From 6abb43d6dc87335a6e515b0bc0b254ebc6fde8e6 Mon Sep 17 00:00:00 2001 From: nshen121 Date: Thu, 3 Mar 2016 01:46:43 +0800 Subject: [PATCH] translate --- README_cn.md | 80 +++++++++++++++++++++++++++------------------------- 1 file changed, 41 insertions(+), 39 deletions(-) diff --git a/README_cn.md b/README_cn.md index dcb2a50..117c6d3 100644 --- a/README_cn.md +++ b/README_cn.md @@ -1,6 +1,6 @@ # math-as-code -> 译注：英文不好尝试翻译，如有错误请指正。 +> 译注：译者英文与数学水平都非常有限，尝试翻译，如有错误请指正。 这是一份通过对比数学符号和JavaScript代码来帮助开发者了解数学符号的参考。 @@ -8,7 +8,8 @@ 这个指南还没有完成。如果你发现错误或者想提交贡献，请[open a ticket](https://github.com/Jam3/math-as-code/issues)或发一个 PR。 -> **Note**: For brevity, some code examples make use of [npm packages](https://www.npmjs.com/). You can refer to their GitHub repos for implementation details. + +> **注意**： 简单起见，有些代码示例使用了[npm 包](https://www.npmjs.com/)。你可以到他们的GitHub repos来查看实现的详细情况。 # 前言 @@ -16,7 +17,7 @@ 更完整的列表，请看[Wikipedia - List of Mathematical Symbols](https://en.wikipedia.org/wiki/List_of_mathematical_symbols). -简单起见，这里许多的代码示例都操作浮点数值，并不是数字健壮的(numerically robust)。为什么这会是一个问题的更详细信息请看[Robust Arithmetic Notes](https://github.com/mikolalysenko/robust-arithmetic-notes) by Mikola Lysenko. +简单起见，这里许多的代码示例都操作浮点数值，并不是数字健壮的(numerically robust)。为什么这会是一个问题的更详细信息请看[Robust Arithmetic Notes](https://github.com/mikolalysenko/robust-arithmetic-notes) 作者 Mikola Lysenko. # 目录 @@ -28,13 +29,13 @@ - [向量乘法](#vector-multiplication) - [点乘](#dot-product) - [叉乘](#cross-product) -- [sigma `Σ`](#sigma) - *summation* -- [大写 Pi `Π`](#capital-pi) - *products of sequences* +- [sigma `Σ`](#sigma) - *求和* +- [大写 Pi `Π`](#capital-pi) - *序列的积* - [管道 `||`](#pipes) - [绝对值](#absolute-value) - [取模](#euclidean-norm) - [行列式](#determinant) -- [帽子 **`â`**](#hat) - *unit vector* +- [帽子 **`â`**](#hat) - *单位向量* - ["属于" `∈` `∉`](#element) - [常见数字集 `ℝ` `ℤ` `ℚ` `ℕ`](#common-number-sets) - [函数 `ƒ`](#function) @@ -44,12 +45,12 @@ - [撇号 `′`](#prime) - [向下取整和向上取整（floor & ceiling） `⌊` `⌉`](#floor--ceiling) - [箭头](#arrows) - - [material implication `⇒` `→`](#material-implication) - - [equality `<` `≥` `≫`](#equality) - - [conjunction & disjunction `∧` `∨`](#conjunction--disjunction) -- [logical negation `¬` `~` `!`](#logical-negation) -- [intervals](#intervals) -- [more...](#more) + - [实质蕴含（material implication） `⇒` `→`](#material-implication) + - [等式 `<` `≥` `≫`](#equality) + - [与 & 或 `∧` `∨`](#conjunction--disjunction) +- [逻辑非 `¬` `~` `!`](#logical-negation) +- [区间（intervals）](#intervals) +- [更多...](#more) ## 变量名惯例 @@ -957,15 +958,15 @@ A || B ## 逻辑非（logical negation） -有时候，`¬`, `~` 和 `!` 符号都用来表示逻辑`NOT`。例如，只有在A为false的时候，*¬A* 为true。 +有时候，`¬`, `~` 和 `!` 符号都用来表示逻辑 `NOT`。例如，只有在A为false的时候，*¬A* 为true。 -这里是一个使用 *not*符号简单的例子： +这里是一个使用 *not* 符号简单的例子： ![negation](http://latex.codecogs.com/svg.latex?x%20%5Cneq%20y%20%5CLeftrightarrow%20%5Clnot%28x%20%3D%20y%29) -翻译成代码： +翻译成代码的例子： ```js if (x !== y) { @@ -973,63 +974,64 @@ if (x !== y) { } ``` -*Note:* The tilde `~` has many different meanings depending on context. For example, *row equivalence* (matrix theory) or *same order of magnitude* (discussed in [equality](#equality)). +*注意：* 根据上下文的不同，波浪线 `~` 可以有很多种不同的意思。例如，*行等价（row equivalence）*（矩阵理论）或*相同数量级（same order of magnitude）* （在[等式（equality）](#equality)章节讨论过）。 -## intervals +## 区间（intervals） -Sometimes a function deals with real numbers restricted to some range of values, such a constraint can be represented using an *interval* +有时函数会处理被一些值限定范围的实数，这样的约束可以用*区间（interval）*来表示。 For example we can represent the numbers between zero and one including/not including zero and/or one as: +例如我们可以表示0和1之间的数，让他们包含或不包含0和1。 -- Not including zero or one: ![interval-opened-left-opened-right](http://latex.codecogs.com/svg.latex?