# Testing inequalities in sage

I wanted to show if: $$ |a+b| \leq |a| + |b|$$

So I wrote this in sage:

```
var('a','b')
eqn1=abs(a+b)
eqn2=abs(a)+abs(b)
bool(eqn1<=eqn2)
```

The result is False.

I had expected the result to be True. What is the correct way to test this in sage?

Thank you in advance for any help provided.

Interesting, $bool(abs(a) >= a)$ is $True$, but $bool(abs(a+b) >= (a+b))$ is $False$. Weird.

Also, assume(a<0,b>0) results in false too: http://pastebin.com/7Gg5xMA8

If it can't be determined whether a relation holds, `False` will be returned.

This is disturbing: $$assume(a, 'real')$$ $$assume(b, 'real')$$ $$bool(sqrt((a+b)^2) == sqrt(a^2) + sqrt(b^2))$$ is $$True$$ ????

@eviatar-bach returning False in case can't be determined whether a relation holds seems to me unwise ; This should be changed to a tristate-answer, whatever the third state is