HOW TO MAKE THAT AN INEQUALITY BECOME AN ASSUMPTION?

Hi,

I am interested in checking if a huge formula is positive or negative.

Let's say, for example, which sign have for certain values

of . Hence, I would like to know how I can do assumptions

in the values of the variables.

I know, that I can do things like

assume(x>0)
assume(x,'integer')

But I would like to assume things like

assume(a+b-c>0)
assume(b+2c<0)
assume(a>0)

All of that at the same time. Do you know how can I do something like that?

Thank you very much in advance.

Answer 1

[Walter Roberson]

Yes. Just be careful because once an assumption exists on a variable, using assume() for the same variable can delete the previous assumption. It is safer to use assumeAlso()

assume(x>0)
assumeAlso(x, 'integer')
assumeAlso(a+b-c>0)
assumeAlso(b+2*c<0)
assumeAlso(a>0)

You can also chain together assumptions in the form of relations:

assume(x, 'integer')
assumeAlso( x>0 & a+b-c<0 & b+2*c<0 & a>0)

However, the assumption system is not necessarily going to be robust enough for your purposes.

isAlways() might help you.

[idriskameni]

Thank you very much. What do you mean by not robust enough?

And how isAlways() could help me improving it?

[Walter Roberson]

The symbolic engine sometimes ignores assumptions. And sometimes it just does not work through all the implications of assumptions, so it can miss something that a human can prove.

With regards to isAlways(): you cannot directly test the truth of a symbolic expression. For example if you had the above assumptions then you might expect to be able to ask

if a+b-c>0; disp('yes'); end

since there is an assumption that states that as a truth. However, this will fail with failure to convert sym to logical. You can take sign() of a symbolic expression, sign() will not necessarily resolve all assumptions so you can have trouble if you compare the output of sign() to something -- or you can simply get misleading results. You might need to test isAlways() of the expression, which does return a logical value.