinations of backslash with

another character are recognized; when backslash appears before-до any character other than

", \, or a line termination, the backslash is ignored-игнорируется. There is no way to represent-

представить a special character (such as tab, newline, or carriage return) except-

за_исключением by embedding the literal character in the string.

There is no character type in Maxima (это не типично для Maxima); a single character is

represented-представлен as a one-character string.

Maxima strings are implemented-осуществлены as Lisp symbols, not Lisp strings; that

may change in a future version of Maxima. Maxima can display Lisp strings and Lisp characters,

although-хотя some other operations (for example, equality tests) may fail-сбоить.

The stringproc add-on package contains many functions for working with strings.

Примеры:

(%i1) s_1 : "This is a Maxima string.";

(%o1) This is a Maxima string.

(%i2) s_2 : "Embedded \"double quotes\" and backslash \\ characters.";

(%o2) Embedded "double quotes" and backslash \ characters.

(%i3) s_3 : "Embedded line termination

in this string.";

(%o3) Embedded line termination

in this string.

(%i4) s_4 : "Ignore the \line termination \

characters in \

this string.";

(%o4) Ignore the line termination characters in this string.

(%i5) stringdisp : false;

(%o5) false

(%i6) s_1;

(%o6) This is a Maxima string.

(%i7) stringdisp : true;

(%o7) true

(%i8) s_1;

(%o8) "This is a Maxima string."

8.7 Inequality - Неравенства

Maxima has-имеет the inequality operators <, <=, >=, >, #, and notequal. See-смотри

if for-для a description-описания of conditional-условий expressions-выражений.

8.8 Syntax - Синтаксис

It is possible to define new operators with specified precedence-предшествование, to

undefine-переопределить existing operators, or to redefine the precedence of existing

operators. An operator may be unary prefix or unary postfix, binary infix, n-ary infix,

matchfix, or nofix. "Matchfix" means-средства a pair-сравнение of symbols which enclose-

заключены their argument or arguments, and "nofix" means-средство an operator which takes-

берёт no arguments. As examples of the different types of operators, there are the following.

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Примеры:

unary prefix

negation - a

unary postfix

factorial a!

binary infix

exponentiation a^b

n-ary infix

addition a + b

matchfix

list construction [a, b]

(There are no built-in nofix operators; for an example of such an operator, see nofix.)

The mechanism to define a new operator is straightforward-напрямую. It is only

necessary to declare a function as an operator; the operator function might or might not be

defined.

An example of user-defined (определенный пользователем) operators is the following.

Note-заметьте that the explicit-явно function call "dd" (a) is equivalent to dd a, likewise "<-" (a,

b) is equivalent to a <- b. Note also that the functions "dd" and "<-" are undefined in this

example.

Пример (корректен в консоли maxima, но не в графической wmaxima!):

(%i1) prefix ("dd");

(%o1) dd

(%i2) dd a;

(%o2) dd a

(%i3) "dd" (a);

(%o3) dd a

(%i4) infix ("<-");

(%o4) <-

(%i5) a <- dd b;

(%o5) a <- dd b

(%i6) "<-" (a, "dd" (b));

(%o6) a <- dd b

The Maxima functions which define new operators are summarized in this table, stating-

объявлены the default left and right binding-закреплённый powers (lbp and rbp,

respectively-соответственно). (Binding power determines operator precedence-

предшествование. However-однако, since-поскольку left and right binding powers can differ,

binding power is somewhat-несколько more complicated-сложный than precedence-

предшествование .) Some of the operation definition functions take-берут additional

arguments; see the function descriptions for details.

prefix

rbp=180

postfix

lbp=180

infix

lbp=180, rbp=180

nary

lbp=180, rbp=180

matchfix

(binding power not applicable)

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nofix

(binding power not applicable)

For comparison (для сравнения), here are some built-in operators and their left and right

binding powers.

Operator lbp rbp

: 180 20

:: 180 20

:= 180 20

::= 180 20

! 160

!! 160

^ 140 139

. 130 129

* 120

/ 120 120

+ 100 100

- 100 134

= 80 80

# 80 80

> 80 80

>= 80 80

< 80 80

<= 80 80

not 70

and 65

or 60

, 10

$ -1

; -1

Функции remove and kill remove operator properties from an atom. Например,

remove("a",op) removes only the operator properties of a. Функция kill("a") removes

all properties of a, including the operator properties-свойства. Note-заметьте that the name of

the operator must be enclosed-заключено in quotation marks (кавычки).

Примеры:

(%i1) infix ("##");

(%o1) ##

(%i2) "##" (a, b) := a^b;

b

(%o2) a ## b := a

(%i3) 5 ## 3;

(%o3) 125

(%i4) remove ("##", op);

(%o4) done

(%i5) 5 ## 3;

Incorrect syntax: # is not a prefix operator

5Space##

^

(%i5) "##" (5, 3);

(%o5) 125

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(%i6) infix ("##");

(%o6) ##

(%i7) 5 ## 3;

(%o7) 125

(%i8) kill ("##");

(%o8) done

(%i9) 5 ## 3;

Incorrect syntax: # is not a prefix operator

Space5Space##

^

(%i9) "##" (5, 3);

(%o9) ##(5, 3)

8.9 Functions and Variables for Expressions - Функции и переменные

Функция: at (expr, [eqn_1, ..., eqn_n])

Функция: at (expr, eqn)

Evaluates-вычисления the expression-выражения expr with the variables assuming-

принимающие the values-значения as specified for them in the list-списке of equations

[eqn_1, ..., eqn_n] or the single-одиночное equation-уравнение eqn.