%280%2C%201%29) +- 不包含0或1： ![interval-opened-left-opened-right](http://latex.codecogs.com/svg.latex?%280%2C%201%29) -- Including zero or but not one: ![interval-closed-left-opened-right](http://latex.codecogs.com/svg.latex?%5B0%2C%201%29) +- 包含0但不包含1： ![interval-closed-left-opened-right](http://latex.codecogs.com/svg.latex?%5B0%2C%201%29) -- Not including zero but including one: ![interval-opened-left-closed-right](http://latex.codecogs.com/svg.latex?%280%2C%201%5D) +- 不包含0但包含1： ![interval-opened-left-closed-right](http://latex.codecogs.com/svg.latex?%280%2C%201%5D) -- Including zero and one: ![interval-closed-left-closed-right](http://latex.codecogs.com/svg.latex?%5B0%2C%201%5D) +- 包含0和1： ![interval-closed-left-closed-right](http://latex.codecogs.com/svg.latex?%5B0%2C%201%5D) -For example we to indicate that a point `x` is in the unit cube in 3D we say: +例如我们指出一个点 `x` 在3D单位立方体中，我们可以说： ![interval-unit-cube](http://latex.codecogs.com/svg.latex?x%20%5Cin%20%5B0%2C%201%5D%5E3) -In code we can represent an interval using a two element 1d array: +在代码中我们可以用两个元素大小的一维数组表示区间： ```js var nextafter = require('nextafter') -var a = [nextafter(0, Infinity), nextafter(1, -Infinity)] // open interval -var b = [nextafter(0, Infinity), 1] // interval closed on the left -var c = [0, nextafter(1, -Infinity)] // interval closed on the right -var d = [0, 1] // closed interval +var a = [nextafter(0, Infinity), nextafter(1, -Infinity)] // 开区间 +var b = [nextafter(0, Infinity), 1] // 左闭右开区间 +var c = [0, nextafter(1, -Infinity)] // 左开右闭区间 +var d = [0, 1] // 闭区间 ``` -Intervals are used in conjunction with set operations: +区间与集合运算结合符使用： -- *intersection* e.g. ![interval-intersection](http://latex.codecogs.com/svg.latex?%5B3%2C%205%29%20%5Ccap%20%5B4%2C%206%5D%20%3D%20%5B4%2C%205%29) +- *交集（intersection）* e.g. ![interval-intersection](http://latex.codecogs.com/svg.latex?%5B3%2C%205%29%20%5Ccap%20%5B4%2C%206%5D%20%3D%20%5B4%2C%205%29) -- *union* e.g. ![interval-union](http://latex.codecogs.com/svg.latex?%5B3%2C%205%29%20%5Ccup%20%5B4%2C%206%5D%20%3D%20%5B3%2C%206%5D) +- *并集（union）* e.g. ![interval-union](http://latex.codecogs.com/svg.latex?%5B3%2C%205%29%20%5Ccup%20%5B4%2C%206%5D%20%3D%20%5B3%2C%206%5D) -- *difference* e.g. ![interval-difference-1](http://latex.codecogs.com/svg.latex?%5B3%2C%205%29%20-%20%5B4%2C%206%5D%20%3D%20%5B3%2C%204%29) and ![interval-difference-2](http://latex.codecogs.com/svg.latex?%5B4%2C%206%5D%20-%20%5B3%2C%205%29%20%3D%20%5B5%2C%206%5D) +- *差集（difference）* e.g. ![interval-difference-1](http://latex.codecogs.com/svg.latex?%5B3%2C%205%29%20-%20%5B4%2C%206%5D%20%3D%20%5B3%2C%204%29) 还有 ![interval-difference-2](http://latex.codecogs.com/svg.latex?%5B4%2C%206%5D%20-%20%5B3%2C%205%29%20%3D%20%5B5%2C%206%5D) -In code: +代码: ```js var Interval = require('interval-arithmetic') @@ -1051,22 +1053,22 @@ Interval.difference(b, a) // {lo: 5, hi: 6} ``` -See: +见： - [next-after](https://github.com/scijs/nextafter) - [interval-arithmetic](https://github.com/maurizzzio/interval-arithmetic) -## more... +## 更多... -Like this guide? Suggest some [more features](https://github.com/Jam3/math-as-code/issues/1) or send us a Pull Request! +喜欢这份指南？提出[更多的特性](https://github.com/Jam3/math-as-code/issues/1)的建议或给我们发Pull Request！ -## Contributing +## 贡献 -For details on how to contribute, see [CONTRIBUTING.md](./CONTRIBUTING.md). +关于怎样贡献详见 [CONTRIBUTING.md](./CONTRIBUTING.md)。 ## License -MIT, see [LICENSE.md](http://github.com/Jam3/math-as-code/blob/master/LICENSE.md) for details. +MIT, 详见 [LICENSE.md](http://github.com/Jam3/math-as-code/blob/master/LICENSE.md)。 [1]: http://mimosa-pudica.net/improved-oren-nayar.html#images [2]: http://buzzard.ups.edu/courses/2007spring/projects/million-paper.pdf