<html><head><meta name="color-scheme" content="light dark"></head><body><pre style="word-wrap: break-word; white-space: pre-wrap;">%%
%% Package: spectralsequences v1.3.3 2023-01-28
%% Author: Hood Chatham
%% Email: hood@mit.edu
%% Date: 2023-01-28
%% License: Latex Project Public License
%%
%% File: spectralsequencesmanual.tex
%%
%%   Manual content
%%

%
% TODO:
%
%  maybe move more examples into external files?
%
%  consistency issues?
%  perhaps think about ordering, particularly of "Misc commands" section
%  tutorial
%  explain / cross reference examples folder?
%  \sseqlastlabel is not currently documented.
%
\def\version{Version 1.3.3}


\input spectralsequencesmanualpreamble


\begin{document}
\newgeometry{margin = 4cm,nohead}
\begin{titlepage}
\title{\sseqpages}
\author{Hood Chatham\\\mailtoHC}
\date{\version\\\today}
 \maketitle \thispagestyle{empty}

\begin{abstract}
\noindent
The \sseqpages\  package is a specialized tool built on top of \pgfpkg/\tikzpkg\
for drawing spectral sequence charts. It provides a powerful, concise syntax for
specifying the data of a spectral sequence, and then allows the user to print
various pages of a spectral sequence, automatically choosing which subset of the
classes, differentials, structure lines, and extensions to display on each page.
It also handles most of the details of the layout. At the same time, \sseqpages\
is extremely flexible. It is closely integrated with \tikzpkg\  to ensure that
users can take advantage of as much as possible of its expressive power. It is
possible to turn off most of the automated layout features and draw replacements
using \tikzpkg\  commands. \sseqpages\  also has a carefully designed error
reporting system intended to ensure that it is as clear as possible what is
going wrong.

Many thanks to the authors of \tikzpkg\  for producing such a wonderful package
with such thorough documentation. I would have needed to spend a lot more time
reading the \tikzpkg\  code if the documentation weren't so excellent. I took
ideas or code or both from \tikzcdpkg\ (part of the code for turning quotes into
class or edge labels), \pgfplotspkg\ (axes labels), and \sseqpkg\ (the grid
types, the stack). I lifted a fair amount of code from \TeX stack exchange.
Thanks to Eva Belmont for tons of helpful suggestions, bug reports, and
productive conversations. Talking to her has helped to clarify many design
concepts for the package. Thanks to Eric Peterson for being a very early adopter
and reporting many bugs. Also thanks to all my friends, family, and
acquaintances listened to me talk about \LaTeX\ programming even though they
probably found it dreadfully boring.
\end{abstract}
\end{titlepage}

\restoregeometry
\stepcounter{page}
\newpage
\thispagestyle{empty} % Should the table of contents have a page number?
\tableofcontents
\newpage
\section{Introduction}
The \sseqpages\  package consists of two main environments -- the \sseqdataenv\
environment, which specifies the data for a named spectral sequence, and the
\sseqpageenv\  environment, which prints a single page of a spectral sequence.
The |\printpage| command is also available as a synonym for a \sseqpageenv\
environment with an empty body.

Here is a basic example:
\begin{codeexample}[width = 8.7cm]
\begin{sseqdata}[ name = basic, xscale = 0.6,
                  cohomological Serre grading ]
\class(0,0)
\class(0,2)
\class(3,0)
\class(3,2)
\d3(0,2)
\end{sseqdata}
\printpage[ name = basic, page = 3 ]  \quad
\printpage[ name = basic, page = 4 ]
\end{codeexample}
\codeverb|\begin{sseqdata}[name = basic, cohomological Serre grading]| starts
the declaration of the data of a spectral sequence named |basic| with
cohomological Serre grading -- that is, the page $\mathtt{r}$ differentials go
$\mathtt{r}$ to the right and down $\mathtt{r-1}$. Then we specify four classes
and one page 3 differential, and we ask \sseqpages\  to print the third and
fourth pages of the spectral sequence. Note that on the fourth page, the source
and target of the differential have disappeared.

\subsection{Installation}
In both \miktex\ and \texlive\ installation should be automatic -- your \TeX\
distribution should automatically install the package the first time you include
|\usepackage{spectralsequences}| in a document and compile it. However, in 2016,
\texlive\ made an incompatible change to their database, so no new packages will
run on versions of \texlive\ from before 2016. This includes \sseqpages. If you
have an old version of \texlive, you can either perform a manual install, or,
better, you should install an up to date version of \texlive. If you want to do
a manual install, see \href{https://tex.stackexchange.com/a/73017}{this \TeX
stack exchange post} for instructions.

\subsection{Memory Constraints}
In a default \TeX\ install, \pdfLaTeX\ has small static memory caps that prevent
it from using more than about 60 megabytes of total ram. However,
\spectralsequences\ and \pgfpkg/\tikzpkg\ use a large amount of memory. For this
reason, using \pdfLaTeX\ with a default install, you cannot draw more than about
2500 classes across all of your diagrams (fewer if you include differentials,
structure lines, and other features). There are a few solutions to this.

The easiest solution is to run \LuaLaTeX. \LuaLaTeX\ dynamically allocates
memory and so is unlikely to run out of it. Using \LuaLaTeX\ on my computer, I
can compile a document that draws two copies of a diagram with 20,000 classes in
it (so a total of 40,000 classes). This takes about 50 seconds and 250 megabytes
of ram. I expect any real-world use case will compile fine on a modern computer
using \LuaLaTeX. This option has the advantage that any modern \TeX\ install
comes with a copy of \LuaLaTeX, and that \LuaLaTeX\ is the designated successor
to \pdfLaTeX. It has the disadvantage that there are some incompatibilities
between \LuaLaTeX\ and \pdfLaTeX\ so if your document depends on
\pdfLaTeX-specific features, it might be a pain to switch to \LuaLaTeX.

Another option is to increase the static memory caps for \pdfLaTeX. See
\href{https://tex.stackexchange.com/a/26213}{this \TeX stack exchange post} for
instructions on how to do this.

\subsection{A warning about fragile macros}%
All the data in a \sseqpages\  environment is stored and used later. As a
result, most of the \sseqpages\  commands currently cannot tolerate fragile
macros. Unfortunately, it is impossible for \sseqpages\  to warn you about this
situation -- if you use a fragile command in a place that it doesn't belong, the
result will be an incomprehensible error message. If you are getting nonsense
error messages, this might be why. The solution is to convert fragile macros
into robust ones. Common examples of fragile macros include |\widehat| and
|\underline|. My suggested solution to this is to add the following code to your
preamble for each fragile macro (example given for |\mathbb|):
\begin{codeexample}[code only]
\let\oldwidehat\widehat
\protected\def\widehat{\oldwidehat}
\end{codeexample}


\section{Package Options and Environments}
\begin{manualentry}{Draft Mode}%
The drawings that \sseqpages\ produces can be quite slow, especially if they are
large. Draft mode skips drawing the content of the spectral sequence, but still
takes up exactly the same amount of space in the document, so that you can deal
with formatting issues. To active draft mode, load the package by saying
|\usepackage[draft]{spectralsequences}|.
\end{manualentry}

\begin{environment}{{sseqdata}\moptions}%
The \sseqdataenv\  environment is for storing a spectral sequence to be printed
later. This environment is intended for circumstances where you want to print
multiple pages of the same spectral sequence. When using the \sseqdataenv\
environment, you must use the |name| option to tell \sseqpages\  where to store
the spectral sequence so that you can access it later.
\end{environment}

\begin{environment}{{sseqpage}\ooptions}%
This environment is used for printing a page of existing spectral sequence that
was already specified using the \sseqdataenv\  environment. The body of the
environment adds local changes -- classes, differentials, structure lines,
extensions, and arbitrary \tikzpkg\  options that are by default only printed on
this particular page. The \sseqpageenv\  environment can also be used to print a
stand-alone page of a spectral sequence -- that is, if you only want to print a
single page of the spectral sequence, you can skip using the \sseqdataenv\
environment.
\end{environment}

\begin{command}{\printpage\moptions}%
This command prints a single page of an existing spectral sequence as-is. This
is equivalent to a \sseqpageenv\  environment with an empty body.
\end{command}


\section{The Main Commands}
\begin{command}{\class\ooptions\parargtwo{x}{y}}%
This places a class at |(x,y)| where |x| and |y| are integers. If multiple
classes occur at the same position, \sseqpages\  will automatically arrange them
in a pre-specified pattern. This pattern may be altered using the%
|class pattern| option.
\begin{codeexample}[]
\begin{sseqpage}[ no axes, ymirror, yscale = 0.8 ]
\class(0,0)
\class(1,0) \class(1,0)
\class(0,1) \class(0,1) \class(0,1)
\class(1,1) \class(1,1) \class(1,1) \class(1,1)
\class(0,2) \class(0,2) \class(0,2) \class(0,2) \class(0,2)
\class(1,2) \class(1,2) \class(1,2) \class(1,2) \class(1,2) \class(1,2)
\end{sseqpage}
\end{codeexample}

The effect of the |\class| command is to print a \tikzpkg\ node on a range of
pages. Any option that would work for a \tikzpkg\ |\node| command will also work
in the same way for the |\class|, |\replaceclass|, and |\classoptions| commands.