If a subexpression depends on any of the variables for which a value is specified but there

is no atvalue specified and it can't be otherwise-иначе evaluated, then a noun-

существительная form функции of the at is returned which displays in a two-dimensional

form.

Функция at carries out (выполняет) multiple substitutions-замены in series-рядах, not

parallel.

See also atvalue. For other functions which carry out substitutions, see also функции

subst and ev.

Примеры (лучше в КОНСОЛИ):

(%i1) atvalue (f(x,y), [x = 0, y = 1], a^2);

2

(%o1) a

(%i2) atvalue ('diff (f(x,y), x), x = 0, 1 + y);

(%o2) @2 + 1

(%i3) printprops (all, atvalue);

!

d !

--- (f(@1, @2))! = @2 + 1

d@1 !

!@1 = 0

2

f(0, 1) = a

(%o3) done

(%i4) diff (4*f(x, y)^2 - u(x, y)^2, x);

d d

(%o4) 8 f(x, y) (-- (f(x, y))) - 2 u(x, y) (-- (u(x, y)))

dx dx

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(%i5) at (%, [x = 0, y = 1]);

!

2 d !

(%o5) 16 a - 2 u(0, 1) (-- (u(x, y))! )

dx !

!x = 0, y = 1

Функция: box (expr)

Функция: box (expr, a)

Returns expr enclosed in a box. The return value is an expression with box as the

operator and expr as the argument. A box is drawn on the display when display2d is true.

Функция box(expr,a) encloses expr in a box labelled by the symbol a. The label is

truncated-обрезанный if it is longer than the width of the box.

Функция box evaluates its argument. However, a boxed expression does not evaluate to

its content, so boxed expressions are effectively excluded from computations.

boxchar is the character used to draw the box in box and in the dpart and lpart

functions.

Примеры (только в КОНСОЛИ):

(%i1) box (a^2 + b^2);

"""""""""

" 2 2"

(%o1) "b + a "

"""""""""

(%i2) a : 1234;

(%o2) 1234

(%i3) b : c - d;

(%o3) c - d

(%i4) box (a^2 + b^2);

""""""""""""""""""""

" 2 "

(%o4) "(c - d) + 1522756"

""""""""""""""""""""

(%i5) box (a^2 + b^2, term_1);

term_1""""""""""""""

" 2 "

(%o5) "(c - d) + 1522756"

""""""""""""""""""""

(%i6) 1729 - box (1729);

""""""

(%o6) 1729 - "1729"

""""""

(%i7) boxchar: "-";

(%o7) -

(%i8) box (sin(x) + cos(y));

-----------------

(%o8) -cos(y) + sin(x)-

-----------------

Option variable: boxchar

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Default value: "

boxchar is the character used to draw the box in the box and in the dpart and lpart

functions.

All boxes in an expression are drawn with the current value of boxchar; the drawing

character is not stored (не сохраняется) with the box expression.

Функция: carg(z)

Returns the complex argument of z. The complex argument is an angle-угол theta-тэта in

(-%pi, %pi] such that r exp (theta %i) = z where r is the magnitude-величина of z.

carg is a computational function, not a simplifying function.

carg ignores-игнорирует the declaration declare (x, complex), and treats-

трактует x as a real variable. This is a bug.

See also abs (complex magnitude), polarform, rectform, realpart, and imagpart.

Примеры (в КОНСОЛИ):

(%i1) carg (1);

(%o1) 0

(%i2) carg (1 + %i);

%pi

(%o2) ---

4

(%i3) carg (exp (%i));

(%o3) 1

(%i4) carg (exp (%pi * %i));

(%o4) %pi

(%i5) carg (exp (3/2 * %pi * %i));

%pi

(%o5) - ---

2

(%i6) carg (17 * exp (2 * %i));

(%o6) 2

Special operator: constant

declare(a,constant) declares a to be a constant. See declare.

Функция: constantp (expr)

Returns true if expr is a constant expression, otherwise-иначе returns false.

An expression is considered-рассматривается a constant expression if its arguments are

numbers (including rational numbers, as displayed with /R/), symbolic constants such as %pi,

%e, and %i, variables bound to a constant or declared constant by declare, or functions whose-

чей arguments are constant.

Функция constantp evaluates its arguments.

Примеры (в КОНСОЛИ):

(%i1) constantp (7 * sin(2));

(%o1) true

(%i2) constantp (rat (17/29));

(%o2) true

(%i3) constantp (%pi * sin(%e));

(%o3) true

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(%i4) constantp (exp (x));

(%o4) false

(%i5) declare (x, constant);

(%o5) done

(%i6) constantp (exp (x));

(%o6) true

(%i7) constantp (foo (x) + bar (%e) + baz (2));

(%o7) false

(%i8)

Функция: declare (a_1, p_1, a_2, p_2, ...)

Assigns the atom or list of atoms a_i the property or list of properties p_i. When a_i

and/or p_i are lists, each of the atoms gets all of the properties.

declare quotes its arguments. declare always returns done.

As noted in the description for each declaration flag, for some flags featurep(object,

feature) returns true if object has been declared to have feature. However, featurep does not

recognize some flags; this is a bug.

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