Jason S
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 Feb 27 comment Clarification on rings of polynomials / Galois fields edit your answer to include the info about quotient rings + I'll accept. Feb 25 comment Clarification on rings of polynomials / Galois fields ah! Thanks, sounds like I should use something like GF2QuotientRing then. I appreciate it -- when I read formal mathematical documents I get lost in the thicket of terminology. Feb 25 comment Clarification on rings of polynomials / Galois fields OK, thanks. The objects I work have characteristic polynomials that are not always irreducible (e.g. not always a maximum-length LFSR). For the identifier I can only use alphanumeric characters, so I can't use GF(2,n) but I could use GaloisField. (GF would be frowned upon by software engineers for being too terse.) Feb 24 asked Clarification on rings of polynomials / Galois fields Feb 18 comment solving linear diophantine equation with inequalities whee! it worked, I posted a Python version of this in my question. Thanks! Feb 18 revised solving linear diophantine equation with inequalities added 1645 characters in body Feb 17 accepted solving linear diophantine equation with inequalities Feb 17 comment solving linear diophantine equation with inequalities e.g. in the original scaled lattice basis, if I had basis vectors $v_1$ and $v_2$, the continuous analog would be to compute $v_1' = v_1 - kv_2$ with $k = \frac{v_1 \cdot v_2}{v_2 \cdot v_2}$, so the integer version would be to find the nearest integer to k? Feb 16 comment solving linear diophantine equation with inequalities oh never mind, you meant this item from earlier in the post: "Repeatedly look for one vector that can be made shorter by adding or subtracting integer multiples of the other two" Feb 16 comment solving linear diophantine equation with inequalities Got all of that except the "You can reduce this (with a little work) to the basis" part... I don't need to see every step, but what's the basic methodology? Gram-Schmidt orthogonalization? Feb 16 comment solving linear diophantine equation with inequalities no, I get why there's extra space between the preceding text (between the k and mod in $ab \equiv k \mod m$) but don't understand about the space after the mod. Compare to $ab \equiv k \bmod m$. Feb 16 comment solving linear diophantine equation with inequalities Odd that the spacing between "mod" and "m" is so large with \mod, however. I should think that spacing would be the same for both \bmod and \mod, since the difference is really with the pause between the "mod" keyword and the stuff that comes before it. Feb 16 revised solving linear diophantine equation with inequalities fixed modulo spacing Feb 16 comment solving linear diophantine equation with inequalities ah.... so I really have some of each in this question. Fixing now... Feb 16 comment solving linear diophantine equation with inequalities Huh, thanks. I've got to digest this + see what I can make of it. I had been able to visualize the 2-D lattice, hadn't thought of adding a 3rd dimension to handle the modulus $m$, but I think I get the gist of what you're talking about. Feb 16 comment solving linear diophantine equation with inequalities hey, thanks! wait, when does the \mod form get used? Feb 16 revised solving linear diophantine equation with inequalities added 4 characters in body Feb 16 revised solving linear diophantine equation with inequalities added 354 characters in body Feb 16 comment solving linear diophantine equation with inequalities ...and is there supposed to be that much space around ${\rm mod}$? If not, what should I be using for MathJax? Feb 16 asked solving linear diophantine equation with inequalities