Physics

[lambdafu]

It might be worth mentioning physics, too. Close enough to math and programming, and obvious application. In fact, I found this github project because I was going to write my own proposal so I can type the name of elementary particles in Unicode (from the Standard Model, in particular the two other neutrinos \nu\mu and \nu\tau as well as the W^\plus and W^\minus boson). Do you think including physics would water down the proposal?

[stevengj]

In previous proposals for super/subscripts in Unicode, the objection was that people should just use HTML or some other formatting language for formatting, and hence there was no need to support this in Unicode.

I want to focus on programming (including computational physics, of course), because in programming languages using an external formatting system (like HTML or a word processor) is not possible.

[miguelraz]

Sorry to comment on a closed thread, but was redirected here after a comment by @jiahao on Julia slack.

I think there is a case to put forth with Unicode's impact on programming in computational physics in at least one respect: fully fledged Einstein Notation for tensors.

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

Infuriatingly, superscript and subscript for the same letter is needed. For starters, not all greek letters are availabe, which are used to denote 0:3, and latin letters are used to index 1:3. For example, in this link one can see that the greek letters delta, theta, iota have no subscript counterpart, whilst rho has no superscript counterpart. A crucial aspect of using indices in Einstein notation is "lowering" or "raising" them from super/subscripts to the other.

This proposal could at least homogenize such a capability, if not outright allow one to implement it in general.

In particular, heavy duty relativistic codes have run on legacy languages and have simply given up on usability. I think having super and subscripts available would be a great boon to the development, maintainability and, readability of gravitational codes specifically, and physics code in general as well.

[stevengj]

Yes, that falls under programming for computational science. Einstein notation is one of many, many notations where both greek and latin subscripts and superscripts are used extensively.

[miguelraz]

I thought we could use some more (prepared) used cases, hopefully I can keep adding/editing this comment as evidence piles.

Physics:

1. Vectors are indicated by an arrow above, Second rank tensors use a double arrow, higher order tensors use the index notation. [2, p,3]
2. Neutrinos require the \mu and \tau subscripts [2, p.12]
3. Nuclear configuration notation require several fractions as subscripts [2, p.14]
4. The equals symbol with a tilde on top means 'corresponds to'
5. The circumflex accent ( hat vector) can mean maximum, or minimum value, depending on where it points, whilst the squiggle tilde is used for the rms value. [2, p. 51]
6. The universal constants of vacuum permittivity and permeability require a º symbol as a subscript. [2, p. 54]
7. The Kronecker delta \delta^i_j, Levi-Civita symbol \epsilon_ij
8. Special functions make extensive use of a a specified (n) derivative as superscript with respect to a parameter (m) usually denoted at the bottom. See Spherical Harmonics and functions with last names [4].

Chemistry

1. \Deltavap*E{m,b} is the molar energy of vaporization. [1, p. 55]
2. \eta_{inh} is the inherent viscosity - SI Unit m^3 kg ^-1
3. Polymerization reactions require the need for the notation P_x + P_y -> P_{x+y} [1, p. 72]
4. Units for degree of crystallinity are w_{c,h}
5. Modulated smectic mesophases SmÃ, and SmC with a tilde, which can't be currently drawn. [1, p 112]
6. Anisotropy in general requires the squiggle tilde on top of the quantity being referred to, see [1,p. 114]
7. Stochiometric equations sometimes need to describe a molecule/atom as aqueous, with the "aq" subscript.

Mathematics:

1. Limit, max, min, and \Sigma, supremum, infimum, Unions, Intersections, and Multiplication notation have subscripts to delimit the set under consideration, or process.
2. Derivatives up to order n (and not just 1-9), with the use of a parenthesis.
3. Partial derivatives can be annotated as \delta_xx, and second partial derivatives may have a subscripted index number, as well as an exponent of 2.
4. Specifying the neighbourhood of a topological ball - B_\epsilon
5. The negative infinity sign is used as a subscript for integrals
6. X with a caret (^) on top is used as an estimator of state X [3]
7. ...Almost half the notation index of [4] can't be expressed without super/subscripts.
8. The | bar when applied to a domain denotes with superscripts and subscripts the upper and lower bounds of evaluation - amongst many types of set restrictions.
9. In Integral Equations, a degenerate kernel requires a sum over an index j=1<=n with functions \phi_j(x) and \psi*_j(x). [4, p. 556]

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References. [1]. Compendium of Polymer Terminology and Nomenclature IUPAC 2008 [2]. Symbols, Units, Nomenclature and Fundamental Constants in Physics, IUPAP - Commission C2 SUNAMCO 2010 reprint [3]. Stochastic Differential Equations, Bernt Oksendal, Sixth Edition, Springer. [5]. Mathematical Physics - A Modern Introduction to its Foundations, Sadri Hassani, 2013. [4] A Comprehensive introduction to Differential Geometry, Michael Spivak, Vol.1, p. 478, 3rd edition.

*: I attempted to find notation that would fit for CS, but my Knuth Vol. 1 on AOCP and CSLR couldn't give more examples than the standard maths notation.

As usual, critiques welcome.