If a class is the source or the target of a differential on a certain page, then
the page of the class is set to that page, and the class is only rendered on
pages up to that number:
\begin{codeexample}[width = 8cm]
\begin{sseqdata}[ name = class example,
                  Adams grading,
                  yscale = 0.53 ]
\class(1,0)
\class(0,2)
\class(0,3)
\d2(1,0)
\end{sseqdata}
\printpage[ name = class example, page = 2 ]
\quad
\printpage[ name = class example, page = 3 ]
\end{codeexample}

See the \pgfmanualpdfref{class options}{class options} section for a list of the
sort of options available for classes.
\end{command}

\begin{commandlist}{{\replaceclass\ooptions\parargthreeopt{x}{y}{n}},\replaceclass\ooptions\pararg{classname},
\replacesource\ooptions, \replacetarget\ooptions}%
After a class is the source or target of a differential, it disappears on the
next page. However, some differentials are not injective or not surjective.
Using the command |\replaceclass| causes a new symbol to appear on the page
after a class supported or accepted a differential (or both). If there are
multiple classes at the coordinate |(x,y)| you may specify which using an
integer or a |tag| $n$. By default, this command will affect the first class
placed in that position. You can also provide the |class:name| of a class. The
variants |\replacesource| and |\replacetarget| replace the source and target
respectively of the most recent differential.
\begin{codeexample}[]
\begin{sseqdata}[name = replace class example, Adams grading, classes = {draw = none } ]
\class["\mathbb{Z}"](0,3)
\class["\mathbb{Z}"](1,1)
\class["\mathbb{Z}"](1,0)
\d["\cdot 2"]2(1,1)
\replacetarget["\mathbb{Z}/2"] %\replaceclass["\mathbb{Z}/2"](0,3)
\d[-&gt;&gt;]3(1,0)
\replacesource["2\mathbb{Z}"]    % \replaceclass["2\mathbb{Z}"](1,0)
\end{sseqdata}
\printpage[ name = replace class example, page = 2 ] \qquad
\printpage[ name = replace class example, page = 3 ] \qquad
\printpage[ name = replace class example, page = 4 ]
\end{codeexample}
Note that this will not restore any structure lines coming into or off of the
class. If you want to restore all structlines on the class use
|\replacestructlines|. If you want to selectively replace some of the structure
lines, you must use |\structline| again (or use the |structline:page| option).
\end{commandlist}

\begin{command}{\replacestructlines\opt{\pars{\sourcecoord}}}%
This command replaces all structlines touching a class that has been
replaced using |\replaceclass|, |\replacesource|, or |\replacetarget|.
\begin{codeexample}[]
\begin{sseqdata}[name=replacestructlines]
\class(0,1)
\class(0,2)
\structline
\class(1,0)
\d2(1,0)(0,2)
\replacetarget\replacestructlines
\end{sseqdata}
\printpage[name=replacestructlines, page=3]
\end{codeexample}
\end{command}

\begin{commandlist}{{\classoptions\moptions\parargthreeopt{x}{y}{n}},\classoptions\moptions\pararg{classname},
\classoptions\moptions}%
This adds options to an existing class. This can be used in a \sseqpageenv\
environment to modify the appearance of a class for just one drawing of the
spectral sequence, for instance to highlight it for discussion purposes.

If there are multiple classes at the coordinate |(x,y)| you may specify which
using an integer or a |tag| $n$. By default, this command will affect the first
class placed in that position. You can also provide the |class:name| of a class.
If no coordinate is indicated at all, then |\lastclass| is used.
\begin{codeexample}[width = 6cm]
\begin{sseqdata}[ name = class options example,
                  classes = fill ]
\class(2,1)
\foreach \x in {0,...,2} \foreach \y in {0,1} {
    \class(\x,\y)
}
\end{sseqdata}
\begin{sseqpage}[ name = class options example,
                  right clip padding = 0.6cm ]
\classoptions[red](2,1,2) % Only is red on this page!
\node[ background ] at (0.3,-2.2)
    {\textup{The red class is the problem}};
\end{sseqpage}
\end{codeexample}
Another reason to use this is to give a label to one instance of a class that
shows up in a loop or a command defined using |\NewSseqGroup|:
\begin{codeexample}[width = 6cm]
\NewSseqGroup\mygroup {} {
    \class(0,0)
    \class(0,1)
    \class(0,2)
    \class(1,1)
    \class(2,2)
    \structline(0,0)(0,1)
    \structline(0,1)(0,2)
    \structline(0,0)(1,1)
    \structline(1,1)(2,2)
}
\begin{sseqpage}[ classes = fill, class labels = { left = 0.3em } ]
\mygroup(0,0)
\mygroup(1,2)
\classoptions["2"](0,1)
\classoptions["\eta"](1,1)
\end{sseqpage}
\end{codeexample}
See the \pgfmanualpdfref{class options}{class options} section for a list of the
sort of options available for classes.
\end{commandlist}

\begin{commandlist}{
    {\d\ooptions\meta{page}},
    {\d\ooptions\meta{page}\pars{\meta{x},\meta{y}\opt{,\sourcen,\targetn}}},
    {\d\ooptions\meta{page}\pars{\sourcename\opt{,\targetn}}},
    {\d\ooptions\meta{page}\pars{\sourcecoord}\pars{\targetcoord}}%
}%
Calling |\d\meta{page}|\parargtwo{x}{y} creates a differential starting at
\parargtwo{x}{y} of length determined by the specified page. In order to use the
|\d| command like this, you must first specify the |degree| of the differentials
as an option to the \sseqdataenv\  or \sseqpageenv\  environment. The degree
indicates how far to the right and how far up a page $\mathtt{r}$ differential
will go as a function of $\mathtt{r}$. If there is a page $\mathtt{r}$
differential, on page $\mathtt{r+1}$, the source, target, and any structure
lines connected to the source and target of the differential disappear. If no
class is specified, the default is to use |\lastclass|.

If there are multiple nodes in the source or target, you may specify which one
the differential should go to using an index or tag for \sourcen\  or \targetn.
It is also possible to provide the name of the source coordinate and an optional
target, or to separately provide the source and target coordinate, either as
names or as \parargthree{x}{y}{n}. Using |\d| with explicit source and target
coordinates works even if you did not provide a |degree| to the spectral
sequence. If you did provide a |degree|, then \sseqpages\  will check whether
the difference between the source and target is appropriate for a differential
of a given page, and if not it will throw an error. If this is undesirable, you
can use the |lax degree| option.
\begin{codeexample}[width = 7.5cm]
\begin{sseqdata}[ name = d example, degree = {-1}{#1},
                  struct lines = blue, yscale = 1.3 ]
\class(0,2)
\class(1,2)
\class(1,1)
\class(1,0)
\structline(1,2)(0,2)
\structline(1,2)(1,1)
\structline(1,1)(1,0)
\d2(1,0)
\end{sseqdata}
\printpage[ name = d example, page = 2 ] \quad
\printpage[ name = d example, page = 3 ]
\end{codeexample}
If there are multiple nodes in the source or target coordinate, then there is a
funny syntax for indicating which one should be the source and target:
\begin{center}
|\d\meta{page}\pars{\meta{x},\meta{y}\opt{,\sourcen,\targetn}}|
\end{center}
\begin{codeexample}[width = 7.5cm]
\begin{sseqpage}[ Adams grading, yscale = 0.8 ]
\class(1,0) \class(1,0)
\class(0,2) \class(0,2)
\d2(1,0,1,2)
\class(2,0) \class(2,0)
\class(1,2)
\d2(2,0,2)
\class(3,0)
\class(2,2) \class(2,2)
\d2(3,0,,2)
\end{sseqpage}
\end{codeexample}
Negative indices will count from the most recent class in the coordinate (so the
most recent is |-1|, the second most recent is |-2|, etc). You can also use a
|tag|, which works better if the situation is complicated.
\begin{codeexample}[width = 7.5cm]
\begin{sseqpage}[ Adams grading, yscale = 0.65 ]
\class(1,0)
\class(0,2) \class(0,2)
\d[blue]2(1,0,-1,-1)
\class(1,0)
\class(0,2)
\d[orange]2(1,0,-1,-1)
\class(1,0)
\d[red]2(1,0,-1,-2)
\end{sseqpage}
\end{codeexample}
\end{commandlist}

\begin{commandlist}{
    {\doptions\moptions\meta{page}\pars{\meta{x},\meta{y}\opt{,\sourcen,\targetn}}},
    {\doptions\moptions\meta{page}\pars{\sourcename\opt{,\targetn}}},
    {\doptions\moptions\meta{page}\pars{\sourcecoord}\pars{\targetcoord}}%
}%
This command adds options to an existing differential, just like |\classoptions|
except for differentials. Its syntax is identical to that of |\d|.
\end{commandlist}

\begin{command}{\kill\meta{page}\oarg{coord}} This command sets the indicated
coordinate to die on the indicated page, but does not establish a target for the
differential. This is useful if you want to draw your own differential using
tikz (see |\getdtarget|) or if you are not drawing the class on the other side
of the differential for clutter reasons. As usual, if no coordinate is provided,
the default argument is |\lastclass|.
\end{command}

\begin{command}{\structline\ooptions\opt{\pars{\sourcecoord}\pars{\targetcoord}}}
The |\structline| command creates a structure line from \sourcecoord\  to
\targetcoord. The source and target coordinates are either of the form
\pars{\meta{x},\meta{y}\opt{,\meta{n}}} or \pararg{class name}. If there are
multiple classes at $\mathtt{(x,y)}$, then \meta{n} specifies which of the
classes at $\mathtt{(x,y)}$ the structure line starts and ends at -- if n is
positive, then it counts from the first class in that position, if n is
negative, it counts backwards from the most recent. You can also use a |tag| for
n. If the \targetcoord\ is omitted, then |\lastclass| is used, so that
|\structline(\sourcecoord)| connects the most recent class to the specified
coordinate. If both coordinates are omitted, then |\lastclass| and |\lastclass1|
are used, and so |\structline| with no arguments at all will connect the two
most recent classes.

If the source or target of a structure line is hit by a differential, then on
subsequent pages, the structure line disappears.

