Keep in mind that what you consider solid proof that the officer is lying may not appear that way to the judge. Even if your PD had done what you wanted him to do, the impact might have been much less dramatic than you believe. I see little point in making a complaint against your PD.
Algebra is a part of mathematics (often called math in the United States and maths in the United Kingdom ). It uses variables to represent a value that is not yet known. When an equals sign (=) is used, this is called an equation.
abstract algebra: the area of modern mathematics that considers algebraic structures to be sets with operations defined on them, and extends algebraic concepts usually associated with the real number system to other more general systems, such as groups, rings, fields, modules and vector spaces.