Message Boards Message Boards


Understanding Resolve[Exists[...]] type command

Posted 10 years ago
1 Reply
0 Total Likes
Hi everyone,
I'd be most thankful for any and all inputs into understanding what I describe below. I thank you for your patience and time in hearing out my question.
I frequently use
where inq1,...,inqM and eq1,...,eqN are all real multivariable polynomials in x1,...,xL (and x1,..,xL are all positive and so real).
I use the command above to check for the existence of a solution satisfying all the inequalities and equalities as represented by the expressions inq1,...,inqM>0 and eq1==...=eqN==0. The command works perfectly fine.
But now there is one additional inequality
(Polynomial 1 in {x1,...,xL}) - (Polynomial 2 in {x1,...,xL})*Log[(1+x1)/(1-x1*x2)] > 0
that I'd like to introduce into the command above, call it INQ.
In generally, introducing INQ into the above appears to bottleneck Mathematica. In fact, leaving the conditions inq1,...,inqM>0 and eq1==...=eqM==0 aside,
which is obviously true in my case does not terminate. My first question is, is there any reason as to why the commands Resolve[] and Log[] are not compatible?
I tried Resolve[Exists[...],WorkingPrecision->number (say, 10)] to potentially quicken the calculation.
I am not sure why, but regardless of introducing INQ>0, the original command
updated to
does not converge. For example, the original command takes less than 10 seconds, but the new command simply doesn't converge.
My second question is, isn't WorkingPrecision->number supposed to fasten the calculations? Why is this happening?
Finally, my third question is, is there any way of quickening Resolve[Exists[...]] type of command?

Thank you so much in advance for all your help!!

Hello and welcome to the Wolfram Community! Please take a few minutes to read this tutorial about correct posting – especially of Mathematica code:

How to type up a post: editor tutorial & general tips

If you will not follow the tutorial, other members of community may not be able to test your code. To edit your post – click “Edit” in the lower right corner of your post.
POSTED BY: Moderation Team
Reply to this discussion
Community posts can be styled and formatted using the Markdown syntax.
Reply Preview
or Discard

Group Abstract Group Abstract