Display Math in Formula Where is it and where can it go
Or Is T EX really good at math?
The present Basics
Equation Numbering (1) \placeformula \startformula ... \stopformula + + =
Location of equation number (2) \setupformulas[location=left] + + =
(C) Conversion of equation numbers \setupformulas[conversion=Characters] + + + + =
Formatting of equation numbers (4) \setupformulas[numberstyle=bold] + + + =
[5] Formatting of equation numbers \setupformulas[left={[},right={]}] + + + + =
Placement of fomrula (6) \setupformulas[align=left] + + =
Placement of fomrula (7) \setupformulas[align=right] + + + =
The present AMSTeX features
\startformula Gather \NC ... \NR[+] \NC ... \NR[+] \stopalign \stopformula = + + + + = + + + \startalign[ n=1 ]
\startformula Left gather \startalign[n=1, align=left ] \NC ... \NR[+] \NC ... \NR[+] \stopalign \stopformula = + = + + + +
Right gather \startformula \stopalign \NC ... \NR[+] \NC ... \NR[+] \stopformula = + + + + + = + + + + + \startalign[n=1, align=right ]
\startformula Align \NC ... \NC ... \NR[+] \NC ... \NC ... \NR[+] \stopalign \stopformula = + + + = + + \startalign[ n=2 ]
\startformula Alignat \startalign[n=2, m=2, distance=2em ] \NC ... \NC ... \NC ... \NC ... \NR[+] \NC ... \NC ... \NC ... \NC ... \NR[+] \stopalign \stopformula = = = + =
Flaign \startformula \stopalign \NC ... \NC ... \NC ... \NC ... \NR[+] \NC ... \NC ... \NC ... \NC ... \NR[+] \stopformula = + + = + + = + = + + \startalign[n=2, m=2, distance=1em plus 1fill ]
Intertext \startformula \startalign \NC ... \NC ... \NR[+] \intertext{...} \NC ... \NC ... \NR[+] \stopalign \stopformula = + + + + = + +
Multi-column numbered equations (11) \stopalign \stopformula ... \startformula \startalign \stopalign \stopformula ... \startformula \startalign \startformulas \placeformula \stopformulas (10) (9) (8) = + = = + = +
Subformulas (12a) (12b) \startsubformulas \startformula \startalign \NC ... \NC ... \NR[+] \NC ... \NC ... \NR[+] \stopalign \stopformula \stopsubformulas = + + = + + +
The present Subexpressions
Matrix (13) \startformula \startmathmatrix[n=3] \NC ... \NC ... \NC ... \NR \NC ... \NC ... \NC ... \NR \NC ... \NC ... \NC ... \NR \stopmathmatrix \stopformula
Matrix — parenthesis \startformula \NC ... \NC ... \NC ... \NR \NC ... \NC ... \NC ... \NR \NC ... \NC ... \NC ... \NR \stopmathmatrix \stopformula \startmathmatrix[n=3, left={\left(\,}, right={\,\right)}]
Defining matrices \definemathmatrix[pmatrix][left={\left(\,}, right={\,\right)}]
Aligning matrices \startformula ... \stopmathmatrix ... \stopmathmatrix \stopformula \startmathmatrix[ location=low ] \startmathmatrix[ location=middle ] ... \stopmathmatrix \startmathmatrix[ location=high ]
Cases \startformula ... = \startcases \NC ... \NC ... \NR \NC ... \NC ... \NR \stopcases \stopformula , + + = ,
Substacks \startformula \sum_{\startsubstack \NC ... \NR \NC ... \NR \stopsubstack ... \stopformula � + + +
Missing features
Simple yet have no support Arbitrary tag's as equation numbers (Einstein's Formula) Need to come up with a consistent user interface gathered, aligned, etc. Is really simple to code from scratch, hard to reuse parts of mathalign • E = mc 2 •
Not so simple and still have no support Complete support of multline If you do not care about location of equation numbers, support is easy. Proper support for equation numbers in multiline equations Need a two pass algorithm, current support is only a one pass algorithm. Location of equation numbers — ctags, tbtags Currently ConT EXt does not even attempt to do this • • •
Proper support for split Easy once location of equation number is done. Correct support for align when there are multiple columns Find the size of all columns and split the remaining space equally between them Controlling page break between equations Something more fine tuned than the current all or none approach Using \shortdisplayskip Can be done, ( breqn does it), but I don't really understand T EX that well. • • • •
Example
