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MathGroup Archive 2001

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Re: restrictions on parameters

  • To: mathgroup at smc.vnet.net
  • Subject: [mg31985] Re: restrictions on parameters
  • From: atelesforos at hotmail.com (Orestis Vantzos)
  • Date: Sat, 15 Dec 2001 01:30:02 -0500 (EST)
  • References: <9vcgq9$3js$1@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

The problem is that the restrictions are not specified at all!
Evaluating a<0;b>0;... means asking Mathematica whether a is less than
0, b greater than 0, etc. This has absolutely no effect, since
Mathematica knows nothing about a,b,c or d, so it just returns the
inequalities.
The proper way to go around this, is to use the new Experimental`
features of version 4.
So:
<<Experimental`
ImpliesRealQ[{a<0,b>0,c>0,d>0},-b*c+a*d<0]
True
which means that the Determinant is indeed negative.
The first eigenvalue is 
1                2                    2
- (a + d - Sqrt[a  + 4 b c - 2 a d + d ])
2
but the same trick does not work.
If you evaluate:
ImpliesRealQ[{a<0,b>0,c>0,d>0},(a+d)^2 < a^2+4*b*c-2*a*d+d^2]
which is equivalent, you will get True.
Orestis


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