[racecar789]

I know a lot of programming languages, but I have never wrapped my head around math notation.

Question for someone who is familiar math notation...was the abstract of this article easy to understand?

For me, the abstract seems like code but no commentary explaining what each bloc does. But I could be mistaken.

[nightcracker]

For context: I'm a computer science MSc student.

The notation is easy to understand (and as far as mathematical notation goes, really quite tame). I don't know what a nearly shortest vector of a lattice is in this context, but I do understand everything else. Note that means I have no idea how the actual method works, but I can understand what's being claimed.

[sterlind]

Not an expert at all, but you can think of lattices as evenly-spaced grid points in a vector space. Given a set of basis vectors b0..bn, and arbitrary integers a0..an, a0b0 + ... + anbn are points on the lattice b.

You can have a "good basis" where the norms for b are low, or an equivalent "bad basis" with the same lattice points but with high norms. That's one hard problem (lattice reduction), but there are polynomial-time approximations.

The shortest vector problem, iirc, is to find the vector with the smallest norm in the best possible basis of that lattice.

[wtallis]

The first half of the abstract is more akin to declaring the data types and structures used, and the second half is mostly a very high level summary of the overall method and results. It's not supposed to be interpreted like code. It's just setting up the context you need to start interpreting the meat of the paper, and giving you a heads-up about what background topics to Google if anything in the abstract sounds unfamiliar.

[chmod775]

> For me, the abstract seems like code but no commentary explaining what each bloc does. But I could be mistaken.

You are mistaken. (Pretty much) all of mathematics is written as natural language, and those symbols are just abbreviations for stuff that could also be written as words. If I read those sentences out loud, another could write them back down and arrive at something that looks the same.

That's why all of mathematical notation is embedded in sentences - they are part of the sentence and can be read as such.

Further that is really basic notation a first semester student of any STEM discipline should be able to read, though I wouldn't expect them to know what a lattice and some of the other terminology is.

[kfrzcode]

I'd love a "cheat sheet" or dictionary for mathematical notation. I don't know how to pronounce half of the embedded symbology, let alone what rules apply. It seems so esoteric and arbitrary sometimes, though I recognize it's most certainly not.

[chmod775]

> It seems so esoteric and arbitrary sometimes

It kind of is since a lot of it grew organically. Often it isn't even consistent across authors/countries. It wasn't really "designed".

The German Wikipedia has a decent overview of symbols and I often use it as a cheat-sheet for LaTeX, whereas the English equivalent of that article has a better explanation of basic notation.

https://en.wikipedia.org/wiki/Glossary_of_mathematical_symbo...

https://de.wikipedia.org/wiki/Liste_mathematischer_Symbole?o...

Even If you don't speak German, the article might be useful because you can follow the links to the individual articles next to the symbols, then change the language back to English. Or use it as a LaTeX reference if you're like me and have trouble remembering some of the more wonky abbreviations it uses. Of course that article isn't comprehensive, but most of the stuff that is missing is very domain-specific.

[racecar789]

Thanks for the info. I finished calculus years ago but am very rusty now. I am reviewing the notation links provided, the material is dense, but it is understandable.

[kfrzcode]

This is perfect, can't believe I didn't go to Wikipedia right away (duh!) -- thank you. Into the rabbit hole I go.

[dutchmartin]

For someone who took a matrix calculation (linear algebra) course like me, it was kinda understandable.

[woah]

You will not be able to understand the notation if you do not understand the math