 And here we are in lecture 2, we are going to look at printing, now printing as far as iPython notebook is concerned means printing to the screen. Think of it this way, you use a word processing program and you say file print and instead of printing to a physical printer, depending on your operating system and how it's set up you can print to PDF. The same happens here, and Sympi has various printers, instead of printing an answer to my code I can have it print LaTeC code which I then can then use somewhere else. So there's a variety of printers available in Sympi, here I'm going to do as you can see, this line here is going to indicate to this iPython notebook that I want to do what is referred to as pretty printing. So I'm going to say import Sympi as SYM, just an abbreviation for this namespace and then I'm going to invoke this pretty printing. I'm going to tell this notebook that I want SYM, referring to sympi.init underscore printing open and close parenthesis. Then I'm going to set up my symbols x, y, z, r, theta, now look at that theta, there's a variety or long list of words that I can use in Sympi that will export the symbol for that word. Now remember the variable here, the first one maps to the first symbol there, the second variable maps to the second symbol there, note the commas here, note no commas there, and I have theta here and theta there. Now I'm just simply going to print to the screen theta cubed, let's see what that looks like. Beautiful as if you've written it on paper in beautiful handwriting, that really is pretty printing. So remember we can factorize, I have 2x squared plus xy, it's going to factorize by taking x out as a common factor, leaving me with x and then 2x plus y and I can print that out. So because I've invoked this pretty printing here, everything that gets printed to the screen now will be done with pretty printing and indeed I have the x and 2x plus y. Let's look at integration. I'm going to print the string, the indefinite integral dot and I have some dot integral, now we're going to get to differentiation and integration, but look here I've got integral with a capital I and I'm going to say x cubed comma x, that means the indefinite integral of x cubed with respect to x, so I just have my expression there comma with respect to what I want to integrate and if I were to run that look at that, is that not a thing of beauty, the integral of x cubed with respect to x, I can also do the definite integral, I'm going to do a and b, a symbols a and b and I'm going to say some dot integral, again my expression there x cubed comma, now I have to put this part in parentheses, still with respect to x and I have my lower bound and then upper bound, so if I were to print that look at that, the definite integral of x cubed with respect to x, going from a to b. Now there is a keyword just integrate that we can use here that will actually do the integration for me, but I can also use this formal integral and just put the dot do it with open and closed parentheses at the back and that will actually just solve that integral for me, this is not the usual way of doing it, but I can have the printing and then just say dot do it and it will just do the integral for me, let's look at the derivative, some dot derivative with a capital D there, it's y cubed with respect to y, so this comma y and lo and behold look at that, I needn't just take the first derivative though, what if I wanted the third derivative, so here I have x plus y cubed with respect to y three times, I'm just going to have y y and then just hit enter and lo and behold look at this, so I have a partial derivative because it's with respect to y but I have another symbol in the x, so that is a third partial derivative with respect to y of x plus y cubed, now in this last section of code here I'm again going to do the derivative of y cubed and now I needn't put y, y, y, I could also have just said y, let's just do that three, if I do that it is going to still do the third derivative, so I can also do it here but I can also do the dot do it, so it's just going to do the second derivative of y cubed with respect to y for me and just give me the answer, now just getting back I just wanted to show you alpha comma alpha comma beta comma beta and let's map that to symbols and remember parentheses and my quotation marks alpha alpha lower uppercase and lowercase beta and beta, so we can do that and now if I were to print alpha I have the remember if I'm in a cell and I want to execute that cell I can either press the run button there or I can hit shift enter and lo and behold there's a capital alpha and lowercase alpha there's my lowercase alpha uppercase beta and my lowercase beta done all done now through pretty printing and that is mightily impressive indeed