Talk:Diophantine linear system solving

Totally lost

Some questions:
What does any of this actually mean?
What is a basis?
What is the standard basis?
What is a vector space?
What is the dimension of the vector space?
What is linear independence?
What is spanning property?
What is a spanning set?
What is a polynomial ring?
What is a monomial?
What is a monomial basis?
What is the Steinitz exchange lemma?
What is the axiom of choice?
What is the ultrafilter lemma?
What is the dimension theory?

I think you can see where I'm going with this, and I'm not even halfway through the first of, I dunno, 30,000 wikipedia pages I would have to read.

Let's try this: what does this actually mean?

2  1| 2
6  5| 2
7  6| 2

==> P | Hnf

 1 -1  0 |  1  1  1  0
-1  2 -0 | -0  4  5 -0
-2  2  1 |  0  0  0  1  -solution

loop 7 I have a very vague grasp of what the input is, but the output is pure gibberish, and obviously "Transformation matrix P (on the left) and the Hermite normal form" elicits questions as above.

Detailed step-by-step inner workings of all 21 puzzles might be a start... --Pete Lomax (talk) 22:24, 24 December 2021 (UTC)