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Christopher Creutzig
science forum Guru Wannabe

Joined: 03 May 2005
Posts: 107

Posted: Thu Jul 20, 2006 5:32 pm    Post subject: Re: maxima again...

jimmij wrote:

 Quote: (%i12) ratsimp(sqrt(a*b)); (%o12) sqrt(1 - x) sqrt(x + 1) Where is a problem?

Obviously(?), maxima regards sqrt(1-x)*sqrt(x+1) as simpler than
sqrt((1-x)*(x+1)). Note that it *did* use your assumptions.

I do not have maxima installed, but I'd guess that with your assumptions,

ratsimp(sqrt(a*b)-sqrt(a)*sqrt(b))

will equal zero, which without the assumptions would be wrong, as
Richard pointed out.

Regards,
Christopher
jimmij
science forum beginner

Joined: 17 Jul 2006
Posts: 4

Posted: Thu Jul 20, 2006 12:48 pm    Post subject: Re: maxima again...

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

 Quote: 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.

Thanks for explainations.
Lets then assume something:

(%i1) a: 1-x;
(%o1) 1 - x
(%i2) b: 1+x;
(%o2) x + 1
(%i3) assume(x<1);
(%o3) [x < 1]
(%i4) assume(x>0);
(%o4) [x > 0]
(%i5) sign(x);
(%o5) pos
(%i6) sign(a);
(%o6) pos
(%i7) sign(b);
(%o7) pos
(%i sign(sqrt(a));
(%o pos
(%i9) sign(sqrt(b));
(%i10) a*b;
(%o10) (1 - x) (x + 1)
(%i11) ratsimp(a*b);
2
(%o11) 1 - x
(%i12) ratsimp(sqrt(a*b));
(%o12) sqrt(1 - x) sqrt(x + 1)

Where is a problem?

--
jimmij
rjf
science forum beginner

Joined: 05 May 2006
Posts: 5

Posted: Thu Jul 20, 2006 6:22 am    Post subject: Re: maxima again...

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:
 Quote: (%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
jimmij
science forum beginner

Joined: 17 Jul 2006
Posts: 4

 Posted: Wed Jul 19, 2006 5:28 pm    Post subject: maxima again... (%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
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