If the source or target has had multiple generations (i.e., they got hit and you
used |\replaceclass|), then the |\structline| will only appear starting on the
first page where the current generation of both the source and target are
present. If this is undesirable, you can use the |structline:page| option or the
to change it. Also, the structline will disppear the first time after this the
source or target has a differential, but this can be changed with the
|\replacestructlines| command.
\begin{codeexample}[width = 7.5cm]
\DeclareSseqGroup\tower {} {
    \class(0,0)
    \foreach \y in {1,...,5} {
        \class(0,\y)
        \structline
    }
    \class(0,2)
    \structline(0,1,-1)
    \structline(0,3,-1)
}
\begin{sseqdata}[ name = structline example,
                  classes = { circle, fill },
                  Adams grading, no axes,
                  yscale = 1.28 ]
\class(1,1) \class(1,2)
\class(2,3) \class(2,3) \class(2,5)
\tower[classes = blue](0,0)
\tower[struct lines = dashed,orange](1,0)
\tower[struct lines = red](2,0)
\d2(1,1,2)
\end{sseqdata}
\printpage[ name = structline example, page = 2 ] \quad
\printpage[ name = structline example, page = 3 ]
\end{codeexample}
\end{command}

\begin{command}{\structlineoptions\moptions\opt{\pars{\sourcecoord}\pars{\targetcoord}}}
This command adds options to an existing structure line, just like
|\classoptions| except for structure lines. Its syntax is identical to
|\structline|.
\end{command}

\begin{command}{\extension\ooptions\opt{\pars{\sourcecoord}\pars{\targetcoord}}}
The |\extension| command has an identical syntax to the |\structline| command
and most of the same options. Instead of adding a structline, it adds an
extension. The extensions are only shown on page $\infty$ or page ranges ending
at $\infty$.

\begin{codeexample}[width = 7.5cm]
\begin{sseqdata}[ name = extension example,
                  classes = { circle, fill },
                  Adams grading, no axes,
                  yscale = 1.28 ]
\class(0,0) \class(0,1)
\extension
\end{sseqdata}
\printpage[ name = extension example, page = 2 ] \quad
\printpage[ name = extension example, page = \infty ]
\end{codeexample}    
\end{command}

\begin{command}{\extensionoptions\moptions\opt{\pars{\sourcecoord}\pars{\targetcoord}}}
This command adds options to an existing extension. Its syntax is identical to
|\extension|.
\end{command}

\begin{command}{\circleclasses\ooptions\pars{\sourcecoord}\pars{\targetcoord}}
This command is a lot like |\structline| except that it puts a circle around the
classes instead of connecting them with a line. It might take a certain amount
of fiddling with options to get |\circleclasses| to produce good results. There
is no |\circleclassesoptions| command because it doesn't seem necessary.
\end{command}

\begin{commandlist}{\draw,\path,\node,\clip}
Any code that would work in a \tikzpictureenv\  environment will also work
unchanged in a \sseqdataenv\  or \sseqpageenv\  environment, with a few minor
differences. This is a very flexible way to add arbitrary background or
foreground features to the spectral sequence:
\codeexample[from file=tikz]
\end{commandlist}


\section{Options for the main commands}
\subsection{Universal options}
The following options work with all of the drawing commands in this package,
including |\class|, |\d|, and |\structline|, |\extension|, their friends |\replaceclass|,
|\classoptions|, |\doptions|, |\structlineoptions|, |\extensionoptions|and |\replacestructlines|, as well as with \tikzpkg\
primitives.
\begin{keylist}{xshift = \meta{integer},yshift = \meta{integer}}
Shifts by integer values are the only coordinate changes that are allowed to be
applied to |\class|, |\d|, |\structline|, |\extension| their relatives, or to a \scopeenv\
environment that contains any of these commands. These shift commands help with
reusing code. For instance:
\begin{codeexample}[width = 6cm]
\begin{sseqpage}[ cohomological Serre grading, yscale = 0.45 ]
\foreach \x in {0,1} \foreach \y in {0,1} {
    \begin{scope}[ xshift = \x, yshift = \y ]
    \class(2,0)
    \class(0,1)
    \d2(0,1)
    \end{scope}
}
\end{sseqpage}
\end{codeexample}
This code segment is very useful so \sseqpages\  has the command |\NewSseqGroup|
which to make code like this more convenient. The following code produces the
same output as above:
\begin{codeexample}[code only,width = 6cm]
\NewSseqGroup\examplegroup {} {
    \class(2,0)
    \class(0,1)
    \d2(0,1)
}
\begin{sseqpage}
\examplegroup(0,0)
\examplegroup(0,1)
\examplegroup(1,0)
\examplegroup(1,1)
\end{sseqpage}
\end{codeexample}


A word of warning: the behavior of |xshift| in \sseqpages\  is incompatible with
the normal behavior of |xshift| in \tikzpkg. For some reason, saying%
|xshift = 1| in \tikzpkg\ does not shift the coordinate |(0,0)| to the
coordinate |(1,0)| -- instead it shifts by 1pt. In \sseqpages\ , saying%
|xshift = 1| moves the coordinate |(0,0)| to the coordinate |(1,0)|. This
includes \tikzpkg\ primitives: saying%
\codeverb|\draw[ xshift = 1 ] (0,0) -- (1,0);| inside a \sseqdataenv\  or
\sseqpageenv\  environment is the same as saying \codeverb|\draw(1,0) -- (2,0);|
despite the fact that this is not the case in the \tikzpictureenv\ environment.
\end{keylist}

\begin{manualentry}{Colors}
These come from the \LaTeX\  \colorpkg\  package via \tikzpkg, so see the
\href{\colormanualurl}{\colorpkg\  package documentation} for more information.
\begin{codeexample}[width = 6cm]
\begin{sseqpage}[ classes = {fill,inner sep = 0.4em},
                  no axes, scale = 1.3 ]
\class[red](0,0)
\class[blue](1,0)
\class[green](2,0)
\class[cyan](0,1)
\class[magenta](1,1)
\class[yellow](2,1)
\class[blue!50!red](0,2) % a 50-50 blend of blue and red
\class[green!30!yellow](1,2) % 30% green, 70% yellow
\class[blue!50!black](2,2)
\end{sseqpage}
\end{codeexample}
\end{manualentry}

\begin{manualentry}{\pgfmanualpdflabel{""quotes}{}|"|\meta{text}|"|\opt{\meta{options}}}
Specify a label for a class, a differential, or a structure line. This uses the
\tikzpkg\ quotes syntax. If the label text includes an equal sign or comma, you
need to enclose the entire label in braces, e.g., \codeverb|\class["{x =
y}"](0,0)|. The options include anything you might pass as an option to a
\tikzpkg\ node, including arbitrary coordinate transforms, colors, opacity
options, shapes, fill, draw, etc. The behavior is a little different depending
on whether you use it on a class or on a differential or structure line.

For a class, the \meta{text} is placed in the position |inside| the node by
default -- in effect, the \meta{text} becomes the label text of the node (so
saying |\class["label text"](0,0)| causes a similar effect to saying%
|\node at (0,0) {label text};|). There are other position options such as%
|left|, |above left|, etc which cause the label text to be placed in a separate
node positioned appropriately. If the placement is above, left, etc, then any
option that you may pass to a \tikzpkg\ node will also work for the label,
including general coordinate transformations. If the placement is ``inside'',
then the only relevant \opt{\meta{options}} are those that alter the appearance
of text, such as opacity and color.
\begin{codeexample}[width = 4cm]
\begin{sseqpage}[ classes = { minimum width = width("a") + 0.5em }, no axes ]
\class["a"](0,0)
\class["a", red](1,0)
\class["a" black, red](2,0)
\class["b" above](0,1)
\class["b" { below right, yshift = 0.1cm }](1,1)
\class["a" { above right = {1em} }](2,1)
\end{sseqpage}
\end{codeexample}
You can adjust the default behavior of class labels using the |labels| style
option or its relatives |class labels|, |inner class labels| or%
|outer class labels|. Note that it is also possible to give a label to a |\node|
this way, although the behavior is slightly different. In particular, the label
defaults to the |above| position instead of going in the |\node| text by
default. Also, this won't respect the various label style options like |labels|,
etc.
\begin{codeexample}[width = 6cm]
\begin{sseqpage}[ no axes ]
\class(0,0)
\class(2,0)
\node[circle, fill, "a"] at (1,0) {};
\end{sseqpage}
\end{codeexample}

\begin{key}{pin = \meta{style}} %
The |pin| key makes \sseqpages\ draw a line connecting the label to the relevant
class, which can provide necessary clarification in dense diagrams. The pin key
itself can take options which adjust the way that the line is drawn:
\begin{codeexample}[width = 6cm]
\begin{sseqpage}
\class(0,0)
\class["xy" { above, xshift = -4pt, pin = red }](0,0)
\class(0,0)
\class(0,1)
\structline
\end{sseqpage}
\end{codeexample}
\end{key}


The label normally goes on the right side of the edge. The special option |'|
makes it go in the opposite position from the default. I imitated the label
handling in the \tikzcdpkg\ package, so if you use \tikzcdpkg, this should be
familiar.
\begin{codeexample}[width = 6cm]
\begin{sseqpage}[ Adams grading, yscale = 0.63 ]
\class(0,0)
\class(0,1)
\class(0,2)
\structline["a"' blue](0,0)(0,1)
\class(1,0)
\class(1,1)
\structline["b"](1,0)(1,1)
\d[ "\cdot 2" { pos = 0.7, yshift = -5pt } ] 2 (1,0)
\end{sseqpage}
\end{codeexample}
You can use the style options |labels|, |edge labels|, |differential labels|,
|struct line labels|, and |extension labels| to adjust the styling of edge labels. For instance, if
you would prefer for the labels to default to the left hand side of the edge
rather than the right hand side, you could say |edge labels = {auto = left}|.
You can also use quotes to label edges drawn with \tikzpkg\ primitives:
\begin{codeexample}[width = 6cm]
\begin{sseqpage}[ yscale = 0.58, no axes ]
\class(0,0)
\class(1,1)
\draw (1,0) to["hi"'{ pos = 0.7, yshift = -0.5em }] (0,1);
\end{sseqpage}
\end{codeexample}

