[Maxima-bugs] [ maxima-Bugs-2852992 ] sqrt(-1/x)-%i/sqrt(x) not zero

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Bugs item #2852992, was opened at 2009-09-06 17:42
Message generated for change (Comment added) made by crategus
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Category: Lisp Core - Simplification
Group: None
>Status: Closed
>Resolution: Fixed
Priority: 5
Private: No
Submitted By: Dieter Kaiser (crategus)
Assigned to: Nobody/Anonymous (nobody)
Summary: sqrt(-1/x)-%i/sqrt(x) not zero

Initial Comment:
For any real value sqrt(-1/x) should simplify to %i/sqrt(x).

We try a positive symbol and get a wrong sign:

(%i1) assume(x>0)$

(%i2) sqrt(-1/x);
(%o2) -%i/sqrt(x)

This should be zero:

(%i3) sqrt(-1/x)-%i/sqrt(x);
(%o3) -2*%i/sqrt(x)

For numbers all is correct. We get the expected answers for positive and negative numbers:

(%i15) sqrt(-1/2)-%i/sqrt(2);
(%o15) 0
(%i16) sqrt(-1/(-2))-%i/sqrt(-2);
(%o16) 0

For a general real value we get a wrong simplification too:

(%i18) kill(all)$

(%i1) expr:sqrt(-1/x)-%i/sqrt(x);
(%o1) 1/sqrt(-x)-%i/sqrt(x)

The expression is wrongly simplified. We should get zero for positive and negative numbers:

(%i2) expr,x=2;
(%o2) -sqrt(2)*%i

(%i3) expr,x=-2;
(%o3) 0

This bug is related to the bug ID: 1010768 "sqrt(1/z) - 1/sqrt(z) => 0".

Dieter Kaiser


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>Comment By: Dieter Kaiser (crategus)
Date: 2010-01-17 02:24

Message:
Fixed in simp.lisp revision 1.96.

For a real argument Maxima simplifies:

(%i1) sqrt(-1/x);
(%o1) %i/sqrt(x)

The example of this bug report simplifies to zero:

(%i2) sqrt(-1/x)-%i/sqrt(x);
(%o2) 0

No simplification if the argument is complex:

(%i3) declare(z,complex)$

(%i4) sqrt(-1/z);
(%o4) sqrt(-1/z)

Closing this bug report as fixed.
Dieter Kaiser

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