% ---------------------------------------------------------------------------
%
% atableau - Andrew Mathas (C) 2022-2025
%
% A latex package for symmetric group combinatorics, including:
% - abacuses
% - multitableau
% - ribbon tableau
% - shifted tableau
% - skew tableau
% - tableaux
% - tabloids
% - Young diagrams
%
% E-mail:
[email protected]
% Released under the LaTeX Project Public License v1.3c or later
% See
http://www.latex-project.org/lppl.txt
% ---------------------------------------------------------------------------
% load TikZ early to avoid \ExplSyntaxOn...\ExplSyntaxOff wrappers
\RequirePackage{tikz}
\usetikzlibrary{shapes.geometric,matrix}
% Correct for negative signs in contents being too long to fit in a tableau
\RequirePackage{amsfonts} %% <- also included by amssymb
\DeclareMathSymbol{\shortminus}{\mathbin}{AMSa}{"39}
% ---------------------------------------------------------------------------
% package date and version
\def\atableau@version{2.1.0}
\def\atableau@release{2025-01-24}
\providecommand\DeclareRelease[3]{}
\providecommand\DeclareCurrentRelease[2]{}
\DeclareRelease{\atableau@version}{\atableau@release}{atableau.sty}
\DeclareCurrentRelease{}{\atableau@release}
\ProvidesExplPackage{atableau} {\atableau@release} {\atableau@version}
{A latex package for symmetric group combinatorics }
% Give a warning if the LaTeX installation is older than TeXLive 2024
\IfFormatAtLeastTF { 2024-04-13 } {}
{
\PackageWarning {aTableau}
{
The~aTableau~package~uses~many~recent~features~from~
~LaTeX3.~Your~LaTeX ~installation~appears~to~be~quite~,
~which~might~result~in~errors~from~the ~package.~You~
~may~need~to~update~your~LaTeX~installation~to~at~
~least~TeXLive~2024
}
}
% ---------------------------------------------------------------------------
% package errors
\msg_new:nnnn { aTableau } { empty-tableau-row }
{ Row~#1~of~tableau~is~empty }
{ Empty~tableau~rows~are~not~supported}
\msg_new:nnnn { aTableau } { missing-runner-labels }
{ Your~abacus~has~a~different~number~of~runners~and~runner~labels }
{ The~number~of~labels~given~to~the~'runner~labels'~must~match~the~number~of~abacus~runners }
\msg_new:nnnn { aTableau } { missing-style }
{ The~'#1'~styles~key~is~missing~a~value }
{ The~styles~key~accepts~a~comma~separated~list~of~key-value~pairs~for~defining~TikZ~styles }
\msg_new:nnnn { aTableau } { invalid-dots}
{ Invalid~specifications~for~dotted~rows~or~dotted~cols }
{ You~can~only~use~these~options~for~interior~rows~and~columns~in~the~diagrams}
\msg_new:nnnn { aTableau } { invalid-ribbon-head }
{ Invalid~ribbon~head:~the~row~and~column~indices~of~the~ribbon~head~must~be~given:~'#1'}
{ Ribbon~specifications~must~be~for~the~form:~(optional~ribbon~style)[style]<row><col>+sequences~of~r's~and~c's~with~style}
\msg_new:nnnn { aTableau } { invalid-ribbon-specification }
{ Invalid~ribbon~specification~'#1':~expecting~r~or~c. }
{ Ribbon~specifications~must~be~for~the~form:~[optional~style]<row><col>~sequences~of~r's and~c's~with~style}
\msg_new:nnnn { aTableau } { unrecognised-abacus-label }
{ Unrecognised~abacus~label~'#1'. }
{ The~possible~abacus~labels~are~betas,~residues,~rows~and~shape}
\msg_new:nnnn { aTableau } { unrecognised-entries }
{ Unrecognised~entries~value:~'#1' }
{ The~possible~diagram~values~for~entries~are:~contents,~first,~hooks,~last,~and~residues}
\msg_new:nnnn { aTableau } { unrecognised-style }
{ Unrecognised~style:~'#1' }
{ The~available~tableau~styles~are~australian,~english,~french~and~ukrainian~and~the~available~abacus~styles~are~north,~south,~east~and~west~}
\msg_new:nnnn { aTableau } { unknown-abacus-ends }
{ Unrecognised~abacus~ends~setting:~'#1' }
{ The~supported~ends~for~the~top/bottom~of~the~abacus~are:~-,~_~,.~,|,~and~>}
\msg_new:nnnn { aTableau } { unknown-cartan }
{ Unrecognised~Cartan~type~'#1' }
{ The~supported~Cartan~types~are~(affine)~types~A,~AA,~C~and~DD}
\msg_new:nnnn { aTableau } { unknown-baseline }
{ Unrecognised~baseline~option:~'#1' }
{ The~supported~halign~options~are~bottom,~centre,~left,~and~top }
\msg_new:nnnn { aTableau } { unknown-halign }
{ Unrecognised~halign~option:~'#1' }
{ The~supported~halign~options~are~centre,~left,~and~right }
\msg_new:nnnn { aTableau } { unknown-top }
{ Unrecognised~format~for~abacus~top;~'#1' }
{ The~supported~formats~are:~blank,~dots,~and~frame}
\msg_new:nnnn { aTableau } { unknown-valign }
{ Unrecognised~valign~option:~#1 }
{ The~supported~valign~options~are~bottom,~centre~and~top }
% ---------------------------------------------------------------------------
% package variables
\bool_new:N \l__atableau_beta_numbers_bool% true if specifying beta numbers
\bool_new:N \l__atableau_frame_bool % true if drawing framed abacus runners
\bool_new:N \l__atableau_conjugate_bool % true if drawing conjugate tableau/diagram
\bool_new:N \l__atableau_border_bool % true if drawing tableau border
\bool_new:N \l__atableau_boxes_bool % true if drawing inner tableau walls
\bool_new:N \l__atableau_shifted_bool % true if a shifted tableau
\bool_new:N \l__atableau_skew_border_bool % true if drawing skew border
\bool_new:N \l__atableau_skew_boxes_bool % true if drawing skew boxes
\bool_new:N \l__atableau_tabloid_bool % true if a tabloid
\bool_new:N \l__atableau_separators_bool % true if drawing separators for multishapes
\fp_new:N \l__atableau_ab_col_dx_fp % change in x-coordinate between columns in an abacus
\fp_new:N \l__atableau_ab_col_dy_fp % change in y-coordinate between columns in an abacus
\fp_new:N \l__atableau_ab_row_dx_fp % change in x-coordinate between rows in an abacus
\fp_new:N \l__atableau_ab_row_dy_fp % change in y-coordinate between rows in an abacus
\fp_new:N \l__atableau_abacus_ht_fp % height of the tableaux nodes/separation between abacus beads
\fp_new:N \l__atableau_abacus_wd_fp % width of the tableaux nodes/separation between abacus runners
\fp_new:N \l__atableau_bead_size_fp % bead radius
\fp_new:N \l__atableau_box_ht_fp % height of a tableau box
\fp_new:N \l__atableau_box_wd_fp % width of a tableau box
\fp_new:N \l__atableau_rows_fp % number of rows in abacus/tableau
\fp_new:N \l__atableau_separation_fp % distance between multitableau
\fp_new:N \l__atableau_script_fp % scaling when used as a subscript
\fp_new:N \l__atableau_sscriptscript_fp % scaling when used as a subsubscript
\fp_new:N \l__atableau_tab_col_dx_fp % change in x-coordinate between columns in a tableau
\fp_new:N \l__atableau_tab_col_dy_fp % change in y-coordinate between columns in a tableau
\fp_new:N \l__atableau_tab_row_dx_fp % change in x-coordinate between rows in a tableau
\fp_new:N \l__atableau_tab_row_dy_fp % change in y-coordinate between rows in a tableau
\fp_new:N \l__atableau_tick_length_fp % half the length of the abacus ticks
\fp_new:N \l__atableau_x_fp % x-coordinate of the origin of the diagram
\fp_new:N \l__atableau_xa_fp % scratch x-coordinate of a node/bead
\fp_new:N \l__atableau_xb_fp % scratch x-coordinate of a node/bead
\fp_new:N \l__atableau_xl_fp % x-coordinate of a tableau node/bead
\fp_new:N \l__atableau_xmax_fp % maximum x-coordinate for multidiagrams and multitableaux
\fp_new:N \l__atableau_xoffsets_seq % x-offsets for the (1,1)-nodes in a multi-tableau
\fp_new:N \l__atableau_xscale_fp % scaling in the x-direction
\fp_new:N \l__atableau_xsep_fp % x-coordinate difference to next separator for multishapes
\fp_new:N \l__atableau_y_fp % y-coordinate of the origin of the diagram
\fp_new:N \l__atableau_ya_fp % scratch y-coordinate of a node/bead
\fp_new:N \l__atableau_yb_fp % scratch y-coordinate of a node/bead
\fp_new:N \l__atableau_yl_fp % y-coordinate of a tableau node/bead
\fp_new:N \l__atableau_ymax_fp % maximum y-coordinate for multidiagrams and multitableaux
\fp_new:N \l__atableau_ymin_fp % minimum y-coordinate for multidiagrams and multitableaux
\fp_new:N \l__atableau_yoffsets_seq % t-offsets for the (1,1)-nodes in a multi-tableau
\fp_new:N \l__atableau_yscale_fp % scaling in the x-direction
\int_new:N \l__atableau_beads_int % number of beads in abacus
\int_new:N \l__atableau_charge_int % charge for current component
\int_new:N \l__atableau_col_int % current column index
\int_new:N \l__atableau_c_int % scratch column counter
\int_new:N \l__atableau_cols_int % number of columns in a multitableau/abacus
\int_new:N \l__atableau_component_int % component in multidiagrams and tableaux
\int_new:N \l__atableau_e_int % quantum characteristic
\int_new:N \l__atableau_row_int % current row index
\int_new:N \l__atableau_r_int % scratch row counter
\int_new:N \l__atableau_rows_int % number of rows in abacus
\seq_new:N \l__atableau_charge_seq % sequences of charges = residue/content offset
\seq_new:N \l__atableau_component_seq % multipartition
\seq_new:N \l__atableau_conjugate_seq % conjugate partition
\seq_new:N \l__atableau_dotted_cols_seq % columns with dots
\seq_new:N \l__atableau_dotted_rows_seq % rows with dots
\seq_new:N \l__atableau_multidotted_cols_seq % sequence of dotted columns for multi shapes
\seq_new:N \l__atableau_multidotted_rows_seq % sequence of dotted rows for multi shapes
\seq_new:N \l__atableau_multilabel_seq % a sequence of labels for multi shapes
\seq_new:N \l__atableau_multipaths_seq % a sequence of ribbon paths for multi shapes
\seq_new:N \l__atableau_multiribbons_seq % a sequence of ribbon for multi shapes
\seq_new:N \l__atableau_multiskew_seq % a sequence of skew partitions for multi shapes
\seq_new:N \l__atableau_multisnobs_seq % a sequence of snobs for multi shapes
\seq_new:N \l__atableau_paths_seq % ribbon paths to add to tableau/diagram
\seq_new:N \l__atableau_rcs_seq % ribbon row, column indices
\seq_new:N \l__atableau_ribbons_seq % ribbons to add to tableau/diagram
\seq_new:N \l__atableau_runner_labels_seq % labels for the abacus runners
\seq_new:N \l__atableau_shape_seq % a partition
\seq_new:N \l__atableau_skew_seq % the inner partition for a skew shape
\seq_new:N \l__atableau_snobs_seq % snob ribbons to add to tableau/diagram
\seq_new:N \l__atableau_styles_seq % ribbon/bead styles
\seq_new:N \l__atableau_texts_seq % ribbon/bead texts
\seq_new:N \l__atableau_xsep_seq % x-coordinates separators for multishapes
\tl_new:N \l__atableau_abacus_bottom_tl % specifies the bottom of the abacus
\tl_new:N \l__atableau_abacus_top_tl % specifies the top of the abacus
\tl_new:N \l__atableau_bead_font_tl % font for abacus beads
\tl_new:N \l__atableau_bead_shape_tl % shape of abacus beads
\tl_new:N \l__atableau_bead_text_tl % text colour of abacus beads
\tl_new:N \l__atableau_bead_tl % abacus head colour
\tl_new:N \l__atableau_border_tl % diagram border
\tl_new:N \l__atableau_box_fill_tl % fill colour for tableau boxes
\tl_new:N \l__atableau_box_font_tl % font for tableau boxes
\tl_new:N \l__atableau_box_shape_tl % shape of tableau boxes
\tl_new:N \l__atableau_box_text_tl % text colour for tableau boxes
\tl_new:N \l__atableau_capture_exp_tl % contains captured exponent
\tl_new:N \l__atableau_capture_part_tl % contains captured part
\tl_new:N \l__atableau_capture_style_tl % contains captured style
\tl_new:N \l__atableau_capture_txt_tl % contains captured text
\tl_new:N \l__atableau_cartan_tl % the Cartan type
\tl_new:N \l__atableau_empty_tl % symbol for empty tableau/diagram in a multi tableau/diagram
\tl_new:N \l__atableau_entries_tl % custom entries in tableau
\tl_new:N \l__atableau_inner_tl % colour of tableau inner walls
\tl_new:N \l__atableau_label_tl % a label to print on an tableau/diagram
\tl_new:N \l__atableau_left_delimiter_tl % the left delimiter for multitableau and multidiagrams
\tl_new:N \l__atableau_multiprefix_tl % prefix used when constructing multinode names
\tl_new:N \l__atableau_name_tl % name of a tableau node
\tl_new:N \l__atableau_outer_tl % colour of tableau outer walls
\tl_new:N \l__atableau_path_box_tl % node for ribbon paths
\tl_new:N \l__atableau_prefix_tl % prefix for node names
\tl_new:N \l__atableau_ribbon_box_tl % box entry for ribbons
\tl_new:N \l__atableau_ribbon_style_tl % optional style used for current path< ribbon or snob
\tl_new:N \l__atableau_ribbon_path_tl % a ribbon in the ribbon tableau
\tl_new:N \l__atableau_ribbon_type_tl % the type of ribbon, which is either path, ribbon or snob
\tl_new:N \l__atableau_right_delimiter_tl % the right delimiter for multitableau and multidiagrams
\tl_new:N \l__atableau_runner_tl % abacus runner colour
\tl_new:N \l__atableau_snob_box_tl % box entry for snobs
\tl_new:N \l__atableau_separator_fg_tl % foreground colour of the separator
\tl_new:N \l__atableau_separator_tl % the separator between multitableau: | or , or ...
\tl_new:N \l__atableau_shading_tl % the type of shading to use for the abacus beads
\tl_new:N \l__atableau_show_tl % automatic tableau/bead labelling
\tl_new:N \l__atableau_skew_border_tl % skew border colour
\tl_new:N \l__atableau_starstyle_tl % current star style in use
\tl_new:N \l__atableau_styled_nodes_tl % token lists of nodes with non-default style
\tl_new:N \l__atableau_tick_tl % abacus tick colour
\tl_new:N \l__atableau_tikz_after_tl % TikZ commands for after the diagram
\tl_new:N \l__atableau_tikz_before_tl % TikZ commands for before the diagram
\tl_new:N \l__atableau_tikzpicture_tl % TikZ environment settings
\tl_new:N \l__atableau_unstyled_nodes_tl % token lists of nodes with efault style
% ---------------------------------------------------------------------------
% Variable defaults -- most defaults are given in the settings: \keys_set:nn {aTableau} {...}
\tl_set:Nn \l__atableau_ribbon_type_tl {ribbon} % by default, ribbons are ribbons
% ---------------------------------------------------------------------------
% default colours
\definecolor{aTableauMain} {HTML} {00008B}
\definecolor{aTableauInner} {HTML} {0073e6}
\definecolor{aTableauSkew} {HTML} {818589}
\definecolor{aTableauSkewFill} {HTML} {F8F8F8}
\definecolor{aTableauStarStyle} {HTML} {E6F7FF}
% ---------------------------------------------------------------------------
% TikZ styling of aTableau components
\tikzset{
% -----------------------------------------------------------------------
% Allow ball shading to be disabled via shade=none.
% The essential idea comes from
https://tex.stackexchange.com/a/85750/234252
no~shade/.code={ \tikz@addmode{\tikz@mode@shadefalse } },
% -----------------------------------------------------------------------
% all tikz settings are in the aTableau family
aTableau/.is~family,
aTableau/.cd,
% -----------------------------------------------------------------------
% Styles for tableaux and diagrams
% -----------------------------------------------------------------------
% inner tableau wall
innerWall/.style = {
line~cap = rect,
thin,
},
% outer tableau wall
borderStyle/.style = {
% shifting allows us to use \__atableau_set_box_coordinates:nnn when drawing the border
shift = {(\fp_eval:n{-(\l__atableau_tab_row_dx_fp+\l__atableau_tab_col_dx_fp)*\l__atableau_box_wd_fp/2},
\fp_eval:n{-(\l__atableau_tab_row_dy_fp+\l__atableau_tab_col_dy_fp)*\l__atableau_box_ht_fp/2})},
line~cap = rect,
very~thick,
draw = \l__atableau_outer_tl,
},
% skew walls
skewBorder/.style = {
% shifting allows us to use \__atableau_set_box_coordinates:nnn when drawing the border
shift = {(\fp_eval:n{-(\l__atableau_tab_row_dx_fp+\l__atableau_tab_col_dx_fp)*\l__atableau_box_wd_fp/2},
\fp_eval:n{-(\l__atableau_tab_row_dy_fp+\l__atableau_tab_col_dy_fp)*\l__atableau_box_ht_fp/2})},
draw = \l__atableau_skew_border_tl,
thick
},
% styles for tableau boxes in Young diagrams
% -----------------------------------------------------------------------
node/.style = {
anchor = center,
inner~sep = 0pt,
minimum~height = \fp_use:N \l__atableau_box_ht_fp cm,
minimum~width = \fp_use:N \l__atableau_box_wd_fp cm,
shape = \l__atableau_box_shape_tl,
font = \l__atableau_box_font_tl,
text = \l__atableau_box_text_tl,
},
boxStyle/.style = {
aTableau/node,
aTableau/innerWall,
draw = \l__atableau_inner_tl,
fill = \l__atableau_box_fill_tl,
},
% default skew box style
skewBox/.style = {
aTableau/node,
aTableau/innerWall,
draw = \l__atableau_skew_border_tl,
fill = aTableauSkewFill,
},
% box styles for paths, ribbons and snobs
% -----------------------------------------------------------------------
pathBox/.style = {
aTableau/node,
draw = none, % border disabled by default
},
ribbonBox/.style = {
aTableau/node,
},
snobBox/.style = {
aTableau/node,
},
% styles for paths, ribbons and snobs
% -----------------------------------------------------------------------
% default path style
pathStyle/.style = {
draw = \l__atableau_inner_tl,
},
ribbonStyle/.style = {
aTableau/innerWall,
draw = \l__atableau_inner_tl,
},
% default ribbon style
snobStyle/.style = {
aTableau/innerWall,
draw = \l__atableau_inner_tl,
},
% label styles
% -----------------------------------------------------------------------
labelStyle/.style = {
shift = {(\fp_eval:n{-0.2*(\l__atableau_tab_row_dx_fp+\l__atableau_tab_col_dx_fp)*\l__atableau_box_wd_fp},
\fp_eval:n{-0.2*(\l__atableau_tab_row_dy_fp+\l__atableau_tab_col_dy_fp)*\l__atableau_box_ht_fp})},
font=\scriptsize,
text = \l__atableau_inner_tl,
},
% tableau star style
% -----------------------------------------------------------------------
tableauStarStyle/.style = {
fill = aTableauStarStyle,
text = \l__atableau_box_text_tl,
},
% cleared boxes for dotted rows and columns
% -----------------------------------------------------------------------
clearBoxes/.style = {
draw = white,
fill = white,
},
% dots used for dotted rows and columns
% -----------------------------------------------------------------------
dottedLine/.style = {
densely~dotted,
thick,
draw = \l__atableau_outer_tl,
},
% separators and delimiters
% -----------------------------------------------------------------------
separatorSymbol/.style = {
text = \l__atableau_separator_fg_tl,
},
% default separator line style
separatorLine/.style = {
thick,
draw = \l__atableau_separator_fg_tl,
},
% Delimiters around multitableaux and multidiagrams. To change the colour
% of the delimiters we need to use \path[aTableau/delimiterPath] (x,y) node...
