# Question:How to do parametric comparisons?

## Question:How to do parametric comparisons?

Maple

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); interface(showassumed=0);
 (1)
 > 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(%));
 (2)
 > plot3d([f__1,f__2], sigma__v=0.001..10, sigma__d=0.001..10, view=0..5, color=[red,blue]);
 >
 >