a very basic derivative solver i made to test my understanding of simple calculus:
- chain rule
- product rule
- power rule
this is a toy project, considered finished. i don't plan on adding any other major features.
a Term is an abstract math expression.
the following operations are supported between Terms:
Add(t1, t2)(subtraction is done using negative coefficients)Mul(t1, t2)(division is done using negative exponents)Pow(t1, t2)Ln(t1)(log_a of b must be represented as ln(b)/ln(a))Sin(t1)Cos(t1)
in addition, the following constants/variables are given:
X(the only variable)E(euler's constant)PiInt(i)(uses 64-bit signed integers)
Term::estimate() allows you to plug in a 64-bit floating point value and approximate the result of substituting that number for X
NaN is returned on failure.
Term::derivative() returns the simplified derivative of the term. derivatives are always guaranteed to be correct - however, note that expressions usually aren't reduced optimally, so some results may be more complex than necessary.
if you want the second derivative, you can simply do t1.derivative().derivative()... and so on.
Term::simplified() does very basic reductions on a term, for example:
Add(Mul(Int(1), Int(2)), Int(3))->Int(5)Ln(E)->Int(1)Mul(Int(0), Ln(Pow(X, Int(8))))->Int(0)Mul(Pow(X, Int(2)), Pow(X, Int(-2)))->Int(1)
i'm pretty sure all of my reductions are mathematically correct (hopefully they are). my goal is for these to be good enough, not perfect. i know i'm missing a lot of reductions.
also, the way i did reduction is probably not super efficient - i wouldn't be surprised if it could be 10+ times faster. but it's good enough for me.
i actually did implement the property that sin(x)^2 + cos(x)^2 = 1, and it should be able to simplify that in the most basic of cases.
i'm aware that there are way too many parentheses when you print a term. however, i don't really feel like fixing it.