delimiterStyle/.style = {
align = center,
inner~sep = 0pt,
minimum~height = \fp_use:N\l__atableau_ymax_fp cm,
},
% hack to set the colour
delimiterPath/.style = {
every~delimiter/.style = { \l__atableau_separator_fg_tl, },
},
leftDelimiter/.style = {
aTableau/delimiterStyle,
left~delimiter = \l__atableau_left_delimiter_tl,
xshift = 2pt,
},
rightDelimiter/.style = {
aTableau/delimiterStyle,
right~delimiter = \l__atableau_right_delimiter_tl,
xshift = -2pt,
},
% -----------------------------------------------------------------------
% abacus beads and runners
% -----------------------------------------------------------------------
% abacus beads
beadStyle/.style = {
ball~color = \l__atableau_bead_tl,
font = \l__atableau_bead_font_tl,
minimum~height = \fp_to_decimal:N \l__atableau_bead_size_fp cm,
minimum~width = \fp_to_decimal:N \l__atableau_bead_size_fp cm,
shading = \l__atableau_shading_tl,
shape = \l__atableau_bead_shape_tl,
text = \l__atableau_bead_text_tl,
anchor = center,
inner~sep = 0pt,
},
% abacus runners
runnerStyle/.style = {
line~cap = rect,
very~thick,
draw = \l__atableau_runner_tl,
},
runnerLabelStyle/.style = {
aTableau/node,
text = aTableauInner,
font = \scriptsize
},
% style for the top and bottom of the abacus
abacusEnds/.style = {
aTableau/runnerStyle,
},
% abacus star style
abacusStarStyle/.style = {
text = aTableauMain,
ball~color = aTableauStarStyle,
},
% abacus ticks
tickStyle/.style = {
draw = \l__atableau_tick_tl,
semithick,
},
% the named coordinate for an abacus tick
namedTick/.style = {
minimum~height = \fp_to_decimal:N \l__atableau_bead_size_fp cm,
minimum~width = \fp_to_decimal:N \l__atableau_bead_size_fp cm,
shape = \l__atableau_bead_shape_tl,
draw=none,
}
}
% ---------------------------------------------------------------------------
% usage: \__atableau_set_style:nn {abacus|tableau} {style}
% sets the basic styles for the tableaux and abacus commands
\cs_new:Npn \__atableau_set_style:nn #1 #2
{
\str_case:enF { #1/#2 }
{
{tableau/english}
{
\fp_set:Nn \l__atableau_tab_col_dx_fp {1}
\fp_set:Nn \l__atableau_tab_col_dy_fp {0}
\fp_set:Nn \l__atableau_tab_row_dx_fp {0}
\fp_set:Nn \l__atableau_tab_row_dy_fp {-1}
\fp_set:Nn \l__atableau_box_ht_fp {\l__atableau_yscale_fp*0.5}
\fp_set:Nn \l__atableau_box_wd_fp {\l__atableau_xscale_fp*0.5}
\tl_set:Nn \l__atableau_box_shape_tl {rectangle}
}
{tableau/french}
{
\fp_set:Nn \l__atableau_tab_col_dx_fp {1}
\fp_set:Nn \l__atableau_tab_col_dy_fp {0}
\fp_set:Nn \l__atableau_tab_row_dx_fp {0}
\fp_set:Nn \l__atableau_tab_row_dy_fp {1}
\fp_set:Nn \l__atableau_box_ht_fp {\l__atableau_yscale_fp*0.5}
\fp_set:Nn \l__atableau_box_wd_fp {\l__atableau_xscale_fp*0.5}
\tl_set:Nn \l__atableau_box_shape_tl {rectangle}
}
{tableau/australian}
{
\fp_set:Nn \l__atableau_tab_col_dx_fp {0.5}
\fp_set:Nn \l__atableau_tab_col_dy_fp {-0.5}
\fp_set:Nn \l__atableau_tab_row_dx_fp {-0.5}
\fp_set:Nn \l__atableau_tab_row_dy_fp {-0.5}
\fp_set:Nn \l__atableau_box_ht_fp {\l__atableau_yscale_fp*0.7012} % 1/sqrt(2)
\fp_set:Nn \l__atableau_box_wd_fp {\l__atableau_xscale_fp*0.7012}
\tl_set:Nn \l__atableau_box_shape_tl {diamond}
}
{tableau/ukrainian}
{
\fp_set:Nn \l__atableau_tab_col_dx_fp {0.5}
\fp_set:Nn \l__atableau_tab_col_dy_fp {0.5}
\fp_set:Nn \l__atableau_tab_row_dx_fp {-0.5}
\fp_set:Nn \l__atableau_tab_row_dy_fp {0.5}
\fp_set:Nn \l__atableau_box_ht_fp {\l__atableau_yscale_fp*0.7012}
\fp_set:Nn \l__atableau_box_wd_fp {\l__atableau_xscale_fp*0.7012}
\tl_set:Nn \l__atableau_box_shape_tl {diamond}
}
{abacus/south}
{
\fp_set:Nn \l__atableau_ab_col_dx_fp {1}
\fp_set:Nn \l__atableau_ab_col_dy_fp {0}
\fp_set:Nn \l__atableau_ab_row_dx_fp {0}
\fp_set:Nn \l__atableau_ab_row_dy_fp {-1}
\fp_set:Nn \l__atableau_abacus_ht_fp {\l__atableau_yscale_fp*0.5}
\fp_set:Nn \l__atableau_abacus_wd_fp {\l__atableau_xscale_fp*0.5}
\tl_set:Nn \l__atableau_bead_shape_tl {circle}
}
{abacus/north}
{
\fp_set:Nn \l__atableau_ab_col_dx_fp {1}
\fp_set:Nn \l__atableau_ab_col_dy_fp {0}
\fp_set:Nn \l__atableau_ab_row_dx_fp {0}
\fp_set:Nn \l__atableau_ab_row_dy_fp {1}
\tl_set:Nn \l__atableau_bead_shape_tl {circle}
\fp_set:Nn \l__atableau_abacus_wd_fp {\l__atableau_xscale_fp*0.5}
\fp_set:Nn \l__atableau_abacus_ht_fp {\l__atableau_yscale_fp*0.5}
}
{abacus/east}
{
\fp_set:Nn \l__atableau_ab_col_dx_fp {0}
\fp_set:Nn \l__atableau_ab_col_dy_fp {-1}
\fp_set:Nn \l__atableau_ab_row_dx_fp {1}
\fp_set:Nn \l__atableau_ab_row_dy_fp {0}
\tl_set:Nn \l__atableau_bead_shape_tl {circle}
\fp_set:Nn \l__atableau_abacus_wd_fp {\l__atableau_xscale_fp*0.5}
\fp_set:Nn \l__atableau_abacus_ht_fp {\l__atableau_yscale_fp*0.5}
}
{abacus/west}
{
\fp_set:Nn \l__atableau_ab_col_dx_fp {0}
\fp_set:Nn \l__atableau_ab_col_dy_fp {1}
\fp_set:Nn \l__atableau_ab_row_dx_fp {-1}
\fp_set:Nn \l__atableau_ab_row_dy_fp {0}
\tl_set:Nn \l__atableau_bead_shape_tl {circle}
\fp_set:Nn \l__atableau_abacus_wd_fp {\l__atableau_xscale_fp*0.5}
\fp_set:Nn \l__atableau_abacus_ht_fp {\l__atableau_yscale_fp*0.5}
}
}
{
\msg_error:nnx {aTableau} {unrecognised-style} {#1/#2}
}
}
% usage: \__atableau_set_xscale:n {x-scale} : rescale the x-dimension
\cs_new_protected:Npn \__atableau_set_xscale:n #1
{
\fp_set:Nn \l__atableau_xscale_fp {#1} % makes scale persistent
\fp_set:Nn \l__atableau_abacus_wd_fp {#1*\l__atableau_abacus_wd_fp}
\fp_set:Nn \l__atableau_box_wd_fp {#1*\l__atableau_box_wd_fp}
\fp_set:Nn \l__atableau_separation_fp {#1*\l__atableau_separation_fp }
}
% usage: \__atableau_set_yscale:n {y-scale} : rescale the y-dimension
\cs_new_protected:Npn \__atableau_set_yscale:n #1
{
\fp_set:Nn \l__atableau_yscale_fp {#1} % makes scale persistent
\fp_set:Nn \l__atableau_abacus_ht_fp {#1*\l__atableau_abacus_ht_fp}
\fp_set:Nn \l__atableau_box_ht_fp {#1*\l__atableau_box_ht_fp}
}
% usage: \__atableau_set_delimiters:nn {left delimiter} {right delimiter}
\cs_new_protected:Npn \__atableau_set_delimiters:nn #1 #2
{
\tl_set:Nn \l__atableau_left_delimiter_tl #1
\tl_set:Nn \l__atableau_right_delimiter_tl #2
}
% usage: \__atableau_set_multiseq_key:nn {name} {value}
% Set up a sequence, for keys used with multishapes
\cs_new_protected:Npn \__atableau_set_multiseq_key:nn #1 #2
{
\tl_if_in:nnTF {#2} {|}
{
% unpack the ribbons into \l__atableau_multiribbons_seq
\seq_set_split:cnn {l__atableau_multi#1_seq} {|} {#2}
}
{ \seq_set_from_clist:cn {l__atableau_#1_seq} {#2} }
}
% usage: \__atableau_set_abacus_ends:nn {top} {top}
% Set the abacus ends abacus_top and abacus_bottom and give an error
% message if the ends are not one of =,-,.,|,>
\cs_new_protected:Npn \__atableau_set_abacus_ends:nn #1 #2
{
\tl_set:Nn \l__atableau_abacus_top_tl {#1}
\str_if_in:nnF {-.>|\c_underscore_str*} {#1}
{ \msg_error:nne {aTableau} {unknown-abacus-ends} {#1}}
\tl_set:Nn \l__atableau_abacus_bottom_tl {#2}
\str_if_in:nnF {-.>|\c_underscore_str*} {#2}
{ \msg_error:nne {aTableau} {unknown-abacus-ends} {#2}}
}
% ---------------------------------------------------------------------------
% command variants
\cs_generate_variant:Nn \fp_add:Nn {NV}
\cs_generate_variant:Nn \int_set:Nn {No}
\cs_generate_variant:Nn \seq_put_right:Nn {Nx}
\cs_generate_variant:Nn \seq_set_item:Nnn {NVx, Nnx, Nox}
\cs_generate_variant:Nn \seq_set_from_clist:Nn {co}
\cs_generate_variant:Nn \seq_set_split:Nnn {cnn}
\cs_generate_variant:Nn \__atableau_add_ribbon:n {V}
\cs_generate_variant:Nn \__atableau_count_row:n {x}
\cs_generate_variant:Nn \__atableau_draw_tableau:n {V}
\cs_generate_variant:Nn \__atableau_entry:n {x}
\cs_generate_variant:Nn \__atableau_draw_abacus_end:nnn {noo}
\cs_generate_variant:Nn \__atableau_set_bead_coordinates:nnn {nVV, nnV, noo, non, noV}
\cs_generate_variant:Nn \__atableau_set_box_coordinates:nnn {nVV, nVn, noo }
\cs_generate_variant:Nn \__atableau_set_partition:nn {no}
\cs_generate_variant:Nn \__atableau_tl_put_right_braced:Nn { NV, Nx, No, Ne }
% ---------------------------------------------------------------------------
% utility functions
% usage: \__atableau_tl_put_right_braced:Nn #1 #2
% Add braces around #2 and append to #1
\cs_new_protected:Nn \__atableau_tl_put_right_braced:Nn
{
\tl_put_right:Nn #1 { {#2} }
}
% ---------------------------------------------------------------------------
% expandable residue functions
% usage: \__atableau_residue_A:nn
% Computes the residue of #1 mod #2. This is positive integer remainder when
% dividing by #2. As with \int_mod:n, the result is left in the input stream.
\cs_new:Npn \__atableau_residue_A:nn #1 #2
{
\int_compare:nNnTF {#1} > {0}
{ \int_mod:nn {#1} {#2} }
{ \int_eval:n {\int_mod:nn {#2 + \int_mod:nn {#1} {#2}} {#2}} }% \int_mod:nn is negative
}
% usage: \__atableau_residue_C:nn
% Computes the residue of #1 in affine type C. When e=3 this residue pattern is
% 0 1 2 3 2 1 0 1 2 3 2 1 0 1 ...
% As with \int_mod:n, the result is left in the input stream.
\cs_new:Npn \__atableau_residue_C:nn #1 #2
{
\int_compare:nNnTF {#1} < {0}
{ % #1 is negative
\int_compare:nNnTF {\int_mod:nn {#1} {2*#2}} < {-#2}
{ \int_eval:n { 2*#2 + \int_mod:nn {#1} {2*#2} } }
{ \int_eval:n { \int_mod:nn {-#1} {2*#2} } }
}
{ % #1 is non-negative
\int_compare:nNnTF {\int_mod:nn {#1} {2*#2}} > {#2}
{ \int_eval:n { 2*#2 - \int_mod:nn {#1} {2*#2} } }
{ \int_eval:n { \int_mod:nn {#1} {2*#2} } }
}
}
% usage: \__atableau_residue_AA:nn
% Computes the residue of #1 in twisted type A. When e=3 this residue pattern is
% 0 1 2 3 3 2 1 0 1 2 3 3 2 1 0 1 ...
% As with \int_mod:n, the result is left in the input stream.
\cs_new:Npn \__atableau_residue_AA:nn #1 #2
{
\int_compare:nNnTF {#1} < {0}
{ % #1 is negative
\int_compare:nNnTF {\int_mod:nn {#1} {2*#2+1}} < {-#2}
{ \int_eval:n { 2*#2+1 + \int_mod:nn {#1} {2*#2+1}} }
{ \int_eval:n { \int_mod:nn {-#1} {2*#2+1} } }
}
{ % #1 is non-negative
\int_compare:nNnTF {\int_mod:nn {#1} {2*#2+1}} > {#2}
{ \int_eval:n { 2*#2+1 - \int_mod:nn {#1} {2*#2+1} } }
{ \int_eval:n { \int_mod:nn {#1} {2*#2+1} } }
}
}
% usage: \__atableau_residue_D:nn
% Computes the residue of #1 in affine type C. When e=3 this residue pattern is
% 0 1 2 3 3 2 1 0 0 1 2 3 3 2 1 0 0 1 ...
% As with \int_mod:n, the result is left in the input stream.
\cs_new:Npn \__atableau_residue_DD:nn #1 #2
{
\int_compare:nNnTF {#1} < {0}
{ % #1 is negative
\int_compare:nNnTF {\int_mod:nn {#1} {2*#2+2}} < {-#2}
{ \int_eval:n {2*#2+1 + \int_mod:nn {#1} {2*#2+2}} }
{ \int_eval:n { -\int_mod:nn {#1} {2*#2+2} } }
}
{ % #1 is non-negative
\int_compare:nNnTF {\int_mod:nn {#1} {2*#2+2}} > {#2}
{ \int_eval:n {2*#2+1- \int_mod:nn {#1} {2*#2+2} } }
{ \int_eval:n { \int_mod:nn {#1} {2*#2+2} } }
}
}
% use type A residues by default
\cs_set_eq:NN \__atableau_residue:nn \__atableau_residue_A:nn
% ---------------------------------------------------------------------------
% Parsing input
% \seq_set_split:Nnn does not respect braces around singleton entries
% such as in { 1345, 8{10}, {11}, {12} }, with the result that {11}
% and {12} are treated as {1}{1} and {1}{2}, respectively. As this is
% not what we want, we use \peek_charcode:NTF to do this ourselves.
\cs_new_protected:Npn \__atableau_peek_tableau:w
{
\peek_remove_spaces:n { % ignore spaces
\peek_charcode_remove:NTF ,
{
% record the column index in the shape for drawing the border
\seq_put_right:NV \l__atableau_shape_seq \l__atableau_col_int
% increment the row index
\int_incr:N \l__atableau_row_int
% reset the column index, and update the skew shape for shifted tableau
\bool_if:NTF \l__atableau_shifted_bool
{
\seq_put_right:No \l__atableau_skew_seq {\int_use:N \l__atableau_row_int}
\int_set_eq:NN \l__atableau_col_int \l__atableau_row_int
}
{
\int_set:Nn \l__atableau_col_int { 0\seq_item:Nn \l__atableau_skew_seq {\l__atableau_row_int+1}}
}
% look for the next entry
\__atableau_peek_tableau:w
}
{
\__atableau_peek_style:nw {draw_entry:nn}
}
}
}
% ---------------------------------------------------------------------------
% usage: \__atableau_peek_style:nw {command suffix}
% Read the next entry in the input sequence, with any optional style given by
% a * or [...], and then pass this data to the command \__atableau_#1.
\cs_new_protected:Npn \__atableau_peek_style:nw #1
{
\peek_remove_spaces:n { % ignore spaces
\peek_charcode:NTF [
{ \use:c{__atableau_#1} }
{
\peek_charcode_remove:NTF *
{ \use:c{__atableau_#1} [\l__atableau_starstyle_tl] }
{ \use:c{__atableau_#1} [] }
}
}
}
% To parse the bead specifications used by \Abacus we need to accept the
% a "bead specification" of the following form
% [style]m^k_txt
% where the [style] could simply be a *, the m is an integer, a part of the
% partition being constructed, the k its exponent and txt is the text for the
% node. Except for m, all of of these components are optional, with the
% exponent being 1 if it is omitted. As is customary, the order of the
% superscript and subscript is interchangeable. To parse these expressions we
% first use \__atableau_peek_style:nw to strip off the style specification, via
% \__atableau_record_style:nn, and then pass between \__atableau_peek_beads:nw
% and \__atableau_record:nn to look ahead for the characters ^ and _ to decide
% which of the following token lists the next character is added to:
\cs_new_protected:Npn \__atableau_record_style:nn [#1] #2
{
% clear the bead token lists
\tl_set:Nn \l__atableau_capture_style_tl {#1}
\tl_set:Nn \l__atableau_capture_part_tl {#2}
\tl_clear:N \l__atableau_capture_exp_tl
\tl_clear:N \l__atableau_capture_txt_tl
\__atableau_peek_beads:nw {part}
}
% look for a caret or an underscore and pass on to \__atableau_record_bead:nn
\cs_new_protected:Npn \__atableau_peek_beads:nw #1
{
\peek_remove_spaces:n { % ignore spaces
\peek_charcode_remove:NTF _
{ \__atableau_record_bead:nn {txt} {}}
{
\peek_charcode_remove:NTF ^ { \__atableau_record_bead:nn {exp} {}}
{ \__atableau_record_bead:nn {#1} }
}
}
}
% #1 is one of part, exp or txt
\cs_new_protected:Npn \__atableau_record_bead:nn #1 #2
{
\quark_if_recursion_tail_stop_do:nn {#2}
{
% the data in the sequences \l__atableau_capture_exp_tl times
\tl_if_empty:NT \l__atableau_capture_exp_tl { \tl_set:Nn \l__atableau_capture_exp_tl {1}}
\int_step_inline:nn { \l__atableau_capture_exp_tl }
{
\int_incr:N \l__atableau_beads_int
\seq_put_right:NV \l__atableau_shape_seq \l__atableau_capture_part_tl
\seq_put_right:NV \l__atableau_texts_seq \l__atableau_capture_txt_tl
\seq_put_right:NV \l__atableau_styles_seq \l__atableau_capture_style_tl
}
}
\tl_put_right:cn {l__atableau_capture_#1_tl} {#2}
\__atableau_peek_beads:nw {#1}
}
% usage: \__atableau_count_entries:nn [style] {entry}
% Count the number of entries in the row, storing the result in c_int
\cs_new_protected:Npn \__atableau_count_entries:nn [#1] #2
{
% exit when we reach the end of the row
\quark_if_recursion_tail_stop:n {#2}
\int_incr:N \l__atableau_c_int
\__atableau_peek_style:nw {count_entries:nn}
}
% usage: \__atableau_count_row:n {entries}
\cs_new_protected:Npn \__atableau_count_row:n #1
{
\__atableau_peek_style:nw {count_entries:nn} #1 \q_recursion_tail \q_recursion_stop
}
% ---------------------------------------------------------------------------
% creating custom diagrams
% usage: \__atableau_compute_conjugate_partition:N {seq}
% compute the conjugate partition of <seq> and store in \l__atableau_conjugate_seq
\cs_new_protected:Npn \__atableau_compute_conjugate_partition:N #1
{
\seq_clear:N \l__atableau_conjugate_seq
\int_zero:N \l_tmpa_int % previous part
\int_set:No \l__atableau_r_int {\seq_count:N #1}
\int_while_do:nn {\l__atableau_r_int > 0}
{
\int_set:No \l_tmpb_int {\seq_item:NV #1 \l__atableau_r_int }
\int_step_inline:nn { \l_tmpb_int - \l_tmpa_int }
{
\seq_put_right:NV \l__atableau_conjugate_seq \l__atableau_r_int
}
\int_set_eq:NN \l_tmpa_int \l_tmpb_int
\int_decr:N \l__atableau_r_int
}
}
% usage: \__atableau_set_partition:nn {shape|skew} {csv for partition}
% This function allows the partition to be given either as a comma separated
% list of integers, or as a comma separated list of integers with exponents
% giving the multiplicity of each part. For example, 4,3,3,3,2 and 4,3^3,2
% are both supported.
% TODO? Rewrite using quarks?
