[Maxima-bugs] [ maxima-Bugs-1977146 ] radexpand does not work as explained in documentation

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Bugs item #1977146, was opened at 2008-05-28 23:37
Message generated for change (Comment added) made by crategus
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Category: Lisp Core - Simplification
Group: None
Status: Open
Resolution: None
Priority: 5
Private: No
Submitted By: Robert Marik (robertmarik)
Assigned to: Nobody/Anonymous (nobody)
Summary: radexpand does not work as explained in documentation

Initial Comment:
>From maxima discussion list:

Maxima manual states the following

---------------------
When radexpand is false, certain transformations are inhibited. radcan (sqrt (1-x)) remains sqrt (1-x) and is not simplified to %i sqrt (x-1). radcan (sqrt (x^2 - 2*x + 11)) remains sqrt (x^2 - 2*x + 1) and is not
simplified to x - 1.
---------------------

Neglecting the typo in radcan (sqrt (x^2 - 2*x + 11)) which should be probably radcan (sqrt (x^2 - 2*x + 1)), I get the answer x-1 also with radexpand:false. Moreover, sqrt(1-x) remains sqrt(1-x) even with radexpand:true.

Is the documentation of radcan obsolete?

Robert Marik



reponse of Richard Fateman

radexpand was inserted by someone else, after the code was written in 1970. I do not know if the documentation or the program is buggy, since I'm not sure what was intended.
RJF




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>Comment By: Dieter Kaiser (crategus)
Date: 2009-11-28 23:40

Message:
I think the option variable radexpand controls the simplification of the
power function, but does not control the function radcan. This is wrongly
documented.

radexpand works for expressions like (x*y)^a and (x^a)^b. Some examples
are:

(%i2) radexpand:false$

(%i3) (x*y)^a;
(%o3) (x*y)^a

(%i4) (x*y)^a,radexpand:true;
(%o4) (x*y)^a

The expression simplifies, if radexpand is set to ALL:

(%i5) (x*y)^a,radexpand:all;
(%o5) x^a*y^a


(%i6) (x^a)^b;
(%o6) (x^a)^b

(%i7) (x^a)^b,radexpand:true;
(%o7) (x^a)^b

The expression simplifies, if radexpand is set to ALL:

(%i8) (x^a)^b,radexpand:all;
(%o8) x^(a*b)

Both expressions simplify only, if radexpand is set to ALL. Therefore, the
value ALL has the effect, that all variables are assumed to be positive and
real.

With a value of TRUE, radexpand controls the simplifcation of the power
function for even and odd rational numbers.

For an even rational power we do not get a simplification:

(%i12) (x*y)^(1/2);
(%o12) sqrt(x*y)

(%i13) (x*y)^(1/2),radexpand:true;
(%o13) sqrt(x*y)

But we get a simplification for an odd power, if radexpand is set to
TRUE:

(%i14) (x*y)^(1/3);
(%o14) (x*y)^(1/3)

(%i15) (x*y)^(1/3),radexpand:true;
(%o15) x^(1/3)*y^(1/3)

The function radcan simplifies the above expressions with power functions
too, but does not depend on the flag radexpand:

The flag is set to FALSE:

(%i34) radexpand;
(%o34) false

radcan simplifies the expressions. The flag radexpand does not matter:

(%i35) radcan((x*y)^a);
(%o35) x^a*y^a

(%i36) radcan((x^a)^b);
(%o36) x^(a*b)

Therefore, radcan always assumes the variables to be positive and real.

In a first step, all of these should be documented more clearly.

Dieter Kaiser

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