assume certain properties of the output of a function
I've just started using SAGE and I want to "declare" a symbolic function f(t) and to be able to hint that f(t) > 5 && f(t) < 100, for any value of t (the values are just for the purpose of example).
I know I can use assume for variables, but it seems it doesn't also work on functions, so I'm trying to see what alternatives I have left.
I have thought of "defining" the function f(t), with some mock values which don't contradict my assumptions(I don't actually know f(t), I only know some of it's properties), but I'm not sure how to force sage not to expand the function. I have tried f(t, hold=True) but it didn't seem to work(while this works for the default functions like sin).
Edit: Upon the comment made by @eric_g I add the following information:
f = function('f') ; t = var('t') (f(t) > 4).assume() assume(f(3)>5) assume(t>1) assume(f(t)>5) print(assumptions()) print('a) bool(f(3)>5) : '+str(bool(f(3)>5))) print('b) bool(f(3)>4) : '+str(bool(f(3)>4))) print('c) bool(f(2)>5) : '+str(bool(f(2)>5))) print('d) bool(f(t)>5) : '+str(bool(f(t)>5)))
[f(t) > 4, f(3) > 5, t > 1, f(t) > 5] a) bool(f(3)>5) : True b) bool(f(3)>4) : False c) bool(f(2)>5) : False d) bool(f(t)>5) : False
Two things puzzle me:
- How to get "c)" and "d)" to return true
- While "a)" returns true probably due to the second assumption, I would expect "b)" to also be true
Is the behavior I'm seeing incorrect, or am I just using SAGE wrong?