\cs_new_protected:Npn \__atableau_set_partition:nn #1 #2
{
\seq_clear:c {l__atableau_#1_seq}
\clist_map_inline:nn {#2} { \__atableau_add_to_partition:nn {#1} {##1} }
}
% add parts to the partition \l__atableau_#1_seq given input
% of the form k or k^r
\cs_new_protected:Npn \__atableau_add_to_partition:nn #1 #2
{
% split #1 on ^: the trailing ^1 sets the exponent to 1 if it's omitted
\seq_set_split:Nnn \l_tmpa_seq {^} {#2 ^1}
% given k or k^r, set \l_tmpa_int=k and \l_tmpb_int=r, where r=1 with input k
\seq_pop_left:NN \l_tmpa_seq \l_tmpa_tl % part
\seq_pop_left:NN \l_tmpa_seq \l_tmpb_tl % exponent
% now add \l_tmpa_int to \l__atableau_#1_seq b times
\int_step_inline:nn {\l_tmpb_tl} { \seq_put_right:ce {l__atableau_#1_seq} {\l_tmpa_tl} }
}
% usage: \__atableau_diagram_for_shape:N {partition}
% Young diagrams are drawn using the \Tableau command by generating
% a sequence of ~ for the partition. For example,
% it replaces the sequence 3,2,2,1 with
% the dot-sequence ~~~,~~,~~,~,
\cs_new_protected:Npn \__atableau_diagram_for_shape:N #1
{
\tl_clear:N \l__atableau_entries_tl
\tl_set:Nn \l_tmpb_tl {}
\seq_map_inline:Nn #1
{
\tl_put_right:No \l__atableau_entries_tl \l_tmpb_tl
\tl_put_right:Nx \l__atableau_entries_tl { \prg_replicate:nn {##1} {{{~}}} }
\tl_set:Nn \l_tmpb_tl {,}
}
}
% usage: \__atableau_shape_to_content:Nn {partition sequence}
% Return the content sequence to for a tableau of this shape
\cs_new_protected:Npn \__atableau_shape_to_content:N #1
{
\tl_clear:N \l__atableau_entries_tl
\int_zero:N \l__atableau_row_int
\tl_set:Nn \l_tmpb_tl {}
\seq_map_inline:Nn #1
{
\tl_put_right:No \l__atableau_entries_tl \l_tmpb_tl
\int_incr:N \l__atableau_row_int
\int_step_inline:nn {##1}
{
\int_set:Nn \l_tmpa_int { \l__atableau_charge_int + ####1 - \l__atableau_row_int + 0\seq_item:NV \l__atableau_skew_seq \l__atableau_row_int }
\int_compare:nNnTF {\l_tmpa_int} < {0}
{ \__atableau_tl_put_right_braced:Ne \l__atableau_entries_tl {\exp_not:N\shortminus\int_eval:n{-\l_tmpa_int}} }
{ \__atableau_tl_put_right_braced:No \l__atableau_entries_tl {\int_use:N \l_tmpa_int} }
}
\tl_set:Nn \l_tmpb_tl {,}
}
}
% Diagrams with show=last are drawn using the \Tableau command, with
% usage: \__atableau_shape_to_last:N {partition sequence}
\cs_new_protected:Npn \__atableau_shape_to_last:N #1
{
% compute conjugate of #1 as \l__atableau_conjugate_seq
%\__atableau_compute_conjugate_partition:N #1
% initialise \l_tmpc_seq -- should not be necessary but otherwise \seq_item:NV fails
\seq_clear:N \l_tmpc_seq % construct the tableau in this sequence and then decant
\seq_map_inline:Nn #1 {\seq_put_right:Nn \l_tmpc_seq {}}
% value of last entry added to the tableau
\int_set:Nn \l__atableau_c_int {\l__atableau_charge_int}
% length of the first row of the partition/seq #1
\int_set:Nn \l__atableau_row_int {0\seq_item:Nn #1 {1}}
\int_step_inline:nn {\l__atableau_row_int} % ##1 is the column index
{
\int_zero:N \l__atableau_r_int % r_int is the row index
\seq_map_inline:Nn #1 % ####1 is the rth entry of the partition #1
{
\int_incr:N \l__atableau_r_int
\tl_set:Nn \l_tmpa_tl { 0\seq_item:NV \l__atableau_skew_seq \l__atableau_r_int}
\bool_if:nT { \int_compare_p:nNn {##1} > {\l_tmpa_tl} && \int_compare_p:nNn {\l_tmpa_tl+####1+1} > {##1}}
{
\int_incr:N \l__atableau_c_int
\tl_set:No \l_tmpa_tl { \seq_item:Nn \l_tmpc_seq {\l__atableau_r_int} }
\__atableau_tl_put_right_braced:No \l_tmpa_tl {\int_use:N \l__atableau_c_int}
\seq_set_item:NVx \l_tmpc_seq \l__atableau_r_int {\l_tmpa_tl}
}
}
}
% finally, unpack \l_tmpc_tl into l__atableau_entries_tl
\tl_clear:N \l__atableau_entries_tl
\tl_set:Nn \l_tmpb_tl {}
\seq_map_inline:Nn \l_tmpc_seq {
\tl_put_right:No \l__atableau_entries_tl \l_tmpb_tl
\tl_put_right:Nn \l__atableau_entries_tl {##1}
\tl_set:Nn \l_tmpb_tl {,}
}
}
% Diagrams with show=first are drawn using the \Tableau command, with
% usage: \__atableau_shape_to_first:N {partition sequence}
\cs_new_protected:Npn \__atableau_shape_to_first:N #1
{
\tl_clear:N \l__atableau_entries_tl
\int_set:Nn \l__atableau_r_int {\l__atableau_charge_int}
\tl_set:Nn \l_tmpb_tl {}
\seq_map_inline:Nn #1
{
\tl_put_right:No \l__atableau_entries_tl \l_tmpb_tl
\int_step_inline:nn {##1}
{
\int_incr:N \l__atableau_r_int
\__atableau_tl_put_right_braced:NV \l__atableau_entries_tl \l__atableau_r_int
}
\tl_set:Nn \l_tmpb_tl {,}
}
\seq_put_right:No \l__atableau_charge_seq {\int_use:N\l__atableau_r_int}
}
% usage: \__atableau_shape_to_hook:N {partition_seq}
% Return a string for the hooks length tableau
% Diagrams with show=hooks are drawn using the \Tableau command
\cs_new_protected:Npn \__atableau_shape_to_hook:N #1
{
% now construct the hook tableau
\tl_clear:N \l__atableau_entries_tl
\bool_if:NTF \l__atableau_shifted_bool
{ % shifted tableau
% initialise l_tmpc_seq because we will construct the entries in it and unpack at the end
\seq_clear:N \l_tmpc_seq
\seq_map_inline:Nn #1 {\seq_put_right:Nn \l_tmpc_seq {}}
\int_set:Nn \l__atableau_col_int { 0\seq_item:Nn #1 {1} } % length of first row
\int_step_inline:nn { \l__atableau_col_int }
{ % add hooks column by column, starting by determining the rows in columns ##1
\int_zero:N \l__atableau_row_int
\seq_map_inline:Nn #1
{
\bool_if:nT { \int_compare_p:nNn {##1} > {\l__atableau_row_int} && \int_compare_p:nNn {####1+\l__atableau_row_int+1} > {##1} }
{
\int_incr:N \l__atableau_row_int
}
}
% record length of row col+1
\int_set:Nn \l_tmpa_int {0\seq_item:Nn #1 {##1+1}}
% loop through rows 1,...,row and add the hook lengths
\int_step_inline:nn {\l__atableau_row_int}
{
\tl_set:Nx \l_tmpa_tl { \seq_item:Nn \l_tmpc_seq {####1} }
\tl_set:Nx \l_tmpb_tl { \int_eval:n {\seq_item:Nn #1 {####1} + \l__atableau_row_int - ##1 + \l_tmpa_int } }
\__atableau_tl_put_right_braced:NV \l_tmpa_tl \l_tmpb_tl
\seq_set_item:Nnx \l_tmpc_seq {####1} {\l_tmpa_tl}
}
}
\tl_set:Nx \l__atableau_entries_tl { \seq_use:Nn \l_tmpc_seq {,} }
}
{ % unshifted (although could be skew, when all bets are off...)
% compute conjugate of #1 as \l__atableau_conjugate_seq
\int_zero:N \l__atableau_row_int
\tl_set:Nn \l_tmpb_tl {}
\__atableau_compute_conjugate_partition:N #1
\seq_map_inline:Nn #1
{
\tl_put_right:No \l__atableau_entries_tl \l_tmpb_tl
\int_incr:N \l__atableau_row_int
\int_step_inline:nn {##1}
{
\tl_set:Ne \l_tmpc_tl { \int_eval:n {##1+\seq_item:Nn \l__atableau_conjugate_seq {####1} -\l__atableau_row_int-####1+1} }
\__atableau_tl_put_right_braced:NV \l__atableau_entries_tl \l_tmpc_tl
}
\tl_set:Nn \l_tmpb_tl {,}
}
}
}
% Residue diagrams are drawn using the \Tableau command, with
% usage: \__atableau_shape_to_residue:N {partition sequence}
\cs_new_protected:Npn \__atableau_shape_to_residue:N #1
{
\tl_clear:N \l__atableau_entries_tl
\int_zero:N \l__atableau_row_int
\tl_set:Nn \l_tmpb_tl {}
\seq_map_inline:Nn #1
{
\tl_put_right:No \l__atableau_entries_tl \l_tmpb_tl
\int_incr:N \l__atableau_row_int
\int_step_inline:nn {##1}
{
\int_set:Nn \l_tmpa_int { \l__atableau_charge_int + ####1 - \l__atableau_row_int }
\int_add:Nn \l_tmpa_int { + 0\seq_item:NV \l__atableau_skew_seq \l__atableau_row_int }
\tl_set:Nx \l_tmpa_tl { \__atableau_residue:nn { \l_tmpa_int } {\l__atableau_e_int} }
\__atableau_tl_put_right_braced:Nx \l__atableau_entries_tl { \l_tmpa_tl }
}
\tl_set:Nn \l_tmpb_tl {,}
}
}
% ---------------------------------------------------------------------------
% draw diagram border
% usage: \__atableau_draw_border:nn #1 #2 {name of sequence} {name of style}
% The name of the sequence is either skew or shape
\cs_new_protected:Npn \__atableau_draw_border:nn #1 #2
{
\int_zero:N \l__atableau_r_int % row index
\int_zero:N \l__atableau_c_int % column index
\tl_clear:N \l__atableau_border_tl % will hold the border
\seq_map_inline:cn {l__atableau_#1_seq}
{
% compute the endpoints of this row
\str_if_eq:nnF {skew} {#1}
{
\int_set:Nn \l__atableau_c_int { 0\seq_item:Nn \l__atableau_skew_seq {\l__atableau_r_int+1}}
\bool_if:nT { \l__atableau_tabloid_bool && \int_compare_p:nNn {\l__atableau_r_int} > {0} }
{
\int_set:Nn \l__atableau_c_int { \int_min:nn {\l__atableau_c_int} {0\seq_item:Nn \l__atableau_skew_seq {\l__atableau_r_int}} }
}
}
\__atableau_set_box_coordinates:nVV {a} \l__atableau_r_int \l__atableau_c_int
\__atableau_set_box_coordinates:nVn {b} \l__atableau_r_int {##1}
\bool_if:nTF { \int_compare_p:n {\l__atableau_r_int = 0} || \l__atableau_tabloid_bool }
{
% add line along "top" of the row
\tl_put_right:Nx \l__atableau_border_tl {(\fp_use:N\l__atableau_xa_fp,\fp_use:N\l__atableau_ya_fp)--(\fp_use:N\l__atableau_xb_fp,\fp_use:N\l__atableau_yb_fp)}
\__atableau_add_row_ends:
}
{
% add lines for second and later rows
\tl_put_left:Nx \l__atableau_border_tl {(\fp_use:N\l__atableau_xa_fp,\fp_use:N\l__atableau_ya_fp)--}
\tl_put_right:Nx \l__atableau_border_tl {--(\fp_use:N\l__atableau_xb_fp,\fp_use:N\l__atableau_yb_fp)}
\__atableau_add_row_ends:
}
\int_incr:N \l__atableau_r_int
}
% draw the border that we have constructed
\tl_if_empty:NF \l__atableau_border_tl
{
% fill in the last line
\bool_if:nT { \l__atableau_tabloid_bool && \int_compare_p:nNn {\l__atableau_r_int} > {0} }
{
\int_set:Nn \l__atableau_c_int { 0\seq_item:NV \l__atableau_skew_seq \l__atableau_r_int }
\__atableau_set_box_coordinates:nVV {a} \l__atableau_r_int \l__atableau_c_int
}
\tl_put_right:Nx \l__atableau_border_tl {(\fp_use:N\l__atableau_xa_fp,\fp_use:N\l__atableau_ya_fp)--(\fp_use:N\l__atableau_xb_fp,\fp_use:N\l__atableau_yb_fp)}
% draw the border
\draw[aTableau/#2] \l__atableau_border_tl;
}
}
% usage: \__atableau_remove_dotted_tableau_rows:
% Poke some holes in the border for the rows in dotted_rows_seq
\cs_new_protected:Nn \__atableau_remove_dotted_tableau_rows:
{
% To collect repeated rows in dotted_rows_seq
% we use \seq_map_inline:Nn and then compare ##1 with \l__atableau_r_int to
% determine if this is a new row.
% take a copy of \l__atableau_dotted_rows_seq so that the pop_left's below
% do not destroy it
\seq_set_eq:NN \l_tmpb_seq \l__atableau_dotted_rows_seq
\bool_do_until:nn { \seq_if_empty_p:N \l_tmpb_seq }
{
\seq_pop_left:NN \l_tmpb_seq \l_tmpa_tl
\int_set:Nn \l__atableau_row_int {\l_tmpa_tl}
\int_set:Nn \l__atableau_r_int {\l__atableau_row_int+1}
% LaTeX3 does not provide \seq_if_in_p:NN, so ...
\bool_set_true:N \l_tmpa_bool
\bool_do_while:nn { \l_tmpa_bool }
{
\int_set:Nn \l_tmpa_int {0\seq_item:Nn \l_tmpb_seq 1}
\int_compare:nNnTF {\l__atableau_r_int} = {\l_tmpa_int}
{
\seq_pop_left:NN \l_tmpb_seq \l_tmpa_tl
\int_incr:N \l__atableau_r_int
}
{ \bool_set_false:N \l_tmpa_bool }
}
% We want to blank out the rows between the four coordinates
% a=(row,tmpa) .... b=(row,col)
% | |
% c=(r,tmpb) .... d=(r,c)
% set tmpa and tmpb to the column index for rows row and r, respectively
\int_set:No \l__atableau_col_int { 0\seq_item:NV \l__atableau_shape_seq \l__atableau_row_int } % mu_row
\int_set:No \l__atableau_c_int { 0\seq_item:NV \l__atableau_shape_seq \l__atableau_r_int } % mu_r
% shift in col-direction
\fp_set:Nn \l__atableau_xa_fp {\l__atableau_tab_col_dx_fp*\l__atableau_box_wd_fp}
\fp_set:Nn \l__atableau_ya_fp {\l__atableau_tab_col_dy_fp*\l__atableau_box_ht_fp}
% shift in row-direction
\fp_set:Nn \l__atableau_xb_fp {\l__atableau_tab_row_dx_fp*\l__atableau_box_wd_fp}
\fp_set:Nn \l__atableau_yb_fp {\l__atableau_tab_row_dy_fp*\l__atableau_box_ht_fp}
% a draw between the coordinates a, b, c, d
\__atableau_set_box_coordinates:noo {l} {\l__atableau_row_int-1} {\l__atableau_col_int-1} % point b
\draw[aTableau/clearBoxes]
(\fp_eval:n{\l__atableau_xl_fp+0.58*\l__atableau_xa_fp-0.42*\l__atableau_xb_fp},
\fp_eval:n{\l__atableau_yl_fp+0.58*\l__atableau_ya_fp-0.42*\l__atableau_yb_fp})
--++(\fp_eval:n{(\l__atableau_r_int-\l__atableau_row_int)*\l__atableau_xb_fp},
\fp_eval:n{(\l__atableau_r_int-\l__atableau_row_int)*\l__atableau_yb_fp})
--++(\fp_eval:n{(\l__atableau_c_int-\l__atableau_col_int)*\l__atableau_xa_fp},
\fp_eval:n{(\l__atableau_c_int-\l__atableau_col_int)*\l__atableau_ya_fp})
--++(\fp_eval:n{-0.12*\l__atableau_xb_fp}, \fp_eval:n{-0.12*\l__atableau_yb_fp})
--++(\fp_eval:n{-(0.15+\l__atableau_c_int)*\l__atableau_xa_fp}, \fp_eval:n{-(0.15+\l__atableau_c_int)*\l__atableau_ya_fp})
--++(\fp_eval:n{(\l__atableau_row_int-\l__atableau_r_int+0.12)*\l__atableau_xb_fp},
\fp_eval:n{(\l__atableau_row_int-\l__atableau_r_int+0.12)*\l__atableau_yb_fp})
--cycle
;
% finally, we need to add dots between b and d
\draw[aTableau/dottedLine]
(\fp_eval:n{0.5*\l__atableau_xa_fp-0.5*\l__atableau_xb_fp+\l__atableau_xl_fp},
\fp_eval:n{0.5*\l__atableau_ya_fp-0.5*\l__atableau_yb_fp+\l__atableau_yl_fp})
--++(\fp_eval:n{(\l__atableau_c_int-\l__atableau_col_int)*\l__atableau_xa_fp+(\l__atableau_r_int-\l__atableau_row_int)*\l__atableau_xb_fp},
\fp_eval:n{(\l__atableau_c_int-\l__atableau_col_int)*\l__atableau_ya_fp+(\l__atableau_r_int-\l__atableau_row_int)*\l__atableau_yb_fp})
;
% and between a and c, which is trickier as the skew shape plays a role
\int_set:No \l_tmpa_int { \int_eval:n {0\seq_item:Nn \l__atableau_skew_seq \l__atableau_row_int} }
\int_set:No \l_tmpb_int { \int_eval:n {\int_max:nn{\l_tmpa_int}{0\seq_item:Nn \l__atableau_skew_seq \l__atableau_r_int} }}
\int_decr:N \l__atableau_row_int
\int_decr:N \l__atableau_r_int
\draw[aTableau/dottedLine]
(\fp_eval:n{\l__atableau_x_fp+\l_tmpa_int*\l__atableau_xa_fp+\l__atableau_row_int*\l__atableau_xb_fp},
\fp_eval:n{\l__atableau_y_fp+\l_tmpa_int*\l__atableau_ya_fp+\l__atableau_row_int*\l__atableau_yb_fp})
--(\fp_eval:n{\l__atableau_x_fp+\l_tmpb_int*\l__atableau_xa_fp+\l__atableau_r_int*\l__atableau_xb_fp},
\fp_eval:n{\l__atableau_y_fp+\l_tmpb_int*\l__atableau_ya_fp+\l__atableau_r_int*\l__atableau_yb_fp})
;
\bool_if:nT { \int_compare_p:nNn {\l_tmpa_int}>{0} && \l__atableau_skew_border_bool }
{
\draw[aTableau/dottedLine,draw=\l__atableau_skew_border_tl]
(\fp_eval:n{\l__atableau_x_fp+\l__atableau_row_int*\l__atableau_xb_fp},
\fp_eval:n{\l__atableau_y_fp+\l__atableau_row_int*\l__atableau_yb_fp})
--(\fp_eval:n{\l__atableau_x_fp+\l__atableau_r_int*\l__atableau_xb_fp},
\fp_eval:n{\l__atableau_y_fp+\l__atableau_r_int*\l__atableau_yb_fp})
;
}
}
}
% usage: \__atableau_remove_dotted_tableau_cols:
% Poke some holes in the border for the cols in dotted_rows_seq
\cs_new_protected:Nn \__atableau_remove_dotted_tableau_cols:
{
% To collect repeated columns in dotted_cols_seq
% we use \seq_map_inline:Nn and then compare ##1 with \l__atableau_c_int to
% determine if this is a new column.
% conjugate partition and skew shape
\__atableau_compute_conjugate_partition:N \l__atableau_skew_seq
\seq_set_eq:NN \l_tmpa_seq \l__atableau_conjugate_seq % \l_tmpa_seq is the conjugate skew
\__atableau_compute_conjugate_partition:N \l__atableau_shape_seq % conjugate shape
% take a copy of \l__atableau_dotted_cols_seq so that the pop_left's below
% do not destroy it
\seq_set_eq:NN \l_tmpb_seq \l__atableau_dotted_cols_seq
\bool_do_until:nn { \seq_if_empty_p:N \l_tmpb_seq }
{
\seq_pop_left:NN \l_tmpb_seq \l_tmpa_tl
\int_set:Nn \l__atableau_col_int {\l_tmpa_tl}
\int_set:Nn \l__atableau_c_int {\l__atableau_col_int+1}
% LaTeX3 does not provide \seq_if_in_p:NN, so ...
