@math-blocks/solver

Is able to solve basic equations and simplify basic expressions using steps that are similar to what a human would do. This can then be used by intelligent tutors to provide suggestions to users when they don't know what step to take next or provide a complete worked solution.

API

const solve = (node: types.Eq, ident: types.Ident) => Step | undefined;

Solves an equation for the given identifier. If the identifier doesn't exist in node or if solve doesn't know how to solve the given equation the function will return undefined.

const simplify = (node: types.Node) => Step | undefined;

Simplifies an expression. It will return undefined if the expression is already simplified.

type Step = {
    message: string;
    before: types.Node;
    after: types.Node;
    substeps: Step[];
};

Step is a common type that's used throughout this package to communicate what each step is doing. before is the node that is being changed within a step and may be a descendent of the node passed to solve or simplify. after is the node that before has been replaced with. Use applyStep to compute the new node after applying the step to node.

const applyStep = (node: types.Node, step: Step): types.Node;

Applies a single step to a given node. If step couldn't be applied, the original node is returned.

Notes

Each function that performs steps to simplify an expression or solve an equation should have the following properties:

• applying all substeps to the before should result in a node that is the same as after
• applying each substep to an expression or equation should result in an equivalent expression or equation
  • equivalent expressions have the same value no matter the value of the variables
  • equivalent equations should have all of the same solutions

TODO

• create a helper to check that two expressions are equivalent
• create a helper to check that two equations are equivalent
• update solve to handle linear inequalities
• add tests to check that the general equation of a line can be rewritten in standard for by solving for y