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Appendix G illuminated
Debrecen 7th July, 2006
Bogusław Jackowski
Babylonian tablet with a very precise√
2
XVI– XVIII century B.C.
Yale Babylonian Collection, photo: Bill Casselman
3·2
1·√
2−√
3
B. Jackowski: Appendix G illuminated • Debrecen, 7th July, 2006
Typesetting a radical
√
baselineof the radicand
baselineof the radical
symbol
θdef= hy
dy
hx
dx
3·2
1·√
2−√
3
B. Jackowski: Appendix G illuminated • Debrecen, 7th July, 2006
Typesetting a radical
√θθ
∆
ψ
∆
baseline of theresulting formula
top lineof the radicand
bottom lineof the radicand
ψ =
{ξ8 + 1
4σ5, styles D,D′
54ξ8, other styles
∆ = 12
(dy − (hx + dx + ψ)
)
3·2
2·√
2−√
2+√
3
B. Jackowski: Appendix G illuminated • Debrecen, 7th July, 2006
Typesetting an accented symbol
H hx
1
2wy 1
2wxwx = wd + ic
wd
ic
3·2
2·√
2−√
2+√
3
B. Jackowski: Appendix G illuminated • Debrecen, 7th July, 2006
Typesetting an accented symbol
Hs δ
s – italic correction between the accentee symboland the skewchar
δ = min(x-height, hx)
3·2
2·√
2−√
2+√
3
B. Jackowski: Appendix G illuminated • Debrecen, 7th July, 2006
Typesetting an accented symbol
, hx
s = 0
s – italic correction between the accentee symboland the skewchar
3·2
2·√
2−√
2+√
3
B. Jackowski: Appendix G illuminated • Debrecen, 7th July, 2006
Typesetting an accented symbol
, δ = hx
δ = min(x-height, hx)
3·2
3·√
2−√
2+
√2
+√
3
B. Jackowski: Appendix G illuminated • Debrecen, 7th July, 2006
Typesetting an operator with limits
Q∫
M=1
δ
baseline of theupper limit
baseline of theoperator
baseline of thebottom limit
δ – italic correctionof the operator symbol
3·2
3·√
2−√
2+
√2
+√
3
B. Jackowski: Appendix G illuminated • Debrecen, 7th July, 2006
Typesetting an operator with limits
Q∫
M=1
δ/2
δ/2
ξ13
≥ξ9ξ11
≥ξ10
ξ12
ξ13
math axisbaselineof the result
σ22
3·2
3·√
2−√
2+
√2
+√
3
B. Jackowski: Appendix G illuminated • Debrecen, 7th July, 2006
Typesetting an operator with limits
Q∫
M=1
δ/2
δ/2
ξ13
≥ξ9ξ11
≥ξ10
ξ12
ξ13
math axisbaselineof the result
σ22
1 2dop
1 2dop
3·2
3·√
2−√
2+
√2
+√
3
B. Jackowski: Appendix G illuminated • Debrecen, 7th July, 2006
Typesetting an operator with limits
Q∫
M=1
δ/2
δ/2
ξ13
≥ξ9ξ11
≥ξ10
ξ12
ξ13
math axisbaselineof the result
σ22
3·
24·
√ √ √ √2−
√
2+
√2
+
√2
+√
3
B. Jackowski: Appendix G illuminated • Debrecen, 7th July, 2006
Typesetting a generalized fraction
3·
24·
√ √ √ √2−
√
2+
√2
+
√2
+√
3
B. Jackowski: Appendix G illuminated • Debrecen, 7th July, 2006
Typesetting a generalized fraction
baseline ofthe resulting
formula
math axis θσ8 styles D,D′
σ9 other styles
σ11 styles D,D′
σ12 other styles
θ is either given explicitly (\abovewithdelims) or θ = ξ8
3·
24·
√ √ √ √2−
√
2+
√2
+
√2
+√
3
B. Jackowski: Appendix G illuminated • Debrecen, 7th July, 2006
Typesetting a generalized fraction
baseline ofthe resulting
formula
σ8 styles D,D′
σ10 other styles
σ11 styles D,D′
σ12 other styles
3·
24·
√ √ √ √2−
√
2+
√2
+
√2
+√
3
B. Jackowski: Appendix G illuminated • Debrecen, 7th July, 2006
Typesetting a generalized fraction(resolving collisions)
colliding positionof the numerator
baseline
math axis
baseline ofthe resulting
formula
colliding positionof the denominator
baseline
ϕ
ϕ
∆1
∆2
ϕ =
{
3ξ8, styles D,D′
ξ8, other styles
in general ∆1 6= ∆2
3·
24·
√ √ √ √2−
√
2+
√2
+
√2
+√
3
B. Jackowski: Appendix G illuminated • Debrecen, 7th July, 2006
