@marmot I wrote all of l3draw at present!

@manooooh well, the axioms of a vector space do not say "vector/vector" must be indefined.

@yo' and then we can invent the sets we want... Go to any math book and find that vector/vector is defined

@manooooh well, you have many vector spaces in which division is possible. For instance, the real numbers are a vector space of dimension one over the real numbers, and obviously divison by nonzeros is defined there :-)

@yo' again, you cannot divide a vector by a vector

@JosephWright Oh WOW. What is the logic to store coordinates: do you use the screen coordinates, or do you have an abstract "reference frame"?

@manooooh well, you can take two elements of a vector space and divide them, as long as the division is defined in some way

@manooooh So what? Twofooted beings are able to walk. But ducks can fly, so they aren't twofooted beings. It's the same you're saying about vectors.

@daleif vvvvvvv

@marmot It's just a rip-off heavily inspired by pgf

@egreg sorry, but the division is not defined in vectors but in complex. If you want to extend the vectors to a more general way, do it, of course you can, but in any university you will find that every teacher say "You cannot divide a vector by a vector"

@manooooh The real numbers are a vector space (one-dimensional) and you can do division, can't you?

@manooooh They have very bizarre ideas, at your university.

@manooooh well, you are proving that A is not B because A is C, but A can be both B and C.

@marmot Co-ordinates are relative to a canvas, which can be redefined as required

@JosephWright I see. Translation: conceptual problems in making 3d coordinates referencable and allowing to user to install local transformations at the same time.

@JosephWright Yes. But imagine you had a coordinate (A), say at (1,0,0) in whatever frame you start in. Then you switch to a new frame. Now, obviously (A) has different coordinates. Add a point (B) ad (0,2,0) in the rotated system. There is, so far, to the best of my knowledge no way to find out the Euclidean distance between these two points. The Euclidean distance could be computed if we had an "absolute" coordinate system ACS and stored all coordinates with respect to ACS.

@egreg yes

@egreg as you can note, I am not in a math university...

@egreg From my office, I can see a duck pond. After you typed the message, all ducks disappeared.

@manooooh this is a huge relief. :)

@yo' you have convinced me, but that does not mean that teachers are bad. I am the curious one. It's as if we were asking an engineer to know and explain advanced mathematics, it's crazy!

@marmot The more complex you make the 'back end', the more performance you impact on. At some level you need a 2D frame for output: that's really where l3draw sits

@manooooh yeah, sorry for that. I did not realize it's an engineering school. Well, still if you ask a mathematician (even there), he should know better. If you asked a physicist, then it's ok, they do have bizzare ideas about maths :-)

@JosephWright Yes. I know in principle how to install an "ACS" but what I am not sure is how much this is reinventing something that existed before. That's why I am asking. There are a lot of steps that are absolutely trivial with, say, Mathematica, such as transposing a matrix but redoing them in TeX is tough for users with only very limited knowledge like me....

@manooooh Well, if you talk about mathematics with somebody who has been doing algebra for many years…

@yo' hahaha. Sorry, but what does "bizarre ideas of a physicist" mean? Do you mean that some physicist use math badly, or do they build things firmly even though their ideas are crazy?

@egreg ? I know you wrote a math book, that's awesome! But I had Linear Algebra at the first year of the career, but in that time I did not realize about that every thing can be a vector, so I did not care

More generally, if everything can be a vector, everything can be a math tensor?

@manooooh A certain set may be seen as a vector space when convenient. This point of view is very fruitful when talking about algebraic field extensions (not the physicists' fields).

@manooooh No. Not everything can be a vector. A vector is an element of a vector space, i.e. a space in which you can add things. In general, group elements are not vectors, since you cannot add them.

@egreg I know that you do not use arrows or anything to differentiate a vector of a scalar, but do you write explicitly "Let $v$ be a vector..." or do you just say "Let $v$"?

@manooooh I never differentiate vectors. I could differentiate vector valued functions.

@marmot ok. So let's think about the thing that are indeed a vector space. Can this things be extended to a tensor?

@manooooh No, not in general (unless you are willing to add fake spaces to your set-up).

