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
>
- References:
- Simplify puzzle
- From: Alan <alan.isaac@gmail.com>
- Simplify puzzle