\bool_set_true:N \l_tmpa_bool
\bool_do_while:nn { \l_tmpa_bool }
{
\int_set:Nn \l_tmpa_int {0\seq_item:Nn \l_tmpb_seq 1}
\int_compare:nNnTF {\l__atableau_c_int} = {\l_tmpa_int}
{
\seq_pop_left:NN \l_tmpb_seq \l_tmpa_tl
\int_incr:N \l__atableau_c_int
}
{ \bool_set_false:N \l_tmpa_bool }
}
% We want to blank out the rows between the four coordinates
% a=(row,tmpa) .... b=(r,tmpb)
% | |
% c=(row,col) .... d=(r,c)
% set row and r to the row indices for col and c, respectively
\int_set:No \l__atableau_row_int { 0\seq_item:NV \l__atableau_conjugate_seq \l__atableau_col_int } % mu_row
\int_set:No \l__atableau_r_int { 0\seq_item:NV \l__atableau_conjugate_seq \l__atableau_c_int } % mu_r
% shift in col-direction
\fp_set:Nn \l__atableau_xa_fp {\l__atableau_tab_col_dx_fp*\l__atableau_box_wd_fp}
\fp_set:Nn \l__atableau_ya_fp {\l__atableau_tab_col_dy_fp*\l__atableau_box_ht_fp}
% shift in row-direction
\fp_set:Nn \l__atableau_xb_fp {\l__atableau_tab_row_dx_fp*\l__atableau_box_wd_fp}
\fp_set:Nn \l__atableau_yb_fp {\l__atableau_tab_row_dy_fp*\l__atableau_box_ht_fp}
% a draw between the coordinates a, b, c, d
\__atableau_set_box_coordinates:noo {l} {\l__atableau_row_int-1} {\l__atableau_col_int-1} % point b
\draw[aTableau/clearBoxes]
(\fp_eval:n{\l__atableau_xl_fp-0.42*\l__atableau_xa_fp+0.58*\l__atableau_xb_fp},
\fp_eval:n{\l__atableau_yl_fp-0.42*\l__atableau_ya_fp+0.58*\l__atableau_yb_fp})
--++(\fp_eval:n{(\l__atableau_c_int-\l__atableau_col_int)*\l__atableau_xa_fp},
\fp_eval:n{(\l__atableau_c_int-\l__atableau_col_int)*\l__atableau_ya_fp})
--++(\fp_eval:n{(\l__atableau_r_int-\l__atableau_row_int)*\l__atableau_xb_fp},
\fp_eval:n{(\l__atableau_r_int-\l__atableau_row_int)*\l__atableau_yb_fp})
--++(\fp_eval:n{-0.12*\l__atableau_xa_fp}, \fp_eval:n{-0.12*\l__atableau_ya_fp})
--++(\fp_eval:n{-(0.15+\l__atableau_r_int)*\l__atableau_xb_fp}, \fp_eval:n{-(0.15+\l__atableau_r_int)*\l__atableau_yb_fp})
--++(\fp_eval:n{(\l__atableau_col_int-\l__atableau_c_int+0.12)*\l__atableau_xa_fp},
\fp_eval:n{(\l__atableau_col_int-\l__atableau_c_int+0.12)*\l__atableau_ya_fp})
--cycle
;
% finally, we need to add dots between b and d
\draw[aTableau/dottedLine]
(\fp_eval:n{\l__atableau_xl_fp-0.5*\l__atableau_xa_fp+0.5*\l__atableau_xb_fp},
\fp_eval:n{\l__atableau_yl_fp-0.5*\l__atableau_ya_fp+0.5*\l__atableau_yb_fp})
--++(\fp_eval:n{(\l__atableau_r_int-\l__atableau_row_int)*\l__atableau_xb_fp+(\l__atableau_c_int-\l__atableau_col_int)*\l__atableau_xa_fp},
\fp_eval:n{(\l__atableau_r_int-\l__atableau_row_int)*\l__atableau_yb_fp+(\l__atableau_c_int-\l__atableau_col_int)*\l__atableau_ya_fp})
;
% and between a and c, which is trickier as the skew shape plays a role
\int_set:No \l_tmpa_int { \int_eval:n {0\seq_item:Nn \l_tmpa_seq \l__atableau_col_int} }
\int_set:No \l_tmpb_int { \int_eval:n {\int_max:nn{\l_tmpa_int}{0\seq_item:Nn \l_tmpa_seq \l__atableau_c_int} }}
\int_decr:N \l__atableau_col_int
\int_decr:N \l__atableau_c_int
\draw[aTableau/dottedLine]
(\fp_eval:n{\l__atableau_x_fp+\l_tmpa_int*\l__atableau_xb_fp+\l__atableau_col_int*\l__atableau_xa_fp},
\fp_eval:n{\l__atableau_y_fp+\l_tmpa_int*\l__atableau_yb_fp+\l__atableau_col_int*\l__atableau_ya_fp})
--(\fp_eval:n{\l__atableau_x_fp+\l_tmpb_int*\l__atableau_xb_fp+\l__atableau_c_int*\l__atableau_xa_fp},
\fp_eval:n{\l__atableau_y_fp+\l_tmpb_int*\l__atableau_yb_fp+\l__atableau_c_int*\l__atableau_ya_fp})
;
\bool_if:nT { \int_compare_p:nNn {\l_tmpa_int}>{0} && \l__atableau_skew_border_bool }
{
\draw[aTableau/dottedLine,draw=\l__atableau_skew_border_tl]
(\fp_eval:n{\l__atableau_x_fp+\l__atableau_col_int*\l__atableau_xa_fp},
\fp_eval:n{\l__atableau_y_fp+\l__atableau_col_int*\l__atableau_ya_fp})
--(\fp_eval:n{\l__atableau_x_fp+\l__atableau_c_int*\l__atableau_xa_fp},
\fp_eval:n{\l__atableau_y_fp+\l__atableau_c_int*\l__atableau_ya_fp})
;
}
}
}
% usage: \__atableau_draw_label:
% Add the label to a diagram
\cs_new_protected:Nn \__atableau_draw_label:
{
% determine where the label should be attached, which is the (1,1)-box by default
\fp_set_eq:NN \l__atableau_xa_fp \l__atableau_x_fp
\fp_set_eq:NN \l__atableau_ya_fp \l__atableau_y_fp
\bool_if:nF { \seq_if_empty_p:N \l__atableau_skew_seq || \l__atableau_skew_border_bool }
{ % attach label to the (1,skew_1)-box
\tl_set:Nn \l_tmpa_tl { 0\seq_item:Nn \l__atableau_skew_seq {1} }
\fp_add:Nn \l__atableau_xa_fp {\l_tmpa_tl*\l__atableau_tab_col_dx_fp*\l__atableau_box_wd_fp}
\fp_add:Nn \l__atableau_ya_fp {\l_tmpa_tl*\l__atableau_tab_col_dy_fp*\l__atableau_box_wd_fp}
}
% add the label
\node[aTableau/labelStyle] at (\fp_use:N\l__atableau_xa_fp,\fp_use:N\l__atableau_ya_fp) { \__atableau_entry:n{\l__atableau_label_tl} };
}
% usage: \__atableau_draw_skew_boxes:
% Draw the skew boxes using ribbons
\cs_new_protected:Nn \__atableau_draw_skew_boxes:
{
\group_begin:
% override the style of the skew boxes inside this group
\tikzset{aTableau/ribbonBox/.style=aTableau/skewBox}
\tikzset{aTableau/ribbonStyle/.style={draw=none,fill=none}}
\tl_set:Nn \l__atableau_ribbon_type_tl {ribbon} % change ribbon type to ribbon
\int_zero:N \l__atableau_r_int
\seq_map_inline:Nn \l__atableau_skew_seq
{
\int_incr:N \l__atableau_r_int
\int_compare:nNnT {##1} > {0}
{
\tl_clear:N \l_tmpa_tl
\tl_put_right:Ne \l_tmpa_tl { {\int_use:N \l__atableau_r_int} }
\tl_put_right:Ne \l_tmpa_tl { {##1} }
\tl_put_right:Ne \l_tmpa_tl { \prg_replicate:nn {##1-1} {c} }
\__atableau_add_ribbon:V \l_tmpa_tl
}
}
\group_end:
}
% usage: \__atableau_add_row_ends: increment the (xa,ya) and (xb,yb) coordinates down
% one row and add the lines at the left and right hand ends of the row to
% \l__atableau_border_tl. If this is a tabloid then we only want to add the
% coordinates but otherwise we join them up
\cs_new_protected:Nn \__atableau_add_row_ends:
{
\bool_if:NTF \l__atableau_conjugate_bool
{
% adding to the left-hand side
\fp_add:Nn \l__atableau_xa_fp {\l__atableau_tab_col_dx_fp*\l__atableau_box_wd_fp}
\fp_add:Nn \l__atableau_ya_fp {\l__atableau_tab_col_dy_fp*\l__atableau_box_ht_fp}
% adding to the right-hand side
\fp_add:Nn \l__atableau_xb_fp {\l__atableau_tab_col_dx_fp*\l__atableau_box_wd_fp}
\fp_add:Nn \l__atableau_yb_fp {\l__atableau_tab_col_dy_fp*\l__atableau_box_ht_fp}
\bool_if:NTF \l__atableau_tabloid_bool
{
\tl_put_left:Nx \l__atableau_border_tl {--(\fp_use:N\l__atableau_xa_fp,\fp_use:N\l__atableau_ya_fp)}
\tl_put_right:Nx \l__atableau_border_tl {(\fp_use:N\l__atableau_xb_fp,\fp_use:N\l__atableau_yb_fp)--}
}
{
\tl_put_left:Nx \l__atableau_border_tl {(\fp_use:N\l__atableau_xa_fp,\fp_use:N\l__atableau_ya_fp)--}
\tl_put_right:Nx \l__atableau_border_tl {--(\fp_use:N\l__atableau_xb_fp,\fp_use:N\l__atableau_yb_fp)}
}
}
{
% adding to the left-hand side
\fp_add:Nn \l__atableau_xa_fp {\l__atableau_tab_row_dx_fp*\l__atableau_box_wd_fp}
\fp_add:Nn \l__atableau_ya_fp {\l__atableau_tab_row_dy_fp*\l__atableau_box_ht_fp}
% adding to the right-hand side
\fp_add:Nn \l__atableau_xb_fp {\l__atableau_tab_row_dx_fp*\l__atableau_box_wd_fp}
\fp_add:Nn \l__atableau_yb_fp {\l__atableau_tab_row_dy_fp*\l__atableau_box_ht_fp}
\bool_if:NTF \l__atableau_tabloid_bool
{
\tl_put_left:Nx \l__atableau_border_tl {(\fp_use:N\l__atableau_xa_fp,\fp_use:N\l__atableau_ya_fp)}
\tl_put_right:Nx \l__atableau_border_tl {(\fp_use:N\l__atableau_xb_fp,\fp_use:N\l__atableau_yb_fp)--}
}
{
\tl_put_left:Nx \l__atableau_border_tl {(\fp_use:N\l__atableau_xa_fp,\fp_use:N\l__atableau_ya_fp)--}
\tl_put_right:Nx \l__atableau_border_tl {--(\fp_use:N\l__atableau_xb_fp,\fp_use:N\l__atableau_yb_fp)}
}
}
}
% ---------------------------------------------------------------------------
% Tableaux
% usage: \__atableau_draw_tableau:n {tableau specifications}
% The entries are first primarily because the \Diagram commands need
% to force the entries to expand
\cs_new_protected:Npn \__atableau_draw_tableau:n #1
{
% set the star style
\tl_set:Nn \l__atableau_starstyle_tl {aTableau/tableauStarStyle}
% disable interior boxes if boxes_bool is false
\bool_if:NF \l__atableau_boxes_bool { \__atableau_tikzset_append:nn {boxStyle} {draw=none} }
% initialise the skew shape for a shifted tableaux
\bool_if:NT \l__atableau_shifted_bool
{
\seq_clear:N \l__atableau_skew_seq
\seq_put_right:No \l__atableau_skew_seq {0}
}
% record the tableau shape as we go so that we can draw the border
% in finalise_tableau
\seq_clear:N \l__atableau_shape_seq
% the styled boxes are drawn at the end
\tl_clear:N \l__atableau_styled_nodes_tl
% set initial row and column
\int_zero:N \l__atableau_row_int
\int_set:Nn \l__atableau_col_int { 0\seq_item:Nn \l__atableau_skew_seq {1}}
% Parse #1 into the rows and columns with style. Initially we used
% \seq_set_split:Nnn here, but this required double bracing
% multi-character entries whenever they were he only entry in their
% column. Now we peek for the commas and the style simultaneously.
\__atableau_peek_tableau:w #1 \q_recursion_tail \q_recursion_stop
% add the nodes with style
\l__atableau_styled_nodes_tl
% add the labels, ribbons, snobs and border
\__atableau_finalise_tableau:
}
% usage: \__atableau_finalise_tableau:
% As it is used in several places, collect the code that finishes
% drawing the tableau by adding the ribbons, paths, snobs, skew boxes,
% border and the dotted rows and columns.
\cs_new_protected:Nn \__atableau_finalise_tableau:
{
% prevent paths and ribbons from updating shape
\cs_set_eq:NN \__atableau_update_shape: \prg_do_nothing:
% add paths
\seq_if_empty:NF \l__atableau_paths_seq
{
\tl_set:Nn \l__atableau_ribbon_type_tl {path} % change ribbon type to path
\seq_map_inline:Nn \l__atableau_paths_seq {\__atableau_add_ribbon:n {##1}}
}
% add ribbons
\tl_set:Nn \l__atableau_ribbon_type_tl {ribbon} % change ribbon type to ribbon
\seq_map_inline:Nn \l__atableau_ribbons_seq {\__atableau_add_ribbon:n {##1}}
% paths and ribbons are inside the delimiters, but snobs are not
\cs_set_eq:NN \__atableau_update_extrema:n \use_none:n
% draw border
\tl_if_blank:VF \l__atableau_label_tl { \__atableau_draw_label: }
\bool_if:NT \l__atableau_skew_boxes_bool { \__atableau_draw_skew_boxes: }
\bool_if:NT \l__atableau_skew_border_bool { \__atableau_draw_border:nn {skew} {skewBorder} }
\bool_if:NT \l__atableau_border_bool { \__atableau_draw_border:nn {shape} {borderStyle} }
% remove dotted rows and columns
\seq_if_empty:NF \l__atableau_dotted_rows_seq \__atableau_remove_dotted_tableau_rows:
\seq_if_empty:NF \l__atableau_dotted_cols_seq \__atableau_remove_dotted_tableau_cols:
% add snobs
\tl_set:Nn \l__atableau_ribbon_type_tl {snob} % change ribbon type to snob
\seq_map_inline:Nn \l__atableau_snobs_seq {\__atableau_add_ribbon:n {##1}}
}
% ---------------------------------------------------------------------------
% box and bead coordinates
% usage: \__atableau_update_multi_extrema:n {letter}
% Update xmax, ymax and ymin using the x#1_fp and y#1_fp
\cs_new_protected:Npn \__atableau_update_multi_extrema:n #1
{
% adjust xmax, ymin and ymax for multishapes
\fp_set:Nn \l__atableau_xmax_fp { max(\l__atableau_xmax_fp, \use:c{l__atableau_x#1_fp}) }
\fp_set:Nn \l__atableau_ymax_fp { max(\l__atableau_ymax_fp, \use:c{l__atableau_y#1_fp}) }
\fp_set:Nn \l__atableau_ymin_fp { min(\l__atableau_ymin_fp, \use:c{l__atableau_y#1_fp}) }
}
\cs_new_protected:Npn \__atableau_update_multi_xtrema:n #1
{
% adjust xmax for multishapes
\fp_set:Nn \l__atableau_xmax_fp { max(\l__atableau_xmax_fp, \use:c{l__atableau_x#1_fp}) }
}
% By default, we do not update ymin, ymax and xmax. This only happens for multishapes
\cs_set_eq:NN \__atableau_update_extrema:n \use_none:n
% usage: \__atableau_set_box_coordinates_normal:nnn <letter> <row> <col>: given the row and columns
% indices, row and col, define the corresponding coordinates in a tableau
% - \l__atableau_xl_fp : x-coordinates
% - \l__atableau_yl_fp : y-coordinate
% - \l__atableau_name_tl : the node name
% Used by the tableau and diagram commands. Note that row and col both start
% from 0, so the (1,1)-box has row=col=0.
\cs_new_protected:Npn \__atableau_set_box_coordinates_normal:nnn #1 #2 #3
{
\tl_set:Nx \l__atableau_name_tl {\l__atableau_prefix_tl-\int_eval:n{1+#2}-\int_eval:n {1+#3}}
\fp_set:cn {l__atableau_x#1_fp} {\l__atableau_x_fp+((#2+0.5)*\l__atableau_tab_row_dx_fp+(#3+0.5)*\l__atableau_tab_col_dx_fp)*\l__atableau_box_wd_fp }
\fp_set:cn {l__atableau_y#1_fp} {\l__atableau_y_fp+((#2+0.5)*\l__atableau_tab_row_dy_fp+(#3+0.5)*\l__atableau_tab_col_dy_fp)*\l__atableau_box_ht_fp }
\__atableau_update_extrema:n #1
}
% usage: \__atableau_set_box_coordinates_conjugate:nnn <letter> <row> <col>: given the row and columns
% indices, row and col, define the corresponding coordinates in the conjugate tableau
% - \l__atableau_xl_fp : x-coordinates
% - \l__atableau_yl_fp : y-coordinate
% - \l__atableau_name_tl : the node name
% Used by the tableau and diagram commands
\cs_new_protected:Npn \__atableau_set_box_coordinates_conjugate:nnn #1 #2 #3
{
\tl_set:Nx \l__atableau_name_tl {\l__atableau_prefix_tl-\int_eval:n{1+#3}-\int_eval:n {1+#2}}
\fp_set:cn {l__atableau_x#1_fp} {\l__atableau_x_fp+((#3+0.5)*\l__atableau_tab_row_dx_fp+(#2+0.5)*\l__atableau_tab_col_dx_fp)*\l__atableau_box_wd_fp }
\fp_set:cn {l__atableau_y#1_fp} {\l__atableau_y_fp+((#3+0.5)*\l__atableau_tab_row_dy_fp+(#2+0.5)*\l__atableau_tab_col_dy_fp)*\l__atableau_box_ht_fp }
\__atableau_update_extrema:n #1
}
% by default , normal coordinates are used
\cs_set_eq:NN \__atableau_set_box_coordinates:nnn \__atableau_set_box_coordinates_normal:nnn
% usage: \__atableau_set_bead_coordinates:nnn <letter> <row> <col>: given the row and columns
% indices, row and col, define the corresponding coordinates in a tableau or abacus:
% - \l__atableau_xl_fp : x-coordinates
% - \l__atableau_yl_fp : y-coordinate
% - \l__atableau_name_tl : the node name
% Used by both the tableaux and abacus commands
\cs_new_protected:Npn \__atableau_set_bead_coordinates:nnn #1 #2 #3
{
\tl_set:Nx \l__atableau_name_tl {\l__atableau_prefix_tl-\fp_to_int:n{#2-1}-\fp_to_int:n{#3}}
\fp_set:cn {l__atableau_x#1_fp} {\l__atableau_x_fp+(#2*\l__atableau_ab_row_dx_fp+#3*\l__atableau_ab_col_dx_fp)*\l__atableau_abacus_wd_fp }
\fp_set:cn {l__atableau_y#1_fp} {\l__atableau_y_fp+(#2*\l__atableau_ab_row_dy_fp+#3*\l__atableau_ab_col_dy_fp)*\l__atableau_abacus_ht_fp }
}
% ---------------------------------------------------------------------------
% tableaux boxes/nodes
\cs_new_protected:Npn \__atableau_valign_bottom:n #1 { \vbox_to_zero:n { #1 \vss } }
\cs_new_protected:Npn \__atableau_valign_centre:n #1 { \vbox_to_zero:n { \vss #1 \vss } }
\cs_new_protected:Npn \__atableau_valign_top:n #1 { \vbox_to_zero:n { \vss #1 } }
\cs_set_eq:NN \__atableau_valign_center:n \__atableau_valign_centre:n
% We use \vbox_to_zero:n and \hbox_overlap_center:n to ensure that an entry
% does not change the height or width of the node when it is too large.
\cs_new_protected:Npn \__atableau_entry_math:n #1
{
\__atableau_valign:n
{
\__atableau_halign:n
{
\tl_if_blank:VF \tikz@textcolor {\color{\tikz@textcolor}}
\tikz@textfont $~#1 $
}
}
}
% and a text version
\cs_new_protected:Npn \__atableau_entry_text:n #1
{
\__atableau_valign:n
{
\__atableau_halign:n
{
\tl_if_blank:VF \tikz@textcolor {\color{\tikz@textcolor}}
\tikz@textfont #1
}
}
}
% By default tableau nodes are typeset in math-mode.
