[Maxima-bugs] [ maxima-Bugs-1575120 ] Some laws are still missing

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Bugs item #1575120, was opened at 2006-10-11 02:54
Message generated for change (Comment added) made by robert_dodier
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Category: Lisp Core - Simplification
Group: None
>Status: Pending
>Resolution: Rejected
Priority: 5
Submitted By: Nobody/Anonymous (nobody)
Assigned to: Nobody/Anonymous (nobody)
Summary: Some laws are still missing

Initial Comment:
is(equal((x/y)^z,(x^z/y^z)));
is(equal((x*y)^z,(x^z*y^z)));
is(equal((x^y)^z,(x^(y*z))));

of course they are equal! Those are laws!

--Mario/Mexico

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>Comment By: Robert Dodier (robert_dodier)
Date: 2006-10-21 14:26

Message:
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As mentioned by Barton, Maxima's default behavior is correct
(since there are examples for which those equations fail to
hold). I find that assuming x > 0 and y > 0, Maxima does
evaluate those to true; I believe that is correct. 

assume(x>0,y>0);
is(equal((x/y)^z,(x^z/y^z))); => true
is(equal((x*y)^z,(x^z*y^z))); => true
is(equal((x^y)^z,(x^(y*z)))); => true

A possible enhancement (very far away at this point) would
be for is(equal(...)) to return a result with one or more
guard clauses specifying the applicability of various
particular results. I won't try to spec that here.

Marking this report "rejected" and "pending" (so that it
will be closed automatically in 2 weeks, in case the
original poster comes back).

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Comment By: Barton Willis (willisbl)
Date: 2006-10-11 04:09

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For real x,y,z, the equation (x*y)^z = x^z*y^z isn't an
identity. To see this, let x --> -1, y --> -1, and 
z --> 1/2. If Maxima did 

   is(equal((x*y)^z,(x^z*y^z))) --> true

that would be a bug. Similarly, all your other laws
are not valid for all real numbers.

(1) We're working on improving the function equal; it
has many known problems.

(2) The function 'radcan' does

(%i16) radcan((x*y)^z);
(%o16) x^z*y^z

Maybe you would like to use it.

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