问题
Suppose I have an expression like (actually mine is much more complex, thousands of characters)
expr:a+b*c+b*c*d;
and I want to replace an internal sub-expression with a symbol (useful to avoid recomputation of common subexpressions), say k in place of b*c:
subst(b*c=k,expr);
returns
k+b*c*d+a
How I can make Maxima calculate the "right" substitution so to return (apart from obviuos simplification, here)
k+k*d+a
?
回答1:
Take a look at let and letsimp. E.g.:
(%i2) expr : a + b*c + b*c*d;
(%o2) b*c*d+b*c+a
(%i3) let (b*c, k);
(%o3) b*c --> k
(%i4) letsimp (expr);
(%o4) d*k+k+a
letsimp differs from subst and tellsimp or defrule in that those other functions make only formal substitutions, i.e., replacing subexpressions which are exactly the same as some pattern.
回答2:
You can try optimize
http://maxima.sourceforge.net/docs/manual/en/maxima_6.html#IDX219
(%i14) example(optimize);
(%i15) diff(exp(y+x^2)/(y+x),x,2)
2 2 2 2
2 y + x y + x y + x y + x
4 x %e 2 %e 4 x %e 2 %e
(%o15) ------------- + ---------- - ------------ + ----------
y + x y + x 2 3
(y + x) (y + x)
(%i16) optimize(%)
2 y + %2 1
(%o16) block([%1, %2, %3, %4], %1 : y + x, %2 : x , %3 : %e , %4 : --,
%1
4 x %3 2 %3
4 %2 %4 %3 + 2 %4 %3 - ------ + ----)
2 3
%1 %1
来源：https://stackoverflow.com/questions/22685853/maxima-how-to-replace-common-subexpressions-with-symbols