\cs_set_eq:NN \__atableau_entry:n \__atableau_entry_math:n
% usage: \__atableau_draw_entry:nn [style] {entry}
% Used by draw_tableau to draw the node entry #2 in the tableau using the style #1
\cs_new_protected:Npn \__atableau_draw_entry:nn [#1] #2
{
% exit when we reach the end of the row
\quark_if_recursion_tail_stop_do:nn {#2}
{
% record the column index in the shape for drawing the border
\seq_put_right:NV \l__atableau_shape_seq \l__atableau_col_int
}
% compute the node name and its (x,y)-coordinates
\__atableau_set_box_coordinates:nVV {l} \l__atableau_row_int \l__atableau_col_int
\tl_if_empty:nTF {#1}
{ % draw box if it has the default styling
\node[aTableau/boxStyle] (\l__atableau_name_tl)
at (\fp_use:N\l__atableau_xl_fp, \fp_use:N\l__atableau_yl_fp)
{\__atableau_entry:n{#2}};
}
{ % save the node to \l__atableau_styled_nodes_tl if it is styled
\tl_put_right:Nx \l__atableau_styled_nodes_tl
{
\exp_not:N \node [aTableau/boxStyle,#1] (\l__atableau_name_tl)
at (\fp_use:N\l__atableau_xl_fp, \fp_use:N\l__atableau_yl_fp)
{\exp_not:N\__atableau_entry:n{#2}};
}
}
% look for the next entry, or finish
\int_incr:N \l__atableau_col_int
\__atableau_peek_tableau:w
}
% ---------------------------------------------------------------------------
% diagrams
% usage: \__atableau_draw_diagram:n {partition}
\cs_new_protected:Npn \__atableau_draw_diagram:n #1
{
% convert #1 to the partition \l__atableau_shape_seq
\__atableau_set_partition:nn {shape} {#1}
% set the skew shape for shifted tableaux
\bool_if:NT \l__atableau_shifted_bool
{
\seq_clear:N \l__atableau_skew_seq
\seq_map_inline:Nn \l__atableau_shape_seq
{
\seq_put_right:No \l__atableau_skew_seq {\int_use:N \l__atableau_row_int}
\int_incr:N \l__atableau_row_int
}
\int_zero:N \l__atableau_row_int
}
% depending on \l__atableau_show_tl, generate the tableau entries
\str_case:VnF \l__atableau_show_tl
{
{contents} { \__atableau_shape_to_content:N \l__atableau_shape_seq }
{last} { \__atableau_shape_to_last:N \l__atableau_shape_seq }
{hooks} { \__atableau_shape_to_hook:N \l__atableau_shape_seq }
{first} { \__atableau_shape_to_first:N \l__atableau_shape_seq }
{residues} { \__atableau_shape_to_residue:N \l__atableau_shape_seq }
{} { \__atableau_diagram_for_shape:N \l__atableau_shape_seq }
}
{
\msg_error:nnx {aTableau} {unrecognised-entries} {\l__atableau_show_tl}
}
\__atableau_draw_tableau:V \l__atableau_entries_tl
}
% ---------------------------------------------------------------------------
% multitableau and their diagrams
% usage: \__atableau_draw_multishape:n diagram|tableau
% Draw a multitableau or multidiagram. Most of the work is in calculating the
% x-coordinates of the origins and each diagram, their separators and the
% maximal y-coordinates, for drawing the delimiters. We also need to set
% various keys for the components, so that they work correctly.
\cs_new_protected:Npn \__atableau_draw_multishape:n #1
{
% save the prefix name so that we can modify it
\tl_set_eq:NN \l__atableau_multiprefix_tl \l__atableau_prefix_tl
% check for conjugation
\bool_if:NT \l__atableau_conjugate_bool { \seq_reverse:N \l__atableau_component_seq }
% reset the variables that we need
\int_zero:N \l__atableau_component_int % component index
% We will increment x_fp to give the origins of the component diagrams.
% For now we record the position of the x-coordinates of the left brace,
% which will be placed after the diagrams have been drawn we first have to
% determine their height.
\seq_clear:N \l__atableau_xsep_seq
\seq_put_right:Nx \l__atableau_xsep_seq {\fp_to_decimal:N\l__atableau_x_fp}
% keep track of min/max y-coordinates used and max x-coordinate
\fp_set_eq:NN \l__atableau_xmax_fp \l__atableau_x_fp
\fp_set:Nn \l__atableau_ymax_fp {\l__atableau_y_fp + \l__atableau_tab_row_dy_fp*\l__atableau_box_ht_fp/2} % middle of box
\fp_set_eq:NN \l__atableau_ymin_fp \l__atableau_ymax_fp
\seq_map_inline:Nn \l__atableau_component_seq
{
% increment component and set prefix, charge, skew, ribbons and snobs
\int_incr:N \l__atableau_component_int
% update ymin, ymax and xmax (re-enable each time as this is disabled when placing ribbons)
\fp_compare:nNnTF {\l__atableau_rows_fp} = {0}
{ \cs_set_eq:NN \__atableau_update_extrema:n \__atableau_update_multi_extrema:n } % update xmax, ymin, ymax
{ \cs_set_eq:NN \__atableau_update_extrema:n \__atableau_update_multi_xtrema:n } % update only xmax
% change the node prefix to include the component index
\tl_set:No \l__atableau_prefix_tl {\l__atableau_multiprefix_tl-\int_use:N\l__atableau_component_int}
% charge defaults to zero if not set
\int_set:Nn \l__atableau_charge_int {0\seq_item:NV \l__atableau_charge_seq \l__atableau_component_int}
% set the multi-component keys from the corresponding multi sequence
\clist_map_inline:nn {dotted_rows, dotted_cols, paths, ribbons, snobs}
{
% if multi####1 is empty then clear the ####1 sequence, otherwise set it equal to component value
\seq_if_empty:cTF {l__atableau_multi####1_seq}
{ \seq_clear:c {l__atableau_####1_seq} }
{
\tl_set:Nx \l_tmpb_tl {\seq_item:cV {l__atableau_multi####1_seq} \l__atableau_component_int}
\seq_set_from_clist:co {l__atableau_####1_seq} {\l_tmpb_tl}
}
}
% labels are handled separately because they are not sequences
\seq_if_empty:NTF \l__atableau_multilabel_seq
{ \seq_clear:N \l__atableau_label_seq }
{
\tl_set:Nx \l_tmpb_tl {\seq_item:NV \l__atableau_multilabel_seq \l__atableau_component_int}
\tl_set:No \l__atableau_label_tl {\l_tmpb_tl}
}
% skew is handled separately because it uses set_partition
\seq_if_empty:NTF \l__atableau_multiskew_seq
{ \seq_clear:N \l__atableau_skew_seq }
{
\tl_set:Nx \l_tmpb_tl {\seq_item:NV \l__atableau_multiskew_seq \l__atableau_component_int}
\__atableau_set_partition:no {skew} {\l_tmpb_tl}
}
% determine the coordinates for the diagram/tableau
% - \l__atableau_c_int: number of columns in first row
% - \l__atableau_r_int: number of rows in components
\bool_if:nTF { \str_if_empty_p:n {##1} || \str_if_eq_p:nn {##1} {...} }
{
\int_set:Nn \l__atableau_c_int {1}
\int_set:Nn \l__atableau_r_int {1}
}
{
% the component is nonempty
\tl_if_eq:nnTF {#1} {diagram}
{
\__atableau_set_partition:nn {shape} {##1}
\int_set:No \l__atableau_c_int {\seq_item:Nn \l__atableau_shape_seq {1}+0\seq_item:Nn \l__atableau_skew_seq {1}}
% set r_int equal to the number of nonzero rows in shape_seq
\int_set:No \l__atableau_r_int { \seq_count:N \l__atableau_shape_seq }
}
{ % coordinates for tableaux
\seq_set_from_clist:Nn \l_tmpa_seq {##1}
\int_set:No \l__atableau_c_int {0\seq_item:Nn \l__atableau_skew_seq {1}} % initialise to skew length
\tl_set:Nx \l_tmpc_tl {\seq_item:Nn \l_tmpa_seq {1}} % first row of tableau
\__atableau_count_row:x \l_tmpc_tl % length of first row + skew
% set r_int equal to the number of nonzero rows in shape_seq
\int_set:No \l__atableau_r_int { \seq_count:N \l_tmpa_seq }
}
}
% now that we have the coordinates we need, we compute the
% x-coordinates of the diagram origin and the separators
% need to switch for conjugate partitions
\bool_if:NTF \l__atableau_conjugate_bool
{ % conjugating
% the origin is c * col_dx units from the separator + xoffset
\fp_add:Nn \l__atableau_x_fp
{
abs(\l__atableau_c_int*\l__atableau_tab_row_dx_fp*\l__atableau_box_wd_fp) % number of columns
+ 0\seq_item:NV \l__atableau_xoffsets_seq \l__atableau_component_int % x-offset
}
% the next separator is is r * row_dx units from the origin
\fp_set:Nn \l__atableau_xsep_fp {
abs(\l__atableau_r_int*\l__atableau_tab_col_dx_fp*\l__atableau_box_wd_fp)
+ \l__atableau_separation_fp
}
% compute maximum height of the diagram
\fp_set:Nn \l__atableau_yb_fp
{
\l__atableau_c_int*\l__atableau_tab_row_dy_fp*\l__atableau_box_ht_fp
+ \l__atableau_r_int*abs(\l__atableau_tab_col_dy_fp)*\l__atableau_box_ht_fp
+ 0\seq_item:NV \l__atableau_yoffsets_seq \l__atableau_component_int
}
}
{ % not conjugating
% the origin is r * row_dx units from the separator + xoffset
\fp_add:Nn \l__atableau_x_fp
{
abs(\l__atableau_r_int*\l__atableau_tab_row_dx_fp*\l__atableau_box_wd_fp) % number of columns
+ 0\seq_item:NV \l__atableau_xoffsets_seq \l__atableau_component_int % x-offset
}
% the next separator is is c * col_dx units from the origin
\fp_set:Nn \l__atableau_xsep_fp
{
abs(\l__atableau_c_int*\l__atableau_tab_col_dx_fp*\l__atableau_box_wd_fp) % number of columns
+ \l__atableau_separation_fp
}
% compute maximum height of the diagram
\fp_set:Nn \l__atableau_yb_fp
{
\l__atableau_r_int*\l__atableau_tab_row_dy_fp*\l__atableau_box_ht_fp
+ \l__atableau_c_int*\l__atableau_tab_col_dy_fp*\l__atableau_box_ht_fp
+ 0\seq_item:NV \l__atableau_yoffsets_seq \l__atableau_component_int
}
}
% Having determined the positions of the diagram origins and separators, we are ready to draw the diagram
% First set the y-coordinate for the origin of the current component
\fp_add:Nn \l__atableau_y_fp {0\seq_item:NV \l__atableau_yoffsets_seq \l__atableau_component_int}
% special processing for empty diagrams and ...
\str_case:nnF {##1}
{
{}
{
% an empty diagram -> \l__atableau_empty_tl
\__atableau_set_box_coordinates:nnn {a} {0} {0}
\node[aTableau/separatorSymbol] at (\fp_use:N \l__atableau_xa_fp, \fp_use:N \l__atableau_ya_fp){\l__atableau_empty_tl};
}
{...}
{
% insert dots. ?? Replace \cdots with \l__atableau_dots_tl ??
\__atableau_set_box_coordinates:nnn {a} {0} {0}
\node[aTableau/separatorSymbol] at (\fp_use:N \l__atableau_xa_fp, \fp_use:N \l__atableau_ya_fp){$\cdots$};
}
}
{
% draw the diagram/tableau
\use:c {__atableau_draw_#1:n} {##1}
}
% increment the origin by the separation distance and record the
% x-coordinate of the separator
\fp_set:Nn \l__atableau_x_fp { \l__atableau_xmax_fp+\l__atableau_box_wd_fp/2+\l__atableau_separation_fp }
\seq_put_right:Nx \l__atableau_xsep_seq {\fp_to_decimal:N\l__atableau_x_fp}
% add the separation distance to x_fp for the next component
\fp_add:NV \l__atableau_x_fp \l__atableau_separation_fp % separation
} % end of seq_map_inline to draw component diagrams/tableau
% All of the component diagrams/tableaux have been drawn
% It remains to add the separators. First we adjust ymin and ymax
\bool_if:NT \l__atableau_separators_bool
{
% when rows_fp is nonzero it sets the maximum y-coordinate, otherwise we
% need to adjust ymin and ymax by half the box height
\fp_compare:nNnTF {\l__atableau_rows_fp} > {0}
{
\fp_compare:nNnTF {\l__atableau_tab_row_dy_fp} > {0}
{
\fp_add:Nn \l__atableau_ymax_fp { (\l__atableau_rows_fp-0.5)*\l__atableau_box_ht_fp }
\fp_add:Nn \l__atableau_ymin_fp { -0.5*\l__atableau_box_ht_fp }
}
{
\fp_add:Nn \l__atableau_ymin_fp { (0.5-\l__atableau_rows_fp)*\l__atableau_box_ht_fp }
\fp_add:Nn \l__atableau_ymax_fp { 0.5*\l__atableau_box_ht_fp }
}
}
{
% adjust ymin and ymax count as they count from the centre of the box
\fp_add:Nn \l__atableau_ymax_fp { \l__atableau_box_ht_fp/2}
\fp_add:Nn \l__atableau_ymin_fp {-\l__atableau_box_ht_fp/2}
}
\fp_set:Nn \l__atableau_y_fp {(\l__atableau_ymin_fp+\l__atableau_ymax_fp)/2} % midway between ymin and ymax
\fp_set:Nn \l__atableau_ymax_fp { \l__atableau_ymax_fp-\l__atableau_ymin_fp } % maximum height
% add left delimiter: need to use \path to set the colour
\seq_pop_left:NN \l__atableau_xsep_seq \l_tmpa_tl
\tl_if_blank:VF \l__atableau_left_delimiter_tl
{
\path[aTableau/delimiterPath] (\fp_eval:n{\l_tmpa_tl-\l__atableau_separation_fp/2}, \fp_use:N \l__atableau_y_fp)
node[aTableau/leftDelimiter] {};
}
% add right delimiter
\seq_pop_right:NN \l__atableau_xsep_seq \l_tmpa_tl
\tl_if_blank:VF \l__atableau_right_delimiter_tl
{
\path[aTableau/delimiterPath] (\fp_eval:n{\l_tmpa_tl-\l__atableau_separation_fp/2}, \fp_use:N \l__atableau_y_fp)
node[aTableau/rightDelimiter] {};
}
% the internal separators
\tl_set:Ne \l_tmpa_tl {\fp_to_decimal:N \l__atableau_ymin_fp } % ymin
\tl_set:Ne \l_tmpb_tl {\fp_to_decimal:n {\l__atableau_y_fp + \l__atableau_ymax_fp/2}} % ymax
\seq_map_inline:Nn \l__atableau_xsep_seq
{
% add the separator
\str_case:VnF \l__atableau_separator_tl
{
{|} { \draw[aTableau/separatorLine](##1,\l_tmpa_tl)--(##1,\l_tmpb_tl); }
}
{ % any other separator is assumed to be text
\node[aTableau/separatorSymbol] at (##1,\fp_use:N \l__atableau_y_fp){\l__atableau_separator_tl};
}
}
}
}
% usage: \__atableau_multidiagram:n {entries}
% The entries are first primarily because the \Diagram commands needs
% to force the entries to expand
\cs_new_protected:Npn \__atableau_multidiagram:n #1
{
% separate the component partitions
\seq_set_split:Nnn \l__atableau_component_seq {|} {#1}
% when entries=last, we need to set the charge
\tl_if_eq:NnT \l__atableau_show_tl {last}
{
\seq_clear:N \l__atableau_charge_seq
\int_zero:N \l__atableau_c_int % cumulative total of component sizes
\seq_set_eq:NN \l_tmpc_seq \l__atableau_component_seq
\seq_reverse:N \l_tmpc_seq
\seq_map_inline:Nn \l_tmpc_seq
{
\seq_put_left:No \l__atableau_charge_seq {\int_use:N \l__atableau_c_int}
\__atableau_set_partition:nn {shape} {##1}
\seq_map_inline:Nn \l__atableau_shape_seq { \int_add:Nn \l__atableau_c_int {####1} }
}
}
% determine the coordinates of the components of the diagram
\__atableau_draw_multishape:n {diagram}
}
% usage: \__atableau_multitableau:n {entries}
% The entries are first primarily because the \Diagram commands need
% to force the entries to expand
\cs_new_protected:Npn \__atableau_multitableau:n #1
{
% separate the entries of the component tableaux
\seq_set_split:Nnn \l__atableau_component_seq {|} {#1}
% determine the coordinates of the components of the tableau
\__atableau_draw_multishape:n {tableau}
}
% ---------------------------------------------------------------------------
% Ribbon tableaux
% usage: \__atableau_ribbon_tableau:n {ribbons}
% Draw a ribbon tableau. The ribbons are specified by
% (ribbon style) ij sequences of r's and c's with optional style and
% with text as a subscript. Here i and j are the row and column
% indices of the head of the ribbon
\cs_new_protected:Npn \__atableau_ribbon_tableau:n #1
{
% set the star style
\tl_set:Nn \l__atableau_starstyle_tl {aTableau/tableauStarStyle}
% record the shape as we draw the border
\seq_clear:N \l__atableau_shape_seq
\cs_set_eq:NN \__atableau_update_shape: \__atableau_update_ribbon_tableau_shape:
% draw the ribbon tableau by drawing each of the ribbons
\tl_set:Nn \l__atableau_ribbon_type_tl {ribbon} % change ribbon type to ribbon
\clist_map_inline:nn {#1} { \__atableau_add_ribbon:n {##1} }
% draw the tableau border, adding associated bells and whistles
\__atableau_finalise_tableau:
}
% usage: \__atableau_add_ribbon:n {ribbon} add a ribbon to the tableau
% The code for adding ribbons is slightly different dependning onf on whether
% \l__atableau_ribbbon_ty[e is equal to 'ribbon' or 'path'
\cs_new_protected:Npn \__atableau_add_ribbon:n #1
{
% reset the sequences that store the ribbon specifications data
\seq_clear:N \l__atableau_texts_seq % will contain node text
\seq_clear:N \l__atableau_styles_seq % will contain node styles
\seq_clear:N \l__atableau_rcs_seq % will contain node (row,col)-indices
\__atableau_peek_ribbon_style:w #1 \q_recursion_tail \q_recursion_stop
}
% usage: \__atableau_peek_ribbon_style:w {ribbon specifications}
% look for (ribbon) style inside parentheses: (style)
\cs_new_protected:Npn \__atableau_peek_ribbon_style:w
{
\peek_remove_spaces:n { % ignore spaces
\peek_charcode:NTF (
{ \__atableau_save_ribbon_style:n }
{ \__atableau_save_ribbon_style:n ()}
}
}
% usage: \__atableau_save_ribbon_style:n {style}
% read the style (style) and save in \l__atableau_ribbon_style_tl
% and then peek for [style]rc...
\cs_new_protected:Npn \__atableau_save_ribbon_style:n (#1)
{
\tl_set:Nn \l__atableau_ribbon_style_tl {#1}
\__atableau_peek_style:nw {save_ribbon_head:nnn}
}
% usage: \__atableau_initialise_path_head:
% Start \l__atableau_ribbon_path_tl for a path
\cs_new_protected:Nn \__atableau_initialise_path_head:
{ % adding a ribbon path
\tl_set:Nx \l__atableau_ribbon_path_tl
{
(\fp_use:N\l__atableau_xl_fp,\fp_use:N\l__atableau_yl_fp)
node[aTableau/pathBox,\l__atableau_ribbon_style_tl]{\__atableau_entry:n{\l__atableau_path_box_tl}}
}
}
% usage: \__atableau_initialise_ribbon_head:
% Start \l__atableau_ribbon_path_tl for a ribbon
\cs_new_protected:Nn \__atableau_initialise_ribbon_head:
{
% 1. Make (xl,yl) the top corner of the ribbon and add it
\fp_add:Nn \l__atableau_xl_fp { 0.5*(\l__atableau_tab_col_dx_fp-\l__atableau_tab_row_dx_fp)*\l__atableau_box_wd_fp }
\fp_add:Nn \l__atableau_yl_fp { 0.5*(\l__atableau_tab_col_dy_fp-\l__atableau_tab_row_dy_fp)*\l__atableau_box_ht_fp }
\tl_set:Nx \l__atableau_ribbon_path_tl { (\fp_use:N\l__atableau_xl_fp,\fp_use:N\l__atableau_yl_fp) }
% 2. Make (xa,ya) the top left of the ribbon and add it on the left (decreasing column)
\fp_set:Nn \l__atableau_xa_fp {\l__atableau_xl_fp-\l__atableau_tab_col_dx_fp*\l__atableau_box_wd_fp}
\fp_set:Nn \l__atableau_ya_fp {\l__atableau_yl_fp-\l__atableau_tab_col_dy_fp*\l__atableau_box_ht_fp}
\tl_put_left:Nx \l__atableau_ribbon_path_tl { (\fp_use:N\l__atableau_xa_fp,\fp_use:N\l__atableau_ya_fp)-- }
% 3. Make (xb,yb) the bottom right corner and add it on the right (increasing row)
\fp_set:Nn \l__atableau_xb_fp {\l__atableau_xl_fp+\l__atableau_tab_row_dx_fp*\l__atableau_box_wd_fp}
\fp_set:Nn \l__atableau_yb_fp {\l__atableau_yl_fp+\l__atableau_tab_row_dy_fp*\l__atableau_box_ht_fp}
\tl_put_right:Nx \l__atableau_ribbon_path_tl { --(\fp_use:N\l__atableau_xb_fp,\fp_use:N\l__atableau_yb_fp) }
}
% usage: \__atableau_save_ribbon_head:nnnn {path/ribbon} [style] {row index} {col index}
% save the style, row and column indices for the head of the ribbon
% and then compute the coordinates of the three "external nodes" in the
% head.