\needspace{3\baselineskip}
\begin{key}{description}
The |description| key, stolen from \tikzcdpkg, places the label on top of the
edge. In order to make this option work correctly, if the background coolor is
not the default white, you must inform \sseqpages\ about this using the key
|background color = |\meta{color}. In this document, the background color is
called \textit{graphicbackground}.
\begin{codeexample}[width = 6cm]
\begin{sseqpage}[ no axes, background color = graphicbackground ]
\foreach \x in {0,1,2} \foreach \y in {0,1} {
    \class(\x,\y)
}
\structline["a" red](0,0)(0,1)
\structline["a'"'blue,"b"{yshift = 1em}](1,0)(1,1)
\structline["c" description](2,0)(2,1)
\end{sseqpage}
\end{codeexample}
\end{key}
\end{manualentry}



\subsection{Options for \sectionstring\class}\pgfmanualpdflabel{class options}{}
Because the main job of the |\class| command is to print a \tikzpkg\ |\node| on
the appropriate pages of the spectral sequence, most options that would work for
a \tikzpkg\ node also work for the commands |\class|, |\replaceclass|, and
|\classoptions|. Here are a few that you might care about:
\begin{manualentry}{A \tikzpkg\ shape}
If you give the name of a \tikzpkg\ shape, the class node will be of that shape.
The standard \tikzpkg\ shapes are |circle| and |rectangle|. \sseqpages\ defines
two new shapes:
\begin{key}{circlen = \meta{n}}%
This draws $n$ concentric circles. It's intended for indicating a
$\mathbb{Z}/p^n$ summand. For large values of $n$ the result isn't all that
appealing.
\begin{codeexample}[]
\begin{sseqpage}[ no axes ]
\class[circlen = 2](0,0)
\class[circlen = 2,fill](1,0)
\class[circlen = 3](0,1)
\class[circlen = 4](1,1)
\end{sseqpage}
\end{codeexample}
\end{key}

\begin{keylist}{newellipse,ellipse ratio = \meta{ratio}}%
This shape is used for |\circleclasses|. It's a variant on the |ellipse| shape
that gives more control over the ellipse's aspect ratio.
\end{keylist}

There are many more \tikzpkg\ shapes in the shapes library, which you can load
using the command |\usetikzlibrary{shapes}|. The following are some examples:
\begin{codeexample}[width = 6cm]
\begin{sseqpage}[ no axes, classes = { inner sep = 0.4em },
                  class placement transform = { scale = 1.8 },
                  yscale = 1.63 ]
\class(0,0)
\class[isosceles triangle](2,0)
\class[rectangle](1,0)
\class[diamond](0,1)
\class[semicircle](1,1)
\class[regular polygon, regular polygon sides = 5](2,2)
\class[regular polygon, regular polygon sides = 6](2,2)
\class[regular polygon, regular polygon sides = 7](2,2)
\class[regular polygon, regular polygon sides = 8](2,2)
\end{sseqpage}
\end{codeexample}
See the \href{\pgfmanualurl#section.49}{\tikzpkg\  manual} for more information.
\end{manualentry}

\begin{keylist}{minimum width = \meta{dimension}, minimum height =
\meta{dimension}, minimum size = \meta{dimension}, inner sep = \meta{dimension},
outer sep = \meta{dimension}}%
These options control the size of a node. This is typically useful to make the
size of nodes consistent independent of the size of their label text.  For
instance:
\begin{codeexample}[width = 5cm]
\begin{sseqdata}[ name = minimum width example, no axes, yscale = 0.8 ]
\class["ab"](0,0)
\class["a"](0,1)
\class(0,2)
\end{sseqdata}
\printpage[ name = minimum width example ]
\printpage[ name = minimum width example,
  change classes = { blue, minimum width = width("ab") + 0.5em } ]
\end{codeexample}
\end{keylist}

\begin{key}{class:name = \meta{node name}}%
The |\class| command makes a \tikzpkg\ node on appropriate pages. You can refer
to this node using \tikzpkg\ commands by using its coordinates. Using the
|class:name| option, you can give the node a name, which you can use to refer to
the class. Using names creates more readable code. The |show name| option can be
used to display the names of classes. You can modify the names of classes
systematically using the options |class name prefix|, |class name postfix|, and
|class name handler|.

Named classes are immune to coordinate transformations. For example, in the
following code, |xshift| does not apply to the nodes specified by |(id)| and
|(eta)| but does apply to the coordinate specified by |(1,1)|:
\begin{codeexample}[width = 6cm]
\begin{sseqpage}[classes = { show name=above }]
\class[class:name = 1](0,0)
\class[class:name = \eta](1,1)
\class(2,1)
\structline[xshift = 1] (1) (\eta)
\structline[xshift = 1,blue] (1) (1,1)
\end{sseqpage}
\end{codeexample}
\end{key}

\begin{key}{show name = \meta{label options}}
\declareasstyle{show name}
This option is like saying |"class name"\marg{label options}| if the class has a
name, and does nothing if the class has no name. If the class has multiple
names, only the most recent is used. This is particularly useful with class
styles, . For instance, by saying |this page classes = { show name = above }|
you can display names of all of the sources and targets of differentials on each
page.
\begin{codeexample}[width=7cm]
\begin{sseqdata}[
    name = show name example,
    this page classes = { show name = { above right, pin } }
]
\class[ name = a ](0,2)
\class[ name = b ](0,3)
\class[ name = x ](1,0)
\d2(x)(a)
\replacesource[name=2x]
\d3(x)(b)
\end{sseqdata}

\printpage[ name = show name example, page = 2]

\printpage[ name = show name example, page = 3]
\end{codeexample}
\end{key}

\begin{key}{tag = \meta{tag}}%
This key adds a tag to the current class. Tags are used for identifying which of
multiple classes in the same position you are referring to. They are useful when
you have groups of related classes and want a family of differentials connecting
them.  For instance:
\begin{codeexample}[width = 8cm]
\DeclareSseqGroup\tower {} {
    \class(0,0)
    \foreach \i in {1,...,11} {
        \class(0,\i)
        \structline(0,\i-1,-1)(0,\i,-1)
    }
}
\NewSseqGroup\hvee {} {
    \tower(0,0)
    \foreach \i in {1,...,11} {
        \class(\i,\i)
        \structline(\i-1,\i-1,-1)(\i,\i,-1)
    }
}
\begin{sseqpage}[ degree = {-1}{1}, yscale = 1.1,
                  x range = {0}{5}, y range = {0}{5} ]
\tower(3,0)
\hvee[ tag = id ](0,0)
\hvee[ tag = h21 ](4,2)
\foreach \n in {0,...,5} {
    \d2(4+\n,2+\n,h21,id)
}
\end{sseqpage}
\end{codeexample}
We want each differential to go from the |h21| vee to the |id| vee, independent
of which classes are in the same position of the two vees. The easy way to
accomplish this is by giving tags to each of the two vees.
\end{key}

\begin{key}{insert = \meta{integer}}%
If there are multiple classes in the same position, this option allows you to
insert classes later into earlier positions. This is intended to help you put
logically related classes next to each other. If the integer is positive, it
inserts the class in the specified position, and if the integer is negative, it
counts backwards from the end. Providing |0| is the same as omitting the option
entirely. Values larger in absolute value than the total number of classes are
truncated. Consider:
\codeexample[from file=insert]
\end{key}

\begin{key}{offset = \{\pars{\meta{x offset},\meta{y offset}}\}}%
By default, a class uses the offset specified by |class pattern|. Occasionally
this is undesirable. In this case, you can specify the offset for a particular
class by hand. For example if the sum of two classes is hit by a differential,
it looks better for the class replacing them to be centered:
\begin{codeexample}[width = 9cm]
\begin{sseqdata}[ name = offset example,
    xscale = 0.7,
    Adams grading,
    class placement transform = {scale = 1.8} ]
\class(0,1)
\class(0,2)\class(0,2)
\draw(0,1)--(0,2);
\class(1,0)
\d2(1,0,,1)
\replacetarget
\d2(1,0,,2)
\end{sseqdata}
\printpage[name = offset example, page=2]
\printpage[name = offset example, page=3]
\begin{sseqpage}[name = offset example, page=3]
\classoptions[offset = {(0,0)}](0,2)
\end{sseqpage}
\end{codeexample}
\end{key}

\begin{key}{tooltip = \meta{text}}%
This key generates a ``tooltip'' over the given class. That is, if you hover
your mouse over it, a little window will popup with the tooltip text. This is
particularly useful to give the coordinates or names of classes in large charts
where it may be hard to tell from looking at the picture what position the class
is in, or there may not be room to supply names to classes.

The tooltip is made using the |\pdftooltip| command from the |pdfcomment|
package. The |pdfcomment| package generates two extra auxiliary files, so it is
not included by default. In order to use the |tooltip| option, you have to use
the |tooltips| package option (e.g., load \sseqpages\ with
|\usepackage[tooltips]{spectralsequences}|). This cannot handle math, but it
will print math expressions into \TeX\ input form. Not all pdf viewers will
display the tooltip correctly. If this concerns you, the command |\sseqtooltip|
is used to produce the tooltip, and you can redefine it as any other command
that takes |\sseqtooltip|\marg{text}\marg{tooltip text} and produces a tooltip.
For instance, on \href{https://tex.stackexchange.com/a/164186/23866}{this stack
exchange post}, there is code that supposedly produces tooltips that work with
Evince. I have not tested whether it works by itself or whether it works with my
package, but you could. You could potentially figure out how to get math to work
in tooltips too -- if you find a satisfactory method, please let me know.

