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PROFESSOR: So again, we go here
back up to the Examples, Intro,

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Group Theory, start it up.

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And then our first
example is group theory 1,

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and it just goes through.

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And basically, I came up
with a way in a spreadsheet

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to define the functions
I was looking at,

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and then start creating
combinations of them,

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and then do very simple
tests on associativity

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and [? distribution ?]
and all that stuff.

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If you actually look
at the tests I do,

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you might blanch
and be like, really?

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You said that?

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You declared that it
was fully associative?

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It's not like I went in and did
formal proofs for everything.

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I just did some very
quick numerical tests.

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The semi-ring test actually
takes a while here,

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as you can see.

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And this will take
a minute here.

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It appears to be hanging.

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Oh, no, it's not.

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Good.

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We'll let it go through that.

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In fact, while it does that,
we can look at-- basically,

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these are inputs.

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So basically, I
have my different--

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what I call the key function.

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I have union and
intersection, and then

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I have the three possible
conditions-- v1 less than v2,

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v1 equal to v2, v1
greater than v2,

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and then essentially,
the different types

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of operators, the results
that can occur from those.

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And so this is a CSV
file, and we read it

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in as [? associative ?]
[INAUDIBLE].

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And so it looks
like a spreadsheet,

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and I can actually have
columns named v1 less than v1.

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Very powerful.

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And in fact, I'm even
able to pass that column

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into the Matlab Eval function
and have it actually execute

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it, which is nice.

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So I can actually have code
in my column or row names,

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and then have
operations performed

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based on that,
which is, I think,

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a nice thing that you
can do when you allow

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strings to be in your set.

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Likewise, Matlab will formally
parse nan as nan and plus

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minus inf as minus inf, and so
I can get all that functionality

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out of there,
which is very nice.

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And then it goes
through-- let's see here.

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And these are just different
tests that we do on those.

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STUDENT: Is nan a
special character?

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PROFESSOR: Not a number.

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Yeah, I kind of--
I use that as-- it

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has a lot of the
properties of null

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when you add it to
different functions.

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So I'm using that for that,
and it works out pretty well.

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So it's IEEE failure state modes
or whatever it's-- it appears

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like that.

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I can't remember if there is
a plus nan and negative nan

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as well.

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No.

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It's just nan, yeah.

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And then actually,
it goes through here,

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and I think-- these are just
various ways of inputting--

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these are different values,
different little spreadsheets

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that you can make for
exploring these different types

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of things.

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And you can just write
them as little CSV files.

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Very useful.

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On Instruct here.

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I do apologize for the
length of time it's taking.

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I think having the QuickTime
video recording going

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at the same time is
causing the poor computer

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to sweat a little bit more
than it does normally.

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It usually doesn't
take this long.

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Outputs that it
comes up with-- it

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basically writes all these out.

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Look here.

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This shows-- I ask it
to basically generate

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all those 200 pairs.

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So for each key and whatever,
it can go and generate

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those for me.

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So I create this little thing,
and it goes through and creates

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this whole function, and
then writes that out as a CSV

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itself, which is
very convenient.

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Again, these are
things you can do.

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I think this is the one
where we came up with all the

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[? fields. ?] Oh, yeah.

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It doesn't really fit there.

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But you can see these are
the pairs that it found,

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and it shows this is
the zero operator.

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And again, this is all done
with D4M kinds of values

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that it can store
different types of things.

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This is how we made all the
tables that are in there.

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Oh, it's writing out results.

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That means it's done.

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There we go.

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And so the main
one I want to show

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you is that we [? read in ?]
that function, func range,

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and we permuted it.

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And if we do display
full afunc, you

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can see there is the full
combination of values

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as we saw there.

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So there's really
nothing here for you.

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It's not I expect
you to go using

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D4M to do group theory things.

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That's not really the
point of these examples.

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I did.

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It's more just
showing that you can--

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when you go into this
larger space, problems

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that you might not solve
linear algebraically,

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all the sudden,
it's like, oh yeah,

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if I have strings and
other types of things,

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it really opens up
the flexibility.

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I thought that was very
neat that you could do this.

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It just handled the
data very nicely

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and without any real difficulty.

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So with that, that's
the end of this lecture.

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I don't know if there's
any final questions

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before we proceed.

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All right.

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Very good.

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And please, if you haven't
signed up on the sheet,

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please do so.

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Thank you very much.