Robert Bruner: This is a brief introduction to the basic features of the exit code which I spoke about in the E ch T seminar on the 30th of September, this is the first of three videos this one shows how to find a module and how to compute a minimal resolution part.
Robert Bruner: The modules we're going to use as our samples are those which occur in a little co fiber sequence here let's let me the cosmology of Bo one which is this for cell complex, so the M itself has four generators over if to integrate 046 and seven.
Robert Bruner: With a square for connecting the bottom two and then square two and then square one we're going to.
Robert Bruner: Look at the Co fiber sequence to sits in which has Ko Phi renew sitting at the bottom and six suspension of co fiber to at the top.
Robert Bruner: And this is when we apply cosmology scope every sequence we get sure the exact sequence here where am one is the smallest Magellan which square ones none zero and four is the smallest Magellan which square for is non zero and in.
Robert Bruner: module up here now, the way the code works, the F2 generators have a module are numbered starting with zero so the for generators in em will be number 012 and three will come back to a minute.
Robert Bruner: And what we'll see in a second lecture will be lecture demonstration will be how to compute the.
Robert Bruner: induced maps in X coming from this, but first let's just create the modules Okay, so what we're going to do is create the module definition files for these three will use the command new module to install them in the process will show how to use how to.
Robert Bruner: enhance the sort of obvious parts of the definition to get the complete definition and it will compute the resolution collect all that data.
Robert Bruner: Create Adams charts for them, then we'll actually join all three items charts into one so just a nice little demonstration of how the atoms church are.
Robert Bruner: designed to be used okay so let's go to a directory where we can do all this, I have one called co home test, and since we're going to be working with a modules rather than a two modules.
Robert Bruner: we're going to go down into the directory a now we want to create the first module m m one Okay, so I am going to.
Robert Bruner: read a file m one death in the module definition file for em one says that there are two is two dimensional over if to the two generators are at zero degrees 01 and there's a.
Robert Bruner: generator zero as a square one, acting on it, which has one term in it and that consists of generator one next to that.
Robert Bruner: So, now that we've got that we can install it to the computer a new module am one oh and here's an interesting feature of all the commands if you invoke the command with the wrong number of arguments it'll tell you how to be used.
Robert Bruner: So this tells you that new module needs the name of the module that's going to be the directory, in which the resolution is computed and stored and module def is the module definition okay so and one will be the director and we'll use this file I just created my one F.
Robert Bruner: Okay, it.
Robert Bruner: Created the directory it went to check the module definition for correctness, it had no errors report, so we can just go down into one now.
Robert Bruner: And compute let's say let's go from dimension zero to 40 that'll be nice and quick i'm going to run this in the background, so I can do some other things same time Okay, so now let's go back up to notice we're in em ones directory and then go back up to the aim.
Robert Bruner: steam right algebra a's resolute directory now and I will create and for.
Robert Bruner: me it's definition looks like to generators now, these are in degrees your own for and generator zero has a square for on it, which consists of one term and that's generator one.
Robert Bruner: module.
Robert Bruner: And for him for death.
Robert Bruner: Okay again no problems will go down into him for and start computing actually type it correctly.
Robert Bruner: After will start the.
Robert Bruner: One I mean dot dot C D m for Robert okay there we are okay, so now let's compute the resolution from degrees zero to 40 for this as well.
Robert Bruner: And again we'll run that the background, I actually look at what jobs are running and see both of these are still running here.
Robert Bruner: Okay, so now let's go back up to the modules directory and let's start creating the middle the module definition file for the middle much now if I think about this there's some obvious entries here.
Robert Bruner: mainly the square for the square to in the square one, so first we tell it is for generators there any reserved for six and seven.
Robert Bruner: i'm generator zero there's a square for which is one term is generator one on generator one there's a square to this is one term and that's generator number two on generator to there's a square one, it has one term minute and it's generator number three.
Robert Bruner: Number remember the DEMO relations you'll know that that's not actually going to be that story, but we'll see that happen automatically so it's good okay so let's install the module now new module.
Robert Bruner: And that definition I just created.
Robert Bruner: uh huh now, when we see here, and it was checking the module definition for correctness it reported some errors so let's go down into.
Robert Bruner: The directory for him and see what they are this program new consistency.
Robert Bruner: Know tell us the old program consistency just gives us a very brief summary of what's wrong here, it says the Adem relation that starts out square to square for.
Robert Bruner: when applied to generate or zero didn't produce a zero like it should have okay new consistency tells us.
Robert Bruner: Also, what the whole the DEM relation is okay so jumpy them relation square to script for plus square six plus square five square one.
Robert Bruner: Applying that to the bottom generator here, we see that square square ones, obviously zero there's nothing degree one.
Robert Bruner: square six well we didn't define a square six and that's the problem squared C square for took us from generators here's a generator to its course six should do the same so let's go and look let's go into the definition now and fix it.
Robert Bruner: I will add the square six here which.
Robert Bruner: generator zero the generator to.
Robert Bruner: Alright, so now okay bye now you see also both of the.
Robert Bruner: Jobs are done job one is done in job is done so, the other two resolutions have been computed at to be 40 candidates we've already done next step Okay, so now let's run new consistency and see how it likes it and still not good.
Robert Bruner: Okay, so what's the problem now square one square six plus square seven applied to generate or zero is not zero should be zero of course Okay, so we go back into the definition and there we go there's The problem we should have had a square seven here as well.
Robert Bruner: Okay, so we add that it gives us generator three and you know we we know the damn relations law, and if we also know, there should be a square three on this guy on January one here, so let me just put that in right now so generator one place where three to it.
