I have a very complicated mathematica expression that I'd like to simplify by using a new, possibly dimensionless parameter.
An example of my expression is:
K=a*b*t/((t+f)c*d);
(the actual expression is monstrously large, thousands of characters). I'd like to replace all occurrences of the expression t/(t+f) with p
p=t/(t+f);
The goal here is to find a replacement so that all t's and f's are replaced by p. In this case, the replacement p is a nondimensionalized parameter, so it seems like a good candidate replacement.
I've not been able to figure out how to do this in mathematica (or if its possible). I tried:
eq1= K==a*b*t/((t+f)c*d);
eq2= p==t/(t+f);
Solve[{eq1,eq2},K]
Not surprisingly, this doesn't work. If there were a way to force it to solve for K in terms of p,a,b,c,d, this might work, but I can't figure out how to do that either. Thoughts?
Edit #1 (11/10/11 - 1:30) [deleted to simplify]
OK, new tact. I've taken p=ton/(ton+toff) and multiplied p by several expressions. I know that p can be completely eliminated. The new expression (in terms of p) is
testEQ = A B p + A^2 B p^2 + (A+B)p^3;
Then I made the substitution for p, and called (normal) FullSimplify, giving me this expression.
testEQ2= (ton (B ton^2 + A^2 B ton (toff + ton) +
A (ton^2 + B (toff + ton)^2)))/(toff + ton)^3;
Finally, I tried all of the suggestions below, except the last (not sure how it works yet!)
Only the eliminate option worked. So I guess I'll try this method from now on. Thank you.
EQ1 = a1 == (ton (B ton^2 + A^2 B ton (toff + ton) +
A (ton^2 + B (toff + ton)^2)))/(toff + ton)^3;
EQ2 = P1 == ton/(ton + toff);
Eliminate[{EQ1, EQ2}, {ton, toff}]
A B P1 + A^2 B P1^2 + (A + B) P1^3 == a1
I should add, if the goal is