[Date Prev][Date Next][Thread Prev][Thread Next][Date Index][Thread Index]

**To**:*Multiple recipients of list LATEX-L <LATEX-L@RELAY.URZ.UNI-HEIDELBERG.DE>***Subject**:**gcd and lcm (was: Re: math fonts)****From**:*Johannes Kuester <kuester@MATHEMATIK.TU-MUENCHEN.DE>***Date**: Thu, 10 Apr 1997 17:32:14 +0200- Reply-To: Mailing list for the LaTeX3 project <LATEX-L@RELAY.URZ.UNI-HEIDELBERG.DE>
- Sender: Mailing list for the LaTeX3 project <LATEX-L@RELAY.URZ.UNI-HEIDELBERG.DE>

As I just sent a copy of my own tries at METAFONT to Joerg Knappen, I feel I should comment on some symbols my fonts contain, as I never published them in any way, but I think they could be useful and could be included in the new math fonts. These are delimiters to denote greatest common divisor and least common muptiple. Currently, there is no real standard for these, one is to use gcd(a,b) in English, ggT(a,b) in German and so on, one is to simply use (a,b) which is a notation overloaded with different meanings and often causes confusion when read, also, (a,b) lacks a standard counterpart for lcm (I've seen {a,b} and [a,b] for this, both are very original and unambiguous notations...) So I propose the following symbols for this (first some ASCII art, see below for my metafont code (only base size here; of course, they should come with extensibles, which I have prepared, too): __ __ \ / / \ \ a, b / for the gcd and / a, b, \ for the lcm \ / /_ __\ The idea here is to represent two angles of a downward pointing triangle (as the gcd of a and b is \leq \min(a,b)) and of an upward pointing triangle (analogous reason for the lcm), respectively. These symbols seem to match all criteria I could think of for new math symbols, e.g. they are unambiguous, international, mnemonic, consistent (they are not to far away from at least one existing notation, yet different enough), and concepts belonging together are represented by resembling symbols. So much for this proposal. Here's my metafont code (rather simple changes to cm's slash and backslash programs), I also prepared macros to use these symbols (my suggestion here is \gcd{a,b} and \lcm{a,b}, with \biggcd etc for the other sizes and \Gcd and \Lcm for automatic \left and \right insertion). cmchar "Left least common multiple delimiter"; beginchar(oct"002",10u#,body_height#,paren_depth#); italcorr body_height#*slant-.5u#; adjust_fit(0,0); pickup rule.nib; rt x1=hround(w-u)+eps; top y1=h+eps; lft x2=hround 2u-eps; bot y2=-d-eps; x3=x1; y3=y2; draw z1--z2--z3; % diagonal and horizontal penlabels(1,2,3); endchar; cmchar "Right least common multiple delimiter"; beginchar(oct"003",10u#,body_height#,paren_depth#); adjust_fit(0,0); pickup rule.nib; lft x1=hround u-eps; top y1=h+eps; rt x2=hround(w-2u)+eps; bot y2=-d-eps; x3=x1; y3=y2; draw z1--z2--z3; % diagonal and horizontal penlabels(1,2,3); endchar; cmchar "Left greatest common divisor delimiter"; beginchar(oct"004",10u#,body_height#,paren_depth#); adjust_fit(0,0); pickup rule.nib; lft x2=hround 2u-eps; top y2=h+eps; rt x3=hround(w-u)+eps; bot y3=-d-eps; x1=x3; y1=y2; draw z1--z2--z3; % horizontal and diagonal penlabels(1,2,3); endchar; cmchar "Right greatest common divisor delimiter"; beginchar(oct"005",10u#,body_height#,paren_depth#); italcorr body_height#*slant-.5u#; adjust_fit(0,0); pickup rule.nib; rt x2=hround(w-2u)+eps; top y2=h+eps; lft x3=hround u-eps; bot y3=-d-eps; x1=x3; y1=y2; draw z1--z2--z3; % horizontal and diagonal penlabels(1,2,3); endchar; -- Johannes Kuester kuester@mathematik.tu-muenchen.de Mathematisches Institut der Technischen Universitaet Muenchen

- Prev by Date:
**Re: math fonts** - Next by Date:
**Re: math fonts (and all those glyphs)** - Prev by thread:
**The upright "d" (was: Re: math fonts)** - Next by thread:
**Re: math fonts (and all those glyphs)** - Index(es):