Robert Bruner: That takes you to generate your two and then for their generators Okay, so it should be correct now it's running new consistency and sure enough no errors are reported OK, so now we can do, they can compute.
Robert Bruner: The resolution for this module.
Robert Bruner: set that going well, now that the resolutions for me one and in Florida let's go up there and compute the.
Robert Bruner: create two files for those okay so let's go back here to our little summary of what we're doing.
Robert Bruner: Okay, so we've used new module to install them and we're using the Dems to compute the resolutions now using a report we're going to collect the data is generated and create out of charts using church okay so.
Robert Bruner: Okay, so go over we're down in em one NASA report.
Robert Bruner: It could produce a text summary of the output as well we don't really want that, today, so.
Robert Bruner: If you want more details on any of this, you can go look at the.
Robert Bruner: paper that genre Agnes night put on archive when we posted the database that the N ar ar D database repository.
Robert Bruner: And it just gives it gives a more complete description of file format and all of these techniques okay so church, let me show you the.
Robert Bruner: invocation you give it the high and low, the low and the high filtration so low and the high geometric degrees this file shape and hai malts.
Robert Bruner: Those actually recreated by report so let's look at those here as a files are most recently created after creating all these differentials in computing the.
Robert Bruner: Resolution we have it create the command report generated the file shape and the file hmm bolts here, in particular, those are the ones that we need for the charts Okay, so now let's go back to create the chart let's go from general.
Robert Bruner: filtration zero to 12 i'm gonna it's fairly low, but i'm going to fit all of these into a single file in a minute, so that.
Robert Bruner: The more convenient.
Robert Bruner: hmm models, now the next one is the output file let's just call this one tech, and then the label that goes into the caption the tech caption for the figure that generates so i'll just call it that one alright, so now that we've got that chart.
Robert Bruner: Open is the sort of generic.
Robert Bruner: MAC command to do whatever is appropriate to the file and that's in one tech open will fire up tech shop for me what types at this.
Robert Bruner: And if you're at all familiar with the.
Robert Bruner: My to more space, this should remind this should be quite familiar here the lightning flashes connected by.
Robert Bruner: News hooking the bottoms of the lightning places together up on the edge and then some more stuff here.
Robert Bruner: Okay, and you can see that we calculated out to Internet agree 40 and stop there by this vanishing line along this edge of here okay so put that to sleep for a moment do the same thing, and the other two directories.
Robert Bruner: Report always should do that to bring all the data up to date here and then shirt i'm going to just use practically the same chart command because I went the same size.
Robert Bruner: Of.
Robert Bruner: tech figure here, but now I call it in for him for tech.
Robert Bruner: Type types it that.
Robert Bruner: This may be slightly less familiar secure fiber of new Okay, you see, we killed off new in this release them here, and then it starts to that effect of that, of course, is to create it for sell a fourth dimension for generator starting filtration three here.
Robert Bruner: And you know we'll look at the more detail in a minute, so now let's go to the third much we created em and again run report to collect the data and now the church command now just call it M and tick.
Robert Bruner: Okay types it this.
Robert Bruner: Okay, in this maybe.
Robert Bruner: Even less completely familiar.
Robert Bruner: But.
Robert Bruner: You see, the effect of killing off the new and with the four cell and then actually killed off Ada on the on the for sale here, etc okay now.
Robert Bruner: next thing I want to show you is how to use these tech files and in fact I don't really let's I don't really need him to take anymore, so I got rid of that let's cut be okay let's think about this for a second.
Robert Bruner: We have cool five renewed going into be one with quotient Sigma six collaborative giving us this long exact sequence.
Robert Bruner: So let's put the Co fiber of new at the top of the page, be a one in the middle and m one at the bottom, and then the connecting map will, and then the induced maps in ext and display these module maps or by the geometric maps from go fiber new to be a one etc.
Robert Bruner: Those will map those three x down the page and then the boundary map will go from the bottom around to the top okay so let's do that now let's copy and tech into let's call it le s for long exact sequence.
Robert Bruner: Who would not do that let's actually first put em for.
Robert Bruner: i'm.
Robert Bruner: Here at the top and then we'll add the others after that okay now.
Robert Bruner: So good and now let's just add.
Robert Bruner: The end of Las tech.
Robert Bruner: and one that tech at the bottom.
Robert Bruner: let's go in and Edit.
Robert Bruner: Open this week just watch what it looks like.
Robert Bruner: Okay, if I type set this of course all we're going to see is that first co fiber new sitting here at the top, because we'll see in a second and let's go in and look at the file now.
Robert Bruner: Okay, so you can see here at the top, there is just a tiny little bit of tech header.
Robert Bruner: before it starts to.
Robert Bruner: Do this take the picture here, so the tix the pictures, the vast majority of this.
Robert Bruner: So what we'll do now, if you go down to the end of this you'll see the end document here has caused it to only display and four so we'll get rid of the end document there in the tech hitter and now we'll start in the new figure for me, taking the middle if I now.
Robert Bruner: write this out in three types at this.
Robert Bruner: You see it's now added m tech there, and you can kind of see what the induced map is going to look like from co fiber of new and to be a one here already now let's go ahead and get rid of the other and document.
Robert Bruner: and incorporate the rest of this in one.
Robert Bruner: that take into here.
Robert Bruner: Okay, so now let's make this a little bit bigger and move it over to the middle of the page and there we go this gives us the line exact sequence in X, corresponding to this co fiber sequence that we started with here go fiber new to be open to seeing the six co fiber two.
Robert Bruner: and
Robert Bruner: that's it, I will, in the next section, the next video I will show you how.
Robert Bruner: To start creating the map definition files that link these up.