Unary equation solving

Unary function automatic solution online calculation tool

Newton's method is the core method of solving. Its Wikipedia's definition is: Newton's method is a method of approximating equations in real and complex fields. The method uses the first few terms of the Taylor series of the function f (x) to find the root of the equation f (x) = 0. In short, Newton's method is to iterate over x until x converges to a small range

Therefore, for any unary function, we can try to use Newton's method to find its approximate solution. When the error is less than 10 ^ -9, or when the number of iteration steps exceeds 10 ^ 5, the iteration ends.

When constructing the solver, there are several key issues that need to be solved: parsing the input expression, expressing the function, deriving the function equation, and substituting and evaluating the function. Among them, the first priority is: how do we store (express) functions?

Why choose this binary expression tree? Mainly because it is a tree structure, which is convenient for recursive processing of nodes, and we later use the recursive idea to derive the function, including the idea of substitution and evaluation.

Preprocessing expressions: First, we need to preprocess the input expression string. Because there are some simple or redundant writing in mathematics that need to be standardized here. After the natural input string is preprocessed, it should be an infix expression string, which is an expression form that humans can naturally understand. But in order to store the expression as a binary expression tree, we also need to convert the infix expression into a postfix expression

Scheduling field algorithm: The degree field algorithm is basically similar to the way we use stack to calculate expressions in stack recursion Hanoi. It uses a queue to express the output suffix expression, and uses the stack to store operators and functions