How to use Assuming and If together?

Question

I would like to compare variables t and u and print either Yes or No depending one which is larger.

My code is simply the following:

Assuming[t < u, If[t - u < 0, Print[Yes], Print[No]]]

Since t < u is assumed, t - u < 0 holds. So I should get Yes. But what I get is a repetition of If term. That is,

If[t - u < 0, Print[Yes], Print[No]]

Am I missing something?

You need a Simplify (Assuming[t < u, Simplify[If[t - u < 0, Print[Yes], Print[No]]]]) otherwise the Assumpition has no effect. — Karsten7, Sep 06 '14 at 18:07
@Karsten, It worked! Thank you so much! But one question: Why do I have to simplify it which is already very simple? Do I have to always do this in this case regardless whether If clause is simple or not? — ppp, Sep 06 '14 at 18:09
@Karsten, I see. If has no Assumptions options, so I have to always use Simplify.... Thank you so much! — ppp, Sep 06 '14 at 18:11
Assuming only has an effect on an expression, if the expression has the option Assumptions, like Simplify has. — Karsten7, Sep 06 '14 at 18:11
@ppp I noticed you never accepted any answer to your previous questions. Maybe you would get more responses if you checked "Accept" on some of the earlier answers that you apparently liked. — Jens, Sep 07 '14 at 03:35

Jens · Accepted Answer · 2014-09-06T18:56:42.553

6

What you need to use here is Refine:

Refine[If[t - u < 0, Print[Yes], Print[No]], t < u]

Yes

Ad if you need to work with $Assumptions as well, then you could do this:

$Assumptions = t < u;

Refine[If[t - u < 0, Print[Yes], Print[No]], $Assumptions]

Yes

The last line is also the way it would look if you were to wrap your If statement in Assuming. However, since $Assumptions is also used by default, you can simply do this:

Assuming[t < u, Refine[If[t - u < 0, Print[Yes], Print[No]]]]

Yes

edited Sep 06 '14 at 18:56

answered Sep 06 '14 at 18:21

Jens

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This is very helpful. Thanks a lot! – ppp Sep 06 '14 at 18:25
what about in case of multiple assumptions? Can I do add them with &&? – ppp Sep 06 '14 at 18:47
@ppp Yes, the docs have many examples. – Jens Sep 06 '14 at 18:54

How to use Assuming and If together?

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