How to define piece-wise functions in Z3py

Question

I would like to define a piece-wise (linear) function in Z3py, for example, the function f(x) has the form

f(x) = a*x + b when 0 <= x <= 1
f(x) = exp(c*x) when 1 < x <= 2
f(x) = 1/(1+10^x) when 2 < x <= 3
etc.

where a, b and c are constants.

I guess the z3.If() function will be relevant, but as the number of pieces grows, the expression gets convoluted.

My questions is, does Z3pyprovides the if-else statement, or is there an elegant way to define piece-wise function in Z3py?

Answer 1

Yes, Z3 supports if-then-elses and in Python they can be constructed using the If function. An example from the documentation of If:

>>> x = Int('x')
>>> y = Int('y')
>>> max = If(x > y, x, y)
max = If(x > y, x, y)