@g-js-api/algebra

A parser for G.js that allows you to write mathematical expressions, which gets decomposed into Item Edit triggers efficiently.

Supports:

• Variable assignment (n = ...)
• Arithmetic (+ - * /)
• Exponentiation (^)
• Parentheses
• Unary operators (+ -)
• Factorials (!, only for integers, not variables)
• Some function calls like abs, round, rnd, floor, ceil

Example

Code below generates and runs the Taylor series for sin(x) and cos(x):

import '@g-js-api/g.js';
import { setVariables, equation } from '@g-js-api/algebra';

await $.exportConfig({
    type: 'live_editor',
    options: { info: true, verticalPositioning: false } // verticalPositioning: false because horizontal order is necessary here
});

let result1 = float_counter(); // sin result
let result2 = float_counter(); // cos result
let input = float_counter(25); // 25 degrees
// constant for converting degrees to radians
// we also multiply by 1e+7 because item edit's mod field only has 3 digits of decimal precision,
// so we put as much of the decimal as we can into the integer part before info is lost
let radians_factor = float_counter(Math.PI / 180 * 1e+7);

// text + item displays so the user can see the inputs and outputs
$.add("Input:"
    .to_obj()
    .with(obj_props.X, 88)
    .with(obj_props.Y, 125)
    .with(obj_props.SCALING, 0.25));
input.display(88, 105);

$.add("Sine:"
    .to_obj()
    .with(obj_props.X, 45)
    .with(obj_props.Y, 65)
    .with(obj_props.SCALING, 0.25));
result1.display(45, 45);

$.add("Cosine:"
    .to_obj()
    .with(obj_props.X, 135)
    .with(obj_props.Y, 65)
    .with(obj_props.SCALING, 0.25));
result2.display(135, 45);

// define the variable names in the equations
radians_factor.divide(1e+7); // to bypass item edit's mod field precision
setVariables({
    result1, 
    result2, 
    // here we copy the input degrees and multiply it by radians_factor to convert it to rads
    x: input
        .clone()
        .multiply(radians_factor) 
})

// 6 terms for the Taylor series
let terms = 6;
let sin_str = [];
let cos_str = [];

// sin and cos Taylor series are calcualted simultaneously
// a term for sin(x): ±(x ^ n / n!) where n is an odd number
// a term for cos(x): ±(x ^ n / n!) where n is an even number
// for both cases, the sign alternates between + and -
for (let n = 0; n < terms; n++) {
    let power = 2 * n;
    let sign = n % 2 === 0 ? "" : "-";
    sin_str.push(`${sign}(x ^ ${power + 1} / ${power + 1}!)`);
    cos_str.push(`${sign}(x ^ ${power} / ${power}!)`);
}

// `equation(string)` takes an equation as input and adds Item Edit triggers as output
// here, we sum the terms for sin and cos
equation(`result1 = ${sin_str.join('+')}`); // sin
equation(`result2 = ${cos_str.join('+')}`); // cos