@marmot The group of positive reals with respect to multiplication is well-known to be a one-dimensional vector space over the reals. ;-)

@egreg Yes, there are groups in which there is a + a defined. In general, there is not. If you add two unitary matrices, the result won't be a unitary matrix.

@egreg I was just responding to @manooooh's proposal that everything can be a vector. My take is that the answer is no (as long as you don't stretch it too much, of course you can always define addition in a way that suits you but this is not what is meant here, I think.)

@manooooh Physicists are interested in vector valued functions (that they call vectors), but this is just for elementary mechanics or dynamics. As soon as you go up to Lagrangians and higher theoretical physics, things change very much.

@egreg but suppose that you are going to write the definition of a linear map. So I would say "Let $(V,+_{V},\cdot_{V})$ and $(W,+_{W},\cdot_{W})$ be two $K$-vector spaces. Then a \emph{linear map} is a function $f:V\to W$ that satisfies f(\lambda(v+_{V}v'))=\lambda f(v)+_{W}\lambda f(v'), for all ????" in ???? how would you distinguish a scalar from a vector?

@egreg Well, physicists also call states vectors because they are element of a Hilbert space.

\documentclass{standalone}

\usepackage{l3draw}

\begin{document}

\ExplSyntaxOn
\draw_begin:

	\draw_path_ellipse:nnn
		{ 1.25cm , -0.95cm }
		{ 0.25cm , 0cm }
		{ 0cm , 0.1cm }
	\draw_color_fill:n { yellow!70!blue!40!black }
	\draw_path_use_clear:n { fill }

	\draw_path_ellipse:nnn
		{ 0.75cm , -0.95cm }
		{ 0.25cm , 0cm }
		{ 0cm , 0.1cm }
	\draw_color_fill:n { yellow!70!blue!40!black }
	\draw_path_use_clear:n { fill }

	\draw_path_ellipse:nnn
		{ 1.2cm , 0.95cm }
		{ 0.1cm , 0cm }
		{ 0cm , 0.15cm }

@marmot ^^^

@manooooh We algebraists don't bother to distinguish the + in the two vector spaces, of course. If v is an element of V and a is a scalar, then av is the product of the vector by the scalar. Where's the problem?

@samcarter Impressive! (In tikz this is a one-liner: \tizkz\marmot. ;-)

@samcarter l3ducks and l3marmots are coming soon?

@marmot a mathematician say to me: "In fact, it is easy to use the notion of a free abelian group, to make any set part of a vector space, or in other words, in certain circumstances any mathematical object could be a vector", so I interpreted that as "everything" can be a vector

@manooooh Actually, in my lecture notes I use Greek letters for scalars and boldface letters for vectors. But it's just a convention for helping students. I make no distinction, apart from the alphabet when writing on the blackboard. And there's usually no problem.

@marmot Wrong level, I suspect ;)

@manooooh Yes, because it is Abelian.

@egreg the problem is how you distinguish between a vector from a scalar. You explicitly you wrote "vector" and "scale" instead of putting or not arrows, which is enough. That's what I wanted to know

@JosephWright Maybe start with l3koalas?

@marmot so I was wrong

@manooooh Surprise. ;-) ;-)

xD

@manooooh You can try to convince @egreg to define a new + with A+B\ne B+A.... let me know once you're done. ;-)

What a student of engineering suffers for the impressive (or sometimes null) number of existing notations... Some day I will die of just knowing that two mathematicians write one in Word and another in LaTeX :)

@manooooh Well, as long as the bridges you guys build do not collapse, there is no problem... ;-)

@marmot In my notes for the abstract algebra course, I warn that + is mostly used for commutative operations, but it's not a requirement.

@marmot hahaha, "if it works do not ask", a famous phrase applicable to everything from programming to... computer engineers? :)

@egreg Well, I agree that you can water down any definition but in the end this raises the question what the definition is good for.

@egreg I am a student and if I write it's due to other students (of course!), so as you state a convention for helping students, me or anyone can create a convention, too (e.g. arrows to denote a vector)

@samcarter wow. Are you using expl3 now for the tikzlings?

@marmot hmm Java "a" + "b" is rather different to "b" + "a" :-)

@DavidCarlisle Yes, but isn't Java a chain specialized on selling overpriced coffee? ;-)

@UlrikeFischer The l3-marmot is just an experiment :)

@samcarter WHAT!!?!

