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To define a function in Maxima you use the := operator. E.g.
f(x) := sin(x)
defines a function f.
Anonmyous functions may also be created using lambda.
For example
lambda ([i, j], ...)
can be used instead of f
where
f(i,j) := block ([], ...); map (lambda ([i], i+1), l)
would return a list with 1 added to each term.
You may also define a function with a variable number of arguments, by having a final argument which is assigned to a list of the extra arguments:
(%i1) f ([u]) := u; (%o1) f([u]) := u (%i2) f (1, 2, 3, 4); (%o2) [1, 2, 3, 4] (%i3) f (a, b, [u]) := [a, b, u]; (%o3) f(a, b, [u]) := [a, b, u] (%i4) f (1, 2, 3, 4, 5, 6); (%o4) [1, 2, [3, 4, 5, 6]]
The right hand side of a function is an expression. Thus if you want a sequence of expressions, you do
f(x) := (expr1, expr2, ...., exprn);
and the value of exprn is what is returned by the function.
If you wish to make a return from some expression inside the
function then you must use block and return.
block ([], expr1, ..., if (a > 10) then return(a), ..., exprn)
is itself an expression, and so could take the place of the right hand side of a function definition. Here it may happen that the return happens earlier than the last expression.
The first [] in the block, may contain a list of variables and
variable assignments, such as [a: 3, b, c: []], which would cause the
three variables a,b,and c to not refer to their
global values, but rather have these special values for as long as the
code executes inside the block, or inside functions called from
inside the block. This is called dynamic binding, since the
variables last from the start of the block to the time it exits. Once
you return from the block, or throw out of it, the old values (if
any) of the variables will be restored. It is certainly a good idea
to protect your variables in this way. Note that the assignments
in the block variables, are done in parallel. This means, that if
you had used c: a in the above, the value of c would
have been the value of a at the time you just entered the block,
but before a was bound. Thus doing something like
block ([a: a], expr1, ... a: a+3, ..., exprn)
will protect the external value of a from being altered, but
would let you access what that value was. Thus the right hand
side of the assignments, is evaluated in the entering context, before
any binding occurs.
Using just block ([x], ... would cause the x to have itself
as value, just as if it would have if you entered a fresh Maxima
session.
The actual arguments to a function are treated in exactly same way as the variables in a block. Thus in
f(x) := (expr1, ..., exprn);
and
f(1);
we would have a similar context for evaluation of the expressions as if we had done
block ([x: 1], expr1, ..., exprn)
Inside functions, when the right hand side of a definition,
may be computed at runtime, it is useful to use define and
possibly buildq.
expr is any single Maxima expression and
variables is a list of elements of the form <atom>
or <atom>: <value>.
The elements of the list variables are evaluated left to right (the syntax
atom is equivalent to atom: atom). then these values are substituted
into <expression> in parallel. If any atom appears as a single
argument to the special form splice (i.e. splice (atom)) inside
expr, then the value associated with that atom must be a Maxima
list, and it is spliced into expr instead of substituted.
The arguments to buildq need to be protected from simplification until
the substitutions have been carried out. This code should effect that
by using '.
buildq can be useful for building functions on the fly. One
of the powerful things about Maxima is that you can have your
functions define other functions to help solve the problem.
Further below we discuss building a recursive function, for a
series solution. This defining of functions inside functions
usually uses define, which evaluates its arguments.
A number of examples are included under splice.
buildq.
mprint ([x]) ::= buildq ([u : x], if (debuglevel > 3) print (splice (u)));
Including a call like
mprint ("matrix is", mat, "with length", length(mat))
is equivalent to putting in the line
if (debuglevel > 3) print ("matrix is", mat, "with length", length(mat));
A more non trivial example would try to display the variable values and their names.
mshow (a, b, c)
should become
print ('a, "=", a, ",", 'b, "=", b, ", and", 'c, "=", c)
so that if it occurs as a line in a program we can print values.
