Re: Retypesetting Mathematics now on GitHub

[G. Branden Robinson]

At 2023-06-02T21:54:21+1000, Damian McGuckin wrote:
> I probably need to build the PDF info stuff into my document. I have a
> somewhat different structure so I need to think a bit more about it. I
> have the following Level 1 and 2 headings:
> 
>       .H 1 "Introduction"
>       .H 1 "Encapsulating EQN Code"
>       .H 2 "Displayed Mathematics"
>       .H 2 "In-lined Mathematics"
>       .H 1 "Names, Symbols and Letters"
>       .H 2 "Special Words"
>       .H 2 "Simple Symbols"
>       .H 2 "Advanced Symbols"
>       .H 2 "Miscellaneous Symbols and Names"
>       .H 2 "The Greek Alphabet"
>       .H 1 "Basic Use **"
>       .H 1 "Progressive Examples"
>       .H 2 "Adding Spaces to the Input"
>       .H 2 "Adding Spaces to the Output"
>       .H 2 "Clarity of Expression"
>       .H 2 "?? Superscripts and Subscripts"
>       .H 2 "?? Wrapping"
>       .H 1 "?? Fractions **"
>       .H 1 "?? Square Roots, etc"
>       .H 1 "?? File Inclusion"
>       .H 1 "?? Diacritical Marks"
>       .H 1 "?? Definitions"
>       .H 1 "?? Big Brackets, Braces, etc"
>       .H 1 "?? Size and Font Changes"
>       .H 1 "?? Quoted Text"
>       .H 1 "?? Local Motions"
>       .H 1 "?? Lining Up Equations"
>       .H 1 "?? Linear Algebra"
>       .H 1 "Partial Differential Equations"
>       .H 1 "Operations Between Bounds"
>       .H 1 "?? More Definitions"
>       .H 1 "A Large Example - A"
>       .H 1 "Past Experience"
>       .H 1 "?? Troubleshooting"
>       .H 1 "++ Words Known to Eqn!!"
>       .H 1 "?? Use on a \s-1UNIX\s+1-like System"
> 
>       .HU "References"
> 
>       (Appendices)
>       .H 1 "TROFF Special Character Names"
>       .H 1 "Ted Harding's Slightly Complicated Example"
>       .H 1 "Rewrite - Some Other \*(eQ Definitions"
>       .H 1 "Some Differences Between Classical \*(eQ and GNU's \*(eQ"
>       .H 1 "A Large Example - B"
> 
> Anything with a ?? in it need more thorough checking for copyright
> issues.

Looks ambitious!

> I am hoping that using Brian's and Lorinda's examples is not copyright
> violation.

Generally, at least in the U.S., mathematical equations are not believed
to be subject to copyright protection.  You can find much online support
for this view but a lot of it is glib, in my opinion.  Here's a resource
that digs fairly deep, cites case law extensively with quotations from
precedential decisions, and undertakes analysis.

https://www.comsol.com/blogs/can-models-be-protected-by-copyright-law/

I realize that you live and work in Australia; I apologize but my legal
semi-education is highly U.S.-centric.  There is also the fact that
what I term the "copyright cartels"--publishing, software, and
entertainment companies--have repeatedly used global trade agreements to
effectively impose the copyright laws of the U.S. on its trading
partners.  In this limited case, however, that fact may work to your
benefit.

As an aside, upon reading the following, one hack did occur to me.

        Some models encounter difficulties in clearing the threshold set
        by the idea-expression dichotomy. The 2011 decision in the case
        of Ho v. Taflove is one example. In this case, a federal
        appellate court in Chicago held that an engineering professor
        and graduate student failed to prove that another professor and
        student had copied any protected elements from a “4-level
        2-electron atomic model with Pauli Exclusion Principle for
        simulating the dynamics of active media in a photonic device.”
        The court described this model as “a new mathematical model of
        how electrons behave under certain circumstances.”

        The ruling in the case was that the equations and figures
        contained in the model were not capable of attaining copyright
        protection and that there was no evidence found that it was
        possible to use different equations or figures to depict the
        concepts at issue. The court observed the following: “Although
        equations can be rearranged through the laws of mathematics, the
        substance of the equation nevertheless remains the same.” In
        spite of the creators’ argument that the model reflected
        hypothetical assumptions, the court found no original creative
        authorship in the equations and figures, which attempted to
        describe reality and mimic nature.

If an equation is not copyrightable because it expresses a _fact_, then
it seems to be that one can obtain copyright protection in _false_
equations.  These would be analogous to the trap streets that map
publishers place in their works.[1]

Not saying you _should_ do that in your document...

> For continuity reasons, I wanted to retain their originals. I add
> more examples - some are Ted Harding's and some are totally new.

As far as I know, you are offending neither the law nor general
principles of academic courtesy if you both reuse specific equations and
acknowledge the source of any that isn't common knowledge.  (I don't
think we need to cite sources for Newton's Laws of Motion, Einstein's
mass-energy equivalence, the quadratic equation, the Arrhenius equation,
the ideal gas law...)  Those that are gigantic and weird, like that in
K&C's abstract, I would cite.  I still don't know what the application
of that series of identities is.  Like a word in the Cyrillic alphabet,
I can pronounce it but I don't understand it.  :P

> Is the equivalence of lpile and lcol a GNU thing or is it part of the
> original 'eqn' program too?

A good question.  Five minutes of experimentation didn't answer it.

According to K&C §18, they are distinguished:

        The reason for using a matrix instead of two adjacent piles, by
        the way is that if the elements of the piles don't all have the
        same height, they won't line up properly.  A matrix forces them
        to line up, because it looks at the entire structure before
        deciding what spacing to use.

And sure enough the K&C paper as rendered by groff _appears_ to have the
aforementioned problem; if you look at the example in K&C §17, the piles
are clearly _not_ aligned; the swash on the italic "z" seems to be
sitting on top of the same text baseline as the "c" to its left, instead
of...swashbuckling below it.

But when I try to recreate this ugliness with a minimal input,[2] it
doesn't reproduce...

[some time later]

I've got it.

GNU eqn compels more beauty than AT&T eqn by default, maybe, but you can
still extract ugliness.  Try this.[3]

Regards,
Branden

[1] https://en.wikipedia.org/wiki/Trap_street

[2]

.EQ
A ~=~ left [
  pile { a above b above c }
  ~~ pile { x above y above z }
right ]
.EN
.sp
.EQ
A ~ = ~ matrix {
  ccol { a above b above c }
  ccol { x above y above z }
}
.EN

[3]

.EQ
A ~=~ left [
  pile { a above b above c sup { left ( pile { n over k } right ) } }
  ~~ pile { x above y above z }
right ]
.EN
.sp
.EQ
A ~ = ~ matrix {
  ccol { a above b above c sup { left ( pile { n over k } right ) } }
  ccol { x above y above z }
}
.EN

signature.asc
Description: PGP signature