Here's an example:
\begin{codeexample}[]
\begin{sseqpage}[classes = {tooltip = {(\xcoord,\ycoord)}}]
\class(0,0)
\class(0,1)
\class(1,0)
\class(1,1)
\end{sseqpage}
\end{codeexample}

There's another example at the beginning of the section on the
\hyperref[sec:class stack]{class stack}.
\end{key}

\begin{keylist}{
    class:page = \meta{page}\opt{-{}-\meta{page max}},
    generation = \meta{generation}\opt{-{}-\meta{generation max}}
}
\def\classpagehandler#1#2{\textcolor{keycolor}{\noligs{#2}}}
\declarecustomhandler{class:page}{\classpagehandler}
These options only work in |\classoptions|. The |page| option gives a range of
pages for which the options apply to. If only one page is specified, it is the
minimum page and the option applies to all larger pages.
\begin{codeexample}[width = 6cm]
\begin{sseqdata}[ name = page_example, no axes,
    title = \page, title style = {yshift = -0.5cm} ]
\class(0,0)
\classoptions[class:page = 2 -- 3, fill, blue](0,0)
\end{sseqdata}

\printpage[ name = page_example, page = 1 ] \qquad
\printpage[ name = page_example, page = 2 ] \qquad
\printpage[ name = page_example, page = 4 ]
\end{codeexample}
A ``generation'' of a class is the interval from one call of |\class| or
|\replaceclass| to the page on which it next supports or is hit by a
differential. By default the |\classoptions| command adds options only to the
most recent generation of the class in a \sseqdataenv\  environment, or on the
generation appropriate to the current page in a \sseqpageenv\  environment.
Using the |generation| option allows you to provide a single generation or range
of generations of the class that the options should apply to. The first
generation is generation 0, and the most recent generation is generation -1.
Larger negative values count backwards.
\codeexample[from file=class-page2a]
\codeexample[from file=class-page2b]
\end{keylist}

\begin{commandlist}{\xcoord,\ycoord}
These commands represent the $\mathtt{x}$ and $\mathtt{y}$ coordinate of the
current class when used in class options. The only use I have for them is in the
|tooltip| option, but maybe there is some other purpose for them.
\end{commandlist}


\subsection{Options for \sectionstring\d, \sectionstring\structline, and \sectionstring\extension}
Because the main job of the |\d|, |\structline|, and |\extension| commands is to
print an edge on the appropriate pages of the spectral sequence, most \tikzpkg\
options that you could apply to a \tikzpkg\ ``to'' operator (as in%
|\draw (x1,y1) to (x2,y2);|) can be applied to |\d|, |\structline|, and
|\extension|. Some such options are as follows:

\begin{keylist}{source anchor = \meta{anchor}, target anchor = \meta{anchor}}
Because you can't use the normal \tikzpkg\ mechanism for specifying the source
and target anchors, \sseqpages\  has these two keys for |\d|, |\structline|, and
|\extension|:
\begin{codeexample}[width = 4cm]
\begin{sseqpage}[ no axes, yscale = 1.24 ]
\foreach \x in {0,1} \foreach \y in {0,1} {
    \class(\x,\y)
}
\structline(0,0)(0,1)
\structline[ source anchor = north west, target anchor = -30 ](1,0)(1,1)
\end{sseqpage}
\end{codeexample}
\end{keylist}


\begin{keylist}{shorten &gt; = \meta{distance}, shorten &lt; = \meta{distance}}%
These behave exactly like the corresponding options from \tikzpkg\ , shortening
the end and beginning of the edge respectively. Note that you can lengthen the
edge by shortening by a negative amount.
\end{keylist}

\begin{manualentry}{Dash patterns:}
See the \href{\pgfmanualurl#subsubsection.15.3.2}{\tikzpkg\  manual} for a
complete explanation of the dash pattern related options. Some examples:
\begin{codeexample}[width = 6cm]
\begin{sseqpage}[ no axes, yscale = 1.6 ]
\foreach \x in {0,1,2} \foreach \y in {0,1} {
    \class(\x,\y)
}
\structline[densely dotted](0,0)(0,1)
\structline[dashed, red, "a"](1,0)(1,1)
\structline[dash dot, red, "a" black](2,0)(2,1)
\end{sseqpage}
\end{codeexample}
%
\end{manualentry}

\begin{keylist}{%
    bend left = \meta{angle}, bend right = \meta{angle},%
    *in = \meta{anchor}, *out = \meta{anchor}%
}%
\begin{codeexample}[width = 6cm]
\begin{sseqpage}[no axes,yscale = 1.6]
\foreach \x in {0,1,2} \foreach \y in {0,1} {
    \class(\x,\y)
}
\structline[bend left = 20](0,0)(0,1)
\structline[bend right = 20](1,0)(1,1)
\structline[in = 20, out = north](2,0)(2,1)
\end{sseqpage}
\end{codeexample}
\end{keylist}

%\begin{key}{invisible}
%
% This key is only for |\d|. It prevents a differential from being drawn at all.
% The typical reason you might want this is so that you can draw your own
% differential using \tikzpkg\  commands. See |\getdtarget| for an example of
% this.
%
% \end{key}

\begin{key}{structline:page = \meta{page}\opt{-{}-\meta{page max}}}%
This key is only for |\structline| and |\structlineoptions|. By default, the
|\structline| command only adds a structure line starting on the page where the
most recent generation of the source or target is born:

\begin{codeexample}[width = 7.6cm]
\begin{sseqdata}[ name = structpage example,
                  title = \page, yscale = 0.53 ]
\class(0,2)
\class(0,4)
\class(1,0)
\class(1,1)
\d2(1,0)(0,2) \replacesource
\d3(1,1)(0,4) \replacesource
\structline(1,0)(1,1)
\end{sseqdata}
\printpage[name = structpage example,page = 3]
\qquad
\printpage[name = structpage example,page = 4]
\end{codeexample}

By specifying a page number, you can adjust which page the |\structline| starts
on:

\begin{codeexample}[]
\begin{sseqdata}[ name = structpage example2, title = \page, yscale = 0.5 ]
\class(0,2)
\class(0,4)
\class(1,0)
\class(1,1)
\d2(1,0)(0,2) \replacesource
\d3(1,1)(0,4) \replacesource
\structline[structline:page = 2](1,0)(1,1)
\end{sseqdata}
\printpage[ name = structpage example2, page = 1 ]
\qquad
\printpage[ name = structpage example2, page = 2 ]
\qquad
\printpage[ name = structpage example2, page = 3 ]
\qquad
\printpage[ name = structpage example2, page = 4 ]
\end{codeexample}

Similarly, for |\structlineoptions| you can specify a minimum page on which to
apply the options, or a range of pages.
\end{key}

\subsection{Options for \sectionstring\circleclass}
\begin{key}{fit = \meta{coordinates or nodes}}%
The |\circleclasses| command uses the \href{\pgfmanualurl#section.52}{\tikzpkg\
fitting library}. Sometimes it's desirable to make the resulting node fit extra
things, for example a label. It doesn't necessarily end up looking great though.
\begin{codeexample}[]
\begin{sseqpage}[ Adams grading, axes gap = 0.7cm ]
\class(0,2)
\class(1,0)
% Fit in the label x and also a symmetric invisible label to maintain symmetry
\d["x"{name = x}, "x"'{name = x', opacity = 0}]2(1,0)
\circleclasses[fit = (x)(x'), rounded rectangle](1,0)(0,2)
\end{sseqpage}
\end{codeexample}
\end{key}

\begin{key}{rounded rectangle}
You can put a shape as an option and it will change the shape of the node drawn
by |\circleclasses|. Any shape will do, but I think that an |ellipse| or
|rounded rectangle| are the only particularly appealing options.
\end{key}

\begin{key}{ellipse ratio = \meta{ratio} (initially 1.2)}%
By default, the shape drawn by |\circleclasses| is a ``newelipse'' which is a
custom defined shape that respects the option |elipse ratio| which roughly
controls how long and skinny versus short and fat the ellipse is. If you find
that the ellipse is too long, try a larger value of this option, and conversely
if it's too fat try a smaller value. If no value is satisfactory, try out the
|rounded rectangle| shape. (This is stolen from the following stack exchange
answer: \url{https://tex.stackexchange.com/a/24621}.)
\end{key}

\begin{keylist}{
    cc:class style,cc:permanent cycle style,cc:transient cycle style,
    cc:this page class style,cc:differential style,cc:struct line style,cc:extension style
}
See the \pgfmanualpdfref{class style}{corresponding entry} in the \tikzpkg\
primitives section.
\end{keylist}

\begin{key}{cc:page = \meta{page}\opt{-{}-\meta{page max}}}%
By default, the ellipse will be drawn on the same set of pages that a structure
line between the two classes would be drawn on. This specifies a range of pages
for the ellipse to be drawn. Note that unlike with structure lines, you can
instruct |\circleclasses| to draw the shape even on pages where one or both of
the classes that it is fitting are dead.
\end{key}

\subsection{Options for \tikzpkg\  primitives}
\begin{key}{background}%
This key instructs \sseqpages\  to put the current \tikzpkg\  primitive in the
background. The way that the spectral sequence is printed is as follows:
\begin{itemize}
\item The title, axes, axes ticks, and axes labels are printed (the appropriate
steps are skipped when the |no title|, |no axes|, |no ticks|, or |no labels|
keys are used or if no title or axes labels are provided).

\item The \tikzpkg\  background paths are printed.

\item The clipping is inserted (unless the |no clip| key is used).