(%i1) foo (x,y,z) := mshow (x, y, z); (%i2) foo (1, 2, 3); x = 1 , y = 2 , and z = 3
The actual definition of mshow is the following. Note how buildq
lets you build "quoted" structure, so that the 'u lets
you get the variable name. Note that in macros, the result is
a piece of code which will then be substituted for the macro and evaluated.
mshow ([l]) ::= block ([ans:[], n:length(l)],
for i:1 thru n do
(ans: append (ans, buildq ([u: l[i]], ['u, "=", u])),
if i < n then
ans: append (ans, if i < n-1 then [","] else [", and"])),
buildq ([u:ans], print (splice(u))));
The splice also works to put arguments into algebraic operations:
(%i1) buildq ([a: '[b, c, d]], +splice(a)); (%o1) d + c + b
Note how the simplification only occurs after the substitution,
The operation applying to the splice in the first case is the +
while in the second it is the *, yet logically you
might think splice(a)+splice(a) could be replaced by
2*splice(a). No simplification takes place with the buildq.
To understand what splice is doing with the algebra you must understand
that for Maxima, a formula an operation like a+b+c is really
internally similar to +(a,b,c), and similarly for multiplication.
Thus *(2,b,c,d) is 2*b*c*d.
(%i1) buildq ([a: '[b,c,d]], +splice(a)); (%o1) d + c + b (%i2) buildq ([a: '[b,c,d]], splice(a)+splice(a)); (%o2) 2 d + 2 c + 2 b
but
(%i3) buildq ([a: '[b,c,d]], 2*splice(a)); (%o3) 2 b c d
Finally buildq can be invaluable for building recursive functions.
Suppose your program is solving a differential equation using the
series method, and has determined that it needs to build a
recursion relation
f[n] := -((n^2 - 2*n + 1)*f[n-1] + f[n-2] + f[n-3])/(n^2-n)
and it must do this on the fly inside your function. Now you
would really like to add expand.
f[n] := expand (-((n^2 - 2*n + 1)*f[n-1] + f[n-2] + f[n-3])/(n^2-n))
but how do you build this code. You want the expand
to happen each time the function runs, not before it.
(%i1) val: -((n^2 - 2*n + 1)*f[n-1] + f[n-2] + f[n-3])/(n^2-n)$ (%i2) define (f[n], buildq ([u: val], expand(u)))$
does the job. This might be useful, since when you do
(with expand)
(%i3) f[0]: aa0$
(%i4) f[1]: aa1$
(%i5) f[2]: aa2$
(%i6) f[6];
3 aa2 aa1 7 aa0
(%o6) ----- + -- + -----
10 40 90
where as without it is kept unsimplified, and even after 6 terms it becomes:
(%i7) define (g[n], buildq ([u: val], u))$
(%i8) g[0]: bb0$
(%i9) g[1]: bb1$
(%i10) g[2]: bb2$
(%i11) g[6];
aa2 7 aa2 aa1 11 aa0 aa1 aa0
-- - 25 (- ----- - -- - ------) + -- + ---
4 20 40 120 8 24
(%o11) ---------------------------------------------
30
(%i12) expand (%);
3 aa2 aa1 7 aa0
(%o12) ----- + -- + -----
10 40 90
The expression quickly becomes complicated if not simplified at
each stage, so the simplification must be part of the definition.
Hence the buildq is useful for building the form.
This is useful when it is desired to
compute the arguments to a function before applying that function.
For example, if l is the list [1, 5, -10.2, 4, 3], then apply (min, l)
gives -10.2. apply is also useful when calling functions which do not
have their arguments evaluated if it is desired to cause evaluation of
them. For example, if filespec is a variable bound to the list [test,
case] then apply (closefile, filespec) is equivalent to
closefile (test, case). In general the first argument to apply should
be preceded by a ' to make it evaluate to itself. Since some atomic
variables have the same name as certain functions the values of the
variable would be used rather than the function because apply has its
first argument evaluated as well as its second.
block evaluates expr_1, ..., expr_n in sequence
and returns the value of the last expression evaluated.
