Improve sqrt products simplification

[rwst]

Let the argument be positive. I think the following should give sqrt(6), and 6*sqrt(2) respectively.

sage: (sqrt(2) * sqrt(3)).simplify_full()
sqrt(3)*sqrt(2)
sage: (sqrt(12) * sqrt(6)).simplify_full()
2*sqrt(6)*sqrt(3)

There is a Pynac ticket for this but we appreciate improvements of Maxima as well.

CC: @orlitzky

Component: calculus

Issue created by migration from https://trac.sagemath.org/ticket/22621

[kcrisman]

comment:1

Is this also going to simplify sqrt(-3)*sqrt(-2)==sqrt(6)? We've had this discussion before...

[rwst]

comment:2

Replying to @kcrisman:

Is this also going to simplify sqrt(-3)*sqrt(-2)==sqrt(6)? We've had this discussion before...

I don't remember but I hope it concluded that combining positive arguments is fine.

[rwst]

Description changed:

--- 
+++ 
@@ -1,4 +1,4 @@
-I think this should give `sqrt(6)`, and `6*sqrt(2)` respectively.
+Let the argument be positive. I think the following should give `sqrt(6)`, and `6*sqrt(2)` respectively.
 
 ```
 sage: (sqrt(2) * sqrt(3)).simplify_full()

[kcrisman]

comment:3

#12737 is the main place this sort of thing was discussed, though there are many. Probably for positive is fine, but I'm no expert on this kind of thing.