maxima again...

jimmij · science forum beginner Joined: 17 Jul 2006 Posts: 4

(%i1) a: sqrt(1-x);
(%o1) sqrt(1 - x)
(%i2) b: sqrt(1+x);
(%o2) sqrt(x + 1)
(%i3) a*b;
(%o3) sqrt(1 - x) sqrt(x + 1)

How can I simpify this to sqrt(1-x^2)?

I tried ratsimp, trigsimp, expand, ratexpand, trigexpand...
Nothing works.

--
jimmij

rjf · science forum beginner Joined: 05 May 2006 Posts: 5

in general, sqrt(a)*sqrt(b) is not equal to sqrt(a*b), so most computer
algebra systems are not going to do this for you by some standard
command.

let a=b=-1. Then sqrt(a)*sqrt(b) = i*i = -1.
but sqrt(a*b)=sqrt(1)=1. (at least by convention. really it should be
+/-1 but CAS don't usually make that observation). Of course sqrt(-1)
is +-i, by the same reasoning.

radcan can do some related simplifications, and you can also see
describe(denest);

jimmij wrote:

jimmij · science forum beginner Joined: 17 Jul 2006 Posts: 4

"rjf" <fateman@gmail.com> writes:

Christopher Creutzig · science forum Guru Wannabe Joined: 03 May 2005 Posts: 107

jimmij wrote:

Google