The sequence can be modified by the go, throw, and return functions.
The last expression is expr_n unless return or an expression containing throw
is evaluated.
Some variables v_1, ..., v_m can be declared local to the block;
these are distinguished from global variables of the same names.
If no variables are declared local then the list may be omitted.
Within the block,
any variable other than v_1, ..., v_m is a global variable.
block saves the current values of the variables v_1, ..., v_m (if any)
upon entry to the block,
then unbinds the variables so that they evaluate to themselves.
The local variables may be bound to arbitrary values within the block but when the
block is exited the saved values are restored,
and the values assigned within the block are lost.
block may appear within another block.
Local variables are established each time a new block is evaluated.
Local variables appear to be global to any enclosed blocks.
If a variable is non-local in a block,
its value is the value most recently assigned by an enclosing block, if any,
otherwise, it is the value of the variable in the global environment.
This policy may coincide with the usual understanding of "dynamic scope".
If it is desired to save and restore other local properties
besides value, for example array (except for complete arrays),
function, dependencies, atvalue, matchdeclare, atomgrad, constant, and
nonscalar then the function local should be used inside of the block
with arguments being the names of the variables.
The value of the block is the value of the last statement or the
value of the argument to the function return which may be used to exit
explicitly from the block. The function go may be used to transfer
control to the statement of the block that is tagged with the argument
to go. To tag a statement, precede it by an atomic argument as
another statement in the block. For example:
block ([x], x:1, loop, x: x+1, ..., go(loop), ...). The argument to go must
be the name of a tag appearing within the block. One cannot use go to
transfer to a tag in a block other than the one containing the go.
Blocks typically appear on the right side of a function definition but can be used in other places as well.
exit; the computation resumes.
throw (arg), then the value of the catch is the value of
throw (arg), and no further expressions are evaluated.
This "non-local return" thus goes through any depth of
nesting to the nearest enclosing catch.
If there is no catch enclosing a throw, an error message is printed.
If the evaluation of the arguments does not lead to the evaluation of any throw
then the value of catch is the value of expr_n.
(%i1) lambda ([x], if x < 0 then throw(x) else f(x))$
(%i2) g(l) := catch (map ("%, l))$
(%i3) g ([1, 2, 3, 7]);
(%o3) [f(1), f(2), f(3), f(7)]
(%i4) g ([1, 2, -3, 7]);
(%o4) - 3
The function g returns a list of f of each element of l if l
consists only of non-negative numbers; otherwise, g "catches" the
first negative element of l and "throws" it up.
The Lisp translations are not evaluated, nor is the output file processed by the Lisp compiler.
translate creates and evaluates Lisp translations.
compile_file translates Maxima into Lisp, and then executes the Lisp compiler.
See also translate, translate_file, and compile_file.
COMPILE on each translated function.
compile returns a list of the names of the compiled functions.
compile (all) or compile (functions) compiles all user-defined functions.
compile quotes its arguments;
the double-single-quotes operator '' defeats quotation.
define quotes its first argument in most cases,
and evaluates its second argument unless explicitly quoted.
However, if the first argument is an expression of the form
ev (expr), funmake (expr), or arraymake (expr),
the first argument is evaluated;
this allows for the function name to be computed, as well as the body.
define is similar to the function definition operator :=, but when
define appears inside a function, the definition is created using the value
of expr at execution time rather than at the
time of definition of the function which contains it.
All function definitions appear in the same namespace;
defining a function f within another function g
does not limit the scope of f to g.
