Question: How to do parametric comparisons?

How to compare the magnitude (the absolute value, ignoring the sign) of two multi-parameter functions f_1 and f_2?

Note that all my parameters can only take stricly positive values. Specifically, I want to know the ranges of parameter values for which f_1 > f_2, f_1 < f_2, and f_1 = f_2. Is solve(f_1 > f_2) etc. the best way to do this? If so, how to specify solve() so that it incorporates all three (>,<,=) comparisons and do not ignore the strict positivity assumption? Is there any other command other than solve()?   

Example with only two parameters sigma__v and sigma__d:


 # Parameters always positive

assume(0 < sigma__d, 0 < sigma__v);



Diff('lambda__1', sigma__v) = sqrt(5)/(5*sigma__d);
f__1 := rhs(%);
Diff('lambda__1', sigma__d) = -sqrt(5)*sigma__v/(5*sigma__d^2);
f__2 := abs(rhs(%));

Diff(lambda__1, sigma__v) = (1/5)*5^(1/2)/sigma__d




Diff(lambda__1, sigma__d) = -(1/5)*5^(1/2)*sigma__v/sigma__d^2




plot3d([f__1,f__2], sigma__v=0.001..10, sigma__d=0.001..10, view=0..5, color=[red,blue]);





Note that f_1 depends only on sigma__d but f_2 depends on both sigma__v and sigma__d. Of course I can directly plot the two curves in 3d in this simple case, but I am looking for a systematic way to do parametric comparisons so that I don't have to "eyeball" the threshold values (if any exist). Most importantly, I can't plot at all once my functions depend on more than two parameters.


EDIT: perhaps "variables" is a better word than "parameters" here.

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