\cs_new_protected:Npn \__atableau_save_ribbon_head:nnn [#1] #2 #3
{
% check for syntax errors to prevent an endless loop
\quark_if_recursion_tail_stop_do:nn {#2} { \msg_error:nnn {aTableau} {invalid-ribbon-head} {no~x-coordinate~given} }
\quark_if_recursion_tail_stop_do:nn {#3} { \msg_error:nnn {aTableau} {invalid-ribbon-head} {no~y-coordinate~given} }
% save any style
\seq_put_right:Nx \l__atableau_styles_seq {#1}
% record the row and column indices of the head
\int_set:No \l__atableau_row_int { \int_eval:n {#2-1} }
\int_set:No \l__atableau_col_int { \int_eval:n {#3-1} }
\seq_put_right:NV \l__atableau_rcs_seq \l__atableau_row_int
\seq_put_right:NV \l__atableau_rcs_seq \l__atableau_col_int
% update the shape to include the head node (#3,#4)
\__atableau_update_shape:
% add initial coordinates to \l__atableau_ribbon_path_tl
\__atableau_set_box_coordinates:nVV {l} \l__atableau_row_int \l__atableau_col_int
% initialise the start of the path/ribbon
\use:c {__atableau_initialise_ \l__atableau_ribbon_type_tl _head:}
%\message{row=\int_use:N\l__atableau_row_int,~col=\int_use:N\l__atableau_col_int}
\__atableau_peek_ribbon_text:w
}
% usage: \__atableau_peek_ribbon_text:nw {path/ribbon}
% peek for subscripted text _{text} in the ribbon
\cs_new_protected:Npn \__atableau_peek_ribbon_text:w
{
\peek_remove_spaces:n { % ignore spaces
\peek_charcode_remove:NTF _
{ \__atableau_save_ribbon_text:n }
{
\seq_put_right:Nn \l__atableau_texts_seq {} % empty text
\__atableau_peek_style:nw {save_ribbon:nn}
}
}
}
% usage: \__atableau_save_ribbon_text:n {text}
% save any text for a rode in the ribbon in \l__atableau_texts_seq
\cs_new_protected:Npn \__atableau_save_ribbon_text:n #1
{
\seq_put_right:No \l__atableau_texts_seq {#1}
\__atableau_peek_style:nw {save_ribbon:nn}
}
% usage: \__atableau_add_to_ribbon:n
% Extend a ribbon path. Here #1 is either r or c
\cs_new_protected:Npn \__atableau_extend_ribbon:n #1
{
\str_case:enF {#1}
{
{c} { % move back one column
\int_decr:N \l__atableau_col_int
% Move (xa,ya) back one column add it to the ribbon on the left
\fp_sub:Nn \l__atableau_xa_fp {\l__atableau_tab_col_dx_fp*\l__atableau_box_wd_fp}
\fp_sub:Nn \l__atableau_ya_fp {\l__atableau_tab_col_dy_fp*\l__atableau_box_ht_fp}
\tl_put_left:Nx \l__atableau_ribbon_path_tl { (\fp_use:N\l__atableau_xa_fp,\fp_use:N\l__atableau_ya_fp)-- }
% Move (xb,xb) back one column add it to the ribbon on the right
\fp_sub:Nn \l__atableau_xb_fp {\l__atableau_tab_col_dx_fp*\l__atableau_box_wd_fp}
\fp_sub:Nn \l__atableau_yb_fp {\l__atableau_tab_col_dy_fp*\l__atableau_box_ht_fp}
\tl_put_right:Nx \l__atableau_ribbon_path_tl { --(\fp_use:N\l__atableau_xb_fp,\fp_use:N\l__atableau_yb_fp) }
}
{r} { % move forward one row
\int_incr:N \l__atableau_row_int
% Move (xa,ya) forward one row add it to the ribbon on the left
\fp_add:Nn \l__atableau_xa_fp {\l__atableau_tab_row_dx_fp*\l__atableau_box_wd_fp}
\fp_add:Nn \l__atableau_ya_fp {\l__atableau_tab_row_dy_fp*\l__atableau_box_ht_fp}
\tl_put_left:Nx \l__atableau_ribbon_path_tl { (\fp_use:N\l__atableau_xa_fp,\fp_use:N\l__atableau_ya_fp)-- }
% Move (xb,xb) forward one row add it to the ribbon on the right
\fp_add:Nn \l__atableau_xb_fp {\l__atableau_tab_row_dx_fp*\l__atableau_box_wd_fp}
\fp_add:Nn \l__atableau_yb_fp {\l__atableau_tab_row_dy_fp*\l__atableau_box_ht_fp}
\tl_put_right:Nx \l__atableau_ribbon_path_tl { --(\fp_use:N\l__atableau_xb_fp,\fp_use:N\l__atableau_yb_fp) }
}
}
{
\msg_error:nnx {aTableau} {invalid-ribbon-specification} {#1}
}
}
% usage: \__atableau_add_to_path:n
% Extend a ribbon path. Here #1 is either r or c
\cs_new_protected:Npn \__atableau_extend_path:n #1
{
% the ribbon hasn't finished, so move row and col according to the ribbon
% specification and update the nodes (xa,ya) and (xb,yb) in the ribbon
\str_case:enF {#1}
{
{c} { % move back one column
\int_decr:N \l__atableau_col_int
\fp_sub:Nn \l__atableau_xl_fp {\l__atableau_tab_col_dx_fp*\l__atableau_box_wd_fp}
\fp_sub:Nn \l__atableau_yl_fp {\l__atableau_tab_col_dy_fp*\l__atableau_box_ht_fp}
\tl_put_right:Nx \l__atableau_ribbon_path_tl
{
--(\fp_use:N\l__atableau_xl_fp,\fp_use:N\l__atableau_yl_fp)
node[aTableau/pathBox,\l__atableau_ribbon_style_tl]{\__atableau_entry:n{\l__atableau_path_box_tl}}
}
}
{r} { % move forward one row
\int_incr:N \l__atableau_row_int
\fp_add:Nn \l__atableau_xl_fp {\l__atableau_tab_row_dx_fp*\l__atableau_box_wd_fp}
\fp_add:Nn \l__atableau_yl_fp {\l__atableau_tab_row_dy_fp*\l__atableau_box_ht_fp}
\tl_put_right:Nx \l__atableau_ribbon_path_tl
{
--(\fp_use:N\l__atableau_xl_fp,\fp_use:N\l__atableau_yl_fp)
node[aTableau/pathBox,\l__atableau_ribbon_style_tl]{\__atableau_entry:n{\l__atableau_path_box_tl}}
}
}
}
{
\msg_error:nnx {aTableau} {invalid-ribbon-specification} {#1}
}
}
% For each successive r and c in the ribbon specification, determine the
% surrpouding coordinates in the ribbon and save any custom styles in
% \l__atableau_styles_seq and then repeat
\cs_new_protected:Npn \__atableau_save_ribbon:nn [#1] #2
{
% draw the ribbon when we run out of nodes
\quark_if_recursion_tail_stop_do:nn {#2} { \__atableau_draw_ribbon: }
% Add the new coordinate(s) to \l__atableau_ribbon_path_tl. This is
% different for ribbons and paths
\use:c {__atableau_extend_ \l__atableau_ribbon_type_tl :n} {#2}
% update the shape to include the new node
\__atableau_update_shape:
% save the style and row and column indices
\seq_put_right:No \l__atableau_styles_seq {#1} % record the style of the head
\seq_put_right:NV \l__atableau_rcs_seq \l__atableau_row_int % record the row of the node
\seq_put_right:NV \l__atableau_rcs_seq \l__atableau_col_int % record the column of the node
% check to see if this node has any text
\__atableau_peek_ribbon_text:w
}
% update the shape of the ribbon tableau using the current values of
% \l__atableau_row_int and \l__atableau_col_int
\cs_new_protected:Nn \__atableau_update_ribbon_tableau_shape:
{
% ensure that \l__atableau_shape_seq has at least a 0 in each row
\int_step_inline:nn { \l__atableau_row_int+1 - \seq_count:N \l__atableau_shape_seq }
{
\seq_put_right:Nn \l__atableau_shape_seq {0}
}
% for shifted tableaux we also need to ensure that skew is big enough
\bool_if:NT \l__atableau_shifted_bool
{
\int_set:Nn \l_tmpa_int {\seq_count:N \l__atableau_skew_seq}
\int_step_inline:nn { \l__atableau_row_int+1 - \l_tmpa_int }
{
\seq_put_right:Nx \l__atableau_skew_seq {\int_eval:n{\l_tmpa_int+##1-1 }}
}
}
\int_compare:nNnT {0\seq_item:Nn \l__atableau_shape_seq {\l__atableau_row_int+1}} < {\l__atableau_col_int+1}
{
\seq_set_item:Nox \l__atableau_shape_seq {\l__atableau_row_int+1} { \int_eval:n{\l__atableau_col_int+1} }
}
}
% usage: \__atableau_finalise_ribbon:n
% Add the final node to the ribbon
\cs_new_protected:Nn \__atableau_finalise_ribbon:
{
% Add the last node to the ribbon
\fp_add:Nn \l__atableau_xa_fp {\l__atableau_tab_row_dx_fp*\l__atableau_box_wd_fp}
\fp_add:Nn \l__atableau_ya_fp {\l__atableau_tab_row_dy_fp*\l__atableau_box_ht_fp}
\tl_put_left:Nx \l__atableau_ribbon_path_tl { (\fp_use:N\l__atableau_xa_fp, \fp_use:N\l__atableau_ya_fp)-- }
% add a closing cycle
\tl_put_right:Nn \l__atableau_ribbon_path_tl {--cycle}
}
% usage: \__atableau_finalise_path:n
% We do not need to do anything to finalise a path
\cs_set_eq:NN \__atableau_finalise_path:n \prg_do_nothing:
% by default, snobs have the same styles and coordinates as ribbons
\cs_set_eq:NN \__atableau_extend_snob:n \__atableau_extend_ribbon:n
\cs_set_eq:NN \__atableau_finalise_snob: \__atableau_finalise_ribbon:
\cs_set_eq:NN \__atableau_initialise_snob_head: \__atableau_initialise_ribbon_head:
% \__atableau_draw_ribbon: use the various sequences we have constructed
% to draw the ribbon. We first place the nodes with default styling and
% no text, then draw the ribbon with its supplied style and then,
% finally, add the nodes with custom styling or text.
\cs_new_protected:Nn \__atableau_draw_ribbon:
{
\use:c { __atableau_finalise_ \l__atableau_ribbon_type_tl :}
% We want to first draw the ribbon, with its outline and any filling, and
% then place the node with the default styling (or unstyled), and styled
% nodes in the ribbon. To do this we build the two token lists
% \l__atableau_unstyled_nodes_tl and \l__atableau_styled_nodes_tl for these
% two types of nodes
\tl_clear:N \l__atableau_styled_nodes_tl
\tl_clear:N \l__atableau_unstyled_nodes_tl
% We need to add ribbon_node to every box in a ribbon, so we do the
% check here rather than in \seq_map_inline:Nn
\tl_if_eq:VnTF \l__atableau_ribbon_type_tl {path}
{ \tl_clear:N \l_tmpc_tl }
{ \tl_set_eq:Nc \l_tmpc_tl { l__atableau_ \l__atableau_ribbon_type_tl _box_tl } }
\seq_map_inline:Nn \l__atableau_styles_seq
{
% pop the text and row and column indices
\seq_pop_left:NN \l__atableau_texts_seq \l_tmpa_tl % text
\seq_pop_left:NN \l__atableau_rcs_seq \l_tmpb_tl % row index
\int_set:Nn \l__atableau_row_int {\l_tmpb_tl}
\seq_pop_left:NN \l__atableau_rcs_seq \l_tmpb_tl % column index
\int_set:Nn \l__atableau_col_int {\l_tmpb_tl}
% compute the box coordinates
\__atableau_set_box_coordinates:nVV {l} \l__atableau_row_int \l__atableau_col_int
\tl_if_empty:eTF {##1\l_tmpa_tl}
{ % nodes with default style and no text are added to \l__atableau_unstyled_nodes_tl
\tl_put_right:Nx \l__atableau_unstyled_nodes_tl
{
\exp_not:N \node [aTableau/\l__atableau_ribbon_type_tl Box](\l__atableau_name_tl)
at (\fp_use:N\l__atableau_xl_fp,\fp_use:N\l__atableau_yl_fp)
{ \exp_not:N \__atableau_entry:n{\l_tmpc_tl }};
}
}
{ % nodes with styling are added to \l__atableau_styled_nodes_tl
\tl_put_right:Nx \l__atableau_styled_nodes_tl
{
\exp_not:N \node [aTableau/\l__atableau_ribbon_type_tl Box,##1](\l__atableau_name_tl)
at (\fp_use:N\l__atableau_xl_fp,\fp_use:N\l__atableau_yl_fp)
{\exp_not:N \__atableau_entry:n{\l_tmpa_tl}};
}
}
}
% draw the ribbon, applying any style
\exp_last_unbraced:Ne\draw { [aTableau/\l__atableau_ribbon_type_tl Style,\l__atableau_ribbon_style_tl] } \l__atableau_ribbon_path_tl;
% finally, add the unstyled and the styled nodes on top of the ribbon
\l__atableau_unstyled_nodes_tl
\l__atableau_styled_nodes_tl
}
% ---------------------------------------------------------------------------
% abacuses
% usage: \__atableau_draw_abacus_end:nnn {abacus_top/abacus_bottom} % {0/row index} {±1}
% Draw the top/bottom on gthe abacus. Here #1 is either
% \l__atableau_abacus_top_tl or \l__atableau_abacus_bottom_tl and #2 is
% either 0, for top, or the row index of the last row, for bottom
\cs_new_protected:Npn \__atableau_draw_abacus_end:nnn #1 #2 #3
{
\str_case:Vn #1
{
{-}
{ % draw a line
\__atableau_set_bead_coordinates:non {a} {#2} {0}
\__atableau_set_bead_coordinates:noo {b} {#2} { \int_eval:n {\l__atableau_cols_int-1} }
\draw[aTableau/abacusEnds]
(\fp_eval:n{\l__atableau_xa_fp-\l__atableau_ab_col_dx_fp*\l__atableau_abacus_wd_fp/2},
\fp_eval:n{\l__atableau_ya_fp-\l__atableau_ab_col_dy_fp*\l__atableau_abacus_ht_fp/2})
-- (\fp_eval:n{\l__atableau_xb_fp+\l__atableau_ab_col_dx_fp*\l__atableau_abacus_wd_fp/2},
\fp_eval:n{\l__atableau_yb_fp+\l__atableau_ab_col_dy_fp*\l__atableau_abacus_ht_fp/2});
% set default "row height" of the runner labels for use below
\fp_set:Nn \l_tmpa_fp {-0.4}
}
{_}
{ % draw a line
\__atableau_set_bead_coordinates:non {a} {#2} {0}
\__atableau_set_bead_coordinates:noo {b} {#2} { \int_eval:n {\l__atableau_cols_int-1} }
\draw[aTableau/abacusEnds] (\fp_use:N\l__atableau_xa_fp, \fp_use:N\l__atableau_ya_fp)
-- (\fp_use:N\l__atableau_xb_fp, \fp_use:N\l__atableau_yb_fp);
% set default "row height" of the runner labels for use below
\fp_set:Nn \l_tmpa_fp {-0.4}
}
{.}
{ % draw dots
\int_step_inline:nn {\l__atableau_cols_int}
{
\seq_if_in:NeF \l__atableau_dotted_cols_seq { \int_eval:n{##1-1} }
{
% draw the abacus runners from (xa,ya) to (xb,yb)
\__atableau_set_bead_coordinates:noo {a} { #2 } { \int_eval:n{##1-1} }
\__atableau_set_bead_coordinates:noo {b} { #3 } { \int_eval:n{##1-1} }
\draw[aTableau/abacusEnds, dotted] (\fp_use:N\l__atableau_xa_fp,\fp_use:N\l__atableau_ya_fp)--(\fp_use:N\l__atableau_xb_fp,\fp_use:N\l__atableau_yb_fp);
}
}
% set default "row height" of the runner labels for use below
\fp_set:Nn \l_tmpa_fp {-1.4}
}
{>}
{ % draw dots
\int_step_inline:nn {\l__atableau_cols_int}
{
\seq_if_in:NeF \l__atableau_dotted_cols_seq { \int_eval:n{##1-1} }
{
% draw the abacus runners from (xa,ya) to (xb,yb)
\int_compare:nNnTF {#2} = {0}
{
\__atableau_set_bead_coordinates:noo {a} { \fp_eval:n{#2+0.5} } { \fp_eval:n{##1-1} }
\__atableau_set_bead_coordinates:noo {b} { \fp_eval:n{#3+0.5} } { \fp_eval:n{##1-1} }
}
{
\__atableau_set_bead_coordinates:noo {a} { \fp_eval:n{#2-0.5} } { \fp_eval:n{##1-1} }
\__atableau_set_bead_coordinates:noo {b} { \fp_eval:n{#3-0.5} } { \fp_eval:n{##1-1} }
}
\draw[aTableau/abacusEnds,->] (\fp_use:N\l__atableau_xa_fp,\fp_use:N\l__atableau_ya_fp)--(\fp_use:N\l__atableau_xb_fp,\fp_use:N\l__atableau_yb_fp);
}
}
% set default "row height" of the runner labels for use below
\fp_set:Nn \l_tmpa_fp {-0.8}
}
{*}
{ % draw dots
\int_step_inline:nn {\l__atableau_cols_int}
{
\seq_if_in:NeF \l__atableau_dotted_cols_seq { \int_eval:n{##1-1} }
{
% draw the abacus runners from (xa,ya) to (xb,yb)
\int_compare:nNnTF {#2} = {0}
{
\__atableau_set_bead_coordinates:noo {a} { \fp_eval:n{#2} } { \fp_eval:n{##1-1} }
\__atableau_set_bead_coordinates:noo {b} { \fp_eval:n{#3-0.5} } { \fp_eval:n{##1-1} }
}
{
\__atableau_set_bead_coordinates:noo {a} { \fp_eval:n{#2} } { \fp_eval:n{##1-1} }
\__atableau_set_bead_coordinates:noo {b} { \fp_eval:n{#3+0.5} } { \fp_eval:n{##1-1} }
}
\draw[aTableau/abacusEnds,dotted,->] (\fp_use:N\l__atableau_xa_fp,\fp_use:N\l__atableau_ya_fp)--(\fp_use:N\l__atableau_xb_fp,\fp_use:N\l__atableau_yb_fp);
}
}
% set default "row height" of the runner labels for use below
\fp_set:Nn \l_tmpa_fp {-1.8}
}
{|} {
% set default "row height" of the runner labels for use below
\fp_set:Nn \l_tmpa_fp {-0.4}
}
}
}
% usage: \__atableau_abacus:nn { #runners } { bead specifications }
\cs_new_protected:Npn \__atableau_abacus:nn #1 #2
{
% set the star style
\tl_set:Nn \l__atableau_starstyle_tl {aTableau/abacusStarStyle}
\int_set:Nn \l__atableau_cols_int {#1}
\seq_if_empty:NF \l__atableau_runner_labels_seq
{
\int_set:No \l_tmpa_int { \seq_count:N \l__atableau_runner_labels_seq }
\int_compare:nNnF {\l__atableau_cols_int-\l_tmpa_int } = {0}
{
\msg_error:nn {aTableau} {missing-runner-labels }
}
}
% Extract the bead positions and their styles into
% \l__atableau_shape_seq, \l__atableau_styles_seq and \l__atableau_text_tl
