Maxima - руководство на русском языке
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The user can modify these variables, either to replace the default values or to append
additional directories. For example,
file_search_maxima:["/usr/local/foo/###.mac", "/usr/local/bar/###.mac"]$
replaces the default value of file_search_maxima, while
file_search_maxima:append(file_search_maxima,["/usr/local/foo/###.mac",
"/usr/local/bar/###.mac"])$
appends two additional directories. It may be convenient to put such an expression in the
file maxima-init.mac so that the file search path is assigned automatically when Maxima starts.
Multiple filename extensions and multiple paths can be specified by special "wildcard"
constructions. The string ### expands into the sought-after name, while a comma-separated list
enclosed in curly braces {foo,bar,baz} expands into multiple strings. For example, supposing the
sought-after name is neumann,
"/home/{wfs,gcj}/###.{lisp,mac}"
expands into /home/wfs/neumann.lisp, /home/gcj/neumann.lisp, /home/wfs/neumann.mac,
and /home/gcj/neumann.mac.
Функция: file_type (filename)
Returns a guess about the content of filename, based on the filename extension.
filename need not refer to an actual file; no attempt is made to open the file and inspect the
content.
The return value is a symbol, either object, lisp, or maxima. If the extension starts with m
or d, file_type returns maxima. If the extension starts with l, file_type returns lisp. If none of
the above, file_type returns object.
Функция: grind (expr)
Option variable: grind
The function grind prints expr to the console in a form suitable for input to Maxima.
grind always returns done.
When expr is the name of a function or macro, grind prints the function or macro
definition instead-вместо of just the name.
See also string, which returns a string instead of printing its output. grind attempts to
print the expression in a manner which makes it slightly easier to read than the output of string.
When the variable grind is true, the output of string and stringout has the same format
as that of grind; otherwise no attempt is made to specially format the output of those functions.
The default value of the variable grind is false.
grind can also be specified as an argument of playback. When grind is present,
playback prints input expressions in the same format as the grind function. Otherwise, no
attempt is made to specially format input expressions.
grind evaluates its argument.
Примеры:
(%i1) aa + 1729;
(%o1) aa + 1729
(%i2) grind (%);
aa+1729$
(%o2) done
(%i3) [aa, 1729, aa + 1729];
(%o3) [aa, 1729, aa + 1729]
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(%i4) grind (%);
[aa,1729,aa+1729]$
(%o4) done
(%i5) matrix ([aa, 17], [29, bb]);
[ aa 17 ]
(%o5) [ ]
[ 29 bb ]
(%i6) grind (%);
matrix([aa,17],[29,bb])$
(%o6) done
(%i7) set (aa, 17, 29, bb);
(%o7) {17, 29, aa, bb}
(%i8) grind (%);
{17,29,aa,bb}$
(%o8) done
(%i9) exp (aa / (bb + 17)^29);
aa
-----------
29
(bb + 17)
(%o9) %e
(%i10) grind (%);
%e^(aa/(bb+17)^29)$
(%o10) done
(%i11) expr: expand ((aa + bb)^10);
10 9 2 8 3 7 4 6
5 5
(%o11) bb + 10 aa bb + 45 aa bb + 120 aa bb + 210 aa bb +
252 aa bb
6 4 7 3 8 2
9 10
+ 210 aa bb + 120 aa bb + 45 aa bb + 10
aa bb + aa
(%i12) grind (expr);
bb^10+10*aa*bb^9+45*aa^2*bb^8+120*aa^3*bb^7+210*aa^4*bb^6+252*aa^5
*bb^5
+210*aa^6*bb^4+120*aa^7*bb^3+45*aa^8*bb^2+10*aa^9*bb+aa^10$
(%o12) done
(%i13) string (expr);
(%o13)
