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Question: Why does simplify command turn these three expressions to one single expression?

Question:Why does simplify command turn these three expressions to one single expression?

zenterix 350
simplify
August 03 2024
0

In the code below, I define an expression, then turn it into a function of omega_d.

Consider the results (5) and (6) below.

I take the derivative of the function relative to omega_d, set the derivative to zero and ask Maple to solve for the critical point (ie, the omega_d at which the derivative is zero).

I get the correct result in (5), ie three different critical points. But when I simplify this result, Maple returns only one of the critical points.

Why?

restart

expr := f/sqrt((`ω__0`^2-`ω__d`^2)^2+`γ__b`^2*`ω__d`^2)

f/((omega__0^2-omega__d^2)^2+gamma__b^2*omega__d^2)^(1/2)

 (1)

A := unapply(expr, `ω__d`)

proc (omega__d) options operator, arrow; f/((omega__0^2-omega__d^2)^2+gamma__b^2*omega__d^2)^(1/2) end proc

 (2)

diff(A(`ω__d`), `ω__d`)

-(1/2)*f*(-4*(omega__0^2-omega__d^2)*omega__d+2*gamma__b^2*omega__d)/((omega__0^2-omega__d^2)^2+gamma__b^2*omega__d^2)^(3/2)

 (3)

simplify(diff(A(`ω__d`), `ω__d`))

-f*omega__d*(gamma__b^2-2*omega__0^2+2*omega__d^2)/(omega__d^4+(gamma__b^2-2*omega__0^2)*omega__d^2+omega__0^4)^(3/2)

 (4)

solve(diff(A(`ω__d`), `ω__d`) = 0, `ω__d`)

0, (1/2)*(-2*gamma__b^2+4*omega__0^2)^(1/2), -(1/2)*(-2*gamma__b^2+4*omega__0^2)^(1/2)

 (5)

simplify(solve(diff(A(`ω__d`), `ω__d`) = 0, `ω__d`))

0

 (6)

NULL


This was a problem for me just now because I used the command in (6) first and just could not figure out what the heck was going on. I did the calculations by hand to check, and then finally found out it was this simplify command.

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