answered
**
2011-06-21 02:18:55 -0500
**

```
sage: bool(c^2 - u*v >= 0)
False
```

"`False`

" here means "not known to be true" -- it seems that `bool`

just can't make the following observation:

```
c^2 > c*v > u*v
```

Although if you test each inequality separately, it will recognize them as `True`

. More powerful symbolic manipulation is available through Maxima; see for example the parts of the reference manual having to do with Symbolic Calculus.

Unfortunately you might have to work harder for this -- I tried `test_relation_maxima`

and got the same unsatisfactory results as with `bool`

. You could try looking through the Maxima reference manual to see if there is something more useful there. You can use Maxima directly through Sage with `maxima_console()`

:

```
sage: maxima_console()
;;; Loading #P"/Applications/sage/local/lib/ecl/sb-bsd-sockets.fas"
;;; Loading #P"/Applications/sage/local/lib/ecl/sockets.fas"
;;; Loading #P"/Applications/sage/local/lib/ecl/defsystem.fas"
;;; Loading #P"/Applications/sage/local/lib/ecl/cmp.fas"
Maxima 5.23.2 http://maxima.sourceforge.net
using Lisp ECL 11.1.1
Distributed under the GNU Public License. See the file COPYING.
Dedicated to the memory of William Schelter.
The function bug_report() provides bug reporting information.
(%i1) factor(10!);
8 4 2
(%o1) 2 3 5 7
(%i2)
```