Axiom is  a general purpose Computer Algebra system. It is useful for research and development of mathematical algorithms. It defines a strongly typed, mathematically correct type hierarchy. It has a programming language and a built-in compiler.
Polybutylene is simply a type of plumbing material that was manufactured between the late 70's and early 90's. It is thought that it was installed in over 6 million homes during that time period.
If the sink were the only fixture you had in the house, the plumbing would be simple. The drain would extend horizontally from the P-trap to a tee. The pipe going down from the tee would empty into the sewer, while the pipe going up would extend through the roof to vent the drain.