jmetz

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Hello,

I'm confused about Maple's adjoint function (in the DEtools package). When I take the adjoint of the derivative operator:

DEtools:-adjoint(Dx, [Dx, x])

 

I get back simply "Dx". However, doing the calculation by hand and integrating by parts seems to indicate that this should return the negative of Dx. The inner product I'm using is int(f(x)*conjugate(g(x)), x=0..1). Is Maple perhaps using a different inner product? Or is this a generalization that I'm unaware of? Or is it perhaps just a bug?

 

Thanks!

Hello,

I am trying to get Maple to recognize and reverse the product rule in more than one dimension. In one dimension, this works:

Int((Diff(f(x), x))*g(x)+(Diff(g(x), x))*f(x), x) = int((diff(f(x), x))*g(x)+f(x)*(diff(g(x), x)), x);

Int((Diff(f(x), x))*g(x)+(Diff(g(x), x))*f(x), x) = int((diff(f(x), x))*g(x)+f(x)*(diff(g(x), x)), x).

But in two dimensions, it no longer evaluates:

Int((Diff(f(x, y), x))*g(x, y)+(Diff(g(x, y), x))*f(x, y), x) = int((diff(f(x, y), x))*g(x, y)+f(x, y)*(diff(g(x, y), x)), x)

Int((Diff(f(x, y), x))*g(x, y)+(Diff(g(x, y), x))*f(x, y), x) = int((diff(f(x, y), x))*g(x, y)+f(x, y)*(diff(g(x, y), x)), x)

As far as I can tell, mathematically these should be identical (except for the antiderivatives being defined up to a constant in the first case and a function of y in the second). Is there a way to get Maple to reverse the product rule to integrate in more than one dimension? Or am I missing something mathematically that makes this incorrect?

Thanks for your help,

Johnathan

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