Examples:
(%i1) foo: 2^bar;
bar
(%o1) 2
(%i2) g(x) := (f_1 (y) := foo*x*y,
f_2 (y) := "foo*x*y,
define (f_3 (y), foo*x*y),
define (f_4 (y), "foo*x*y));
bar
(%o2) g(x) := (f_1(y) := foo x y, f_2(y) := 2 x y,
bar
define(f_3(y), foo x y), define(f_4(y), 2 x y))
(%i3) functions;
(%o3) [g(x)]
(%i4) g(a);
bar
(%o4) f_4(y) := a 2 y
(%i5) functions;
(%o5) [g(x), f_1(y), f_2(y), f_3(y), f_4(y)]
(%i6) dispfun (f_1, f_2, f_3, f_4);
(%t6) f_1(y) := foo x y
bar
(%t7) f_2(y) := 2 x y
bar
(%t8) f_3(y) := a 2 y
bar
(%t9) f_4(y) := a 2 y
(%o9) done
Introduces a global variable into the Maxima environment.
define_variable is useful in user-written packages, which are often translated or compiled.
define_variable carries out the following steps:
mode_declare (name, mode) declares the mode of name to the translator.
See mode_declare for a list of the possible modes.
declare (name, special) declares it special.
The value_check property can be assigned to any variable which has been defined
via define_variable with a mode other than any.
The value_check property is a lambda expression or the name of a function of one variable,
which is called when an attempt is made to assign a value to the variable.
The argument of the value_check function is the would-be assigned value.
define_variable evaluates default_value, and quotes name and mode.
define_variable returns the current value of name,
which is default_value if name was unbound before,
and otherwise it is the previous value of name.
Examples:
foo is a Boolean variable, with the initial value true.
(%i1) define_variable (foo, true, boolean); (%o1) true (%i2) foo; (%o2) true (%i3) foo: false; (%o3) false (%i4) foo: %pi; Error: foo was declared mode boolean, has value: %pi -- an error. Quitting. To debug this try debugmode(true); (%i5) foo; (%o5) false
bar is an integer variable, which must be prime.
(%i1) define_variable (bar, 2, integer);
(%o1) 2
(%i2) qput (bar, prime_test, value_check);
(%o2) prime_test
(%i3) prime_test (y) := if not primep(y) then error (y, "is not prime.");
(%o3) prime_test(y) := if not primep(y)
then error(y, "is not prime.")
(%i4) bar: 1439;
(%o4) 1439
(%i5) bar: 1440;
1440 is not prime.
#0: prime_test(y=1440)
-- an error. Quitting. To debug this try debugmode(true);
(%i6) bar;
(%o6) 1439
baz_quux is a variable which cannot be assigned a value.
The mode any_check is like any,
but any_check enables the value_check mechanism, and any does not.
(%i1) define_variable (baz_quux, 'baz_quux, any_check);
(%o1) baz_quux
(%i2) F: lambda ([y], if y # 'baz_quux then error ("Cannot assign to `baz_quux'."));
(%o2) lambda([y], if y # 'baz_quux
then error(Cannot assign to `baz_quux'.))
(%i3) qput (baz_quux, "F, value_check);
(%o3) lambda([y], if y # 'baz_quux
then error(Cannot assign to `baz_quux'.))
(%i4) baz_quux: 'baz_quux;
(%o4) baz_quux
(%i5) baz_quux: sqrt(2);
Cannot assign to `baz_quux'.
#0: lambda([y],if y # 'baz_quux then error("Cannot assign to `baz_quux'."))(y=sqrt(2))
-- an error. Quitting. To debug this try debugmode(true);
(%i6) baz_quux;
(%o6) baz_quux
::=),
an ordinary function (defined with := or define),
an array function (defined with := or define,
but enclosing arguments in square brackets [ ]),
a subscripted function, (defined with := or define,
but enclosing some arguments in square brackets and others in parentheses ( ))
one of a family of subscripted functions selected by a particular subscript value,
or a subscripted function defined with a constant subscript.
dispfun (all) displays all user-defined functions as
given by the functions, arrays, and macros lists,
omitting subscripted functions defined with constant subscripts.
dispfun creates an intermediate expression label
(%t1, %t2, etc.)
for each displayed function, and assigns the function definition to the label.
