How to replace a list/array of variables in the result?

Question

All,

I want to know how to replace multiple variables in the result expression. To be specific, all those variables are inside the array I defined.

For a simple example, if I define input

mm5 = {a, b, c, d};

mm7 = {2, 3, 9, 8};

mm7a = mm7.mm5

Out: 2 a + 3 b + 9 c + 8 d

After that, if I define a new array

mm6 = {3, 4, 5, 7}

And I want to replace every unknown component in mm5 to be the values in mm6, and to let the final result of mm7a be 2*3+3*4+9*5+8*7=119. How should I do that?

I was thinking is there any way similar to

mm7a /. {mm5[[i]] -> mm6[[i]],{i,1,4}}

Of course, what I wrote is wrong. But is there any simple way to use /. to help me achieve this effect?? And after substituting, I want symbols in mm5 be reserved, for example, when I output mm5 result, it is still {a, b, c, d}

I searched the whole web but I didn't find a simple way to do it. Maybe I didn't search it right. So I post my question here and hope get some answer.

Thank you

Answer 1

Clear["Global`*"]

mm5 = {a, b, c, d};

mm7 = {2, 3, 9, 8};

mm7a = mm7 . mm5

(* 2 a + 3 b + 9 c + 8 d *)

mm6 = {3, 4, 5, 7};

If mm5 is known

mm7a /. Thread[mm5 -> mm6]

(* 119 *)

or

((List @@ mm7a)/mm5) . mm6

(* 119 *)

If mm5 is not known

Cases[mm7a, _Integer, ∞] . mm6

(* 119 *)

or

(List @@ mm7a /. n_Integer*_ :> n) . mm6

(* 119 *)

Answer 2

Another approach you might want to consider is to define a function that does the job. So for the specific setup you request:

f[x_, y_] := x . y

Now you can apply f to your desired values:

mm5 = {a, b, c, d};
mm7 = {2, 3, 9, 8};
mm6 = {3, 4, 5, 7};

f[mm5, mm7]
f[mm5, mm6]

and you get something that is generic and can be easily modified for other applications by redefining f[ ].