\item All foreground elements (classes, differentials, structure lines, and
normal \tikzpkg\  paths) are printed.
\end{itemize}

In particular, this means that foreground \tikzpkg\  paths can be clipped by the
standard clipping, but background paths that are outside of the clipping expand
the size of the \tikzpkg\  picture.
\begin{codeexample}[]
\begin{sseqpage}[ no ticks, yscale = 0.9, math nodes = false ]
\class(0,0)
\class(1,1)
\begin{scope}[background]
\draw(0.1,0.1)--(1.1,1.1);
\end{scope}
\node[background] at (0.5,-1) {not clipped};
\node at (0.5,-0.4) {clipped};
\end{sseqpage}
\end{codeexample}
Here is an example where \tikzpkg\ labels with the |background| key are used to
add labels and a grid. Note that this styling is easier to make using the
|title|, |x label|, |y label|, and |grid| options.
\begin{codeexample}[]
\begin{sseqdata}[ name = tikz background example, cohomological Serre grading, classes = fill ]
\begin{scope}[background]
\node at (\xmax/2,\ymax+1.2) {\textup{Page \page}};
\node at (\xmax/2,-1.7) {H^*(B)};
\node[rotate = 90] at (-1.5,\ymax/2) {H^*(F)};
\draw[step = 1cm, gray, very thin] (\xmin-0.5,\ymin-0.5) grid (\xmax+0.4,\ymax+0.5);
\end{scope}
\class(0,0)
\class(3,0)
\class(0,2)
\class(3,2)
\d3(0,2)
\end{sseqdata}
\printpage[name = tikz background example, page = 2]
\printpage[name = tikz background example, page = 3]
\end{codeexample}

For this particular use case, it's probably better to use |title|, |x label|,
and |y label|:
\begin{codeexample}[]
\begin{sseqdata}[ name = tikz background example2, cohomological Serre grading, classes = fill,
                  grid = go, title = { Page \page }, x label = { $H^*(B)$ }, y label = { $H^*(F)$ } ]
\class(0,0)
\class(3,0)
\class(0,2)
\class(3,2)
\d3(0,2)
\end{sseqdata}
\printpage[name = tikz background example2, page = 2]
\printpage[name = tikz background example2, page = 3]
\end{codeexample}

But if you need more flexible labeling, you'll likely want to use tikz
primitives with |background|. See \example{KF3} for an instance where this key
is useful.

One useful tip is that you can ensure consistent bounding boxes between
different diagrams using%
\begin{center}
|\path[background] (smallest x, smallest y) -- (largest x, largest y);|:
\end{center}
\begin{codeexample}[]
\begin{sseqdata}[ name = boundingboxex, x range = {0}{2}, y range = {0}{2}, scale = 0.5 ]
\end{sseqdata}
\printpage[ name = boundingboxex, title = not aligned ]
\quad
\printpage[ name = boundingboxex, x label = Hi ]
\qquad
\begin{sseqpage}[ name = boundingboxex, keep changes, title = aligned ]
\path[background] (\xmin,\ymin-4) -- (\xmax,\ymax+2);
\end{sseqpage}
\quad
\printpage[ name = boundingboxex, x label = Hi, title = {} ]
\end{codeexample}
\end{key}

\begin{keylist}{page constraint = \meta{predicate}, page constraint or = \meta{predicate}}
\declarecustomhandler{page constraint}{\codehandler}
This places a constraint on the pages in which the \tikzpkg\  primitive is
printed. This predicate should look something like \texttt{(\string\page\ &lt;= 4)}
|&amp;&amp;| \texttt{(\string\page\ &gt;= 3)}. The predicate is anded together with any
previous predicates, so that you can use this as an option for a \scopeenv\  and
again for the individual \tikzpkg\ primitive.

\begin{commandlist}{\isalive\pararg{coordinate},\isalive\{\pararg{coordinate 1}$\cdots$\pararg{coordinate n}\}}
This command can only be used with |page constraint|. Saying
\begin{center}
    |page constraint = {\pars{\meta{x},\meta{y}\opt{,}\oarg{index}}}}}|
\end{center}
will print the \tikzpkg\  primitive only on pages where the specified class is alive. Saying
\begin{center}
    |page constraint = {\isalive(\meta{coordinate 1})|$\,\cdots\,$|(\meta{coordinate n})}|
\end{center}
is equivalent to
\begin{center}
    |page constraint = {\isalive\pararg{coordinate 1} &amp;&amp;|$\,\cdots\,$|&amp;&amp; \isalive\pararg{coordinate n}}|
\end{center}
Writing
\begin{center}
    \codeverb|\draw[page constraint = {\isalive(1,0)(2,2)}](1,0)|\texttt{-{}-}|(2,2);|
\end{center}
is the same as |\structline(1,0)(2,2)|, except that you can't later use
|\structlineoptions| on it (and it won't have the |struct lines| style applied).
\end{commandlist}
\end{keylist}

\begin{keylist}{
    class style,permanent cycle style,transient cycle style,
    this page class style,differential style,struct line style,extension style
}
These classes apply the styling of the corresponding element to your \tikzpkg\
commands.
\begin{codeexample}[width = 6cm]
\begin{sseqpage}[ differentials = blue, yscale = 0.65, no axes ]
\class(0,2)
\class(1,0)
% This will be styled as if it were a differential
\draw[differential style] (1,0) -- (0,2);
\end{sseqpage}
\end{codeexample}
See |\getdtarget| for a more natural example.
\end{keylist}



\section{Miscellaneous Commands}
\subsection{Settings}
\begin{command}{\sseqset\marg{keys}}%
The |\sseqset| command is for adjusting the global options for all spectral
sequences in the current scope, or for applying options to the rest of the
current spectral sequence. For instance, if most of the spectral sequences in
the current document are going to be Adams graded, you can say%
|\sseqset{Adams grading}| and all future spectral sequences in the current scope
will have Adams grading (unless you specify a different grading explicitly). As
another example, |\sseqset{no axes}| will suppress axes from spectral sequences
in the current scope. Note that defaults only apply to new \sseqdataenv\
environments or to unnamed \sseqpageenv\ environments; they won't apply to
existing spectral sequences.

You can also use |\sseqset| to create styles to be used in spectral sequences.
\begin{keylist}{
    .global sseq style = \meta{keys},
    .global sseq append style = \meta{keys},
    .sseq style = \meta{keys},
    .sseq append style = \meta{keys}
}%
These handlers create reusable styles to be used in spectral sequences. If this
style is a set of global options, then use the |.global sseq style| handler,
whereas if it is supposed to be applied to individual features (classes,
differentials, structure lines, circle classes, and tikz primitives) then use
the |.sseq style| handler.
\begin{codeexample}[width=6cm]
\sseqset{
    mysseq/.global sseq style = {
        Adams grading, title = Page \page,
        x range = {0}{4}, y range = {0}{2},
        xscale = 0.5, yscale = 1.35
    },
    htwostruct/.sseq style = { gray, thin }
}
\begin{sseqpage}[ mysseq ]
\class(0,0) \class(0,1) \class(0,2) \class(0,3)
\class(3,1) \class(3,2) \class(3,3)
\structline(0,0)(0,1) \structline(0,1)(0,2)
\structline(0,2)(0,3)
\structline(3,1)(3,2) \structline(3,2)(3,3)
\structline[htwostruct](0,0)(3,1)
\structline[htwostruct](0,1)(3,2)
\structline[htwostruct](0,2)(3,3)
\end{sseqpage}
\end{codeexample}
\end{keylist}
\end{command}

\begin{command}{\SseqErrorToWarning\meta{error-name}}%
Turns the error with the given name into a warning. An error message will start
by saying \let\eatclnifpresent\empty|spectralsequences error: "error-name"|.
This is the name you need to put into this command.
\end{command}

\begin{environment}{{quiet}}%
This environment quiets error messages that occur inside of it. \sseqpages\ is
pretty good at error recovery, and so most of commands will fail gracefully and
do nothing if their preconditions aren't met. If there are any parsing errors in
the body of the |{quiet}| environment, prepare to see low level internal error
messages. You might also run into bugs in \sseqpages\ -- the error recovery code
hasn't been that carefully tested. If you do get low level error messages,
remember to comment out the |{quiet}| environment before trying to debug.

This is particularly useful for code reuse commands. Sometimes there is a source
of long differentials that only applies to classes that haven't already
supported shorter differentials. Sometimes there should be a structure line if a
certain class exists, but it might not exist. In these cases, the |{quiet}|
environment will help you out. See also |\DrawIfValidDifferential|, which is a
variant of |\d| that behaves as if it were inside a |{quiet}| environment.
\end{environment}

\subsection{Code reuse commands}
\begin{command}{\foreach }%
This command is from \tikzpkg\  and works in pretty much the same way in
\sseqpages, though with slightly better variants. The |\foreach| command is very
flexible and has a lot of variants. The basic usage is%
|\foreach \x in {\meta{xmin},...,\meta{xmax}} \marg{loop body}| which will
execute |\meta{loop body}| with |\x| set to each value between \meta{xmin} and
\meta{xmax} inclusive. If you want a step greater than 1, try%
%
\begin{center}
|\foreach \x in {\meta{xmin},\meta{xmin}+\meta{xstep},...,\meta{xmax}}\marg{loop body}|.
\end{center}

If you need to do multiple loops with a common body, you can just stack the
|\foreach| commands:
\begin{codeexample}[width=6cm]
\begin{sseqpage}[ xscale = 0.5, x tick step = 2 ]
\foreach \x in {0,2,...,6}
\foreach \y in {0,...,3}{
    \class(\x,\y)
}
\end{sseqpage}
\end{codeexample}

You can also loop through tuples, for instance:
\begin{codeexample}[width=6cm]
\begin{sseqpage}[ xscale = 0.5 ]
\foreach \x/\y/\label in {0/1/a,1/1/b,0/0/c,1/0/d}{
    \class["\label" above](\x,\y)
}
\end{sseqpage}
\end{codeexample}
See the last example for |normalize monomial| for a better example of this
usage.