In contrast, fundef returns the function definition.
dispfun quotes its arguments;
the double-single-quote operator '' defeats quotation.
dispfun always returns done.
Examples:
(%i1) m(x, y) ::= x^(-y)$
(%i2) f(x, y) := x^(-y)$
(%i3) g[x, y] := x^(-y)$
(%i4) h[x](y) := x^(-y)$
(%i5) i[8](y) := 8^(-y)$
(%i6) dispfun (m, f, g, h, h[5], h[10], i[8])$
- y
(%t6) m(x, y) ::= x
- y
(%t7) f(x, y) := x
- y
(%t8) g := x
x, y
- y
(%t9) h (y) := x
x
1
(%t10) h (y) := --
5 y
5
1
(%t11) h (y) := ---
10 y
10
- y
(%t12) i (y) := 8
8
[]
functions is the list of user-defined Maxima functions
in the current session.
A user-defined function is a function constructed by
define or :=.
A function may be defined at the Maxima prompt
or in a Maxima file loaded by load or batch.
Lisp functions, however, are not added to functions.
The argument may be the name of a macro (defined with ::=),
an ordinary function (defined with := or define),
an array function (defined with := or define,
but enclosing arguments in square brackets [ ]),
a subscripted function, (defined with := or define,
but enclosing some arguments in square brackets and others in parentheses ( ))
one of a family of subscripted functions selected by a particular subscript value,
or a subscripted function defined with a constant subscript.
fundef quotes its argument;
the double-single-quote operator '' defeats quotation.
fundef (f) returns the definition of f.
In contrast, dispfun (f) creates an intermediate expression label
and assigns the definition to the label.
name (arg_1, ..., arg_n).
The return value is simplified, but not evaluated,
so the function is not called.
funmake evaluates its arguments.
Examples:
funmake evaluates its arguments, but not the return value.
(%i1) det(a,b,c) := b^2 -4*a*c$ (%i2) x: 8$ (%i3) y: 10$ (%i4) z: 12$ (%i5) f: det$ (%i6) funmake (f, [x, y, z]); (%o6) det(8, 10, 12) (%i7) "%; (%o7) - 284
funmake's return value.
(%i1) funmake (sin, [%pi/2]); (%o1) 1
When the function is evaluated,
unbound local variables x_1, ..., x_m are created.
lambda may appear within block or another lambda;
local variables are established each time another block or lambda is evaluated.
Local variables appear to be global to any enclosed block or lambda.
If a variable is not local,
its value is the value most recently assigned in an enclosing block or lambda, if any,
otherwise, it is the value of the variable in the global environment.
This policy may coincide with the usual understanding of "dynamic scope".
After local variables are established,
expr_1 through expr_n are evaluated in turn.
The special variable %%, representing the value of the preceding expression,
is recognized.
throw and catch may also appear in the list of expressions.
return cannot appear in a lambda expression unless enclosed by block,
in which case return defines the return value of the block and not of the
lambda expression,
unless the block happens to be expr_n.
Likewise, go cannot appear in a lambda expression unless enclosed by block.
lambda quotes its arguments;
the double-single-quote operator '' defeats quotation.
Examples:
(%i1) f: lambda ([x], x^2);
2
(%o1) lambda([x], x )
(%i2) f(a);
2
(%o2) a
(%i3) lambda ([x], x^2) (a);
2
(%o3) a
(%i4) apply (lambda ([x], x^2), [a]);
2
(%o4) a
(%i5) map (lambda ([x], x^2), [a, b, c, d, e]);
2 2 2 2 2
(%o5) [a , b , c , d , e ]
''.