bb^10+10*aa*bb^9+45*aa^2*bb^8+120*aa^3*bb^7+210*aa^4*bb^6+252*aa^5*bb^
5\
+210*aa^6*bb^4+120*aa^7*bb^3+45*aa^8*bb^2+10*aa^9*bb+aa^10
(%i14) cholesky (A):= block ([n : length (A), L : copymatrix (A),
p : makelist (0, i, 1, length (A))], for i thru n do
for j : i thru n do
(x : L[i, j], x : x - sum (L[j, k] * L[i, k], k, 1, i - 1),
if i = j then p[i] : 1 / sqrt(x) else L[j, i] : x * p[i]),
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for i thru n do L[i, i] : 1 / p[i],
for i thru n do for j : i + 1 thru n do L[i, j] : 0, L)$
Warning - you are redefining the Maxima function cholesky
(%i15) grind (cholesky);
cholesky(A):=block([n:length(A),L:copymatrix(A),p:makelist(0,i,1,l
ength(A))],
for i thru n do
(for j from i thru n do
(x:L[i,j],x:x-sum(L[j,k]*L[i,k],k,1,i-1),
if i = j then p[i]:1/sqrt(x) else
L[j,i]:x*p[i])),
for i thru n do L[i,i]:1/p[i],
for i thru n do (for j from i+1 thru n do L[i,j]:0),L)$
(%o15) done
(%i16) string (fundef (cholesky));
(%o16)
cholesky(A):=block([n:length(A),L:copymatrix(A),p:makelist(0,i,1,lengt
h\
(A))],for i thru n do (for j from i thru n do (x:L[i,j],x:x-
sum(L[j,k]*L[i,k],\
k,1,i-1),if i = j then p[i]:1/sqrt(x) else L[j,i]:x*p[i])),for i
thru n do L[i\
,i]:1/p[i],for i thru n do (for j from i+1 thru n do L[i,j]:0),L)
Option variable: ibase
Default value: 10
Integers entered into Maxima are interpreted with respect to the base ibase.
ibase may be assigned any integer between 2 and 35 (decimal), inclusive-
включительно. When ibase is greater than 10, the numerals comprise the decimal numerals 0
through 9 plus capital letters of the alphabet A, B, C, ..., as needed. The numerals for base 35,
the largest acceptable base, comprise 0 through 9 and A through Y.
See also obase.
Option variable: inchar
Default value: %i
inchar is the prefix of the labels of expressions entered by the user. Maxima
automatically constructs a label for each input expression by concatenating inchar and
linenum. inchar may be assigned any string or symbol, not necessarily a single character.
See also labels.
Функция: ldisp (expr_1, ..., expr_n)
Displays expressions expr_1, ..., expr_n to the console as printed output. ldisp assigns
an intermediate expression label to each argument and returns the list of labels.
See also disp.
Примеры:
(%i1) e: (a+b)^3;
3
(%o1) (b + a)
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(%i2) f: expand (e);
3 2 2 3
(%o2) b + 3 a b + 3 a b + a
(%i3) ldisp (e, f);
3
(%t3) (b + a)
3 2 2 3
(%t4) b + 3 a b + 3 a b + a
(%o4) [%t3, %t4]
(%i5) %t3;
3
(%o5) (b + a)
(%i6) %t4;
3 2 2 3
(%o6) b + 3 a b + 3 a b + a
Функция: ldisplay (expr_1, ..., expr_n)
Displays expressions expr_1, ..., expr_n to the console as printed output. Each expression
is printed as an equation of the form lhs = rhs in which lhs is one of the arguments of
ldisplay and rhs is its value. Typically each argument is a variable. ldisp assigns an
intermediate expression label to each equation and returns the list of labels.
See also display.
Примеры:
(%i1) e: (a+b)^3;
3
(%o1) (b + a)
(%i2) f: expand (e);
3 2 2 3
(%o2) b + 3 a b + 3 a b + a
(%i3) ldisplay (e, f);
3
(%t3) e = (b + a)
3 2 2 3
(%t4) f = b + 3 a b + 3 a b + a
(%o4) [%t3, %t4]
(%i5) %t3;
3
(%o5) e = (b + a)
(%i6) %t4;
3 2 2 3
(%o6) f = b + 3 a b + 3 a b + a
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Option variable: linechar
Default value: %t
linechar is the prefix of the labels of intermediate expressions generated by Maxima.
