On Sunday, October 16, 2016 at 4:18:51 PM UTC, saad khalid wrote:
> You are right, however, I don't know any representation theory and 
> wouldn't be able to understand what I'm coding very well. If my course load 
> weren't as significant as it is, and if my research weren't on a time 
> limit, then I would be learning GAP this instant. 

All you need is to know what the character of a linear group is (it is the 
map taking each element to its trace).

Aren't all your groups given by diagonal matrices?
Then they are all commutative, meaning in particular that the character you 
need to find is merely
the trace of each element.


> On Sunday, October 16, 2016 at 3:44:35 AM UTC-5, Dima Pasechnik wrote:
>> On Saturday, October 15, 2016 at 9:39:40 PM UTC, saad khalid wrote:
>>> Hello everyone! 
>>> So, the title is almost a misnomer, because I don't really want to use 
>>> an object from Sage in M2 as much as I want to just use a number from my 
>>> python code in M2. Let me explain what I mean. I have a list in M2 with 
>>> close to 5,000 matrix groups. Lets call the list MatrixList, and it has 
>>> length 5000. I would like M2 to compute the molien series for all 5000 of 
>>> these matrix groups.
>> practically, you are probably better off by doing this in Sage/GAP (GAP 
>> has a command to compute Molien series)
>>> So, ideally I could write a for loop in M2 that does something like:
>>> SeriesList = []
>>> for j from 0 to (5000) do SeriesList = SeriesList|[toString 
>>> molienSeries MatrixList#j]
>>> This would make an empty list called SeriesList, then it would compute 
>>> the molien series of the j'th element of MatrixList, convert that to a 
>>> string, and then append that string to SeriesList, So, in the end, 
>>> SeriesList would have 5000 elements, each elements being the molien series 
>>> for the corresponding matrix group. The issue, however, is that trying to 
>>> do so many at once makes M2 crash. It crashes when I try doing it purely in 
>>> M2, it crashes when I use the sage interface to M2, and it crashes when I 
>>> try using SMC and the Sage/M2 interface (this is my preferred method 
>>> though). 
>>> My solution so far as been the following (this is particularly good for 
>>> me since I use SMC): After a lot of testing, I know that even though doing 
>>> a loop from 0 to 5000 doesn't work, doing it in chunks of 200 tends to work 
>>> fine. So, I make 25 smaller empty lists in M2, called SeriesList1, 
>>> SeriesList2, etc, and then do something like this:
>>> macaulay2.eval("for j from 0 to (199) do SeriesList1 = 
>>> Serieslist1|[toString molienSeries MatrixList#j]")
>>> List1 = macaulay2.eval("SeriesList1")
>>> save(List1, "List1")
>>> macaulay2.eval("SeriesList1 = []")
>>> So, this does exactly what the code above did, except it only does it 
>>> for the first 200 elements, then it saves a string representation of those 
>>> 200 molienseries as a file "List1", and then it goes and clears SeriesList1 
>>> in M2, to clear up the RAM. Running this takes a couple hours usually, and 
>>> then I run the same thing, except from 200 to 399, and I save the file as 
>>> List2, etc. The Main problem I have is that I have to start each one 
>>> manually. As in, I have to keep checking on it until it's done computing, 
>>> and then run the next one. I would much prefer being able to create some 
>>> loop so that it just keeps doing this entire process for me, in chunks of 
>>> 200, for all 5000 elements, and saves it into a bunch of different files. 
>>> I don't know how to do this, however. My original thought had been that 
>>> I would just write something like this:
>>> List = []
>>> for i in [0..24]:
>>>    macaulay2.eval("for j from i*200 to ((i+1)*(200) - 1) do SeriesList 
>>> = Serieslist|[toString molienSeries MatrixList#j]") //this doesn't work
>>>    List.append(macaulay2.eval("SeriesList")
>>>    save(List[i],"List%s", i) //this doesn't work
>>>    macaulay2.eval("SeriesList = []") //just to clear the list, otherwise 
>>> the RAM usage gets too high
>>> So, I could use the iterator in the for loop in the python code to 
>>> change the range of the for loop in macaulay2. However, this doens't work, 
>>> because "i", the iterator in the python for loop, isn't a variable in M2. 
>>> Also, I was hoping that i could use the i from the for loop to make 
>>> different file names. So, when i = 1, it would save the file as List1, and 
>>> then in the next loop around it would save it as List2, etc. Neither of 
>>> those things work. Do you know how I could make that work? Somehow changing 
>>> what happens inside of M2 with numbers that are defined in Sage? And 
>>> dynamically creating file names?
>>> I had some idea of how I could try to do this. My guess was to use the 
>>> exec() command. From what I understand, the exec command runs strings as 
>>> python code. So, I could create a list of the 25 versions of the above 
>>> code, where it would have 0 through 24 already plugged in for "i" in each 
>>> version of the code. Then I could run do 
>>> for i in [0..24]: exec(ListOfCommands[i])
>>> What do you guys think? Is this a viable method? Is this "dangerous" 
>>> somehow? Do you have any tips or alternative methods to do this? Instead of 
>>> using exec, it would be very interesting to know if i could somehow get 
>>> variables defined outside of M2 to be used within M2. The reason I want to 
>>> make this fully automated is so that i can leave it running over night. if 
>>> I only had to do this with one set of 5000 matrix groups, I'd probably do 
>>> it by hand, but I'm going to be generating lots of different sets of 
>>> different sizes of matrix groups, and I want to have a fairly easy method 
>>> where I can just leave the code running and have it do it all. Thanks!

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