Mathematica Stack Exchange is a question and answer site for users of Mathematica. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

I was wondering: how does one use the ForAll function in Reduce? In particular, I am looking for the set $\{w\in \mathbb{R}^2 | \forall x \in \mathbb{R}^2 : \left<w,x\right> \leq f(x)\},$ where $\left<,\right> $ is the inner product and $f: \mathbb{R}^2\rightarrow\mathbb{R}^1$. Thank you!

share|improve this question
Maybe the example in this post will help. Otherwise, you will have to make the question more specific to get a useful answer. – Jens Apr 22 '12 at 19:54
Uri, try to include a few more details about what you're trying to solve. – Eli Lansey Apr 22 '12 at 21:31

This is a simple example. Suppose you have the following equation and you want to get the coefficients of it:

gl = a x^3 + b x^2 + c x + d == -x + (-3 + x) (5 + x^2);
Reduce[ForAll[x, gl]]

Your output will be:

d == -15 && c == 4 && b == -3 && a == 1
share|improve this answer

Perhaps you mean something like this:

f[{x1_, x2_}, {y1_, y2_}] := x1 y2 - x2 y1
Reduce[ForAll[{x1, x2, y1, y2}, 
   {x1, x2}.{y1, y2} <= f[{x1, x2}, {y1, y2}]]]
share|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.