Maxima constructs a label for each intermediate expression (if displayed) by concatenating
linechar and linenum. linechar may be assigned any string or symbol, not necessarily a
single character.
Intermediate expressions might or might not be displayed. See programmode and
labels.
Option variable: linel
Default value: 79
linel is the assumed width (in characters) of the console display for the purpose of
displaying expressions. linel may be assigned any value by the user, although very small or
very large values may be impractical-непрактично. Text printed by built-in Maxima functions,
such as error messages and the output of describe, is not affected by linel.
Option variable: lispdisp
Default value: false
When lispdisp is true, Lisp symbols are displayed with a leading question mark ?.
Otherwise-иначе, Lisp symbols are displayed with no leading-предществующей mark.
Примеры:
(%i1) lispdisp: false$
(%i2) ?foo + ?bar;
(%o2) foo + bar
(%i3) lispdisp: true$
(%i4) ?foo + ?bar;
(%o4) ?foo + ?bar
Функция: load (filename)
Evaluates expressions in filename, thus bringing variables, functions, and other objects
into Maxima. The binding of any existing object is clobbered by the binding recovered from
filename. To find the file, load calls file_search with file_search_maxima and
file_search_lisp as the search directories. If load succeeds, it returns the name of the file.
Otherwise load prints an error message.
load works equally well for Lisp code and Maxima code. Files created by save,
translate_file, and compile_file, which create Lisp code, and stringout, which creates Maxima
code, can all be processed by load. load calls loadfile to load Lisp files and batchload to load
Maxima files.
load does not recognize :lisp constructs in Maxima files, and while processing filename,
the global variables _, __, %, and %th have whatever bindings they had when load was called.
See also loadfile, batch, batchload, and demo. loadfile processes Lisp files;
batch, batchload, and demo process Maxima files.
See file_search for more detail about the file search mechanism.
load evaluates its argument.
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Функция: loadfile (filename)
Evaluates Lisp expressions in filename. loadfile does not invoke file_search, so
filename must include the file extension and as much of the path as needed to find the file.
loadfile can process files created by save, translate_file, and compile_file.
The user may find it more convenient to use load instead of loadfile.
Option variable: loadprint
Default value: true
loadprint tells whether to print a message when a file is loaded.
When loadprint is true, always print a message.
When loadprint is 'loadfile, print a message only if a file is loaded by the function
loadfile.
When loadprint is 'autoload, print a message only if a file is automatically loaded. See
setup_autoload.
When loadprint is false, never print a message.
Option variable: obase
Default value: 10
obase is the base for integers displayed by Maxima.
obase may be assigned any integer between 2 and 35 (decimal), inclusive-
включительно. When obase is greater than 10, the numerals comprise the decimal numerals 0
through 9 plus capital letters of the alphabet A, B, C, ..., as needed. The numerals for base 35,
the largest acceptable base, comprise 0 through 9, and A through Y.
See also ibase.
Option variable: outchar
Default value: %o
outchar is the prefix of the labels of expressions computed by Maxima. Maxima
automatically constructs a label for each computed expression by concatenating outchar and
linenum. outchar may be assigned any string or symbol, not necessarily a single character.
Пример:
(%i1) outchar: "output";
(output1) output
(%i2) expand ((a+b)^3);
3 2 2 3
(output2) b + 3 a b + 3 a b + a
(%i3)
See also labels.
Option variable: packagefile
Default value: false
Package designers who use save or translate to create packages (files) for others to use
may want to set packagefile: true to prevent information from being added to Maxima's
information-lists (e.g. values, functions) except where necessary when the file is loaded in. In
this way, the contents of the package will not get in the user's way when he adds his own data.