(%i6) a: %pi$
(%i7) b: %e$
(%i8) g: lambda ([a], a*b);
(%o8) lambda([a], a b)
(%i9) b: %gamma$
(%i10) g(1/2);
%gamma
(%o10) ------
2
(%i11) g2: lambda ([a], a*"b);
(%o11) lambda([a], a %gamma)
(%i12) b: %e$
(%i13) g2(1/2);
%gamma
(%o13) ------
2
(%i14) h: lambda ([a, b], h2: lambda ([a], a*b), h2(1/2));
1
(%o14) lambda([a, b], h2 : lambda([a], a b), h2(-))
2
(%i15) h(%pi, %gamma);
%gamma
(%o15) ------
2
lambda quotes its arguments, lambda expression i below
does not define a "multiply by a" function.
Such a function can be defined via buildq, as in lambda expression i2 below.
(%i16) i: lambda ([a], lambda ([x], a*x));
(%o16) lambda([a], lambda([x], a x))
(%i17) i(1/2);
(%o17) lambda([x], a x)
(%i18) i2: lambda([a], buildq([a: a], lambda([x], a*x)));
(%o18) lambda([a], buildq([a : a], lambda([x], a x)))
(%i19) i2(1/2);
x
(%o19) lambda([x], -)
2
(%i20) i2(1/2)(%pi);
%pi
(%o20) ---
2
local quotes its arguments.
local returns done.
local may only be used in block, in the body of function
definitions or lambda expressions, or in the ev function, and only one
occurrence is permitted in each.
local is independent of context.
false
macroexpansion controls advanced features which
affect the efficiency of macros. Possible settings:
false -- Macros expand normally each time they are called.
expand -- The first time a particular call is evaluated, the
expansion is remembered internally, so that it doesn't have to be
recomputed on subsequent calls making subsequent calls faster. The
macro call still calls grind and display normally. However, extra memory is
required to remember all of the expansions.
displace -- The first time a particular call is evaluated, the
expansion is substituted for the call. This requires slightly less
storage than when macroexpansion is set to expand and is just as fast,
but has the disadvantage that the original macro call is no longer
remembered and hence the expansion will be seen if display or grind is
called. See documentation for translate and macros for more details.
true
When mode_checkp is true, mode_declare checks the modes
of bound variables.
false
When mode_check_errorp is true, mode_declare calls
error.
true
When mode_check_warnp is true, mode errors are
described.
mode_declare is used to declare the modes of variables and
functions for subsequent translation or compilation of functions.
mode_declare is typically placed at the beginning of a function
definition, at the beginning of a Maxima script, or executed at the interactive prompt.
The arguments of mode_declare are pairs consisting of a variable and a mode which is
one of boolean, fixnum, number, rational, or float.
Each variable may also
be a list of variables all of which are declared to have the same mode.
If a variable is an array, and if every element of the array which is
referenced has a value then array (yi, complete, dim1, dim2, ...)
rather than
array(yi, dim1, dim2, ...)
should be used when first
declaring the bounds of the array.
If all the elements of the array
are of mode fixnum (float), use fixnum (float) instead of complete.
Also if every element of the array is of the same mode, say m, then
mode_declare (completearray (yi), m))
should be used for efficient translation.
Numeric code using arrays might run faster by declaring the expected size of the array, as in:
mode_declare (completearray (a [10, 10]), float)
for a floating point number array which is 10 x 10.
One may declare the mode of the result of a function by
using function (f_1, f_2, ...) as an argument;
here f_1, f_2, ... are the names
of functions. For example the expression,
mode_declare ([function (f_1, f_2, ...)], fixnum)
declares that the values returned by f_1, f_2, ... are single-word integers.
modedeclare is a synonym for mode_declare.
mode_declare and
macros to declare, e.g., a list of lists of flonums, or other compound
data object. The first argument to mode_identity is a primitive value
mode name as given to mode_declare (i.e., one of float, fixnum, number,
list, or any), and the second argument is an expression which is
evaluated and returned as the value of mode_identity. However, if the
return value is not allowed by the mode declared in the first
argument, an error or warning is signalled. The important thing is
that the mode of the expression as determined by the Maxima to Lisp
translator, will be that given as the first argument, independent of
anything that goes on in the second argument.
