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prog to compute all polys of GFpm
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Informal development log by Phil (PhL, 7.2.13) for the Galois book, tied to the July 2013 release. It tracks how he built a Maple routine for conjugate sets of exponents and primitive elements. Topics include converting between sets, lists, sequences and arrays, removing duplicate elements and duplicate sets, sorting, and flagging primitives. He reports the program finished and installed as Chapter 5 (k). Code and output images did not survive extraction.
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Maple Program to Compute Conjugate Sets and mark Primitives PhL 7.2.13
This is all done and installed as Chapter 5 (k), I like it.
I didn't realize I was so close to having this capability! Looking at section below Galois (5.24) I have almost the whole thing done! What I need basically is to mark which ones are primitives and to make Maple filter out stuff which I did by hand.
There are two filters required:
(1) if an exponent set replicates another one, throw the new one out
(2) throw out duplicate elements within a set.
But not quite there yet. I have a series of things to learn how to do.
Here is how to take the exponents, get them into a sequence joe and then a list and sort them into a list bob.
How do I remove duplicate elements from a list? Answer: convert it to a set and then back to a list.
1. Conversion between Set and Sequence
2. Conversion between List and Sequence
3. Conversion between Set and List. Note how to filter duplicate items!
4. Convert between Array and a List
I am now very close to what I want. For example
It only remains to somehow throw out the duplicate sets.
OK, I have now advanced a bit to this point:
I maintain a set of sets, and as a result, duplicate sets of exponents are automatically removed.
Now all that remains is to get a primitive p symbol in there somehow. OK, here we are
I find that the sets are not always sorted, so want to convert to a list and then I can use the sort command because you cannot sort a set.
I have moved a long quite a bit now. One bug is that Prog sometimes goes to the start of my list!
OK, it is now all done and I pronounce it good! It has been installed.