math.md

Displaying Mathematics on the VT340

The VT340 can display the DEC Technical Character Set, which contains Greek letters, mathematical symbols, and logical symbols. Additionally, it contains characters that may be used to construct larger mathematical symbols, such as large integral and summation signs.

_{The whole is greater than the summation of its parts.}

Also see dectech.c, a program that shows a table of the DEC Technical Character Set and its output, dectech.vt which can be sent to a terminal such as the VT340 using cat.

Basic usage from a programmer's perspective:

Until someone [hackerb9?] writes a proper locale charmap so that Unicode can be automatically translated into the DEC Technical Character Set, these characters will not be available to most users without a specialized program. However, programmers can display them easily:

1. Assign the DEC Technical Set to "G3" via SCS (Select Character Set).

   Esc+>

2. Every time you want to print a mathematical character, first send SS3 to temporarily shift to G3...

   EscO

3. And then send an ASCII character from one of the tables below to choose a symbol.

   @ → ∴ (Therefore)

Slightly more detail

1. Assign the DEC Tech character set to G3

Esc+>

You can actually set any of over a dozen different character sets to four different translation tables: G0, G1, G2, and G3.

Character Set	G0	G1	G2	G3
U.S. ASCII	ESC(B	ESC)B	ESC*B	ESC+B
DEC Technical	ESC(>	ESC)>	ESC*>	ESC+>
VT100 Graphics	ESC(0	ESC)0	ESC*0	ESC+0
DEC Supplemental	ESC(<	ESC)<	ESC*<	ESC+<

2. Send SS3 (non-locking shift to G3)

Renders next character using G3: EscO

Name	Mnemonic	Sequence	Hex	Function
Single Shift 3	SS3	ESC O	1B 4F	Use G3 character set just for the next character.

Locking-shifts are also available, see the charset README.

3. Send an ASCII character to display a mathematical character

Display the ∴ symbol: @

Hex	ASCII	Name	Symbol
40	@	Therefore	∴

The full tables of symbols can be found below.

Notes

• Position reserved for future standardization in the DEC technical set are shown as the error character ␦ (reverse question mark) both on the screen and in print.

• Component characters are imaged so that adjacent component characters form connected lines at all pitches.

• DEC compatible printers work the same way as terminals and use the same escape sequences to access different character sets.

DEC Technical Character Set Tables

The following tables are taken mostly from the "Printronix LG Programmers Manual", with corrections, and using Unicode characters found at https://vt100.net/charsets/technical.html.

Individual Technical Characters

Greek

Hex	ASCII	Name	Symbol	Unicode
44	D	Uppercase Delta	Δ	0x0394
46	F	Uppercase Phi	Φ	0x03A6
47	G	Uppercase Gamma	Γ	0x0393
4A	J	Uppercase Theta	Θ	0x0398
4C	L	Uppercase Lambda	Λ	0x039B
50	P	Uppercase Pi	Π	0x03A0
51	Q	Uppercase Psi	Ψ	0x03A8
53	S	Uppercase Sigma	Σ	0x03A3
57	W	Uppercase Omega	Ω	0x03A9
58	X	Uppercase Ksi	Ξ	0x039E
59	Y	Uppercase Upsilon	Υ	0x03A5
61	a	Lowercase Alpha	α	0x03B1
62	b	Lowercase Beta	β	0x03B2
63	c	Lowercase Chi	χ	0x03C7
64	d	Lowercase Delta	δ	0x03B4
65	e	Lowercase Epsilon	ε	0x03B5
66	f	Lowercase Phi	φ	0x03C6
67	g	Lowercase Gamma	γ	0x03B3
68	h	Lowercase Eta	η	0x03B7
69	i	Lowercase Iota	ι	0x03B9
6A	j	Lowercase Theta	θ	0x03B8
6B	k	Lowercase Kappa	κ	0x03BA
6C	l	Lowercase Lambda	λ	0x03BB
6E	n	Lowercase Nu	ν	0x03BD
70	p	Lowercase Pi	π	0x03C0
71	q	Lowercase Psi	ψ	0x03C8
72	r	Lowercase Rho	ρ	0x03C1
73	s	Lowercase Sigma	σ	0x03C3
74	t	Lowercase Tau	τ	0x03C4
77	w	Lowercase Omega	ω	0x03C9
78	x	Lowercase Xi	ξ	0x03BE
79	y	Lowercase Upsilon	υ	0x03C5
7A	z	Lowercase Zeta	ζ	0x03B6

