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Re: Is EULER math?; was: Re: MF ==> (PS type1

dhl> I actually prepared a math article using Concrete + Euler (+ CM).  I
dhl> followed closely (I hope exactly!) the arrangement of fonts laid out in
dhl> gkpmac.tex, the macro package allegedly used for Concrete Mathematics. 

I prepared (but I didn't write it) a whole book using Concrete +
Euler.  The book was prepared using LaTeX(2e).  In the process, I
created the LaTeX packages `beton' and `euler', and I examined closely
the `gkpmac' macro package that indeed was used for preparing Concrete

dhl> The font set CC and EU were intended to go together, with the Concrete
dhl> fonts used for text, the Euler for math. Essentially: 

That's how Knuth originally intended them to be used.  But I find that
the Euler fonts are sufficiently distinctive (i.e., they do not look
like any text font that I know of).  So I have used the Euler fonts in
combination with other text fonts with a weight similar to Concrete.
In particular, I have used them with Bitstream Charter.

dhl> CCR replaces CMR  (and similarly for other text fonts)
dhl> EUR replaces CMMI (but it lacks a 17 glyphs, mostly arrows and
dhl>                    accents)
Euler does not have variants of sigma and rho (so you must use the
regular shapes).
The (harpoon) arrows are in EUEX.
If you need the triangles, the \star, the \vec accent, or hooks for
the arrows, then you still need CMMI.
I do not consider the special symbols \flat, \natural, \sharp, \smile,
and \frown to be math symbols; I believe they were put there because
Knuth did not want to leave any slots empty in the fonts.

dhl> EUS replaces a small part of CMSY (37 glyphs: \cal A...Z, plus 11 more)
The arrows and \infty are in EUEX.  Also, don't forget the EUF fonts
which has parentheses, square brackets, plus, minus, division, equals
sign, and oldstyle numerals (in addition to the Fraktur letters).

dhl> EUEX replaces a small part of CMEX (50 glyphs including sums,
dhl>                    (co)products, integrals, some arrows and all the
dhl>                    various bits of braces)
dhl> For a full featured math setup, the other extensible symbols
dhl> (parentheses, brackets, etc.) are drawn from CMEX. And virtually all the
dhl> specialized relations and binary operations are drawn from CMSY. 

dhl> If the book Concrete Mathematics (as printed) followed the macros in
dhl> gkpmac.tex, then it would certainly have needed CMEX at least (or
dhl> a replacement) and might possibly have needed CMSY. Indeed, I have read
dhl> comments from Knuth that EUEX was needed only for the few cases where
dhl> the CM symbols did not blend well with the EU family. This suggests
dhl> that they were used or at least intended to be used.

Knuth's macros was dictated by the needs of the Concrete Mathematics
book.  He did not intend to create a complete replacement for the CM
fonts, and why should he?  Would it make sense for him to spend time
designing a \cdot, \times, or a \subset sign for the Euler family?
Especially if the new versions would be quite similar to the originals
or if they were not needed at all for the Concrete Mathematics book
(which is the case for many of the specialized operators and relations).

The EUEX font was created when somebody mentioned that it looked
strange with CM sum signs together with the other Euler symbols (the
first few chapters of Concrete Mathematics has especially many sum
signs).  Later came the integral sign and the arrows.

dhl> To me, it makes equally good sense to regard EU as extending CM
dhl> or to regard CM as extending EU, with respect to the math fonts.

Even though Euler must draw on CM for a number of specialized symbols
(typically `simple' shapes such as \times), I would characterize it as
being an alternative to the CM, not an extension.

Would it have made sense to characterize MathTime (before MathTime
Plus was created) as an extension to CM, since it had to draw on CM
for bold latin and greek letters?  I think not.