Re: Retypesetting Mathematics now on GitHub

[Damian McGuckin]

On Thu, 22 Jun 2023, Dave Kemper wrote:

> But I doubt it's that simple.  It seems to me that an original equation 
> that doesn't express any real-world phenomenon, if it's sufficiently 
> nontrivial, could meet the threshold for an original work, and thus be 
> copyrightable.  (IANAL.)
>
> (A "false equation" could be one that incorrectly expresses a fact 
> (e.g., 2 = 3) or one that is mathematically valid but does not have any 
> known real-world application.  I'm not sure whether that distinction 
> would affect the copyrightability, again assuming the equation is 
> nontrivial enough to reasonably be said to express originality.)

Ditto - IANAL.

Thanks for your take on this Dave.

In our new User Guide, we have used as a source for our equations

a)      The trivial equations of the 2nd edition of Kernighan +  Cherry
        - the most complex is the solution of a quadratic polynomial

b)      The big equation of the abstract of that same document
        - this is non-trivial
        - it is a valid real-world equation but not my field
        - the source code has been published in that document for 40+ years

        Note that the 1990s version of that document released by AT&T as
        Open Source in DWB 3.2 (and 3.3) releases has a bug in that
        abstract equation. The ellipsis are in the wrong spot in both the
        equation itself and in the exposition of the source code. The
        ellipsis (3 centered dots) goes from term 1 to term 2 instead of
        correctly between term 2 and term m (as seen in the 2nd edition
        from 1979). Feel free to correct me.

c)      Some of Ted Hardings trivial equations

d)      A simplification of Ted's interesting 'proof' of Euler's formula
        - that equation .... exp(iT) = cos(T) + i sin (T) is 200+ years old
        - it is a perfectly valid equation
        - See https://en.wikipedia.org/wiki/Euler%27s_formula

e)      Given's rotation of elements of a matrix
        - it is a perfectly valid equation
        - first published is the 1950s by Givens
        - See https://en.wikipedia.org/wiki/Givens_rotation
        - See posting of EQN source by Tadziu on Mar 1st 2021 on this list
        - Tadziu's EQN source is superior to my own and looks way nicer
        - Tadziu also introduced a interesting feature which can be a 'gotcha'
        -- we also explain how to avoid getting into the trap
        - I haven Tadziu's permission

f)      Our own trivial matrix and vector equations

g)      A 2dimensional linear stress strain relationship
        - it is a set of partial differential equations
        - it reflects a physical phenomena of (say) a metal under load

h)      A set of equation from an extremely reputable source
        - it exploits piles within a matrix
        - it is a really really interesting use of EQN
        - we have the author's permission to reproduce the equation

i)      Some twists on the solution of a quadratic polynomial

j)      We add some more trivial examples

k)      We might add something about a linear least squares solution

Thanks - Damian