Problem with SetDelay [duplicate]

Question

I am trying to do some calculations on very long and difficult equations. Ultimately, I want to create a function to NIntegrate my result, but I want to set it as SetDelay (to be evaluated after placing the variables).

The problem can be showed at this simple example:

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

EVals = Eigenvalues[A];

EV1 = EVals[[1]];
EV2 = EVals[[2]];

DEV1 = D[EV1, a];
DEV2 = D[EV2, a];

F[b_, c_, d_] := NIntegrate[DEV1 + DEV2, {a, 0, 1}];

But after evaluation, e.g., F[2,3,4], I get the symbolic expression.

I know, that in this example I can just copy-paste DEV1 and DEV2 directly to the F, but I am working with more difficult formulas, where I cannot do this.

Answer 1

Due to ,localization, your parameters b,c,d are not the same variables as those in DEV1 nd DEV2 and therefore get not replaced. You can see this e.g. by:

tmp = {b, c, d};
F[b_, c_, d_] := Print[tmp];
F[2, 3, 4]

{b,c,d}

However, we can replace them explicitly, like e.g.;

tmp = {b, c, d};
F[b0_, c0_, d0_] := Print[tmp /. {b -> b0, c -> c0, d -> d0}];
F[2, 3, 4]

{2,3,4}

This applied to your example:

F[b0_, c0_, d0_] := 
  NIntegrate[DEV1 + DEV2 /. {b -> b0, c -> c0, d -> d0} , {a, 0, 1}];
F[2, 3, 4]

1.