@Section
    @Tag { vpos }
    @Title { Vertical positioning }
@Begin
@PP
Every equation and every object within every equation has an
@I axis running through it which is used to position it vertically
equations. @RawIndex { equations }
equations.axis @SubIndex { axis of }
axis @Index { axis of equation }
with respect to nearby objects.  In the Expert's Guide to Lout
@Cite { $kingston1995lout.expert } this is called a @I { row mark },
but we'll stick with axis.  Here are some examples with the axis
shown as a dashed line:
@ID {
@ShowHMark @Eq { x sup 2 }
||2c
@ShowHMark @Eq { non + }
||2c
@ShowHMark @Eq { @ExA }
}
When these objects are placed adjacent to one another, their
axes are merged, giving the correct vertical positioning:
@ID @ShowHMark @Eq { x sup 2 + @ExA }
Most of the time you do not need to think about vertical
positioning, because for most objects there is just one
sensible place for the axis to go, and Lout puts it there.
@PP
Matrices and the delimiters that enclose them are the two
exceptions.  Lout makes the axis of a matrix pass through
its exact centre, and it shifts the axes of delimiters
so that they exactly enclose the thing delimited.  These
choices are never disastrous, but there are other possibilities
that might be better sometimes.
@PP
The axis of a matrix could reasonably be set to the axis
of any of its rows:
@ID {
@ShowHMark @Eq {
matrix userow { yes } {
  axisrow col { x sup 3 } col { y sup 3 } col { z sup 3 }
  row     col { x sup 2 } col { y sup 2 } col { z sup 2 }
  row     col { x } col { y } col { z }
}
}
||2c
@ShowHMark @Eq {
matrix userow { yes } {
  row     col { x sup 3 } col { y sup 3 } col { z sup 3 }
  axisrow col { x sup 2 } col { y sup 2 } col { z sup 2 }
  row     col { x } col { y } col { z }
}
}
||2c
@ShowHMark @Eq {
matrix userow { yes } {
  row     col { x sup 3 } col { y sup 3 } col { z sup 3 }
  row     col { x sup 2 } col { y sup 2 } col { z sup 2 }
  axisrow col { x } col { y } col { z }
}
}
}
Alternatively, it could be set to where Lout usually places it,
through the exact centre:
@ID {
@ShowHMark @Eq {
matrix {
  row     col { x sup 3 } col { y sup 3 } col { z sup 3 }
  row     col { x sup 2 } col { y sup 2 } col { z sup 2 }
  row     col { x } col { y } col { z }
}
}
}
Delimiters could reasonably keep the axes that they naturally
have (approximately through their centres, but not exactly):
@ID {
@ShowHMark @Eq { pmatrix userow { yes } shiftdelim { no } { @ExA } }
}
or they could have their axes moved in the way that Lout usually does,
to the point which allows them to evenly cover the thing delimited:
@ID {
@ShowHMark @Eq { pmatrix userow { yes } { @ExA } }
}
Altogether then there are four possibilities when these two alternatives
interact:
@CD lines @Break @Tab
  @Fmta { @Col 0.5w @VShift A ! @Col ! @Col B ! @Col ! @Col C }
{
@Rowa
  A { }
  B { Matrix axis
uses row axis }
  C { Matrix axis passes
through centre }
@Rowa
@Rowa
  A { Delimiter
keeps its axis }
  B { @ShowHMark @Eq { pmatrix userow {yes} shiftdelim {no } { @ExA } } }
  C { @ShowHMark @Eq { pmatrix userow {no } shiftdelim {no } { @ExA } } }
@Rowa
@Rowa
  A { Delimiter
axis shifted }
  B { @ShowHMark @Eq { pmatrix userow {yes} shiftdelim {yes} { @ExA } } }
  C { @ShowHMark @Eq { pmatrix userow {no } shiftdelim {yes} { @ExA } } }
}
To supply these possibilities, the @Code "matrix" symbol and all
its variants (@Code "pmatrix" etc.) have two options whose
equations. @RawIndex { equations }
equations.userow @SubIndex { @Code "userow" option }
userow.equations @Index { @Code "userow" option (equations) }
equations. @RawIndex { equations }
equations.shiftdelim @SubIndex { @Code "shiftdelim" option }
shiftdelim.equations @Index { @Code "shiftdelim" option (equations) }
values may be {@Code "yes"} or {@Code "no"}:
@ID @Code @Verbatim {
matrix
    userow { no }
    shiftdelim { yes }
{
    ...
}
}
The @Code "userow" option determines whether the axis of the
matrix will use a row axis; the default is not to, i.e. to
centre the axis instead.  The @Code "shiftdelim" option
determines whether the axis of the delimiter will be shifted
so that the delimiter evenly covers the thing delimited; the
default is to do this.
@PP
If @Code "userow" is {@Code "yes"}, the next question is
which row's axis to use to make the overall axis.  If you
do nothing, the first (or only) row's axis becomes the
overall axis.  To select some other row instead, replace
the @Code "row" symbol that precedes the row by {@Code "axisrow"}:
equations. @RawIndex { equations }
equations.axisrow @SubIndex { @Code "axisrow" symbol }
axisrow.equations @Index { @Code "axisrow" symbol (equations) }
@ID @Code @Tab
  vmargin { 0.5vx }
  hmargin { 1s }
  @Fmta { @Col A ! @Col ! @Col B ! @Col ! @Col C ! @Col ! @Col D ! @Col }
  @Fmtb { @Col A ! @Col " col {" ! @Col B ! @Col "}  col {" ! @Col C ! @Col "}  col {" ! @Col D ! @Col "}" }
{
@Rowa
  A { "matrix userow { yes } {" &0io }
@Rowb
  A { "    row" }
  B { "x sup 3" }
  C { "y sup 3" }
  D { "z sup 3" }
@Rowb
  A { "    axisrow" }
  B { "x sup 2" }
  C { "y sup 2" }
  D { "z sup 2" }
@Rowb
  A { "    row" }
  B { "x" }
  C { "y" }
  D { "z" }
@Rowa
  A { "}" }
}
The result of this is
@ID @ShowHMark @Eq {
matrix userow { yes } {
  row     col { x sup 3 } col { y sup 3 } col { z sup 3 }
  axisrow col { x sup 2 } col { y sup 2 } col { z sup 2 }
  row     col { x } col { y } col { z }
}
}
with the axis through the second row as desired.
@End @Section