Note that this will not solve the problem of possible name conflicts. Also note that the flag simply
affects what is output to the package file. Setting the flag to true is also useful for creating
Maxima init files.
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Option variable: pfeformat
Default value: false
When pfeformat is true, a ratio of integers (целые дроби) is displayed with the solidus
(forward slash) character, and an integer denominator n is displayed as a leading multiplicative
term 1/n. Когда false, то наоборот.
Примеры:
(%i1) pfeformat: false$
(%i2) 2^16/7^3;
65536
(%o2) -----
343
(%i3) (a+b)/8;
b + a
(%o3) -----
8
(%i4) pfeformat: true$
(%i5) 2^16/7^3;
(%o5) 65536/343
(%i6) (a+b)/8;
(%o6) 1/8 (b + a)
Функция: print (expr_1, ..., expr_n)
Evaluates and displays expr_1, ..., expr_n one after another, from left to right, starting at
the left edge of the console display.
The value returned by print is the value of its last argument. Функция print does not
generate intermediate expression labels.
See also display, disp, ldisplay, and ldisp. Those functions display one
expression per line, while print attempts to display two or more expressions per line.
To display the contents of a file, see printfile.
Примеры:
(%i1) r: print ("(a+b)^3 is", expand ((a+b)^3), "log (a^10/b) is",
radcan (log (a^10/b)))$
3 2 2 3
(a+b)^3 is b + 3 a b + 3 a b + a log (a^10/b) is 10 log(a) -
log(b)
(%i2) r;
(%o2) 10 log(a) - log(b)
(%i3) disp ("(a+b)^3 is", expand ((a+b)^3), "log (a^10/b) is",
radcan (log (a^10/b)))$
(a+b)^3 is
3 2 2 3
b + 3 a b + 3 a b + a
log (a^10/b) is
10 log(a) - log(b)
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Функция: tcl_output (list, i0, skip)
Функция: tcl_output (list, i0)
Функция: tcl_output ([list_1, ..., list_n], i)
Prints elements of a list enclosed by curly braces { }, suitable as part of a program in the
Tcl/Tk language.
tcl_output (list, i0, skip) prints list, beginning with element i0 and printing elements i0 +
skip, i0 + 2 skip, etc.
tcl_output (list, i0) is equivalent to tcl_output (list, i0, 2).
tcl_output ([list_1, ..., list_n], i) prints the i'th elements of list_1, ..., list_n.
Примеры:
(%i1) tcl_output ([1, 2, 3, 4, 5, 6], 1, 3)$
{1.000000000 4.000000000
}
(%i2) tcl_output ([1, 2, 3, 4, 5, 6], 2, 3)$
{2.000000000 5.000000000
}
иногда с ошибками...
Функция: read (expr_1, ..., expr_n)
Prints expr_1, ..., expr_n, then reads one expression from the console and returns the
evaluated expression. The expression is terminated with a semicolon ; or dollar sign $.
Аналогична Input в Visual Basic.
See also readonly.
Примеры:
(%i1) foo: 42$
(%i2) foo: read ("foo is", foo, " -- enter new value.")$
foo is 42 -- enter new value.
(a+b)^3;
(%i3) foo;
3
(%o3) (b + a)
Функция: readonly (expr_1, ..., expr_n)
Prints expr_1, ..., expr_n, then reads one expression from the console and returns the
expression (without evaluation). The expression is terminated with a ; (semicolon) or $ (dollar
sign). Аналогична Input в Visual Basic. See also read.
Примеры
(%i1) aa: 7$
(%i2) foo: readonly ("Enter an expression:");
Enter an expression:
2^aa;
aa
(%o2) 2
(%i3) foo: read ("Enter an expression:");
Enter an expression:
2^aa;
(%o3) 128 /* хм...??? */
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Функция: reveal (expr, depth)
Replaces parts of expr at the specified integer depth with descriptive-описательным
summaries-резюме.