% We allow all of the following expressions
% m, m^r, [style]m, [style]m^2, *m, *m^2,
% m_text, m_text^r, [style]m_text, [style]m_text^2, *m_text, *m_text^2,
% m_text^r, [style]m_text^2, *m_text^2
% where m is a part of the partition \l__atableau_shape_seq and r is
% its' exponent. First, clear all of the sequences and zero the bead
% counter
\seq_clear:N \l__atableau_shape_seq % will record the partition
\seq_clear:N \l__atableau_styles_seq % will record the bead style
\seq_clear:N \l__atableau_texts_seq % will record the bead text
\int_zero:N \l__atableau_beads_int % will record the number of beads
% determine the partition/beta numbers
\clist_map_inline:nn {#2}
{
\__atableau_peek_style:nw {record_style:nn} ##1 \q_recursion_tail \q_recursion_stop
}
% unless they have been set, determine the number of abacus rows
\int_compare:nNnT {\l__atableau_rows_int} = {0}
{
\bool_if:NTF \l__atableau_beta_numbers_bool
{ \int_set:Nn \l__atableau_rows_int { 1+\int_div_truncate:nn { 0\seq_item:Nn \l__atableau_shape_seq 1} {#1} } }
{ \int_set:Nn \l__atableau_rows_int { 1+\int_div_truncate:nn {\l__atableau_beads_int-1 + 0\seq_item:Nn \l__atableau_shape_seq 1} {#1} } }
}
% draw the abacus runners
\int_zero:N \l__atableau_col_int
\int_step_inline:nn {\l__atableau_cols_int}
{
\int_set:Nn \l_tmpa_int {##1-1} % save recalculating this many times
% skip the runners in dotted_cols_seq
\seq_if_in:NVF \l__atableau_dotted_cols_seq \l_tmpa_int
{
% draw the abacus runners from (xa,ya) to (xb,yb)
\__atableau_set_bead_coordinates:nnV {a} { 0 } \l_tmpa_int
\__atableau_set_bead_coordinates:noV {b} { \int_eval:n{\l__atableau_rows_int+1} } \l_tmpa_int
\draw[aTableau/runnerStyle] (\fp_use:N\l__atableau_xa_fp,\fp_use:N\l__atableau_ya_fp)--(\fp_use:N\l__atableau_xb_fp,\fp_use:N\l__atableau_yb_fp);
% draw ticks
\int_step_inline:nn {\l__atableau_rows_int}
{
\__atableau_set_bead_coordinates:noV {l} { ####1 } \l_tmpa_int
% add a named node
\node[aTableau/namedTick] (\l__atableau_name_tl) at (\fp_use:N\l__atableau_xl_fp,\fp_use:N\l__atableau_yl_fp){};
% add and subtract (half) tick width
\fp_set:Nn \l__atableau_xa_fp {\l__atableau_xl_fp+\l__atableau_tick_length_fp*\l__atableau_ab_col_dx_fp}
\fp_set:Nn \l__atableau_ya_fp {\l__atableau_yl_fp+\l__atableau_tick_length_fp*\l__atableau_ab_col_dy_fp}
\fp_set:Nn \l__atableau_xb_fp {\l__atableau_xl_fp-\l__atableau_tick_length_fp*\l__atableau_ab_col_dx_fp}
\fp_set:Nn \l__atableau_yb_fp {\l__atableau_yl_fp-\l__atableau_tick_length_fp*\l__atableau_ab_col_dy_fp}
\draw[aTableau/tickStyle,name=\l__atableau_name_tl] (\fp_use:N\l__atableau_xa_fp,\fp_use:N\l__atableau_ya_fp)--(\fp_use:N\l__atableau_xb_fp,\fp_use:N\l__atableau_yb_fp);
}
}
}
% set e when entries=residues
\tl_if_eq:VnT \l__atableau_show_tl {residues}
{
% if it is not set already, then set e based on the number of runners and the Cartan type
\int_compare:nNnT {\l__atableau_e_int} = {0}
{
\str_case:Vn \l__atableau_cartan_tl
{
{A } { \int_set_eq:NN \l__atableau_e_int \l__atableau_cols_int }
{C } { \int_set:Nn \l__atableau_e_int {\l__atableau_cols_int/2} }
{AA} { \int_set:Nn \l__atableau_e_int {(\l__atableau_cols_int-1)/2} }
{DD} { \int_set:Nn \l__atableau_e_int {\l__atableau_cols_int/2-1} }
}
}
}
% draw the beads on the abacus
\int_step_inline:nn { \l__atableau_beads_int } % finally, add the beads, with labels and styles
{
% determine the row and column indices for the bead
\bool_if:NTF \l__atableau_beta_numbers_bool
{
\int_set:No \l_tmpa_int { \seq_item:Nn \l__atableau_shape_seq {##1} } % beta number
}
{
\int_set:No \l_tmpa_int { \l__atableau_beads_int - ##1 + \seq_item:Nn \l__atableau_shape_seq {##1} } % part -> beta number
}
\int_set:Nn \l__atableau_row_int { \int_div_truncate:nn {\l_tmpa_int} {\l__atableau_cols_int} }
\int_set:Nn \l__atableau_col_int { \int_mod:nn {\l_tmpa_int} {\l__atableau_cols_int} }
% determine the bead coordinates: push everything 0.5 of a
% unit down to allow space of the top of the abacus
\__atableau_set_bead_coordinates:noV {l} {\int_eval:n{\l__atableau_row_int+1} } \l__atableau_col_int
\seq_if_in:NVF \l__atableau_dotted_rows_seq \l__atableau_row_int
{
\seq_if_in:NVF \l__atableau_dotted_cols_seq \l__atableau_col_int
{
\str_case:VnF \l__atableau_show_tl
{
{betas} { \tl_set:No \l_tmpa_tl { \int_use:N\l_tmpa_int } }
{residues} {
\int_set:Nn \l_tmpb_int { \l__atableau_charge_int+\l_tmpa_int-\l__atableau_beads_int }
\tl_set:No \l_tmpa_tl { \__atableau_residue:nn {\l_tmpb_int} {\l__atableau_e_int} }
}
{rows } {
\int_set:Nn \l_tmpb_int { \l_tmpa_int-\l__atableau_beads_int+##1 }
\int_compare:nNnTF {\l_tmpb_int} > {0}
{ \tl_set:No \l_tmpa_tl { ##1 } }
{ \tl_set:No \l_tmpa_tl { {-} } }
}
{shape} { \tl_set:No \l_tmpa_tl { \seq_item:Nn \l__atableau_shape_seq {##1} } }
{} { \tl_set:No \l_tmpa_tl { \seq_item:Nn \l__atableau_texts_seq {##1} } }
}
{
\msg_error:nnx {aTableau} {unrecognised-abacus-label} { \l__atableau_show_tl }
}
% draw the bead with style
\tl_set:No \l_tmpb_tl { \seq_item:Nn \l__atableau_styles_seq {##1} }
\exp_last_unbraced:Nx \node{[aTableau/beadStyle, \l_tmpb_tl]}
at (\fp_use:N\l__atableau_xl_fp,\fp_use:N\l__atableau_yl_fp){\__atableau_entry:x {\l_tmpa_tl}};
}
}
}
% draw the top ends of the abacus -- and set \l_tmpa_fp for the runner labels
\__atableau_draw_abacus_end:nnn \l__atableau_abacus_top_tl {0} {-1}
\int_zero:N \l__atableau_c_int
% add the runner labels using the "row height" \l_tmpa_fp
\int_zero:N \l__atableau_c_int
\seq_map_inline:Nn \l__atableau_runner_labels_seq
{
\__atableau_set_bead_coordinates:nVV {a} \l_tmpa_fp \l__atableau_c_int
\seq_if_in:NVF \l__atableau_dotted_cols_seq \l__atableau_c_int
{
\node[aTableau/runnerLabelStyle] at (\fp_use:N\l__atableau_xa_fp,\fp_use:N\l__atableau_ya_fp){ \__atableau_entry:n{##1} };
}
\int_incr:N \l__atableau_c_int
}
% draw the bottom ends of the abacus
\__atableau_draw_abacus_end:noo \l__atableau_abacus_bottom_tl {\int_eval:n {\l__atableau_rows_int+1}} {\int_eval:n {\l__atableau_rows_int+2}}
% remove dotted rows and columns
\seq_if_empty:NF \l__atableau_dotted_rows_seq \__atableau_remove_dotted_abacus_rows:
\seq_if_empty:NF \l__atableau_dotted_cols_seq \__atableau_remove_dotted_abacus_cols:
}
% usage: \__atableau_remove_dotted_abacus_cols:
% Add dots to the columns of the abacus in \l__atableau_dotted_cols_seq
\cs_new_protected:Nn \__atableau_remove_dotted_abacus_cols:
{
% shift in row-direction
\fp_set:Nn \l_tmpa_fp {\l__atableau_ab_row_dx_fp*\l__atableau_abacus_wd_fp}
\fp_set:Nn \l_tmpb_fp {\l__atableau_ab_row_dy_fp*\l__atableau_abacus_ht_fp}
% take a copy of \l__atableau_dotted_cols_seq so that the pop_left's below
% do not destroy it
\seq_set_eq:NN \l_tmpb_seq \l__atableau_dotted_cols_seq
\bool_do_until:nn { \seq_if_empty_p:N \l_tmpb_seq }
{
\seq_pop_left:NN \l_tmpb_seq \l_tmpa_tl
\int_set:Nn \l__atableau_col_int {\l_tmpa_tl}
\int_set:Nn \l__atableau_c_int {\l__atableau_col_int+1}
% LaTeX3 does not provide \seq_if_in_p:NN, so ...
\bool_set_true:N \l_tmpa_bool
\bool_do_while:nn { \l_tmpa_bool }
{
\int_set:Nn \l_tmpa_int {0\seq_item:Nn \l_tmpb_seq 1}
\int_compare:nNnTF {\l__atableau_c_int} = {\l_tmpa_int}
{
\seq_pop_left:NN \l_tmpb_seq \l_tmpa_tl
\int_incr:N \l__atableau_c_int
}
{ \bool_set_false:N \l_tmpa_bool }
}
\__atableau_set_bead_coordinates:nnV {l} { 0 } \l__atableau_col_int
% set (xa,ya) and (xb,yb) to the "left" and "right" hand coordinates that we want remove
\fp_set:Nn \l__atableau_xa_fp {\l__atableau_xl_fp-0.35*\l__atableau_ab_col_dx_fp*\l__atableau_abacus_wd_fp}
\fp_set:Nn \l__atableau_ya_fp {\l__atableau_yl_fp-0.35*\l__atableau_ab_col_dy_fp*\l__atableau_abacus_ht_fp}
\fp_set:Nn \l__atableau_xb_fp {\l__atableau_xl_fp+(\l__atableau_c_int-\l__atableau_col_int-0.65)*\l__atableau_ab_col_dx_fp*\l__atableau_abacus_wd_fp}
\fp_set:Nn \l__atableau_yb_fp {\l__atableau_yl_fp+(\l__atableau_c_int-\l__atableau_col_int-0.65)*\l__atableau_ab_col_dy_fp*\l__atableau_abacus_ht_fp}
% blank out any line at the top of the abacus and replace it with dots
\tl_if_in:nVT {-_} \l__atableau_abacus_top_tl
{
\draw[aTableau/clearBoxes]
(\fp_eval:n{\l__atableau_xa_fp-0.1*\l_tmpa_fp}, \fp_eval:n{\l__atableau_ya_fp-0.1*\l_tmpb_fp})
--++(\fp_eval:n{0.2*\l_tmpa_fp},\fp_eval:n{0.2*\l_tmpb_fp})
--(\fp_eval:n{\l__atableau_xb_fp+0.1*\l_tmpa_fp}, \fp_eval:n{\l__atableau_yb_fp+0.1*\l_tmpb_fp})
--++(\fp_eval:n{-0.2*\l_tmpa_fp},\fp_eval:n{-0.2*\l_tmpb_fp})
--cycle
;
% first blank out the possible header line and replace with dots
%\draw[fill=white,draw=none](\fp_use:N\l__atableau_xa_fp,\fp_use:N\l__atableau_ya_fp)--(\fp_use:N\l__atableau_xb_fp,\fp_use:N\l__atableau_yb_fp);
\draw[aTableau/dottedLine](\fp_use:N\l__atableau_xa_fp,\fp_use:N\l__atableau_ya_fp)--(\fp_use:N\l__atableau_xb_fp,\fp_use:N\l__atableau_yb_fp);
}
% now draw the dots
\int_zero:N \l__atableau_row_int
\int_step_inline:nn {\l__atableau_rows_int}
{
\fp_add:Nn \l__atableau_xa_fp {\l_tmpa_fp}
\fp_add:Nn \l__atableau_ya_fp {\l_tmpb_fp}
\fp_add:Nn \l__atableau_xb_fp {\l_tmpa_fp}
\fp_add:Nn \l__atableau_yb_fp {\l_tmpb_fp}
\draw[aTableau/dottedLine](\fp_use:N\l__atableau_xa_fp,\fp_use:N\l__atableau_ya_fp)--(\fp_use:N\l__atableau_xb_fp,\fp_use:N\l__atableau_yb_fp);
}
% blank out any line at the bottom of the abacus and replace it with dots
\tl_if_in:nVT {-_} \l__atableau_abacus_bottom_tl
{
\fp_add:Nn \l__atableau_xa_fp {\l_tmpa_fp}
\fp_add:Nn \l__atableau_ya_fp {\l_tmpb_fp}
\fp_add:Nn \l__atableau_xb_fp {\l_tmpa_fp}
\fp_add:Nn \l__atableau_yb_fp {\l_tmpb_fp}
\draw[aTableau/clearBoxes]
(\fp_eval:n{\l__atableau_xa_fp-0.1*\l_tmpa_fp}, \fp_eval:n{\l__atableau_ya_fp-0.1*\l_tmpb_fp})
--++(\fp_eval:n{0.2*\l_tmpa_fp},\fp_eval:n{0.2*\l_tmpb_fp})
--(\fp_eval:n{\l__atableau_xb_fp+0.1*\l_tmpa_fp}, \fp_eval:n{\l__atableau_yb_fp+0.1*\l_tmpb_fp})
--++(\fp_eval:n{-0.2*\l_tmpa_fp},\fp_eval:n{-0.2*\l_tmpb_fp})
--cycle
;
% first blank out the possible header line and replace with dots
\draw[aTableau/dottedLine](\fp_use:N\l__atableau_xa_fp,\fp_use:N\l__atableau_ya_fp)--(\fp_use:N\l__atableau_xb_fp,\fp_use:N\l__atableau_yb_fp);
}
}
}
% usage: \__atableau_remove_dotted_abacus_rows:
% Add dots to the rows of the abacus in \l__atableau_dotted_rows_seq
\cs_new_protected:Nn \__atableau_remove_dotted_abacus_rows:
{
% shift in column-direction
\fp_set:Nn \l_tmpa_fp {\l__atableau_ab_col_dx_fp*\l__atableau_abacus_wd_fp}
\fp_set:Nn \l_tmpb_fp {\l__atableau_ab_col_dy_fp*\l__atableau_abacus_ht_fp}
% take a copy of \l__atableau_dotted_rows_seq so that the pop_left's below
% do not destroy it
\seq_set_eq:NN \l_tmpb_seq \l__atableau_dotted_rows_seq
\bool_do_until:nn { \seq_if_empty_p:N \l_tmpb_seq }
{
\seq_pop_left:NN \l_tmpb_seq \l_tmpa_tl
\int_set:Nn \l__atableau_row_int {\l_tmpa_tl}
\int_set:Nn \l__atableau_r_int {\l__atableau_row_int+1}
% LaTeX3 does not provide \seq_if_in_p:NN, so ...
\bool_set_true:N \l_tmpa_bool
\bool_do_while:nn { \l_tmpa_bool }
{
\int_set:Nn \l_tmpa_int {0\seq_item:Nn \l_tmpb_seq 1}
\int_compare:nNnTF {\l__atableau_r_int} = {\l_tmpa_int}
{
\seq_pop_left:NN \l_tmpb_seq \l_tmpa_tl
\int_incr:N \l__atableau_r_int
}
{ \bool_set_false:N \l_tmpa_bool }
}
\__atableau_set_bead_coordinates:non {l} { \int_eval:n{\l__atableau_row_int+1} } { 0 }
% set (xa,ya) and (xb,yb) to the "left" and "right" hand coordinates that we want remove
\fp_set:Nn \l__atableau_xa_fp {\l__atableau_xl_fp-0.35*\l__atableau_ab_row_dx_fp*\l__atableau_abacus_wd_fp}
\fp_set:Nn \l__atableau_ya_fp {\l__atableau_yl_fp-0.35*\l__atableau_ab_row_dy_fp*\l__atableau_abacus_ht_fp}
\fp_set:Nn \l__atableau_xb_fp {\l__atableau_xl_fp+(\l__atableau_r_int-\l__atableau_row_int-0.65)*\l__atableau_ab_row_dx_fp*\l__atableau_abacus_wd_fp}
\fp_set:Nn \l__atableau_yb_fp {\l__atableau_yl_fp+(\l__atableau_r_int-\l__atableau_row_int-0.65)*\l__atableau_ab_row_dy_fp*\l__atableau_abacus_ht_fp}
\draw[aTableau/clearBoxes]
(\fp_eval:n{\l__atableau_xa_fp-0.12*\l_tmpa_fp}, \fp_eval:n{\l__atableau_ya_fp-0.12*\l_tmpb_fp})
--++(\fp_eval:n{(\l__atableau_cols_int+0.24)*\l_tmpa_fp},\fp_eval:n{(\l__atableau_cols_int+0.24)*\l_tmpb_fp})
--(\fp_eval:n{\l__atableau_xb_fp+(\l__atableau_cols_int+0.12)*\l_tmpa_fp}, \fp_eval:n{\l__atableau_yb_fp+(\l__atableau_cols_int+0.12)*\l_tmpb_fp})
--(\fp_eval:n{\l__atableau_xb_fp-0.12*\l_tmpa_fp}, \fp_eval:n{\l__atableau_yb_fp-0.12*\l_tmpb_fp})
--cycle
;
% first blank out the possible header line and replace with dots
\draw[aTableau/dottedLine](\fp_use:N\l__atableau_xa_fp,\fp_use:N\l__atableau_ya_fp)--(\fp_use:N\l__atableau_xb_fp,\fp_use:N\l__atableau_yb_fp);
% now draw the dots
\int_step_inline:nnn {2} {\l__atableau_cols_int}
{
\fp_add:Nn \l__atableau_xa_fp {\l_tmpa_fp}
\fp_add:Nn \l__atableau_ya_fp {\l_tmpb_fp}
\fp_add:Nn \l__atableau_xb_fp {\l_tmpa_fp}
\fp_add:Nn \l__atableau_yb_fp {\l_tmpb_fp}
\draw[aTableau/dottedLine](\fp_use:N\l__atableau_xa_fp,\fp_use:N\l__atableau_ya_fp)--(\fp_use:N\l__atableau_xb_fp,\fp_use:N\l__atableau_yb_fp);
}
}
}
% ---------------------------------------------------------------------------
% Keys for the package options and their defaults
% setting TikZ styles via styles = { ... }
\cs_new_protected:Npn \__atableau_tikzset:nn #1 #2 { \pgfqkeys{/tikz}{#1/.style={#2}} }
% appending to aTableau styles
\cs_new_protected:Npn \__atableau_tikzset_append:nn #1 #2 { \pgfqkeys{/tikz/aTableau}{#1/.append~style={#2}} }
% aTableau options/keys
\keys_define:nn { atableau }
{
% ---------------------------------------------------------------------------
% general settings
% tableaux alignment
align .choice:,
align/top .code:n = { \tikzset{baseline=(current~bounding~box.north)} },
align/north .code:n = { \tikzset{baseline=(current~bounding~box.north)} },
align/center .code:n = { \tikzset{baseline=(current~bounding~box.center)}},
align/centre .code:n = { \tikzset{baseline=(current~bounding~box.center)}},
align/bottom .code:n = { \tikzset{baseline=(current~bounding~box.south)} },
align/south .code:n = { \tikzset{baseline=(current~bounding~box.south)} },
align .unknown .code:n = { \msg_error:nnn { aTableau } { unknown-baseline } {#1} },
align .initial:n = centre,
% set the Cartan type
cartan .choices:nn = { A, C, AA, DD }
{
% record the Cartan type for use in abacuses
\tl_set:Nn \l__atableau_cartan_tl {#1}
% define all of the type dependent functions here...
\cs_set_eq:Nc \__atableau_residue:nn {__atableau_residue_#1:nn}
},
cartan/unknown .code:n = { \msg_error:nne { aTableau } { unknown-cartan } {#1} },
cartan .initial:n = A,
charge .code:n =
{
% To cater for multipartitions, the charge is a sequence .
