
Re: can your CAS help proving inequalities?
Posted:
Mar 10, 2013 3:27 PM


On 3/10/2013 11:57 AM, clicliclic@freenet.de wrote:
> > Since the Mathematica variables are complex by default, they must here > perhaps be explicitly restricted to real.
Sure.
 FindInstance[ Min[r[a, b, c, d], r[a, c, b, d], r[a, d, c, b]] > 0, {a, b, c, d}, Reals]
FindInstance[ Min[r[a, b, c, d], r[a, c, b, d], r[a, d, c, b]] > 0, {a, b, c,
d}, Reals] FindInstance[ Min[t[a, b, c, d], t[a, c, b, d], t[a, d, c, b]] > 0, {a, b, c, d}, Reals] 
{} {} {} 
> Judging form the "Notes On > Internal Implementation" it looks like Mathematica's Reduce[] might be > able to do reduce such inequalities: among other techniques, it fields > cylindrical algebraic decomposition (CAD). > > Martin. >
yes:
 Reduce[Min[r[a, b, c, d], r[a, c, b, d], r[a, d, c, b]] > 0, {a, b, c, d}, Reals]
Reduce[Min[r[a, b, c, d], r[a, c, b, d], r[a, d, c, b]] > 0, {a, b, c, d}, Reals]
Reduce[Min[t[a, b, c, d], t[a, c, b, d], t[a, d, c, b]] > 0, {a, b, c, d}, Reals]  False False False 
Nasser