Sums-суммы and differences-разности are replaced by sum(n) where n is the number of
operands of the sum.
Products-произведения are replaced by product(n) where n is the number of operands of
the product.
Exponentials-экспоненты are replaced by expt.
Quotients-скобки are replaced by quotient.
Unary negation (унарный знак МИНУС) is replaced by negterm.
When depth is greater than or equal to the maximum depth of expr, reveal (expr,
depth) returns expr unmodified.
reveal evaluates its arguments. reveal returns the summarized expression.
Пример:
(%i1) e: expand ((a - b)^2)/expand ((exp(a) + exp(b))^2);
2 2
b - 2 a b + a
(%o1) -------------------------
b + a 2 b 2 a
2 %e + %e + %e
(%i2) reveal (e, 1);
(%o2) quotient /* коэффициент */
(%i3) reveal (e, 2);
sum(3)
(%o3) ------
sum(3)
(%i4) reveal (e, 3);
expt + negterm + expt
(%o4) ------------------------
product(2) + expt + expt
(%i5) reveal (e, 4);
2 2
b - product(3) + a
(%o5) ------------------------------------
product(2) product(2)
2 expt + %e + %e
(%i6) reveal (e, 5);
2 2
b - 2 a b + a
(%o6) --------------------------
sum(2) 2 b 2 a
2 %e + %e + %e
(%i7) reveal (e, 6);
2 2
b - 2 a b + a
(%o7) -------------------------
b + a 2 b 2 a
2 %e + %e + %e
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Option variable: rmxchar /* знак правой квадр. скобки */
Default value: ]
rmxchar is the character drawn on the right-hand side of a matrix.
See also lmxchar.
Функция: save (filename, name_1, name_2, name_3, ...)
Функция: save (filename, values, functions, labels, ...)
Функция: save (filename, [m, n])
Функция: save (filename, name_1=expr_1, ...)
Функция: save (filename, all)
Функция: save (filename, name_1=expr_1, name_2=expr_2, ...)
Stores the current values of name_1, name_2, name_3, ..., in filename. The arguments
are the names of variables, functions, or other objects. If a name has no value or function
associated with it, it is ignored. save returns filename.
save stores data in the form of Lisp expressions. The data stored by save may be
recovered by load (filename).
The global flag file_output_append governs whether save appends or truncates the
output file. When file_output_append is true, save appends to the output file. Otherwise,
save truncates the output file. In either case, save creates the file if it does not yet exist.
The special form save (filename, values, functions, labels, ...) stores
the items named by values, functions, labels, etc. The names may be any specified by the
variable infolists. values comprises all user-defined variables.
The special form save (filename, [m, n]) stores the values of input and output
labels m through n. Note that m and n must be literal integers. Input and output labels may also
be stored one by one, e.g., save ("foo.1", %i42, %o42). save (filename, labels) stores
all input and output labels. When the stored labels are recovered, they clobber existing labels.
The special form save (filename, name_1=expr_1, name_2=expr_2, ...)
stores the values of expr_1, expr_2, ..., with names name_1, name_2, .... It is useful to apply
this form to input and output labels, e.g., save ("foo.1", aa=%o88). The right-hand side of the
equality in this form may be any expression, which is evaluated. This form does not introduce
the new names into the current Maxima environment, but only stores them in filename.
These special forms and the general form of save may be mixed at will. For example,
save (filename, aa, bb, cc=42, functions, [11, 17]).
The special form save (filename, all) stores the current state of Maxima. This
includes all user-defined variables, functions, arrays, etc., as well as some automatically defined
items. The saved items include system variables, such as file_search_maxima or
showtime, if they have been assigned new values by the user; see myoptions.
save evaluates filename and quotes all other arguments.
Option variable: savedef
Default value: true
When savedef is true, the Maxima version of a user function is preserved when the
function is translated. This permits the definition to be displayed by dispfun and allows the
function to be edited.
When savedef is false, the names of translated functions are removed from the
functions list.
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