# max_symbolic with assumptions?

I am in need of a symbolic engine for Python to calcultate max expressions. It is important that we can pass assumptions like "x is a positive symbol" and "y is greater than x" to the engine (the latter is why sympy does not suffice AFAIK).

I am currently testing sage and ran into some disappointing results... Am I doing something wrong here or is this sage's limit?

```
import sage.all as sage
x = sage.var('x')
y = sage.var('y')
myMax = sage.max_symbolic(x, 2*x)
print(sage.simplify(myMax)) # gives max(x, 2*x) as expected
sage.assume(x, 'integer')
sage.assume(x > 0)
print(sage.simplify(myMax)) # simplifies to 2*x (nice!)
sage.assume(y > 0)
sage.assume(y, 'integer')
myMax = sage.max_symbolic(x, y)
print(sage.simplify(myMax)) # gives max(x, y) as expected
sage.assume(y > x)
print(sage.simplify(myMax)) # now gives y (nice!)
print(sage.simplify(sage.max_symbolic(20*x, 20*y))) # gives 20*y (nice!)
print(sage.simplify(sage.max_symbolic(19*x, 20*y))) # gives max(19*x, 20*y)... why?
print(sage.simplify(sage.max_symbolic(19*x, 20*x))) # gives 20*x, so the above should be deducable
```

We tell sage that x and y are positive integers and that y > x. Sage can deduce that 20*y > 20*x (and also 20*x > 19*x), but it cannot deduce that 20*y > 19*x? :(

Do I need to do somehing differently or is this how things are in sage?

Thanks for the much appreciated help!

If constraints are linear it's worth employing Integer Linear Programming rather than symbolic machinery.

It's not given that the symbols are integers in the actual usecase, but rather reals.

That's fine - just Linear Programming then, which is computationally easier than integer one. In Sage, there is a common interface for them called Mixed Integer Linear Programming - eg., see this tutorial: https://doc.sagemath.org/html/en/them...

Using giac:

Does giac exist as a Python module?