(.) (.) Now, (.) given by generated. Further, First draft – August , 4 b 1 t ( x t , y 2 t , u 2 t , s 2 t − 1 ) � � Y 1 , t = y 1 , t , U 1 , t = u 1 , t ; 4 ϕ t − 1 � X t = x t , Y 2 t = y 2 t , U 2 t = u 2 t , S 2 t − 1 = s 2 � = Pr � t − 1 � � t − 1 Y 1 , t = y 1 , t , U 1 , t = u 1 , t ; 3 ϕ t − 1 , g 2 � U 2 t = u 2 � X t = x t , Y 2 t = y 2 t , S 2 t − 1 = s 2 = Pr � t t � � � X t = x t , Y 2 t = y 2 t , S 2 t − 1 = s 2 � Y 1 , t = y 1 , t , U 1 , t = u 1 , t ; 3 ϕ t − 1 , g 2 × Pr � t − 1 t ( c ) � � u 2 t = g 2 t ( y 2 t , s 2 t − 1 ) = I � � � Y 1 , t = y 1 , t , U 1 , t = u 1 , t ; 3 ϕ t − 1 � X t = x t , Y 2 t = y 2 t , S 2 t − 1 = s 2 × Pr � t − 1 � 3 b 1 � u 2 t = g 2 t ( y 2 t , s 2 t ( x t , y 2 t , s 2 t − 1 ) t − 1 ) = I = : 3 F 1 ( 3 b 1 t , g 2 t )( x t , y 2 t , s 2 t − 1 ) where ( c ) follows from the sequential order in which the system variables are t = ( y 1 , t , u 1 , t ) ∈ ( Y 1 , t × U 1 , t ) , y 1 . Consider 4 o 1 t + 1 ∈ Y 1 , x t + 1 ∈ X , s 2 t ∈ S 2 , and t ) of a realization 1 b 1 1 ϕ t = ( 4 ϕ t − 1 , l 2 t ) . Then a component ( x t + 1 , s 2 t + 1 of 1 B 1 t + 1 is � � t ; 1 ϕ t � 1 b 1 X t + 1 = x t + 1 , S 2 t = s 2 � Y 1 t + 1 = y 1 t + 1 , 4 O 1 t = 4 o 1 t + 1 = Pr � t � � 4 O 1 � t ; 1 ϕ t � X t + 1 = x t + 1 , S 2 t = s 2 t , Y 1 t + 1 = y 1 t = 4 o 1 Pr � t + 1 = � � t ; 1 ϕ t � Y 1 t + 1 = y 1 � 4 O 1 t = 4 o 1 Pr � t + 1 � � t ; 1 ϕ t � X t + 1 = x t + 1 , S 2 t = s 2 t , Y 1 t + 1 = y 1 � 4 O 1 t = 4 o 1 Pr � t + 1 � � t ; 1 ϕ t � Y 1 t + 1 = y 1 � X t + 1 = x t + 1 , S 2 t = s 2 t , 4 O 1 t = 4 o 1 = Pr � t + 1 � X t + 1 = x t + 1 , S 2 t = s 2 � � 4 O 1 t = 4 o 1 t ; 1 ϕ t � × Pr � t t ∈ N 1 : y 1 � � n 1 t + 1 = h 1 t ( x t + 1 , n 1 = P N 1 t + 1 ) � t ; 1 ϕ t � X t + 1 = x t + 1 , S 2 t = s 2 � � 4 O 1 t = 4 o 1 × Pr � t
Theorem . (Structure of optimal control laws of agent ). Consider variation variation into a model similar to variation . gies of agent . These properties are subsequently used to convert the model of of agent that are true for every arbitrary but fixed control and state-update strate- In this section, we provide structural/qualitative properties of optimal control laws Structural properties (.) generated. Combining (.)–(.) we get (.) of the model of Problem .. For any arbitrary but fixed control and state-update strategies First draft – August , � � t ; 1 ϕ t � X t + 1 = x t + 1 , S 2 t = s 2 � 4 O 1 t = 4 o 1 Pr � t � � X t + 1 = x t + 1 , X t = x t , Y 2 t = y 2 t , U 2 t = u 2 Pr = t , x t ∈X , y 2 t ∈Y 2 t ; 1 ϕ t � S 2 t − 1 = s 2 t − 1 , S 2 t = s 2 t | 4 O 1 t = 4 o 1 u 2 t ∈U 2 , s 2 t − 1 ∈S 2 � � X t + 1 = x t + 1 | X t = x t , Y 2 t = y 2 t , U 2 t = u 2 Pr = t , x t ∈X , y 2 t ∈Y 2 t ; 1 ϕ t � S 2 t − 1 = s 2 t − 1 , S 2 t = s 2 t , 4 O 1 t = 4 o 1 u 2 t ∈U 2 , s 2 t − 1 ∈S 2 � S 2 t = s 2 t | X t = x t , Y 2 t = y 2 t , U 2 t = u 2 × Pr t , � S 2 t − 1 = s 2 t − 1 , 4 O 1 t = 4 o 1 t ; 4 ϕ t − 1 , l 2 t � � X t = x t , Y 2 t = y 2 t , U 2 t = u 2 t , S 2 t − 1 = s 2 t − 1 , 4 O 1 t = 4 o 1 t ; 4 ϕ t − 1 , l 2 × Pr t ( d ) � � � � � w t ∈ W : x t + 1 = f ( x t , u 1 t , u 2 s 2 t = l 2 t ( y 2 t , u 2 t , s 1 P W t , w t ) t − 1 ) = I x t ∈X , y 2 t ∈Y 2 � t − 1 , 4 O 1 t ; 4 ϕ t − 1 � X t = x t , Y 2 t = y 2 t , U 2 t = u 2 t , S 2 t − 1 = s 2 t = 4 o 1 × Pr u 2 t ∈U 2 , s 2 t − 1 ∈S 2 � � � � � w t ∈ W : x t + 1 = f ( x t , u 1 t , u 2 s 2 t = l 2 t ( y 2 t , u 2 t , s 1 P W t , w t ) t − 1 ) = I x t ∈X , y 2 t ∈Y 2 × 4 b 1 t ( x t , y 2 t , u 2 t , s 2 t − 1 ) . u 2 t ∈U 2 , s 2 t − 1 ∈S 2 where ( d ) follows from the sequential order in which the system variables are 1 b 1 t ) = : 4 F 1 ( 4 b 1 t + 1 ( x t + 1 , s 2 t , l 2 t , y 1 t + 1 , u 1 t )( x t + 1 , s 2 t ) where 4 F 1 is given by (.)–(.). �
The Future?
What is wrong with current math support in T EX?
Separation of content from presentation
Display math is becoming write once format
Automatic line breaks
Can luaT EX help?
Allow non-T EXperts to experiment with line breaking algorithms
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