Typesetting a generalized fraction(resolving collisions)
colliding positionof the numerator
baseline
baseline ofthe resulting
formula
colliding positionof the denominator
baseline
ϕ
∆1
∆2
ϕ =
{
7ξ8, styles D,D′
3ξ8, other styles
always ∆1 = ∆2
3·
25·
√ √ √ √ √2−
√ √ √ √2
+
√
2+
√2
+
√2
+√
3
B. Jackowski: Appendix G illuminated • Debrecen, 7th July, 2006
Typesetting indices
δ
s
horizontal placementof a superscript
3·
25·
√ √ √ √ √2−
√ √ √ √2
+
√
2+
√2
+
√2
+√
3
B. Jackowski: Appendix G illuminated • Debrecen, 7th July, 2006
Typesetting indices
s
horizontal placementof a subscript
3·
25·
√ √ √ √ √2−
√ √ √ √2
+
√
2+
√2
+
√2
+√
3
B. Jackowski: Appendix G illuminated • Debrecen, 7th July, 2006
Typesetting indices
δs
s
horizontal placementof a superscript and a subscript
3·
25·
√ √ √ √ √2−
√ √ √ √2
+
√
2+
√2
+
√2
+√
3
B. Jackowski: Appendix G illuminated • Debrecen, 7th July, 2006
Typesetting indices
σ13σ14σ15
σ16σ17
vertical placement of indicesfor the kernel being a symbol
3·
25·
√ √ √ √ √2−
√ √ √ √2
+
√
2+
√2
+
√2
+√
3
B. Jackowski: Appendix G illuminated • Debrecen, 7th July, 2006
Typesetting indices
σ↑18
σ↓19
vertical placement of indicesfor the kernel being a boxed formula
3·
25·
√ √ √ √ √2−
√ √ √ √2
+
√
2+
√2
+
√2
+√
3
B. Jackowski: Appendix G illuminated • Debrecen, 7th July, 2006
Typesetting indices
1
4σ5
placement of indices – resolving collisions
3·
25·
√ √ √ √ √2−
√ √ √ √2
+
√
2+
√2
+
√2
+√
3
B. Jackowski: Appendix G illuminated • Debrecen, 7th July, 2006
Typesetting indices
1
4σ5
4
5σ5
placement of indices – resolving collisions
3·
25·
√ √ √ √ √2−
√ √ √ √2
+
√
2+
√2
+
√2
+√
3
B. Jackowski: Appendix G illuminated • Debrecen, 7th July, 2006
Typesetting indices
1
4σ5
4
5σ5 4ξ8
placement of indices – resolving collisions
3·
25·
√ √ √ √ √2−
√ √ √ √2
+
√
2+
√2
+
√2
+√
3
B. Jackowski: Appendix G illuminated • Debrecen, 7th July, 2006
Typesetting indices
1
4σ5
4
5σ5 4ξ8
4ξ84
5σ5
placement of indices – resolving collisions
3·
26·
√ √ √ √ √ √2−
√ √ √ √ √2
+
√ √ √ √2
+
√
2+
√2
+
√2
+√
3
B. Jackowski: Appendix G illuminated • Debrecen, 7th July, 2006
Future of (math) typesetting
3·
26·
√ √ √ √ √ √2−
√ √ √ √ √2
+
√ √ √ √2
+
√
2+
√2
+
√2
+√
3
B. Jackowski: Appendix G illuminated • Debrecen, 7th July, 2006
Future of (math) typesetting
3 · 26 ·
√√√√√√2−
√√√√√2 +
√√√√2 +
√
2 +
√2 +
√2 +√
3
3·
26·
√ √ √ √ √ √2−
√ √ √ √ √2
+
√ √ √ √2
+
√
2+
√2
+
√2
+√
3
B. Jackowski: Appendix G illuminated • Debrecen, 7th July, 2006
Future of (math) typesetting
3 · 26 ·
√√√√√√2−
√√√√√2 +
√√√√2 +
√
2 +
√2 +
√2 +√
3 ≈ π
3·
27·
√ √ √ √ √ √ √2−
√ √ √ √ √ √2
+
√ √ √ √ √2
+
√ √ √ √2
+
√
2+
√2
+
√2
+√
3
B. Jackowski: Appendix G illuminated • Debrecen, 7th July, 2006
Main obstacle: the discrete nature of fonts
3·
27·
√ √ √ √ √ √ √2−
√ √ √ √ √ √2
+
√ √ √ √ √2
+
√ √ √ √2
+
√
2+
√2
+
√2
+√
3
B. Jackowski: Appendix G illuminated • Debrecen, 7th July, 2006
Main obstacle: the discrete nature of fonts
3·
28·
√ √ √ √ √ √ √ √2−
√ √ √ √ √ √ √2
+
√ √ √ √ √ √2
+
√ √ √ √ √2
+
√ √ √ √2
+
√
2+
√2
+
√2
+√
3
B. Jackowski: Appendix G illuminated • Debrecen, 7th July, 2006
Paradoxically, due to its outmodeness and beingdiscreteness-oriented, as long as fonts endure tobe discrete, TEX’s algorithm of the typesetting
of math formulas seems indomitable
Thank you!
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