Sympy替代数学表达式

Question

I am trying to simplify a large expression by substitution of common smaller expressions. Here is the full expression:

For instance, I would like to do:

exp.subs(L_r*cos(alpha)-L_p*sin(alpha),L_r_tilde))

The expression can be found twice in the 1 . I also tried to substitute a smaller expression with the same approach, but SymPy requires factorization in the first step to perform the substitution.

This one works:

small_exp = L_p*sin(alpha)**2-L_r*sin(alpha)*cos(alpha)
small_exp_factorized = small_exp.factor()
small_exp_factorized.subs(L_p*sin(alpha)-L_r*cos(alpha),L_r_tilde)

leading to L_r_tilde*sin(alpha) but without prior factorization SymPy fails to substitute.

Is it possible to substitute all common expressions without factorization or further manipulation of the large expression from above?

Answer 1

SymPy's subs is only going to replace things that appear exactly in an expression. It has a couple of minor heuristics (like handling of (x**4).subs(x**2, y) , but nothing that will factor or otherwise rewrite expressions for you.

One trick is to rearrange the substitution so that you are only substituting one term, like

small_exp.subs(L_p*sin(alpha), L_r*cos(alpha) + L_r_tilde)

After simplification, everything should cancel out.

For your specific expression, it looks like every instance of your subexpression is multiplied by sin(alpha) , so you could just include that term in your definition of L_r_tilde , or you can replace L_r*cos(alpha)*sin(alpha) -L_p*sin(alpha)**2 with L_r_tilde*sin(alpha) .

I'll also point out the cse() function, which pulls out common subexpressions automatically.