abs and sign simplification

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Corey Richardson 2016-9-29

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评论： Corey Richardson 2016-9-29

In some symbolic manipulations, I get a result which has something like abs(e)*sign(e). Why is this not simplified away, even by simplify? It's surely an identity that e = abs(e)*sign(e). For example, with this code:

syms x
diff(norm(diff(cos(x))))
% ans = (abs(sin(t))*sign(sin(t))*cos(t))/(abs(sin(t))^2)^(1/2)

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Massimo Zanetti 2016-9-29

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编辑：Massimo Zanetti 2016-9-29

It happens because for the scalar case norm(y)=|y| (here y=y(x) is any function), therefore Matlab computes derivative by splitting the two cases in the derivative of|y|: y>=0 and y<0. Then it combines the results in a signle function by the sign*|.| trick.