There are tons of other things you can do with |\foreach|, though I haven't yet
found need for them in combination with \sseqpages. See the
\href{\pgfmanualurl#section.64}{\tikzpkg\  manual} for more details.
\end{command}

\begin{commandlist}{
    \Do\marg{iterations}\meta{loop body},
    \DoUntilOutOfBounds\meta{loop body},
    \DoUntilOutOfBoundsThenNMore\marg{extra iterations}\meta{loop body},
    \iteration
}%
The one use case that |\foreach| doesn't cover all that well is if you want the
loop to always repeat until the features you are drawing go off the page. This
is what |\DoUntilOutOfBounds| and |\DoUntilOutOfBoundsThenNMore| are for. These
help ensure that if you change the range of your chart, infinite families will
automatically be drawn correctly without the need to adjust a bunch of loop
bounds. The purpose of |\DoUntilOutOfBoundsThenNMore| is for towers that are
receiving a differential. If your spectral sequence is Adams graded, and a tower
is receiving a $d_r$ differential from another tower, you should use
|\DoUntilOutOfBoundsThenNMore{r}|:
\begin{codeexample}[width=7cm]
\begin{sseqpage}[
    Adams grading, classes = fill,
    x range = {0}{10}, y range = {0}{6},
    x tick step = 2,
    xscale = 0.3,yscale = 0.7,
    run off differentials = {-&gt;}
]
\class(0,0)
\DoUntilOutOfBoundsThenNMore{3}{
    \class(\lastx+1,\lasty+1)
    \structline
}
\class(4,0)
\d3
\DoUntilOutOfBounds{
    \class(\lastx+1,\lasty+1)
    \structline
    \d3
}
\end{sseqpage}
\end{codeexample}
You can also nest |\DoUntilOutOfBounds| reasonably:
\begin{codeexample}[width=7cm]
\begin{sseqpage}[
    x range = {0}{6}, y range = {0}{6},
    tick step = 2,
    scale = 0.6
]
\class(0,0)
\DoUntilOutOfBounds{
    \class(\lastx+1,\lasty+1)
    \structline
    \DoUntilOutOfBounds{
        \class(\lastx,\lasty+1)
        \structline
    }
}
\end{sseqpage}
\end{codeexample}
One important difference between |\foreach| and the |\Do| family of commands is
that |\Do| has no effect on the stack. This is in order to ensure that they nest
properly.

Note that if you are using these commands and you are planning to draw several
pictures of the chart with restricted range, you need to specify a range for the
\sseqdataenv\ that contains all of the ranges of pages that you want to draw. If
you then want to set a smaller default range, specify the smaller range the
first time you use \sseqpageenv\ or |\printpage| to draw the spectral sequence,
and include the |keep changes| key.

The |\Do| command is less general than |\foreach|; the purpose is to provide a
syntax for stack-based looping that is similar to |\DoUntilOutOfBounds| but with
a fixed range. So |\Do{n}\marg{loop body}| repeats \meta{loop body} |n| times.
The assumption is that the loop body draws something relative to the position of
the |\lastclass|.

If you need to know how many iterations one of these three commands has gone
through, this is stored in the variable |\iteration|.
\end{commandlist}
\begin{commandlist}{\NewSseqCommand    \cmdarg{command}\marg{argspec}\marg{body},
                    \DeclareSseqCommand\cmdarg{command}\marg{argspec}\marg{body}}
% TODO: Explain the difference between NewSseqCommand and DeclareSseqCommand!
The \xparsepkg\ package provides these very powerful commands for defining
macros. They are used internally to the \sseqpages\  package to define |\class|,
|\d|, etc. To help you create variants of these commands, I will record here the
argument specifications for each of them. See the \href{\xparseurl}{\xparsepkg\
manual} for a better explanation and more information.

To make a command like |\class|, you can use the argument specification
|O{}r()|. The argument type \texttt{O\marg{default}} stands for a bracket
delimited optional argument with default value \meta{default}. In this case,
we've specified the default to be empty. |r()| stands for a ``required''
argument delimited by |(| and |)|. In the command definition, access the
optional argument with |#1| and the coordinate with |#2|.
\begin{codeexample}[width = 6.5cm,vbox]
\DeclareDocumentCommand\demo{ O{} r() }
    {  \#1 = \textcolor{purple}{\{#1\}};
       \#2 = \textcolor{purple}{\{#2\}} }
\hbox{\demo[key = value](x,y)}
\bigskip
\hbox{\demo(1,2,3)}
\end{codeexample}
% TODO: explain what u does better
If you want to separate out the coordinates into different arguments, you can
use |O{}u(u,u)|. The argument type |u| stands for ``until'' and scans up until
the next instance of the given character. So in this case, |#1| is of argument
type |O| which is an option list, |#2| corresponds to the |u(| which is a
throw-away argument, then |#3| corresponds to |u,| and contains the $\mathtt{x}$
coordinate, and |#4| corresponds to |u)| and contains the $\mathtt{y}$
coordinate. Note however that this will not match balanced parenthetical
expressions.
\begin{codeexample}[width = 6.5cm,vbox]
\DeclareDocumentCommand\demo{ O{} u( u, u)}
    {  \#1 = \textcolor{purple}{\{#1\}};
       \#3 = \textcolor{purple}{\{#3\}};
       \#4 = \textcolor{purple}{\{#4\}}  }
\hbox{\demo[hi](x,y)}
\bigskip
\hbox{\demo(1,2)}
\bigskip
\hbox{\demo((1+1)*2,2)}
\bigskip
\hbox{\demo(1,(1+1)*2)} % uh-oh -- *2) is left off!
\end{codeexample}
You can specify an optional argument delimited by parentheses using |d()|. Use
the commands |\IfNoValueTF|, |\IfNoValueT|, and |\IfNoValueF| to test whether
the user provided a value.
\begin{codeexample}[width = 6.5cm,vbox]
\DeclareDocumentCommand\demo{ O{} d() } {
       \#1 = \textcolor{purple}{\{#1\}};
       \#2 = \textcolor{purple}{
              \{\IfNoValueTF{#2}{no value}{#2}\} }
}
\hbox{\demo[hi](x,y)}
\bigskip
\hbox{\demo[options]}
\bigskip
\hbox{\demo(1,2)}
\bigskip
\hbox{\demo}
\end{codeexample}
An example where this is actually useful:
\begin{codeexample}[width = 6.5cm]
\DeclareSseqCommand\etaclass{ O{} d() }{
    \IfNoValueF{#2}{ \pushstack(#2) }
    \class[#1] (\lastx+1, \lasty+1)
    \structline
}
\begin{sseqpage}[ classes = fill, yscale = 0.55 ]
\class(0,0)
\class(0,1)
\etaclass\etaclass
\etaclass[blue](0,0)\etaclass
\end{sseqpage}
\end{codeexample}


%The |\d| command has argument specification |O{} U( r()|. The argument type |U| is special to \sseqpages, and is a variant of until that reinserts the delimiting token. This allows the |(| token to also delimit the beginning of the |r()| argument. Note that the argument type |U| is specially added by \sseqpages\ and might be removed in the future if the \LaTeX3 team yells at me or something.
%    \ExplSyntaxOn
%    \cs_set_eq:NN \__xparse_add_type_U:w \sseq__xparse_add_type_U:w
%    \cs_set_eq:NN \__xparse_normalize_type_U:w \sseq__xparse_normalize_type_U:w
%    \sseq@install@xparse@Uarggrabber
%    \ExplSyntaxOff
%\begin{codeexample}[width = 7cm,vbox]
%\DeclareDocumentCommand {\demo} { O{} U( r() }
%    {  \#1 = \textcolor{purple}{\{#1\}};
%       \#2 = \textcolor{purple}{\{#2\}};
%       \#3 = \textcolor{purple}{\{#3\}}  }
%\hbox{\demo[opts]page(x,y)}
%\bigskip
%\hbox{\demo5(x,y)}
%\end{codeexample}

The |\structline| and |\changeclasses| commands have argument specification |O{}r()r()|.
\begin{codeexample}[width = 7cm,vbox]
\DeclareDocumentCommand\demo{ O{} r() r() }
    {  \#1 = \textcolor{purple}{\{#1\}};
       \#2 = \textcolor{purple}{\{#2\}};
       \#3 = \textcolor{purple}{\{#3\}}  }
\hbox{\demo[hi](x,y)(x',y')}
\bigskip
\hbox{\demo(x,y,2)(x',y',-1)}
\end{codeexample}
\end{commandlist}

\begin{commandlist}{\NewSseqGroup\cmdarg{command}\marg{argspec}\marg{body},
                    \DeclareSseqGroup\cmdarg{command}\marg{argspec}\marg{body}}%
These are similar to |\NewSseqCommand| and |\DeclareSseqCommand| except that the
commands defined take an optional square bracket delimited options list,
followed by an optional parenthesis delimited |(x,y)| pair and wraps the body of
the code in%
\begin{center}
|\begin{scope}[xshift = \meta{xcoord}, yshift = \meta{ycoord}, options]|.
\end{center}
For instance:
\begin{codeexample}[width = 8cm]
\DeclareSseqGroup\tower {m} {
    \class(0,0)
    \foreach \n in {1,...,#1} {
        \class(0,\n)
        \structline(0,\n-1)(0,\n)
    }
}
\begin{sseqpage}
\tower[orange]{4}
\tower(1,1){2}
\end{sseqpage}
\end{codeexample}
Here we define a command which takes an options list, a coordinate, and a single
mandatory argument. The options are applied to all the classes and structlines,
the coordinate shifts the origin, and the mandatory argument is the length of
the tower.
\end{commandlist}

\begin{command}{\SseqCopyPage\cmdarg{command}\marg{spectral sequence name}\marg{page}}%
This defines \cmdarg{command} to print all of the classes and structlines on
page |\meta{page}| of the spectral sequence named%
|\meta{spectral sequence name}|, throwing out differentials and tikz primitives.
The resulting command has syntax as if you had used |\DeclareSseqGroup| with no
extra arguments -- that is, it takes an optional options list, which are passed
to a scope, and an optional coordinate pair.
\end{command}

\subsection{Families}
\spectralsequences\ has a concept of ``class families'' that can be drawn or
suppressed as a group, and that can have styling options applied to them as a
group.
\begin{command}{\SseqNewFamily\marg{family name}}%
This makes a new family with name \meta{family name}. The effect of this is to
define global options |\meta{family name} style| which apply options to all
classes in the family, |draw \meta{family name}| which causes the family to be
drawn, and |no \meta{family name}| which suppresses the family (drawing is the
default behavior of course). It also defines an option |\meta{family name}|
which puts a feature into the family -- so it can be used as an option to any of
the normal commands like |\class|, |\d|, |\structline|, etc and to a scope.

