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How to remove "Abs" from "Simplify" output?

Zhenyu Zeng
Posted 14 days ago

Hello,

In Mathemtiaca

Simplify[Sqrt[(a  b  c + d  e  g)^2], a  b  c + d  e  g > 0]

will produce

Abs[a b c + d e g]

It is a little wired, as I think the answer should be 

a b d+ d e g
POSTED BY: Zhenyu Zeng
15 Replies
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Sqrt[(a   b   c + d   e   g)^2] // PowerExpand
POSTED BY: Robert Nowak
Zhenyu Zeng
Zhenyu Zeng
Posted 12 days ago

Weird. Your way works.
POSTED BY: Zhenyu Zeng
Hans Milton
Hans Milton
Posted 13 days ago

Try this:

Simplify[Sqrt[(a b c+d e f)^2],(a b c+d e f)\[Element]NonNegativeReals]

It gives:

a b c + d e f
POSTED BY: Hans Milton
Zhenyu Zeng
Zhenyu Zeng
Posted 12 days ago

Your way is very good. Do you feel a lilttle weird as \[Element] NonNegativeReals works but >0 doesn't?
POSTED BY: Zhenyu Zeng
Hans Milton
Hans Milton
Posted 12 days ago

Well, looking at this further I see that this would also work:

Simplify[Sqrt[(a b c + d e f)^2], (a b c + d e f) >= 0]

So zero needs to be included in the domain of this case.

But when the expression is shorter there is no such need:

Simplify[Sqrt[(a b + d e)^2], (a b + d e) > 0]

This is puzzling
POSTED BY: Hans Milton
Zhenyu Zeng
Zhenyu Zeng
Posted 12 days ago

If in this situation

Simplify[Sqrt[1/(a  b  c + d  e  f)^2], (a  b  c + d  e  f) > 0]

we can't use

>=0

here.
POSTED BY: Zhenyu Zeng
Bill Nelson
Bill Nelson
Posted 13 days ago

Simplify[Sqrt[(a b c + d e g)^2], a b c>0&&d e g>0]

returns

a b c+d e g

You might be able to loosen that up a little bit by indicating the result is still positive if one of those triples is negative
POSTED BY: Bill Nelson
David G
David G
Posted 13 days ago

Misread OP.

Deleted
POSTED BY: David G
Hans Milton
Hans Milton
Posted 13 days ago

Your example shows the square of the root. In that case no domain specification is needed. The OP asked for the root of the square,
POSTED BY: Hans Milton
David G
David G
Posted 13 days ago

You are of course correct. Apologies.
POSTED BY: David G

Does this help?

  Assuming[a  b  c + d  e  g > 0,  Simplify[Sqrt[(a  b  c + d  e  g)^2]]]

Out[22]= Abs[a b c + d e g]

Never mind; that's what you started with!
POSTED BY: Marvin Ray Burns

The easiest would just be removing the absolutes:

yourexpression /. Abs -> Identity
POSTED BY: Sander Huisman
Zhenyu Zeng
Zhenyu Zeng
Posted 12 days ago

May you tell why does this work? I don't know the reason. For example, this doesn't work

List[{a, b, c, d}] /. List -> Identity
POSTED BY: Zhenyu Zeng

Just my guess. Simplify transforms the condition a*b*c + d*e*f>0 into the complicated result of Reduce[a*b*c + d*e*f>0] and then gets bogged down. It does not recognize that it fits the pattern Simplify[Sqrt[x^2], x > 0]. Funny that the following does work:

With[{x = Sin[a*b*c + d*e*f ]},
 Simplify[Sqrt[x^2], x > 0]]
POSTED BY: Gianluca Gorni
Zhenyu Zeng
Zhenyu Zeng
Posted 13 days ago

Yes. It is fuuny. Is there a way to 

Simplify[Sqrt[(a  b  c + d  e  g)^2], a  b  c + d  e  g > 0]
POSTED BY: Zhenyu Zeng
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