RE: Problems with SIMPLIFY and SOLVE
- To: mathgroup at smc.vnet.net
- Subject: [mg34138] RE: [mg34111] Problems with SIMPLIFY and SOLVE
- From: "DrBob" <majort at cox-internet.com>
- Date: Sun, 5 May 2002 04:48:47 -0400 (EDT)
- Reply-to: <drbob at bigfoot.com>
- Sender: owner-wri-mathgroup at wolfram.com
Hannes,
(1) The statement
Element[{a, b, n, m}, Reals]
has no effect on expressions following it. It's an assertion, which may
or not be true --- it's not a command telling Mathematica to assume it
IS true, except when used properly... as the second argument of
Simplify, for instance. (Try {a>0, b>0, n>0, m>0, a+b+n>1} as the
second argument, perhaps. Note that a>0 implies "a" is real.)
(2) The part 1 expression isn't defined if m = 0 and its exponent is
negative (you haven't ruled that out), and it isn't real if m is
negative and the exponent isn't an integer (you haven't ruled that out
either).
(3) When I rule out those possibilities, Mathematica STILL doesn't know
the expression has to be positive. I don't know why, but it doesn't
particularly surprise me.
(4) Your part 2 expression is once again NOT affected by the Element
expression preceding it.
(5) I was able to solve for m as follows:
Clear[j,k,m]
j=k/.Solve[a/(a+b+n)-
m^(-1+a+b+n)*(a/(a+b+n))^a*((b+n)/(a+b+n))^(b+n)*(a+b+n)==0
/.m^(-1+a+b+n)->k,k]//First
Off[Solve:ifun]
m/.Solve[m^(-1+a+b+n)==j,m]//First
Bobby Treat
-----Original Message-----
From: Hannes Egli [mailto:hannes.egli at uni-greifswald.de]
To: mathgroup at smc.vnet.net
Subject: [mg34138] [mg34111] Problems with SIMPLIFY and SOLVE
Hello
1)
After the following input, I would expect the output TRUE, since after
my mathematical understanding, the expression is unambiguously
negative. Mathematica, however, only restates the expression.
Element[{a, b, n, m}, Reals]
Simplify[-m^(-2 + a + b + n)*(-1 + a + b + n)*(a/(a + b + n))^a
*((b + n)/(a + b + n))^(b + n)*(a + b + n) < 0, {a > 0, b > 0, n > 0,
a + b + n > 1}]
2)
The second problem may be similar. Given the restriction on the
parameter values, the following equation should can be solved for m:
Element[{a, b, n, m}, Reals]
Solve[a/(a + b + n) - m^(-1 + a + b + n)*(a/(a + b + n))^a
*((b + n)/(a + b + n))^(b + n)*(a + b + n) == 0, m]
Does somebody see what I am doing wrong?
Thanks
Hannes