莉萨：是数学程序。
把多路径的反射加入数学程序之后，处理器不仅可以外推出讯号的方向，还可以算出用户行动电话的确切位置。
By including the multipath reflections in the mathematical equations, the processor can extrapolate not only the direction of the signal but also the exact position of the user's cell phone.
函数语言的名称源于这样一种概念：程序行为应该像数学函数一样；换句话说，给定一组输入，函数应始终返回相同的输出。
Functional languages get their name from the concept that programs should behave like mathematical functions; in other words, given a set of inputs, a function should always return the same output.
逐渐地，计算机也开始满足其他教学领域的需求，从计算机辅助阅读教学、数学练习程序一直到研究协助装置。
Slowly and steadily, though, computers started to fulfill other teaching needs as well, from computer-aided reading instruction to mathematics drill programs to research facilitators.
他试图去剖析人类是如何与语言建立起联系，以及如何利用数学和程序设计让机器获得同样的能力。
He wanted to understand how people established a relationship to language and how, using mathematics and computer programming, machines could be equipped with an analogous skill.
函数性编程范式使用数学函数表达程序。
The functional-programming paradigm uses mathematical functions to express programs.
帮助人们解决他们所选领域的数学问题的计算机程序并不缺乏。
And there is no lack of computer programs to assist people in solving mathematical problems in their chosen field.
副作用把验证程序正确的数学问题复杂化。
Side effects complicate the math required to prove program correctness.
对于初学者或通常认为自己无意从事该领域的读者，本文描述的数学和程序也是引人入胜的。
For the beginner or for those who do not normally consider themselves to be inclined to the field, mathematics and the programs described in this article can be entertaining as well.
有些程序可以证明数学定理。
现有的程序利用试错法，指导折叠的已知数学规则也用到预编程中。
The existing program uses trial and error, and pre-programmed mathematical rules that govern folding as understood today.
与“自动数学家”及其后继者不同的是，他们的程序事先只加载了一组简单的基础数学功能和要求其分析的数据。
Unlike the Automated Mathematician and its heirs, their program is primed only with a set of simple, basic mathematical functions and the data it's asked to analyze.
它们还可以更为严格，不过我们大部分人选择的是程序设计而非数学，因为我们不能忍受数学的单调，也不能忍受它的符号。
They can be done much more rigorously, but many of us chose programming instead of mathematics because we can't stand the tedium of mathematics nor its notation.
可以使用许多计算机程序来帮助您解决数字和符号数学问题，但是还有些程序可以帮助您学习数学。
Many computer programs are available to assist you in solving numerical and symbolic mathematical problems, but there are also programs to help you learn about mathematics.
程序始于基本数学过程的随机组合——加、减、乘、除和一些代数运算。
The program started with near-random combinations of basic mathematical processes - addition, subtraction, multiplication, division and a few algebraic operators.
这也许会被视为无聊的消遣，然而已有学者提出数学方程序解释人们的拖延症。
It might seem an idle pastime but academics have come up with a mathematical equation for why people procrastinate.
这种叫“试探法”的简单定律，可以转化成简单，并且适合电脑模型的数学方程序。
Such simple rules, called heuristics, can be transformed into simple mathematical formulas fit for computer models.
电脑程序必须在数学上下功夫。
接下来它还要经过一些数学处理程序，比如小波分解，多重分辨率傅立叶分析，多相过滤，离散余弦变换等。
It is then subject to such mathematical indignities as wavelet decomposition, multi-resolution Fourier analysis, polyphase filtering and discrete cosine transformation.
编写一个程序用来显示数学常量的值
Write a program that displays the value of the mathematical constant
存在许多在程序中表示数学对象的方法，而MartinJohansen的Dcas系统则证明了这些方法可以如何的千差万别。
There are many ways of representing the objects of mathematics in programs, and Martin Johansen's Dcas system demonstrates just how different these methods can be.
称作Haskell的函数式编程语言展示了一个用于符号数学的程序，名为DoCon。
The functional programming language known as Haskell features a program for symbolic mathematics known as DoCon.
学者创造数学方程序解释人们的拖延症。
Academics invent a mathematical equation for why people procrastinate.
早期的程序员们很快发现了数字的文本表示与程序能在上面执行数学运算的数字变量显著不同。
Beginning programmers quickly discover that the textual representation of a number differs distinctly from a numeric variable on which programs can perform mathematical operations.
说点题外话，我承认这是一个完全无用的程序，跟我们之前写的两个程序一样,我们为什么需要写个程序来解决这个数学运算呢？
Now as an aside, I'll admit this is a completely useless program, much like the first couple of ones we did because why would you write a program just to solve this?
数学是程序员和分析人员的流行主题，从而导致了大量不同的工具可供选择。
Math is a popular topic with programmer and analyst types, leading to a huge diversity of tools to choose from.
不止是下棋或数学这类跟数理有关的事，你知道，有些程序甚至能创作音乐。
Not just in sort of mathematical things like chess or math, there are, as you know, programs that can write music.
原理虽然很简单，但它却可以为强大的科学或数学应用程序提供一个基础。
This idea is rather simple, but it can provide a foundation for a strong scientific or mathematical application.
但是复杂不仅仅是数学问题：副作用还使得测试、理解、分析和记录程序的行为更加困难。
But the complications go beyond the math: Side effects make it harder to test, understand, analyze, and document a program's behavior.
但是复杂不仅仅是数学问题：副作用还使得测试、理解、分析和记录程序的行为更加困难。
But the complications go beyond the math: Side effects make it harder to test, understand, analyze, and document a program's behavior.
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