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What is the internal LaTeX working logic for left and right with delimiters?
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I am reading about latex and in several books is written that to be able to size the delimiter to the vertical size of formula I need to use left and right. I understand that part. But I am interested what is the internal LaTeX working logic for left and right with delimiters? What left and right are doing at the software level?
tex-core delimiters
asked Sep 1 at 13:49
vasili111
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up vote
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I am reading about latex and in several books is written that to be able to size the delimiter to the vertical size of formula I need to use left and right. I understand that part. But I am interested what is the internal LaTeX working logic for left and right with delimiters? What left and right are doing at the software level?
tex-core delimiters
asked Sep 1 at 13:49
vasili111
1547
1
The exact algorithm for sizing and the parameters it uses is explained in appendix G of the TeXBook (it is controlled by the underlying TeX engine, not by LaTeX)
– David Carlisle
Sep 1 at 14:15
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up vote
6
down vote
favorite
up vote
6
down vote
favorite
I am reading about latex and in several books is written that to be able to size the delimiter to the vertical size of formula I need to use left and right. I understand that part. But I am interested what is the internal LaTeX working logic for left and right with delimiters? What left and right are doing at the software level?
tex-core delimiters
asked Sep 1 at 13:49
vasili111
1547
I am reading about latex and in several books is written that to be able to size the delimiter to the vertical size of formula I need to use left and right. I understand that part. But I am interested what is the internal LaTeX working logic for left and right with delimiters? What left and right are doing at the software level?
tex-core delimiters
asked Sep 1 at 13:49
vasili111
1547
edited Sep 1 at 19:50
asked Sep 1 at 13:49
vasili111
1547
asked Sep 1 at 13:49
vasili111
1547
asked Sep 1 at 13:49
vasili111
1547
1547
1
The exact algorithm for sizing and the parameters it uses is explained in appendix G of the TeXBook (it is controlled by the underlying TeX engine, not by LaTeX)
– David Carlisle
Sep 1 at 14:15
add a comment |Â
1
The exact algorithm for sizing and the parameters it uses is explained in appendix G of the TeXBook (it is controlled by the underlying TeX engine, not by LaTeX)
– David Carlisle
Sep 1 at 14:15
1
1
The exact algorithm for sizing and the parameters it uses is explained in appendix G of the TeXBook (it is controlled by the underlying TeX engine, not by LaTeX)
– David Carlisle
Sep 1 at 14:15
The exact algorithm for sizing and the parameters it uses is explained in appendix G of the TeXBook (it is controlled by the underlying TeX engine, not by LaTeX)
– David Carlisle
Sep 1 at 14:15
add a comment |Â
2 Answers
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When TeX encounters material in math mode, it creates a math list.
A math list is a list of nodes (they are called noad here), sometimes containing sublists, representing all the things written in math mode.
If you write
$fleft( stuff right)$
the block with the delimiters is put into a sublist with math class inner, as if you wrote
$fmathinnerleft( stuff right)$
Then TeX converts the mathinner part without left( and right) into a horizontal list to determine it's height and depth. Then TeX tries to add delimiters with height+depth equal to 2*max(height,depth) from this inner material.
How does TeX create this delimiters? The delcode of the delimiter points to a character in a font, if this is big enough, TeX inserts it. Otherwise the character might contain a next field indicating the codepoint of the next larger variant. Then TeX tries again with the bigger one. This repeats until TeX found a delimiter large enough or an extensible delimiter. Extensible delimiters have multiple parts which can be stacked on top of each other and repeated to form arbitrary large delimiters. They are always big enough, but they have to consist mostly of vertical segments.
The last part can be customized with the just released new version of LuaTeX.
For further details, it is best to read The TeXbook, Appendix G, Rule 19 (see also p. 152).
edited Sep 2 at 0:07
GuM
15.5k2253
answered Sep 1 at 14:24
Marcel Krüger
10.4k11032
+1, great answer, maybe Moriambar should have made a post about that in his "appendix G question series".
– TeXnician
Sep 1 at 14:31
To be fussy, the field that points to the next larger character is labeledNEXTLARGERin the output of thetftoplprogram. (I wouldn’t have remarked this if you hadn’t writtennextwithin backticks… ;-)
– GuM
Sep 1 at 23:48
@GuM I recently worked a lot with the LuaTeX font table, so I used the name from there and expected it to be the "standard" name. But you're right,tftoplmight be a better reference. Feel free to edit it in.
– Marcel Krüger
Sep 1 at 23:59
I think that it is more than enough to have the name used bytftoplcited in the comments! :-) Added: Rather, I’m going to improve the reference to Appendix G.
– GuM
Sep 2 at 0:03
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This is not quite an answer, but in a comment, the formatting is lost. Let's start with line 22328 and following of tex.web:
@ We have dealt with all constructions of math mode except `.\left' and
`.\right', so the picture is completed by the following sections of
the program.
@<Put each...@>=
primitive("left",left_right,left_noad);
@!@:left_}.\left primitive@>
primitive("right",left_right,right_noad);
@!@:right_left_noad.\left primitive@>
primitive("right",left_right,right_noad);
@!@:right_left_noad.\left primitive@>
primitive("right",left_right,right_noad);
@!@:right_Â
up vote
3
down vote
up vote
3
down vote
This is not quite an answer, but in a comment, the formatting is lost. Let's start with line 22328 and following of tex.web:
@ We have dealt with all constructions of math mode except `.\left' and
`.\right', so the picture is completed by the following sections of
the program.
@<Put each...@>=
primitive("left",left_right,left_noad);
@!@:left_.\left primitive@>
primitive("right",left_right,right_noad);
@!@:right_left_noad.\left primitive@>
primitive("right",left_right,right_noad);
@!@:right_{.\right primitive@>
So what does this say? This has nothing to do with LaTeX, they are TeX primitives. And basically, this says you should read the TeX book (as David Carlisle already commented the important part for this is appendix G) to understand what's going on here.
Alternatively, you may dig into the source code which is documented (see link above). So you could simply look up the missing references and you would, for instance, go on with line 13514:
And finally, we have |left_noad| and |right_noad| types, to implement
TeX's .\left and .\right.
But as it would take quite some time to find all the corresponding source code, I come back to my recommendation to read the TeX book.
answered Sep 1 at 14:21
TeXnician
20.5k52880
answered Sep 1 at 14:21
TeXnician
20.5k52880
answered Sep 1 at 14:21
TeXnician
20.5k52880
answered Sep 1 at 14:21
TeXnician
20.5k52880
20.5k52880
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1
The exact algorithm for sizing and the parameters it uses is explained in appendix G of the TeXBook (it is controlled by the underlying TeX engine, not by LaTeX)
– David Carlisle
Sep 1 at 14:15