Compute Engine

The CortexJS Compute Engine performs calculations on MathJSON expressions.

Evaluating

Use the ComputeEngine.evaluate() function to evaluate an expression.

The result of evaluate() is an expression. If the expression can be evaluated numerically, the expression is a number. If it can’t be evaluated numerically, the expression will be a symbolic expression.

import { evaluate } from 'compute-engine';

console.log(evaluate(["Add", 2, 3]);
// ➔ 5
console.log(evaluate(["Add", 2, "x", 3]);
// ➔ ["Add", 5, x]

Formating

A given mathematical expression can be represented in multiple equivalent ways as a MathJSON expression. A form is used to specify a representation. The most common forms are "full" where only transformations necessary to make the expression a valid JSON expression are applied and "canonical" that applies rules to perform some basic simplifications and ordering of the elements of the expression.

To transform an expression using the rules for a particular form, use the format() function.

import { format } from 'compute-engine';

console.log(format(["Add", 2, +Infinity], 'full');
// ➔ ["Add", 2, "+Infinity"]

console.log(format(["Add", 2, "x", 3], 'canonical');
// ➔ ["Add", 2, 3, "x"]

See Compute Engine Forms for more info.

Comparing

Use the ComputeEngine.same() function to compare two expressions.

The comparison between expressions is structural so that $$x + 1$$ is not equal to $$1 + x$$. To obtain the desired result, you may need to apply a canonical form to the expressions using ComputeEngine.canonical(), or evaluate them using ComputeEngine.evaluate().

const engine = new ComputeEngine();

const variable = 'x';
console.log(engine.same(
  ['Add', 'x', 1], 
  ['Add', variable, 1]
));
// ➔ true: the two expressions are the same

console.log(engine.same(
  ['Add', 'x', 1], 
  ['Add', 1, 'x']
));
// ➔ false: the two expressions are **not** the same

console.log(engine.same(
  engine.canonical(['Add', 'x', 1]),
  engine.canonical(['Add', 1, 'x'])
));
// ➔ true: the two expressions are the same in canonical form

console.log(engine.same(
  ['Add', 2, 2],
  ['Add', 3, 1]
));
// ➔ false: the two expressions are **not** the same

console.log(engine.same(
  engine.evaluate(['Add', 2, 2]),
  engine.evaluate(['Add', 3, 1])
));
// ➔ true: the two expressions are the same once evaluated

Advanced Usage

To improve performance, particularly when calling format()/evaluate() repeatedly, use an instance of the ComputeEngine class. When the instance is constructed, the dictionaries defining the symbols are compiled, and subsequent invocations of the format() and evaluate() methods can skip that step.

Using a compute engine instance, it is possible to customize which symbol dictionaries are used.

const engine = new ComputeEngine(ComputeEngine.getDictionary('arithmetic'));
engine.evaluate(['Add', 5, 2]);