We've added this notion of a function.
我们明白了函数的概念。
The prototype of a function can be defined in header files.
可以在头文件中定义函数原型。
And, it would be going towards higher values of a function.
它应指向函数值较大的一边。
So, here I have a contour plot of a function, and I have a blue vector.
我这里有一个函数的等值线图，还有一个蓝色的向量。
But they won't be the level curves of a function for which this is the gradient.
但它们不一定是，某个以该向量场为梯度的函数的等值线。
And, each of them has a number next to it which tells us the value of a function there.
每条线都被一个数标出，每个值都代表了一个函数值。
Only the string field is significant; it is the name of a function that is the main program.
只有字符串字段是至关重要的；它表示构成主程序的函数的名称。
An operation is a programmer's tool, offered to them in the familiar guise of a function call.
“操作”是给程序员的工具，它们打扮成程序员熟悉的函数调用。
The definition of an interface of a function is quite direct and intuitive -- just think about
定义功能接口非常直接和直观——只需考虑
So, if the gradient of a function is a vector, the divergence of a vector field is a function.
如果说函数的梯度是向量，那么向量场的散度就是函数。
But then, when we are looking for the minimum of a function, well, it is not at a critical point.
接着，我们找最小值点，会发现它不是临界点。
Shor's algorithm, for example, is able to find the period of a function of N bits in polynomial time.
例如 Shor的算法能在多项式时间内找到一个N位函数的周期。
Sometimes poor performance can be a result of a function being used more frequently than expected.
有时候，不必要地频繁调用一个函数会造成性能问题。
One could also foresee custom iterators being created and used entirely within the scope of a function.
人们也可以预先自定义一些迭代器，在函数的整个作用域内创建并使用。
There should be no space between the name of a function and the left parenthesis of its parameter list.
函数名与((左括号)之间不应该有空格。)
Careful readers of Listing 4 will have noted the use of a function, speakize , which is not detailed here.
细心的读者可能会发现清单4使用了speakize函数，这里我们不打算详细解释。
And then, for each little piece, you take the value of a function, and you multiply by the width of a piece.
对每个小段，用函数的值，与那一小段的长度相乘。
It tells you, if you take the line integral of the gradient of a function, what you get back is the function.
它说，如果你对一个函数的梯度做线积分，就能得到原函数。
Function annotations associate expressions with parts of a function, such as parameters, at compile time.
函数注释会在编译时将表述与函数的某些部分(比如参数)相关联。
y Can we think of a function whose derivative with respect to x is y, and derivative with respect to y is x?
可以想到哪个函数关于x的偏导是，关于y的偏导是x吗？
So, here's version two of my plot where I've added the contour plot of a function, xy on top of the vector field.
这是第二张函数图,我在上面添加了函数xy的轮廓，放在了向量场上面。
The way we actually think of the double integral is really as summing the values of a function all around this region.
就二重积分来讲,它是对区域里函数值求总和。
Lotus Connections displays an error page (see figure 3) when an exception is thrown during the execution of a function.
当在执行一个函数期间抛出一个异常时，LotusConnections就会显示一个错误页面(见图3)。
These handles' lifetime is determined by a handle scope, which is often created at the beginning of a function call.
这些句柄的生存时间由句柄范围决定，句柄范围经常在一个函数的开始的时候被创建。
The first line of a function definition, also known as the method signature, begins with def (shorthand for define).
函数定义的第一行也称为方法签名(method signature)，以def开头(def是define这个单词的缩写)。
The following example annotates the return value of a function. This is useful for checking the return type of a function.
如下的示例则注释了某函数的返回值。
Except, of course, we haven't see the graph of a function of three variables because that would live in 4-dimensional space.
当然我们还不能看到，三元函数的图像，因为它处在一个四维空间里。
In this scenario, performance would be superb, and transactions would complete in times approaching those of a function call.
在这种情况下，性能会非常出色，完成事务的时间可以接近一次函数调用的时间。
Tracing of exit/return value of a function is possible by applying trace hook at exit point and specifying function prototype.
通过在出口点应用跟踪钩子并指定函数原型，可以探测函数的退出/返回值。
I mean we'd seen in last time, but the gradient is perpendicular to the level and points towards higher values of a function.
我的意思是，上一次我们讨论过了，这个梯度是垂直于等高线，并且是指向方程增长的方向的。
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