The following works as expected:
var('b')
with assuming(b>1):
v = max_symbolic(7*b-5,0).full_simplify()
print(v)
yields 7*b - 5
The following does not (maybe my expectations are unrealistic)
with assuming(b>1):
v = max_symbolic(b^2-b+1,0).full_simplify()
print(v)
yields max(0, b^2 - b + 1), even though the latter expression is always > 3/4
I have a bunch of expressions such as the one below, that I want to analyze, to get a piecewise-defined function:
print(myexpr,"\n\n")
print(myexpr.full_simplify(),"\n\n")
with assuming(a>2):
print(myexpr.full_simplify(),"\n\n")
max(max(3, a + 1) + 2*max(2*max(3, a + 1) + 1, a + max(3, a + 1)), a*max(3, a + 1) + max(2*max(3, a + 1) + 1, a + max(3, a + 1)))
max(max(3, a + 1) + 2*max(2*max(3, a + 1) + 1, a + max(3, a + 1)), a*max(3, a + 1) + max(2*max(3, a + 1) + 1, a + max(3, a + 1)))
max(5*a + 7, a^2 + 3*a + 3)
This is good, however:
with assuming(a>2000):
print(myexpr.full_simplify())
yields max(5a + 7, a^2 + 3a + 3)
Can such expressions, as above, in max_symbolic be converted into piecewise defined functions? (I would also be interested in having more than one parameter, and having SAGE partition the parameter space appropriately and automatically).