@samcarter but it looks quite clean.

@marmot I think they do a good line in Hawaiian pizzas to go with the coffee.

@UlrikeFischer Who is "it" ???

@marmot Oh, sorry! Of course marmots as such are no experiment, just the l3draw version of it :)

@marmot the code. I would never dare to say it to a marmot.

@samcarter Oh phhhh ;-)

@marmot Don't worry, no tikzmarmots were harmed while drawing it

@samcarter Now I am relieved.... ;-)

@UlrikeFischer I think it (the code) looks strange with so many _

@manooooh they sense of proper maths is limited. They seem ok and it's rarely a cause of a disaster, but we mathematicians cry :-)

@samcarter one gets used to it. At first it looked like ants everywhere to me too.

@marmot Do you have a GitHub account?

@UlrikeFischer ants crawling though the code? This might take a bit to get used to!

@HenriMenke To my own surprise, I found I have one. Now I need to find out which user name I used. Most likely it is easier to add a new one?

@marmot Don't bother. If you had one I would have assigned this issue to you: github.com/pgf-tikz/pgf/issues/640

@HenriMenke Yes, as soon as I have some real time and some idea how I can sync github I will be doing that.

@DavidCarlisle David, I tried to edit your answer tex.stackexchange.com/a/391541 to bring it up to date, and I think I might have made a mistake. Please feel free to double-check. I apologize.

@user49915 didn't you just put capital letters at start of sentences? (with the second edit)

Not only. I think it was you who added "You may also want to set SOURCE_DATE_EPOCH_TEX_PRIMITIVES=1" later, and I erroneously edited it.

@user49915 it still says that if I look now? If I had more time I'd add some words about what it does, perhaps another day

@HenriMenke how can I add a pgf module to the preamble of pgfmanual? I currently try to write some documentation, but including examples proves hard without the used macros.

@user49915 sorry been a long day I'll look another time, I thought you'd just updated to use the new environment name i didn't notice you'd changed anything else

@Skillmon is it feasible to load all needed modules into one run?, for the latex companion examples we used a makefile that ran each as a separate document then included the result and the source separately

@DavidCarlisle I haven't looked into the Makefile of PGF. I just took a look at how the documentation for other modules is wrote.

@Skillmon yes I haven't looked at all either (I haven't checked out a local copy yet:-) but for the 1st edition companion they did the entire book loading all needed packages in one run but it was hard to avoid conflicts between packages or artefacts in unrelated examples, so for the 2nd edition we isolated each example into separate documents so demonstrating a font package in one chapter didn't accidentally change the fonts used in an unrelated example somewhere else. I was just wondering..

@DavidCarlisle the pgfmanual uses an environment called codeexpample (I didn't looked into that one either) which seems to execute the code as well as printing it.

@Skillmon Add it to the list of other libraries in pgfmanual-en-main-preamble.tex.

@HenriMenke there is a \usetikzlibrary but no \usepgfmodule. Should I just add that?

@Skillmon If you have code examples which require it, then sure.

@HenriMenke in the end the pull request will be rejected anyway :)

@HenriMenke thanks.

@Skillmon But I recall you saying that your module is an extension of pgfmath, so it might be more appropriate to integrate it directly into pgfmath.

@Skillmon Why do you think it will be rejected?

@HenriMenke nope, pgfparse not on math.

@HenriMenke black humour. Spend some time on it now, especially to make it pgf conformant (I hope).

@DavidCarlisle Alright, no hurry.

Good morning/afternoon/night for everyone!

@DavidCarlisle that stupid \outer:

Runaway definition?
#1->\expandafter
! Forbidden control sequence found while scanning definition of \pgfparserx@new
if.
<inserted text>
                }
<to be read again>
                   \newif
l.163     \expandafter\newif
                            \csname if\pgfparserx@ifname{#1}\endcsname

How can I change JUST ONE mathmatical typo (in my case the \sum)? I'm using the font package \usepackage{eulervm} but I want to just \sum symbol stays as a default.

@M.N.Raia I think there are questions on the network regarding using single symbols from different fonts.

Thanks, I'll look up.