Maxima – 201 – Definire funzioni – 2

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Continuo da qui, copio dal Reference Manual, PDF scaricabile da qui, sono a p.606.

Macros

buildq (L, expr)
Substitutes variables named by the list L into the expression expr, in parallel, without evaluating expr. The resulting expression is simplified, but not evaluated, after buildq carries out the substitution.

The elements of L are symbols or assignment expressions symbol: value, evaluated in parallel. That is, the binding of a variable on the right-hand side of an assignment is the binding of that variable in the context from which buildq was called, not the binding of that variable in the variable list L. If some variable in L is not given an explicit assignment, its binding in buildq is the same as in the context from which buildq was called.

Then the variables named by L are substituted into expr in parallel. That is, the substitution for every variable is determined before any substitution is made, so the substitution for one variable has no effect on any other.

If any variable x appears as splice (x) in expr, then x must be bound to a list, and the list is spliced (interpolated) into expr instead of substituted.

Any variables in expr not appearing in L are carried into the result verbatim, even if they have bindings in the context from which buildq was called.

a is explicitly bound to x, while b has the same binding (namely 29) as in the calling context, and c is carried through verbatim. The resulting expression is not evaluated until the explicit evaluation ''%.

(%i1) (a: 17, b: 29, c: 1729)$

(%i2) buildq ([a: x, b], a + b + c);
(%o2)                             x + c + 29
(%i3) ''%;
(%o3)                              x + 1758

e is bound to a list, which appears as such in the arguments of foo, and interpolated into the arguments of bar.

(%i1) buildq ([e: [a, b, c]], foo (x, e, y));
(%o1)                        foo(x, [a, b, c], y)
(%i2) buildq ([e: [a, b, c]], 2 * splice (e));
(%o2)                               2 a b c

The result is simplified after substitution. If simplification were applied before substitution, these two results would be the same.

(%i1) buildq ([e: [a, b, c]], splice (e) + splice (e));
(%o1)                           2 c + 2 b + 2 a
(%i2) buildq ([e: [a, b, c]], 2 * splice (e));
(%o2)                               2 a b c

The variables in L are bound in parallel; if bound sequentially, the first result would be foo (b, b). Substitutions are carried out in parallel; compare the second result with the result of subst, which carries out substitutions sequentially.

(%i1) buildq ([a: b, b: a], foo (a, b));
(%o1)                              foo(b, a)
(%i2) buildq ([u: v, v: w, w: x, x: y, y: z, z: u],
              bar (u, v, w, x, y, z));
(%o2)                        bar(v, w, x, y, z, u)
(%i3) subst ([u=v, v=w, w=x, x=y, y=z, z=u],
             bar (u, v, w, x, y, z));
(%o3)                        bar(u, u, u, u, u, u)

Construct a list of equations with some variables or expressions on the left-hand side and their values on the right-hand side. macroexpand shows the expression returned by show_values.

(%i1) show_values ([L]) ::= buildq ([L], map ("=", 'L, L));
(%o1)          show_values([L]) ::= buildq([L], map("=", 'L, L))
(%i2) (a: 17, b: 29, c: 1729)$

(%i3) show_values (a, b, c - a - b);
(%o3)                 [a = 17, b = 29, c - b - a = 1683]
(%i4) macroexpand (show_values (a, b, c - a - b));
(%o4)           map(=, '([a, b, c - b - a]), [a, b, c - b - a])

Given a function of several arguments, create another function for which some of the arguments are fixed.

(%i1) curry (f, [a]) :=
             buildq ([f, a], lambda ([[x]], apply (f, append (a, x))))$

(%i2) by3 : curry ("*", 3);
(%o2)               lambda([[x]], apply(*, append([3], x)))
(%i3) by3 (a + b);
(%o3)                              3 (b + a)

macroexpand (expr)
Returns the macro expansion of expr without evaluating it, when expr is a macro function call. Otherwise, macroexpand returns expr.

If the expansion of expr yields another >macro function call, that macro function call is also expanded.

macroexpand quotes its argument. However, if the expansion of a macro function call has side effects, those side effects are executed.

See also ::=, macros, and macroexpand1.

(%i1) g (x) ::= x / 99;
                                           x
(%o1)                             g(x) ::= --
                                           99
(%i2) h (x) ::= buildq ([x], g (x - a));
(%o2)                   h(x) ::= buildq([x], g(x - a))
(%i3) a: 1234;
(%o3)                                1234
(%i4) macroexpand (h (y));
                                     y - a
(%o4)                                -----
                                      99
(%i5) h (y);
                                   y - 1234
(%o5)                              --------
                                      99

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