simplify sqrt(x/y^2)*y

asked 2015-09-20 18:03:09 +0200

miguelython
13 ●1 ●4

updated 2015-09-27 11:44:29 +0200

Hello my problem is with a bigger equation but the problem is bassicly this : sage: var('x','y', domain=real)
sage: assume(x>0)
sage: assume(y>0)
sage: e = sqrt(1/y^2)y
sage: e.simplify_full()
1
sage: e = sqrt(x/y^2)y
sage: e.simplify_full()
y*sqrt(x/y^2)

Anyone explain me how to get just sqrt(x) and why it doesn't do directly? Thanks

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answered 2015-09-20 20:29:23 +0200

nbruin
4143 ●3 ●45 ●90

I hope there is no way to coerce Sage into returning just x, because your expression is only equal to that for a very limited number of choices for x. Sage (Maxima, really) can be convinced to make branch choices to simplify the expression to sqrt(x), but not via assumptions, apparently. This does work:

sage: var('x,y')
(x, y)
sage: E=sqrt(x/y^2)*y
sage: E.canonicalize_radical()
sqrt(x)

See the documentation of canonicalize_radical for details.

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thank you, I edited

miguelython ( 2015-09-27 11:43:56 +0200 )edit

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answered 2015-09-20 21:52:52 +0200

miguelython
13 ●1 ●4

Yes, I mean just "x" part so sqrt(x)... sorry for not to be clear. Thanks. It works, but I wonder why canonicalize_radical isn't part of simplify_full?

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This is because

sage: x = var('x', domain='real')
sage: assume(x<0)
sage: sqrt(x^2).canonicalize_radical()
x

and I guess you don't want this (note the x<0 assumption).

eric_g ( 2015-09-20 23:28:18 +0200 )edit

Miguel, note that sqrt(x^2) != x for x<0.

rws ( 2015-09-21 09:50:22 +0200 )edit

I don't want this beacause is false. I want sqrt(x^2)=abs(x) or in case ofassume(x>0) or assume(x<0) : sqrt(x^2)=x or sqrt(x^2)=-x resp

miguelython ( 2015-09-27 12:17:05 +0200 )edit

I mean if I had the time and knowleage, I change it in the source code. Nevertheless, I'm thankful to all community of sagemath

miguelython ( 2015-09-27 12:24:09 +0200 )edit

A fix should be possible with pynac-0.4.x (pynac is part of Sage); pynac git master already does sqrt(x^2) --> x for x>0 as side effect of other changes.

rws ( 2015-09-27 16:39:58 +0200 )edit

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