E.g., x: 3.3; mode_identity (fixnum, x); yields an error. mode_identity (flonum, x)
returns 3.3 .
This has a number of uses, e.g., if you knew that first (l) returned a
number then you might write mode_identity (number, first (l)). However,
a more efficient way to do it would be to define a new primitive,
firstnumb (x) ::= buildq ([x], mode_identity (number, x));
and use firstnumb
every time you take the first of a list of numbers.
true
When transcompile is true, translate and translate_file generate
declarations to make the translated code more suitable for compilation.
compfile sets transcompile: true for the duration.
translate (all) or translate (functions) translates all user-defined functions.
Functions to be translated should include a call to mode_declare at the
beginning when possible in order to produce more efficient code. For
example:
f (x_1, x_2, ...) := block ([v_1, v_2, ...],
mode_declare (v_1, mode_1, v_2, mode_2, ...), ...)
where the x_1, x_2, ... are the parameters to the function and the v_1, v_2, ... are the local variables.
The names of translated functions
are removed from the functions list if savedef is false (see below)
and are added to the props lists.
Functions should not be translated unless they are fully debugged.
Expressions are assumed simplified; if they are not, correct but non- optimal code gets
generated. Thus, the user should not set the simp switch to false
which inhibits simplification of the expressions to be translated.
The switch translate, if true, causes automatic
translation of a user's function to Lisp.
Note that translated
functions may not run identically to the way they did before
translation as certain incompatabilities may exist between the Lisp
and Maxima versions. Principally, the rat function with more than
one argument and the ratvars function should not be used if any
variables are mode_declare'd canonical rational expressions (CRE).
Also the prederror: false setting
will not translate.
savedef - if true will cause the Maxima version of a user
function to remain when the function is translate'd. This permits the
definition to be displayed by dispfun and allows the function to be
edited.
transrun - if false will cause the interpreted version of all
functions to be run (provided they are still around) rather than the
translated version.
The result returned by translate is a list of the names of the
functions translated.
translate_file returns a list of three filenames:
the name of the Maxima file, the name of the Lisp file, and the name of file
containing additional information about the translation.
translate_file evaluates its arguments.
translate_file ("foo.mac"); load("foo.LISP") is the same as
batch ("foo.mac") except for certain restrictions,
the use of '' and %, for example.
translate_file (maxima_filename) translates a Maxima file maxima_filename
into a similarly-named Lisp file.
For example, foo.mac is translated into foo.LISP.
The Maxima filename may include a directory name or names,
in which case the Lisp output file is written
to the same directory from which the Maxima input comes.
translate_file (maxima_filename, lisp_filename) translates
a Maxima file maxima_filename into a Lisp file lisp_filename.
translate_file ignores the filename extension, if any, of lisp_filename;
the filename extension of the Lisp output file is always LISP.
The Lisp filename may include a directory name or names,
in which case the Lisp output file is written to the specified directory.
translate_file also writes a file of translator warning
messages of various degrees of severity.
The filename extension of this file is UNLISP.
This file may contain valuable information, though possibly obscure,
for tracking down bugs in translated code.
The UNLISP file is always written
to the same directory from which the Maxima input comes.
translate_file emits Lisp code which causes
some declarations and definitions to take effect as soon
as the Lisp code is compiled.
See compile_file for more on this topic.
See also tr_array_as_ref,
tr_bound_function_applyp,
tr_exponent,
tr_file_tty_messagesp,
tr_float_can_branch_complex,
tr_function_call_default,
tr_numer,
tr_optimize_max_loop,
tr_semicompile,
tr_state_vars,
tr_warnings_get,
tr_warn_bad_function_calls,
tr_warn_fexpr,
tr_warn_meval,
tr_warn_mode,
tr_warn_undeclared,
tr_warn_undefined_variable,
and tr_windy.
true
When transrun is false will cause the interpreted
version of all functions to be run (provided they are still around)
rather than the translated version.
true
If translate_fast_arrays is false, array references in
Lisp code emitted by translate_file are affected by tr_array_as_ref.
