Why does FullSimplify not work with assumptions in Mathematica?

[daudaudaudau]

Anyone have an explanation for this? It can simplify the first one but not the second...

 

[daudaudaudau]

And what about this:

FullSimplify[Abs[(x*y)]^2, x > 0 && y > 0]

the result is still Abs[x*y]^2

But there is no trouble doing this one

FullSimplify[Abs[(x/y)]^2, x > 0 && y > 0]

is simply returns x^2/y^2...

 

[bpet]

I had similar problems and asked tech support about it - they recommend as a workaround e.g.

PiecewiseExpand[Abs[(x*y)]^2, Reals]

 

[flatmaster]

And what about this:

FullSimplify[Abs[(x*y)]^2, x > 0 && y > 0]

the result is still Abs[x*y]^2

But there is no trouble doing this one

FullSimplify[Abs[(x/y)]^2, x > 0 && y > 0]

is simply returns x^2/y^2...

x > 0 && y > 0
Well, if this was an equals sign rather than >, it would need to be a double equqals "==". Not sure what the expression would be for >

 

[flatmaster]

For the top one, x and y could still be imaginary, giving a negative product. For division, a comlex number squared is real, making the Abs redundant.

i'm assuming that Mathematica's assumes all vars can be complex. See if you can convince mathematica that x,y belong to reals

Not quite what you wanted to do, but it's a starting place.

http://reference.wolfram.com/mathematica/tutorial/ExpressionsInvolvingComplexVariables.html

 

[CompuChip]

flatmaster, I don't understand your remarks about "==" ... it clearly says > doesn't it?

Also, AFAIK Mathematica automatically assumes they are real when you use a comparison operator, i.e. "x > 0" implies "Element[x, Reals]"

 

[daudaudaudau]

I had similar problems and asked tech support about it - they recommend as a workaround e.g.

PiecewiseExpand[Abs[(x*y)]^2, Reals]

I see. When you want to assume that both x and y are real, you simply write ", Reals" ? Because this doesn't work for FullSimplify, e.g.

FullSimplify[Abs[x/y]^2, Reals]

is not the same as

FullSimplify[Abs[x/y]^2, _ \[Element] Reals]