2d-algebra 中文文档教程

Question

2D Algebra Typescript Module

一个用于以编程方式建立用于数值分析的大型方程组的库。

Technologies

Project is created with:

• Typescript version: 3.6.2
• Node version: 12.10.0
• No external dependencies

Setup

要使用此库

npm install 2d-algebra yarn add 2d-algebra

然后在您的代码中，您可以导入并使用 expression(...) 函数来流畅地构建表达式。

import expression from "2d-algebra";

const m = 3; // slope
const b = 4; // point
const x = Symbol("x");
const y = Symbol(); // naming your symbols is optional
const line = expression(m).times(x).plus(b).eq(y);

const solution = new Map([
  [x, 7483],
  [y, 22453],
]);

const err = line.eval(solution);
// err === 0

const dxLine = line.derivative(x);
const xSlope = dxLine.eval(solution);
// xSlope === 0

const dyLine = line.derivative(y);
const ySlope = dyLine.eval(solution);
// ySlope === 0

const dx2Line = dxLine.derivative(x);
const xCup = dx2Line.eval(solution);
// xCup > 0

const dy2Line = dyLine.derivative(y);
const yCup = dx2Line.eval(solution);
// yCup > 0

// https://en.wikipedia.org/wiki/Second_partial_derivative_test
const dxdyLine = dxLine.derivative(y);
const hessianDet = dx2Line.times(dy2Line).minus(dxdyLine.squared());
const xySaddle = hessianDet.eval(solution);
// xySaddle === 0

API

创建一个新的 Expression 很容易，只需从第一个 symbol 或 number 开始。

const one = expression(1).eval(new Map());

从那里您可以使用以下方法来增加复杂性。 所有方法都不会更改现有的 Expression，而是返回一个新的 Expression（也称为不可变）。 b 参数必须是 symbol、number 或 Expression。

Method	Description
plus(b)	add the top term to b and simplifies
minus(b)	equivalent to plus(-b)
times(b)	multiplies the top term with b and simplifies
dividedBy(b)	equivalent to push(b).toThe(-1).times()
toThe(n)	raises the top term by the number n.
squared()	equivalent to toThe(2)
sin()	replaces the top term with the sine
cos()	replaces the top term with the cossine
tan()	equivalent to this.sin().push(this).cos().divide()
eq(b)	equivalent to minus(b).squared()
abs()	replaces the top term with the absolution value

表达式完成后，您可以使用以下方法

Method	Description
eval(Map)	fully evaluate the expression. throw error if not all of the symbols are defined.
apply(Map)	substitute one or more variables with different term and return the new expression.
derivative(symbol)	compute the partial derivative with respect to one symbol.
toString()	makes a ASCII art tree diagram of the expression tree.

Why no parentheses? ( or )

此时您可能遇到了一个表达式，您只想将下一个 times 或 squared 应用于仅一部分之前发生的事情。 例如，单位（半径为 1）圆可能会错误地将其定义为：

const r = 1;
const x = Symbol();
const y = Symbol();

// EXAMPLE OF HOW TO DO IT WRONG
const circle = expression(x)
  .squared() //   x^2
  .plus(y) //   x^2 + y
  .squared() //  (x^2 + y)^2
  .eq(r) //  (x^2 + y)^2 - r)^2
  .squared(); // ((x^2 + y)^2 - r)^2)^2

会产生 ((x^2 + y)^2 - r)^2)^2。 当我期望 (x^2 + y^2 - r^2)^2 时。 请注意，在错误的表达式中，squared() 的每个应用程序如何应用于到该点定义的整个表达式。 为了解决这个问题，我将引入 push(b) 方法，该方法启动一个新的迷你表达式，与目前定义的内容分开。 当使用 push 时，plus()、minus()、times()、< code>divide() 和 eq() 可用于使两个迷你表达式再次合并为一个。

更正后的代码现在如下所示：

const circle = expression(x)
  .squared() //  x^2
  .push(y) //  x^2 | y   <---- y here is separate from x^2
  .squared() //  x^2 | y^2 <---- now that y is squared on its own
  .plus() //  x^2 + y^2 <---- merge y^2 by adding it to x^2
  .push(r) //  x^2 + y^2 | r
  .squared() //  x^2 + y^2 | r^2
  .eq(); // (x^2 + y^2 - r^2)^2

Contributing

提交对项目的更改

1. fork and clone the git repository
2. make changes to the tests and source.

• If making changes to the Expression class make sure matching changes are made to ExpressionStack.
• Changes to simplification logic can be quite tricky with all the symbiotic recursion.

1. run yarn test. if they fail goto step 2
2. push changes to your fork
3. submit pull request

Other ussful commands

• yarn compile: compile the typescript code to POJS
• yarn test: run unit tests once.
• yarn watch: continuously run unit tests.