RFC: rename trace to tr

[JeffBezanson]

In math this is always written as tr(A), and trace could potentially mean other things.

[ViralBShah]

I have never seen it written as tr in math. It is a pretty standard name, and I have always seen it as trace. More so, I don't think we should be taking up 2 letter names like this.

[JeffBezanson]

See https://en.wikipedia.org/wiki/Trace_(linear_algebra). tr for days.

[mbauman]

It also helps that this is now behind a using LinearAlgebra in order to bring it into your namespace. I think it's totally ok for LinearAlgebra to export a two-letter function like this. Base would be a much tougher sell, I agree.

[ViralBShah]

I still feel that being in Stdlib is special. And something like LinearAlgebra will be widely used.

[innerlee]

I support tr. The math books (maybe old books) I used use tr. Until recently, I noticed that engineering books like the verbose trace. It is understandable because the target audience is different.

[GlenHertz]

Functions should have long verbose names so users variables can have short names. Otherwise people will write t = tr(a) and it will not be obvious what it does. If people want they can tr = trace themselves.

[strickek]

SciPy and Matlab also use "trace". And it is short, so why change it?

[antoine-levitt]

There are already two letter names (qr, lu) and abbreviations (det, inv). tr for trace is very standard (I haven't ever seen trace written down in full)

[haampie]

Wolfram Language also usesTr.

It could be confused with a shorthand for transpose, though.

[KristofferC]

Googling on images for trace matrix math and counting I got 18 tr and 4 trace. Science.

[vtjnash]

tr seems a bit less common, so it's harder for someone to google than trace, but it does seem to go right along with the glorious tradition of using truncated names (I'm looking at you "sine"): cos, atan, exp, det, log, log1p, sqrt, pow, mul, hypot, etc.

[ajkeller34]

In physics, I rarely if ever see trace written out in full; almost always I see tr. The context makes it clear though. If tr lived in Base I'd be against this change, but if it lived in LinearAlgebra I think it'd be fine.

[Keno]

No love for https://en.wikipedia.org/wiki/Tr_(Unix)?

[ararslan]

I've seen both tr and trace in math, but more often than not I've seen this written as tr. That said, I'm against this change. While we usually adhere to mathematical names, take for example transpose; no one writes the word out in math. I think in this case trace is perfectly clear and not without precedent. What else could trace(::AbstractMatrix) mean?

[StefanKarpinski]

I've only ever seen the mathematical trace operator written in equations as tr(A). In prose it's referred to as "the trace" but as an operator this is called tr so I'm in favor of changing it.

[GlenHertz]

I can foresee tr being in an html package (table row), tr is also a common Unix command, Total Return in finances, etc. Someone doing financial stuff may want to generate html reports and use linear algebra. If Julia is general purpose then to gain the full benefits of multi-dispatch shouldn't function names be long enough so people can combine packages and still be able to write generic code? Maybe this is better now but in the past it was problematic. Please consider other factors than popularity and people what don't have word auto-complete in there text editor.

[DNF2]

I agree with @GlenHertz here (except I don't like verbosity in general). It is nice to write

tr = trace(A)

While tr is common in mathematics, where the context is always totally obvious, trace is common in programming languages.

It's even monosyllabic.

[antoine-levitt]

It is nice to write
tr = trace(A)

It's the same argument for det & co. I usually write detA = det(A).

I think in this case trace is perfectly clear and not without precedent. What else could trace(::AbstractMatrix) mean?

In Julia there is at least https://github.com/MikeInnes/Traceur.jl (although in macro form). Trace in non-numerical programming languages usually means to examine the execution of a command, e.g. strace, dtrace, python's trace, etc.

[andyferris]

Personally I find trace more readable - I like to consider that people (eg at work) who aren’t mathematicians will read my code and have enough breadcrumbs to figure out what it means. tr wouldn’t Google well (though there is the docsting, I guess).

[JeffBezanson]

I think readability by non-mathematicians is not a real requirement --- tr is the standard notation, like sin, cos, and det.

[StefanKarpinski]

This seems to me to be exactly the same situation as the determinant which is always, always, always written as det(A) in math textbooks; similarly tr(A) is always how the trace of A is written as an operator. You do not write determinant(A) or trace(A).

[StefanKarpinski]

Evidence: just look through this google image search (courtesy of @mbauman):

https://www.google.com/search?tbm=isch&q=linear%20algebra%20trace&tbs=imgo:1

[StefanKarpinski]

This one's for @fredrikekre!

[JeffBezanson]

Ok, looks like the "aye"s have it.