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Re: Simplify puzzle

  • To: mathgroup at smc.vnet.net
  • Subject: [mg124655] Re: Simplify puzzle
  • From: Bob Hanlon <hanlonr357 at gmail.com>
  • Date: Sun, 29 Jan 2012 05:14:49 -0500 (EST)
  • Delivered-to: l-mathgroup@mail-archive0.wolfram.com
  • References: <201201271111.GAA12491@smc.vnet.net>

myassumptions = a > 0 && b > 0 && c > 0 && 1 > d > 0 && 1 > e > 0;

FullSimplify[a*b + c*(1 - d*(1 - e)) > 0,
 Assumptions -> myassumptions]

a b + c + c d e > c d

I don't know why Mathematica doesn't fully simplify the result;
however, for an expression with Plus as its Head you can automate what
you did

eachPartGreaterThanZero[x_Plus, assume_: {}] :=
  Simplify[And @@ Thread[(List @@ x) > 0], assume];

eachPartGreaterThanZero[
 a*b + c*(1 - d*(1 - e)), myassumptions]

True

This test is more restrictive than the original so while if it is True
then the original is True; however, if it is False the original could
still be True.


Bob Hanlon


On Fri, Jan 27, 2012 at 6:11 AM, Alan <alan.isaac at gmail.com> wrote:
> Why does the first simplification below fail?
> (Each term succeeds!)
> Thanks,
> Alan Isaac
>
> In[205]:=
> myassumptions = a > 0 && b > 0 && c > 0 && 1 > d > 0 && 1 > e > 0;
> Simplify[a*b + c*(1 - d*(1 - e)) > 0, Assumptions -> myassumptions]
> Simplify[a*b > 0, Assumptions -> myassumptions]
> Simplify[c*(1 - d*(1 - e)) > 0, Assumptions -> myassumptions]
>
> Out[206]= a b + c + c d e > c d
>
> Out[207]= True
>
> Out[208]= True
>



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