% Set l__atableau_charge_int is the first item in the sequence
\regex_split:nnN {[,\|]} {#1} \l__atableau_charge_seq
\int_set:Nn \l__atableau_charge_int { \seq_item:Nn \l__atableau_charge_seq {1} }
},
charge .value_required:n = true,
charge .initial:n = 0,
% dotted rows and columns for tableaux and abacuses
dotted~cols .code:n = { \__atableau_set_multiseq_key:nn {dotted_cols} {#1} },
dotted~cols .value_required:n = true,
dotted~rows .code:n = { \__atableau_set_multiseq_key:nn {dotted_rows} {#1} },
dotted~rows .value_required:n = true,
e .int_set:N = \l__atableau_e_int,
e .initial:n = 0,
entries .tl_set:N = \l__atableau_show_tl, % automatic bead labelling
entries .value_required:n = false,
entries .initial:n = ,
halign .choice:,
halign/center .code = {\cs_set_eq:NN \__atableau_halign:n \hbox_overlap_center:n},
halign/centre .code = {\cs_set_eq:NN \__atableau_halign:n \hbox_overlap_center:n},
halign/left .code = {\cs_set_eq:NN \__atableau_halign:n \hbox_overlap_left:n},
halign/right .code = {\cs_set_eq:NN \__atableau_halign:n \hbox_overlap_right:n},
halign .unknown .code:n = { \msg_error:nne { aTableau } { unknown-halign } {#1} },
halign .initial:n = centre,
% math/text mode for boxes and beads
math~entries .code:n = { \cs_set_eq:NN \__atableau_entry:n \__atableau_entry_math:n },
text~entries .code:n = { \cs_set_eq:NN \__atableau_entry:n \__atableau_entry_text:n },
% tableau node name prefix
name .tl_set:N = \l__atableau_prefix_tl,
name .value_required:n = true,
name .initial:n = A,
% scaling
scale .code:n = { \__atableau_set_xscale:n {#1} \__atableau_set_yscale:n {#1} },
scale .value_required:n = true,
% subscript an subsubscript scalinmg
script .fp_set:N = \l__atableau_script_fp,
script .value_required:n = true,
script .initial:n = 0.5,
scriptscript .fp_set:N = \l__atableau_scriptscript_fp,
scriptscript .value_required:n = true,
scriptscript .initial:n = 0.4,
star~style .code:n = { \__atableau_tikzset_append:nn {tableauStarStyle} {#1} },
star~style .value_required:n = true,
% shortcut for setting TikZ styles, following a suggestion of Skillmon to use \keyval_parse:nnn
styles .code:n =
{ \keyval_parse:nnn { \msg_error:nnn {aTableau}{missing-style} } { \__atableau_tikzset:nn } { #1 } },
% tikzpicture environment
tikzpicture .tl_set:N= \l__atableau_tikzpicture_tl,
tikzpicture .value_required:n = true,
tikzpicture .initial:n =,
% tikz code after
tikz~after .tl_set:N = \l__atableau_tikz_after_tl,
tikz~after .value_required:n = true,
tikz~after .initial:n = ,
% tikz~ code before
tikz~before .tl_set:N = \l__atableau_tikz_before_tl,
tikz~before .value_required:n = true,
tikz~before .initial:n = ,
valign .choices:nn = { bottom, center, centre, top }
{
\cs_set_eq:Nc \__atableau_valign:n { __atableau_valign_#1:n }
},
valign .unknown .code:n = { \msg_error:nne { aTableau } { unknown-valign } {#1} },
valign .initial:n = centre,
xscale .code:n = { \__atableau_set_xscale:n {#1} },
xscale .value_required:n = true,
xscale .initial:n =1,
yscale .code:n = { \__atableau_set_yscale:n {#1} },
yscale .value_required:n = true,
yscale .initial:n =1,
% ---------------------------------------------------------------------------
% tableau settings
% convention switches
Australian .code:n = \__atableau_set_style:nn {tableau} {australian},
australian .code:n = \__atableau_set_style:nn {tableau} {australian},
australian .value_required:n = false,
English .code:n = \__atableau_set_style:nn {tableau} {english},
english .code:n = \__atableau_set_style:nn {tableau} {english},
english .value_required:n = false,
english .initial:n =, % default style
French .code:n = \__atableau_set_style:nn {tableau} {french},
french .code:n = \__atableau_set_style:nn {tableau} {french},
french .value_required:n = false,
ukrainian .code:n = \__atableau_set_style:nn {tableau} {ukrainian},
Ukrainian .code:n = \__atableau_set_style:nn {tableau} {ukrainian},
ukrainian .value_required:n = false,
Russian .code:n = \__atableau_set_style:nn {tableau} {ukrainian},
russian .code:n = \__atableau_set_style:nn {tableau} {ukrainian},
border .bool_set:N = \l__atableau_border_bool,
border .default:n = true,
border .initial:n = true,
no~border .bool_set_inverse:N = \l__atableau_border_bool,
no~border .default:n = true,
% border colours
border~color .tl_set:N = \l__atableau_outer_tl, % an alias
border~color .value_required:n = true,
border~colour .tl_set:N = \l__atableau_outer_tl,
border~colour .value_required:n = true,
border~colour .initial:n = aTableauMain,
border~style .code:n = { \__atableau_tikzset_append:nn {borderStyle} {#1} },
border~style .value_required:n = true,
% node height and width
box~height .fp_set:N = \l__atableau_box_ht_fp,
box~height .value_required:n = true,
box~height .initial:n = 0.5,
box~width .fp_set:N = \l__atableau_box_wd_fp,
box~width .value_required:n = true,
box~width .initial:n = 0.5,
% box styling
box~fill .tl_set:N = \l__atableau_box_fill_tl,
box~fill .value_required:n = true,
box~fill .initial:n = white,
box~font .tl_set:N = \l__atableau_box_font_tl,
box~font .value_required:n = true,
box~font .initial:n =,
box~shape .tl_set:N = \l__atableau_box_shape_tl,
box~shape .value_required:n = true,
box~shape .initial:n = rectangle,
box~text .tl_set:N = \l__atableau_box_text_tl,
box~text .value_required:n = true,
box~text .initial:n = aTableauMain,
box~style .code:n = { \__atableau_tikzset_append:nn {boxStyle} {#1} },
box~style .value_required:n = true,
boxes .bool_set:N = \l__atableau_boxes_bool,
boxes .default:n = true,
boxes .initial:n = true,
no~boxes .bool_set_inverse:N = \l__atableau_boxes_bool,
no~boxes .default:n = true,
conjugate .code:n =
{
\tl_set:Nx \l_tmpa_tl {\str_lowercase:n {#1}}
\str_if_eq:VnTF \l_tmpa_tl {true}
{
\bool_set_true:N \l__atableau_conjugate_bool
\cs_set_eq:NN \__atableau_set_box_coordinates:nnn \__atableau_set_box_coordinates_conjugate:nnn
}
{
\bool_set_false:N \l__atableau_conjugate_bool
\cs_set_eq:NN \__atableau_set_box_coordinates:nnn \__atableau_set_box_coordinates_normal:nnn
}
},
conjugate .default:n = true,
conjugate .initial:n = false,
inner~wall .tl_set:N = \l__atableau_inner_tl,
inner~wall .value_required:n = true,
inner~wall .initial:n = aTableauInner,
inner~style .code:n = { \__atableau_tikzset_append:nn {innerWall} {#1} },
inner~style .value_required:n = true,
% label
label .code:n = {
\tl_if_in:nnTF {#1} {|}
{
% unpack the ribbons into \l__atableau_multiribbons_seq
\seq_set_split:cnn {l__atableau_multilabel_seq} {|} {#1}
}
{ \tl_set:No \l__atableau_label_tl {#1} }
},
label~style .code:n = { \__atableau_tikzset_append:nn {labelStyle} {#1} },
label~style .value_required:n = true,
% -- paths ---------------------------------------
paths .code:n = { \__atableau_set_multiseq_key:nn {paths} {#1} },
paths .initial:n = ,
path~style .code:n = { \__atableau_tikzset_append:nn {pathStyle} {#1} },
path~style .value_required:n = true,
path~style .initial:n =,
path~box .tl_set:N = \l__atableau_path_box_tl,
path~box .initial:n = ,
path~box~style .code:n = { \__atableau_tikzset_append:nn {pathBox} {#1} },
path~box~style .value_required:n = true,
path~box~style .initial:n =,
% -- ribbons ---------------------------------------
ribbons .code:n = { \__atableau_set_multiseq_key:nn {ribbons} {#1} },
ribbons .initial:n = ,
ribbon~style .code:n = { \__atableau_tikzset_append:nn {ribbonStyle} {#1} },
ribbon~style .value_required:n = true,
ribbon~style .initial:n =,
ribbon~box .tl_set:N = \l__atableau_ribbon_box_tl,
ribbon~box .initial:n = ,
ribbon~box~style .code:n = { \__atableau_tikzset_append:nn {ribbonBox} {#1} },
ribbon~box~style .value_required:n = true,
ribbon~box~style .initial:n =,
% -- snobs ---------------------------------------
snobs .code:n = { \__atableau_set_multiseq_key:nn {snobs} {#1} },
snobs .initial:n = ,
snob~style .code:n = { \__atableau_tikzset_append:nn {snobStyle} {#1} },
snob~style .value_required:n = true,
snob~style .initial:n =,
snob~box .tl_set:N = \l__atableau_snob_box_tl,
snob~box .initial:n = ,
snob~box~style .code:n = { \__atableau_tikzset_append:nn {snobBox} {#1} },
snob~box~style .value_required:n = true,
snob~box~style .initial:n =,
% -- shifted, skew and tabloid shapes ------------
shifted .bool_set:N = \l__atableau_shifted_bool,
shifted .initial:n = false,
skew .code:n =
{
\tl_if_in:nnTF {#1} {|}
{
% unpack the skew tableau into \l__atableau_multiskew_seq
\seq_set_split:Nnn \l__atableau_multiskew_seq {|} {#1}
}
{ \__atableau_set_partition:nn {skew} {#1} }
},
skew .value_required:n = true,
skew .initial:n = 0,
skew~border .bool_set:N = \l__atableau_skew_border_bool,
skew~border .initial:n = false,
no~skew~border .bool_set_inverse:N = \l__atableau_skew_border_bool,
no~skew~border .default:n = true,
skew~border~style .code:n = { \__atableau_tikzset_append:nn {skewBorder} {#1} },
skew~border~style .value_required:n = true,
skew~boxes .bool_set:N = \l__atableau_skew_boxes_bool,
skew~boxes .default:n = true,
skew~boxes .initial:n = false,
no~skew~boxes .bool_set_inverse:N = \l__atableau_skew_boxes_bool,
skew~box~style .code:n = { \__atableau_tikzset_append:nn {skewBox} {#1} },
skew~box~style .value_required:n = true,
skew colour .tl_set:N = \l__atableau_skew_border_tl,
skew color .tl_set:N = \l__atableau_skew_border_tl,
skew colour .initial:n = aTableauSkew,
tabloid .bool_set:N = \l__atableau_tabloid_bool,
tabloid .initial:n = false,
% -- multitableaux and multidiagrams --------------------
delimiters .code:n = { \__atableau_set_delimiters:nn #1 },
delimiters .value_required:n = true,
delimiters .initial:n = (),
left~delimiter .tl_set:N = \l__atableau_left_delimiter_tl,
left~delimiter .value_required:n = true,
right~delimiter .tl_set:N = \l__atableau_right_delimiter_tl,
right~delimiter .value_required:n = true,
empty .tl_set:N = \l__atableau_empty_tl,
empty .initial:n = \textendash,
separators .bool_set:N = \l__atableau_separators_bool,
separators .default:n = true,
separators .initial:n = true,
no~separators .bool_set_inverse:N = \l__atableau_separators_bool,
no~separators .default:n = true,
separation .fp_set:N = \l__atableau_separation_fp,
separation .value_required:n = true,
separation .initial:n = 0.3,
separator .tl_set:N = \l__atableau_separator_tl,
separator .value_required:n = true,
separator .initial:n = |,
separator~colour .tl_set:N = \l__atableau_separator_fg_tl,
separator~colour .value_required:n = true,
separator~colour .initial:n = aTableauMain,
separator~color .tl_set:N = \l__atableau_separator_fg_tl,
separator~color .value_required:n = true,
% set rows in abacuses, multitableau and multidiagrams
rows .code:n = {
\fp_set:Nn \l__atableau_rows_fp {#1}
\int_set:No \l__atableau_rows_int {\fp_to_int:N \l__atableau_rows_fp}
},
rows .value_required:n = true,
rows .initial:n = 0,
xoffsets .code:n = { \regex_split:nnN {[\|,]} {#1} \l__atableau_xoffsets_seq },
xoffsets .value_required:n = true,
xoffsets .initial:n = 0,
yoffsets .code:n = { \regex_split:nnN {[\|,]} {#1} \l__atableau_yoffsets_seq },
yoffsets .value_required:n = true,
yoffsets .initial:n = 0,
% ---------------------------------------------------------------------------
% abacus keys
south .code:n = \__atableau_set_style:nn {abacus} {south},
south .initial:n =,
east .code:n = \__atableau_set_style:nn {abacus} {east},
north .code:n = \__atableau_set_style:nn {abacus} {north},
west .code:n = \__atableau_set_style:nn {abacus} {west},
% abacus style
abacus~ends .code:n = { \__atableau_set_abacus_ends:nn #1 },
abacus~ends .value_required:n = true,
abacus~ends .initial:n = {-|},
abacus~ends~style .code:n = { \__atableau_tikzset_append:nn {abacusEnds} {#1} },
abacus~ends~style .value_required:n = true,
abacus~star~style .code:n = { \__atableau_tikzset_append:nn {abacusStarStyle} {#1} },
abacus~star~style .value_required:n = true,
bead .tl_set:N = \l__atableau_bead_tl, % bead colour
bead .value_required:n = true,
bead .initial:n = aTableauMain,
bead~font .tl_set:N = \l__atableau_bead_font_tl, % bead font
bead~font .initial:n = \small,
bead~font .value_required:n = true,
bead~size .fp_set:N = \l__atableau_bead_size_fp,
bead~size .initial:n = 0.4,
bead~sep .fp_set:N = \l__atableau_abacus_ht_fp, % bead separation
bead~sep .value_required:n = true,
bead~sep .initial:n = 0.42,
bead~shape .tl_set:N = \l__atableau_bead_shape_tl, % bead shape colour
bead~shape .value_required:n = true,
bead~shape .initial:n = circle,
bead~style .code:n = { \__atableau_tikzset_append:nn {beadStyle} {#1} },
bead~style .value_required:n = true,
bead~text .tl_set:N = \l__atableau_bead_text_tl, % bead text colour
bead~text .value_required:n = true,
bead~text .initial:n = white,
beta~numbers .bool_set:N = \l__atableau_beta_numbers_bool,
beta~numbers .initial:n = false,
no~shade .code:n = { \__atableau_tikzset_append:nn {beadStyle} {no~shade,} },
no~shade .value_required:n = false,
runner .tl_set:N = \l__atableau_runner_tl, % runner colour
runner .value_required:n = true,
runner .initial:n = aTableauInner,
runner~style .code:n = { \__atableau_tikzset_append:nn {runnerStyle} {#1} },
runner~style .value_required:n = true,
runner~labels .code:n = { \seq_set_split:Nnn \l__atableau_runner_labels_seq {,} {#1} },
runner~labels .value_required:n = true,
runner~label~style .code:n = { \__atableau_tikzset_append:nn {runnerLabelStyle} {#1} },
runner~label~style .value_required:n = true,
runner~sep .fp_set:N = \l__atableau_abacus_wd_fp, % runner separation
runner~sep .value_required:n = true,
runner~sep .initial:n = 0.42,
shading .tl_set:N = \l__atableau_shading_tl,
shading .value_required:n = true,
shading .initial:n = ball,
tick .tl_set:N = \l__atableau_tick_tl, % tick colour
tick .initial:n = aTableauInner,
tick~length .code:n = { \fp_set:Nn \l__atableau_tick_length_fp {#1/2} }, % (half) tick width separation
tick~length .value_required:n = true,
tick~length .initial:n = 0.1,
tick~style .code:n = { \__atableau_tikzset_append:nn {tickStyle} {#1} },
tick~style .value_required:n = true,
}
% ---------------------------------------------------------------------------
% Usage: \__atableau_set_origin:nn (x,y)
% Set the Cartesian coordinates for the corner of the (1,1) box
% TODO: allow general TikZ-coorindates. To do this we could, for example, use ideas from
%
https://tex.stackexchange.com/questions/33703/extract-x-y-coordinate-of-an-arbitrary-point-in-tikz
\cs_new_protected:Npn \__atableau_set_origin:nn (#1,#2)
{
\fp_set:Nn \l__atableau_x_fp {#1}
\fp_set:Nn \l__atableau_y_fp {#2}
}
% usage: \__atableau_tikzpicture:nnn {settings} {origin} {aTableau command}
% where
% - #1: settings are a comma separated list of aTableau settings
% - #2: origin are Cartesian coordinates in the form x,y, or NoValue
% - #3: an internal aTableau command with parameters for drawing something
% Apply settings and wrap an aTableau command inside a tikzpicture environment.
% Add any tikzpicture environments settings and before and after TikZ commands
\cs_new_protected:Npn \__atableau_tikzpicture:nnn #1 #2 #3
{
\group_begin:
% keep changes to settings local by working inside a group
\keys_set:nn {atableau} {#1}
\IfNoValueTF {#2}
{ % wrap inside a tikzpicture environment, placing the picture at (0,0)
\__atableau_set_origin:nn (0,0)
\mode_if_math:TF
{
% We want to automatically rescale when used as a subscript, which
% we do by putting the tikz code inside a box and then using
% \mathchoice to adjust for script size, using an idea of cfr's
\hbox_set:Nw \l_tmpa_box
\exp_last_unbraced:Ne \tikz{[\l__atableau_tikzpicture_tl]}
{ \l__atableau_tikz_before_tl #3 \l__atableau_tikz_after_tl }
\hbox_set_end:
\mathchoice
{ % display style: do nothing
\box_use:N \l_tmpa_box
}
{ % text style: do nothing
\box_use:N \l_tmpa_box
}
{ % script style: rescale
\box_scale:Nnn \l_tmpa_box {\l__atableau_script_fp*\l__atableau_xscale_fp}
{\l__atableau_script_fp*\l__atableau_yscale_fp}
\box_use:N \l_tmpa_box
}
{ % scriptscript style: rescale
\box_scale:Nnn \l_tmpa_box {\l__atableau_scriptscript_fp*\l__atableau_xscale_fp}
{\l__atableau_scriptscript_fp*\l__atableau_yscale_fp}
\box_use:N \l_tmpa_box
}
}
{ % Not in maths-mode. tcolorbox objects to using a box here
\exp_last_unbraced:Ne \tikz{[\l__atableau_tikzpicture_tl]}
{ \l__atableau_tikz_before_tl #3 \l__atableau_tikz_after_tl }
}
}
{ % already inside a tikzpicture environment
\__atableau_set_origin:nn (#2)
\l__atableau_tikz_before_tl #3 \l__atableau_tikz_after_tl
}
\group_end:
}
% ---------------------------------------------------------------------------
% Public facing package commands
% Almost all public-facing routines call \__atableau_tikzpicture:nnn,
% which applies the settings, sets the coordinates of the origin and
% then ensures that the requested diagram is drawn inside a tikzpicture
% environment.
% \Abacus (x,y) [style] {#runners} {partition}
\NewDocumentCommand\Abacus{ d() O{} m m }
{
\__atableau_tikzpicture:nnn {#2} {#1} { \__atableau_abacus:nn {#3} {#4} }
}
% \Diagram (x,y) [style] {shape}
\NewDocumentCommand\Diagram{ d() O{} m }
{
\__atableau_tikzpicture:nnn {#2} {#1} { \__atableau_draw_diagram:n {#3} }
}
% \Multidiagram (x,y) [style] {entries}
\NewDocumentCommand\Multidiagram{ d() O{} m }
{
\__atableau_tikzpicture:nnn {#2} {#1} { \__atableau_multidiagram:n {#3} }
}
% \Multitableau (x,y) [style] {entries}
\NewDocumentCommand\Multitableau{ d() O{} m }
{
\__atableau_tikzpicture:nnn {#2} {#1} { \__atableau_multitableau:n {#3} }
}
% \RibbonTableau (x,y) [style] {entries}
\NewDocumentCommand\RibbonTableau{ d() O{} m }
{
\__atableau_tikzpicture:nnn {#2} {#1} { \__atableau_ribbon_tableau:n {#3} }
}
% \ShiftedDiagram (x,y) [style] {entries}
\NewDocumentCommand\ShiftedDiagram{ d() O{} m }
{
\__atableau_tikzpicture:nnn {shifted,#2} {#1} { \__atableau_draw_diagram:n {#3} }
}
% \ShiftedTableau (x,y) [style] {entries}
\NewDocumentCommand\ShiftedTableau{ d() O{} m }
{
\__atableau_tikzpicture:nnn {shifted,#2} {#1} { \__atableau_draw_tableau:n {#3} }
}
% \SkewDiagram (x,y) [style] {skew shape} {entries}
\NewDocumentCommand\SkewDiagram{ d() O{} m m }
{
\__atableau_tikzpicture:nnn {skew={#3},#2} {#1} { \__atableau_draw_diagram:n {#4} }
}
% \SkewTableau (x,y) [style] {skew shape} {entries}
\NewDocumentCommand\SkewTableau{ d() O{} m m }
{
\__atableau_tikzpicture:nnn {skew={#3},#2} {#1} { \__atableau_draw_tableau:n {#4} }
}
% \Tableau (x,y) [style] {entries}
\NewDocumentCommand\Tableau{ d() O{} m }
{
\__atableau_tikzpicture:nnn {#2} {#1} { \__atableau_draw_tableau:n {#3} }
}
% \Tabloid (x,y) [style] {entries}
\NewDocumentCommand\Tabloid{ d() O{} m }
{
\__atableau_tikzpicture:nnn {tabloid,#2} {#1} { \__atableau_draw_tableau:n {#3} }
}
\NewDocumentCommand\aTabset{ m }{ \keys_set:nn { atableau } {#1} }
% ---------------------------------------------------------------------------
% Finally, now that everything is defined, process the package options.
\IfFormatAtLeastTF { 2022-06-01 }
{ \ProcessKeyOptions [ atableau ] }
{
\RequirePackage { l3keys2e }
\ProcessKeysOptions { atableau }
}
\endinput
% ---------------------------------------------------------------------------
% CHANGE LOG
%
% Version 1.0.0 - 2023-10-06
% - initial version
% - Young diagrams, tabloids, tableaux, shifted tableaux, Ukrainian tableaux, abacuses, braids
%
% Version 2.0.0 - 2025-01-22
% - completely rewritten using LaTeX3
% - key interface for the tableaux options
% - macros can be used both in and outside tikzpicture environments
% - a quark-based interface allows styles to be applied to each tableau entry
% - support for different conventions (english, french, ukrainian, australian)
% - support diagrams, tableaux, including tabloids, skew and shifted tableaux and ribbon tableaux
% - stars and styles
%
% Version 2.1.0 - 2025-01-24
% - support for using aTableau commands in super and subscripts
% - warning about using older versions of LaTeX3
% ---------------------------------------------------------------------------
%
% Copyright (C) 2022-25 by Andrew Mathas <
[email protected]>
%
% This work may be distributed and/or modified under the
% conditions of the LaTeX Project Public License (LPPL), either
% version 1.3c of this license or (at your option) any later
% version. The latest version of this license is in the file:
%
%
http://www.latex-project.org/lppl.txt
%
% This work is "maintained" (as per LPPL maintenance status) by
% Andrew Mathas.
%
% This package consists of the files:
% atableau.ini
% atableau.pdf
% atableau.sty
% atableau.tex
% LICENSE
% README.md
%
% ---------------------------------------------------------------------------
% end of atableau.sty