When tr_array_as_ref is true,
array names are evaluated,
otherwise array names appear as literal symbols in translated code.
tr_array_as_ref has no effect if translate_fast_arrays is true.
true
When tr_bound_function_applyp is true, Maxima gives a warning if a bound
variable (such as a function argument) is found being used as a function.
tr_bound_function_applyp does not affect the code generated in such cases.
For example, an expression such as g (f, x) := f (x+1) will trigger
the warning message.
false
When tr_file_tty_messagesp is true,
messages generated by translate_file during translation of a file are displayed
on the console and inserted into the UNLISP file.
When false, messages about translation of the
file are only inserted into the UNLISP file.
true
Tells the Maxima-to-Lisp translator to assume that the functions
acos, asin, asec, and acsc can return complex results.
The ostensible effect of tr_float_can_branch_complex is the following.
However, it appears that this flag has no effect on the translator output.
When it is true then acos(x) is of mode any
even if x is of mode float (as set by mode_declare).
When false then acos(x) is of mode
float if and only if x is of mode float.
general
false means give up and
call meval, expr means assume Lisp fixed arg function. general, the
default gives code good for mexprs and mlexprs but not macros.
general assures variable bindings are correct in compiled code. In
general mode, when translating F(X), if F is a bound variable, then it
assumes that apply (f, [x]) is meant, and translates a such, with
apropriate warning. There is no need to turn this off. With the
default settings, no warning messages implies full compatibility of
translated and compiled code with the Maxima interpreter.
false
When tr_numer is true numer properties are used for
atoms which have them, e.g. %pi.
tr_optimize_max_loop is the maximum number of times the
macro-expansion and optimization pass of the translator will loop in
considering a form. This is to catch macro expansion errors, and
non-terminating optimization properties.
false
When tr_semicompile is true, translate_file and compfile
output forms which will be macroexpanded but not compiled into machine
code by the Lisp compiler.
[transcompile, tr_semicompile, tr_warn_undeclared, tr_warn_meval, tr_warn_fexpr, tr_warn_mode, tr_warn_undefined_variable, tr_function_call_default, tr_array_as_ref,tr_numer]
The list of the switches that affect the form of the translated output. This information is useful to system people when trying to debug the translator. By comparing the translated product to what should have been produced for a given state, it is possible to track down bugs.
true
- Gives a warning when when function calls are being made which may not be correct due to improper declarations that were made at translate time.
compfile
- Gives a warning if any FEXPRs are encountered. FEXPRs should not normally be output in translated code, all legitimate special program forms are translated.
compfile
- Gives a warning if the function
meval gets called. If meval is called that indicates problems in the
translation.
all
- Gives a warning when variables are assigned values inappropriate for their mode.
compile
- Determines when to send warnings about undeclared variables to the TTY.
all
- Gives a warning when undefined global variables are seen.
true
- Generate "helpfull" comments and programming hints.
compile_file returns a list of the names of four files:
the original Maxima file, the Lisp translation, notes on translation, and the compiled code.
If the compilation fails,
the fourth item is false.
Some declarations and definitions take effect as soon
as the Lisp code is compiled (without loading the compiled code).
These include functions defined with the := operator,
macros define with the ::= operator,
alias, declare,
define_variable, mode_declare,
and
infix, matchfix,
nofix, postfix, prefix,
and compfile.
Assignments and function calls are not evaluated until the compiled code is loaded.
In particular, within the Maxima file,
assignments to the translation flags (tr_numer, etc.) have no effect on the translation.
filename may not contain :lisp statements.
compile_file evaluates its arguments.
(MFUNCTION-CALL fn arg1 arg2 ...) is generated when
the translator does not know fn is going to be a Lisp function.
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