Mathematical

Hex	ASCII	Name	Symbol	Unicode
3C	<	Less Than or Equal To	≤	0x2264
3D	=	Not Equal	≠	0x2260
3E	>	Greater Than or Equal To	≥	0x2265
3F	?	Integral	∫	0x222B
41	A	Variation or Proportional To	∝	0x221D
42	B	Infinity	∞	0x221E
43	C	Division or Divided By	÷	0xF7
45	E	Nabla or Del	∇	0x2207
48	H	Is Approximate To	∼	0x223C
49	I	Similar or Equal To	≃	0x2243
4B	K	Times or Cross Product	×	0xD7
56	V	Radical	√	0x221A
6F	o	Partial Derivative	∂	0x2202
76	v	Function	ƒ	0x0192
7B	{	Left Arrow	←	0x2190
7C	|	Upward Arrow	↑	0x2191
7D	}	Right Arrow	→	0x2192
7E	~	Downward Arrow	↓	0x2193

Logic

Hex	ASCII	Name	Symbol	Unicode
40	@	Therefore	∴	0x2234
4D	M	If and Only If	⇔	0x21D4
4E	N	Implies	⇒	0x21D2
4F	O	Identical To	≡	0x2261
5A	Z	Is Included In	⊂	0x2282
5B	[	Includes	⊃	0x2283
5C	\	Intersection	∩	0x2229
5D	]	Union	∪	0x222A
5E	^	Logical And	∧	0x2227
5F	_	Logical Or	∨	0x2228
60	`	Logical Not	¬	0xAC

Building Large Mathematical Symbols

This table shows how to build large mathematical symbols. The characters are designed to connect to adjacent character cells to form technical characters that can occupy several vertically adjacent and/or horizontally adjacent character positions. To use this table, find the character you want to build (along the top of the table). On the left side of the table are various pieces of the characters needed to create the whole. Follow the top row choice, say, INTEGRAL, all the way down the table. Use the hex value beside the symbol name you wish to print. For example, to build an oversize integral, you will need a top integral (hex 24), bottom integral (hex 25), and vertical connector (hex 26).

Component Characters for Large Mathematics

Hex	ASCII	Name	Symbol	Unicode	RADICAL	INTEGRAL	SQUARE BRACKETS	CURLY BRACES	PAREN- THESES	SUM- MATION
21	!	Left Radical	⎷	0x23B7	X
22	"	Top Left Radical	┌	0x250C	X
23	#	Horizontal Connector	─	0x2500	X					X
24	$	Top Integral	⌠	0x2320			X
25	%	Bottom Integral	⌡	0x2321		X
26	&	Vertical Connector	│	0x2502	X	X	X	X	X
27	'	Top Left Square Bracket	⎡	0x23A1			X
28	(	Bottom Left Square Bracket	⎣	0x23A3			X
29	)	Top Right Square Bracket	⎤	0x23A4			X
2A	*	Bottom Right Square Bracket	⎦	0x23A6			X
2B	+	Top Left Parenthesis	⎛	0x239B				X	X
2C	,	Bottom Left Parenthesis	⎝	0x239D				X	X
2D	-	Top Right Parenthesis	⎞	0x239E				X	X
2E	.	Bottom Right Parenthesis	⎠	0x23A0				X	X
2F	/	Left Middle Curly Brace	⎨	0x23A8				X
30	0	Right Middle Curly Brace	⎬	0x23AC				X
31	1	Top Left Summation	␦							X
32	2	Bottom Left Summation	␦							X
33	3	Top Vertical Summation Connector	␦							X
34	4	Bottom Vertical Summation Connector	␦							X
35	5	Top Right Summation	␦							X
36	6	Bottom Right Summation	␦							X
37	7	Right Middle Summation	␦							X

␦ marks characters which Unicode (as of 2023) is unable to reproduce, namely the large summation character. Note that Unicode has summation top (⎲) and bottom (⎳) characters, but those are insufficient even for the simplest mathematics. In contrast, DEC's sigma can grow arbitrarily large in either axis which means it can be centered vertically with the equation to its right and properly span the initial state (e.g., $i=-∞$) beneath it.

One can see a sample of the mathematical symbols at different sizes by catting the file components.vt to a VT340.