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Is there a reason MuPad doesn't find the obvious cancellation?

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Billy
Billy 2011-6-17
I have:
f := 1/2* sqrt( 16-x^2 )
df := diff( f, x )
simplify( f * sqrt( 1 + df^2 ) )
mupad doesn't find the obvious cancellation (sqrt( 16-x^2 ) should go away)
Why not? Is there an algebraic reason I'm missing, or am I using the simplify function incorrectly, or is it something else?

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Matt Tearle
Matt Tearle 2011-6-17
I'm guessing it's something to do with assumptions about squares and square roots, and maybe denominators. Wouldn't swear to it, though. If you want it to do what you'd probably do by hand, you can try this:
Simplify(f * sqrt( 1 + df^2 ),IgnoreAnalyticConstraints)
(Note the capital S)

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Walter Roberson
Walter Roberson 2011-6-17
In particular sqrt(t) * sqrt(1/t) does not cancel if t is 0. Or in your case, if x = +/- 4

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