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So for example I defined p, remember back over here, as a Cartesian point, but I can actually ask for its polar form.
我可以要求返回它的极坐标形式，这里对我是可访问的，好，这很棒，请再记另外一个为什么。
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Another reason I wanted to point this out in terms of the polar coordinates that we're using, is I think they're actually flipped from what you're used to seeing in physics.
另一个我想指出,我们采用极坐标的原因是，我认为它们实际上是,从你们习惯于看到的物理学中出来的。
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And the problem is, that we want to build this abstract data type, but we'd like to basically know what kind of object is it, and what functions actually belong to it, how do we use them?
然后我对它们运行了这个方法，就是这一小段代码这个方法,这有意义么？,当然没有了，对不对？,因为你知道，当你把两个极坐标，表示的点进行相加运算的时候？
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the same as polar point 2, polar point 1 And then I could say well, gee, are they the same point?
和另外一个极坐标点，我如果来试试，和polar，point，2是不是相同的话？
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In terms of the Schrodinger equation, we now can write it in terms of our polar coordinates here.
在薛定谔方程中，我们现在可以用,极坐标的方式来表示了。
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Let me give you, I'm going to create, q a polar point, I'm going to call it q, and we'll give it some random values.
让我给大家讲解下，我要去创建，一个极坐标点，然后我会去命名它为，然后我给它赋一些随机的值，好，现在我想知道。
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Another way to represent a point in a plane is I've got a radius and I've got an angle from the x-axis, right, and that's a standard thing you might do.
平面上面的点的方法,也就是极坐标,上面那种方法其实是，如果你们喜欢我这么说的话,笛卡尔坐标表示法。
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And then I could do things like again, say, okay having done, that let me just run it here, run that, so I've now got polar point 1, and polar point 2.
然后给它们赋值半径和角度，然后我可以进行刚才的操作，也就是说，对刚才的笛卡尔坐标进行的操作，让我们来运行下它吧，运行下，现在我有一个极坐标点。
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Here's the polar representation of it, some random set of numbers which makes sense.
也就是，这里是它的极坐标表示法,一些有意义的随机数字集。
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same point Cartesian to have 1 representation for a point that supports different ways of getting information out, but has gathered within it, a method or a function for dealing with things like how do I know if it's the same point or not.
还有,这是一个比较极坐标的点,是否相同的不同的方法，但是这开始成了一个麻烦事儿了，我真正想要做的事情是,创建一个能支持不同的方式,输出已经收集的信息的点的表示。
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Right, and just to get a sense of this, let's look at a simple little example, so on your hand-out, you'll see I've got a little piece of code that says assuming I've got one of these points, I want to do things with it, for example I might want to add them together.
这些数组中的一个，你怎么能够知道，它是哪种类型的呢？,你怎么知道它是以笛卡尔坐标,表示的还是以极坐标,形式表示的呢？,你没有可以用来区分的东西，你没有说明这种信息,聚集实际上的意义。
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I could say I want to change the radius of this particular thing.
如果我去看看,这个点的极坐标形式。
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If I now say, I'm going to go ahead and change the radius of this, something, my polar form did it right, but what happened to the Cartesian form?
如果我现在说，我要去改变这里的半径,一些这样的操作，我的极坐标形式，进行了正确的改动？
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I've got Cartesian points, I could create a polar points.
我已经有了一些笛卡尔坐标点了，我可以创建一个极坐标点。
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So let me in fact show you an example.
也做了极坐标点的定义。
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And I think in the polar one I said, if, what did I do there, I said, yeah, again if the x and y are greater than the other one, I'm going to return them to it.
然后我要返回一些值，我认为在极坐标的形式下我说过，如果，我在这里做了什么来着,我说过，对，再说一次，如果x和y坐标。
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So what I'm leading up to here is that we've got a problem.
假设实际上p1和p2是,我用极坐标形式表示的。
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Once I've got that, you notice I can now define a polar point, same way. Notice I've now solved one of my problems, which is, in each one of these cases here, I'm creating both x y and radius angle values inside of there.
你们注意到我现在可以，定义一个极坐标点了，以同样的方式,请注意到现在，我已经解决了我的问题之一了，也就是，在这些例子中的每一个,我在里面都创建了x，y值。
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