\codeexample[vbox, from file=imJ]
\end{command}


\subsection{Utilities}
\begin{command}{\SseqParseInt\cmdarg{macro}\marg{integer expression}}%
Stores the result of evaluating an integer expression into \cmdarg{macro}. An
integer expression consists of |+|, |-|, |*|, |/|, parentheses, and macros that
expand to more of the same. The exact rules regarding what is a valid expression
are pretty much what you would expect. Note that juxtaposition is a syntax
error, not multiplication, so |2(1+1)| is invalid, you must say |2*(1+1)|.
\end{command}

\begin{commandlist}{
    \SseqIfEmptyTF\marg{expression}\marg{true code}\marg{false code},
    \SseqIfEmptyT\marg{expression}\marg{true code},
    \SseqIfEmptyF\marg{expression}\marg{false code}
}%
This tests if an expression is the empty expression. This is mainly useful for
giving systematic labels to things.
\end{commandlist}

\begin{commandlist}{
    \IfExistsTF\marg{page}\pararg{coordinate}\marg{true code}\marg{false code},
    \IfExistsT\marg{page}\pararg{coordinate}\marg{true code},
    \IfExistsF\marg{page}\pararg{coordinate}\marg{false code}
}%
Test whether a class of the given description exists. The description can be any
valid coordinate, including a named coordinate. If the coordinate is not valid,
this will return false.
\end{commandlist}

\begin{commandlist}{
    \IfAliveTF\marg{page}\pararg{coordinate}\marg{true code}\marg{false code},
    \IfAliveT\marg{page}\pararg{coordinate}\marg{true code},
    \IfAliveF\marg{page}\pararg{coordinate}\marg{false code}
}%
Test whether a class is alive on the given page. If the class doesn't exist,
this will return false.
\end{commandlist}

\begin{commandlist}{
    \IfOutOfBoundsTF\pararg{coordinate}\marg{true code}\marg{false code},
    \IfOutOfBoundsT\pararg{coordinate}\marg{true code},
    \IfOutOfBoundsF\pararg{coordinate}\marg{false code},
    \IfInBoundsTF\pararg{coordinate}\marg{true code}\marg{false code},
    \IfInBoundsT\pararg{coordinate}\marg{true code},
    \IfInBoundsF\pararg{coordinate}\marg{false code}
}%
Test whether a class is in bounds or out of bounds. If no such class exists,
returns false.
\end{commandlist}

\begin{commandlist}{
    \IfValidDifferentialTF\meta{page}\pararg{coordinate}\opt{\pararg{target coordinate}}\marg{true code}\marg{false code},
    \IfValidDifferentialT\meta{page}\pararg{coordinate}\opt{\pararg{target coordinate}}\marg{true code},
    \IfValidDifferentialF\meta{page}\pararg{coordinate}\opt{\pararg{target coordinate}}\marg{false code},
    \DrawIfValidDifferentialTF\ooptions\meta{page}\pararg{coordinate}\opt{\pararg{target coordinate}}\marg{true code}\marg{false code},
    \DrawIfValidDifferentialT\ooptions\meta{page}\pararg{coordinate}\opt{\pararg{target coordinate}}\marg{true code},
    \DrawIfValidDifferentialF\ooptions\meta{page}\pararg{coordinate}\opt{\pararg{target coordinate}}\marg{false code},
    \DrawIfValidDifferential\ooptions\meta{page}\pararg{coordinate}\opt{\pararg{target coordinate}}\marg{false code}
}%
Test whether a differential is valid. There are many possible reasons for a
differential to not be valid -- the source or target class could not exist, the
target could not be in the correct grading, etc. If any error would be generated
if you supplied the same arguments to |\d|, this tests false. Otherwise, this
tests true. The command |\DrawIfValidDifferental| draws the differential if it
is valid, whereas |\DrawIfValidDifferentalT| draws the differential and executes
the true code if it is valid, |\DrawIfValidDifferentalF| draws the differential
or executes false code if it isn't valid, etc.
\end{commandlist}



\begin{command}{\SseqNormalizeMonomial}
This command simplifies a monomial by combining like variables and removing
bases that are raised to the 0th power, removing exponents of 1, removing 1's,
and replacing the empty monomial with 1. The variables are sorted by first
occurrence, use |\SseqNormalizeMonomialSetVariables| to set a different sort
order. It outputs its result into |\result|. This command is specifically meant
to be used as a value for |class label handler| or |class name handler|. See the
example in the documentation for |class label handler| for a realistic example.
The exponents must be integers or else it will misbehave.
\begin{codeexample}[]
\SseqNormalizeMonomial{x^0y^0} $\result$, \quad
\SseqNormalizeMonomial{x^3yx^{-1}z^0} $\result$, \quad
\SseqNormalizeMonomial{1x_2^2x^2_2} $\result$
\end{codeexample}
\end{command}

\begin{command}{\SseqNormalizeMonomialSetVariables}
This command takes an undelimited list sets up |\SseqNormalizeMonomial| to sort
the variables in the input in the specified order. This is useful for
consistency, and particularly important for when you use it to name classes.
For example:
\begin{codeexample}[]
% We always want a first, then b, then x_1, then x_2, then x_3
\SseqNormalizeMonomialSetVariables{abx_1x_2x_3}
\SseqNormalizeMonomial{ba} $\result$, \quad
\SseqNormalizeMonomial{bx_1} $\result$, \quad
\SseqNormalizeMonomial{abx_2x_3x_1} $\result$
\end{codeexample}
\SseqNormalizeMonomialSetVariables{}
\end{command}


\begin{command}{\SseqAHSSNameHandler}
This command expects an argument of the form%
|\meta{monomial}[\meta{integer expression}]| and defines |\result| to be |m[n]|
where |m| is the result of applying |\SseqNormalizeMonomial| to the monomial,
and |n| is the result of evaluation the integer expression plus any |yshift|
that is present. This is intended for use with in drawing Atiyah Hirzebruch
spectral sequences. See |class name handler| for an example of the calculation
of $KO^*\mathbb{R}\mathrm{P}^8$.
\end{command}

\subsection{Coordinate parsers and related}
%    \parsecoordinate and \parsedifferential
\begin{command}{\parsecoordinate\cmdarg{macro}(\meta{coordinate})}%
This command parses the coordinate and puts the triple |(x,y,n)| into
\cmdarg{macro}. It also puts the components of the coordinate into macros, for
instance if \cmdarg{macro} is |\coord|, then |\xcoord| will contain the x
coordinate, |\ycoord| will contain the y coordinate, and |\ncoord| will contain
the index. The coordinate can be anything that would be valid to use in a
differential or structure line; this is the macro that is used internally to
handle coordinates.
\end{command}

\begin{command}{\getdtarget\cmdarg{macro}\marg{page}\pars{\sourcecoord}}%
Sets \cmdarg{macro} equal to the coordinates of the target position of a length
\meta{page} differential starting at \sourcecoord. This helps to make commands
that draw fancy differentials.
\end{command}

\begin{command}{\parsedifferential\meta{page}(\meta{differential coordinate})\opt{\pararg{differential target}}}%
This has the same weird syntax of |\d|, except that you are required to put
braces around the page (if it has multiple digits) and you are required to
provide at least one coordinate (you have to say
|\parsedifferential{2}(\lastclass)| for instance). This command is similar in
effect to saying both |\parsecoordinate\source\meta{source coordinate}| and
|\parsecoordinate\target\meta{target coordinate}|, but it handles determination
of the target coordinate for you.


For instance, consider the following example, suggested by Catherine Ray:
\begin{codeexample}[]
% O{} U( r() is the arg-spec for \d, O{} U( r() mm looks like \d with one extra mandatory arguments
\NewSseqCommand{\twods}{ O{} U( r() d()  m }{
    \parsedifferential{#2}(#3)(#4)             % Store the target position in \target
    \nameclass{source}(\sourcecoord,\nsource)  % give names to the three classes
    \nameclass{target1}(\targetcoord,\ntarget)
    \nameclass{target2}(\targetcoord,#5)
%
    \circleclasses[ cc:differential style, name path = circ,
                    #1, page = #2--#2 ]
                    (target1)(target2)         % Circle the classes, use differential style
%
    % record source and targets as hit.
    \kill#2(source) \kill#2(target1) \kill#2(target2)
%
    \path(target1)--(target2)
                coordinate[midway](midpt);% put a coordinate in the center of the two classes
    \path[name path = lin] (source) -- (midpt);% save path from start to midpoint
%
    % draw line in "differential style" from start to intersection point of circ and lin
    \draw[ cc:differential style, #1, page constraint= { \page == #2 },
           name intersections = { of = circ and lin } ]
                (source) -- (intersection-1);
}
\begin{sseqdata}[ name = cathex, Adams grading, differentials = { blue } ]
\class(0,2)\class(0,2)
\class(1,0)\class(1,0)
\twods2(1,0,-1,1){2}
\end{sseqdata}
\printpage[ name = cathex, page = 1 ]
\qquad
\printpage[ name = cathex, page = 2 ]
\qquad
\printpage[ name = cathex, page = 3 ]
\end{codeexample}
\end{command}

\begin{command}{\nameclass\marg{name}\pararg{coordinate}}%
The |\nameclass| command gives a name to a class. It's similar to saying
|\doptions[name = |\meta{name}|]|, but faster. It's also similar to saying
|\pushstack|\pararg{coordinate}. Giving temporary names to coordinates that you
are going to use repeatedly makes the code easier to read and is faster (though
this only matters in very large charts). See |\getdtarget| for an example.
\end{command}

\begin{command}{\tagclass\marg{tag}\pararg{coordinate}}%
The |\tagclass| command gives a tag to a class. It's similar to saying
|\doptions[tag = |\meta{name}|]|, but faster. See \example{tmfmayss} for a use
case for this.
\end{command}

\begin{command}{\gettag\cmdarg{macro}\pararg{coordinate}}%
The |\gettag| command finds the most recent tag applied to the coordinate and
stores it into |\cmdarg{macro}|. This is useful for connecting groups of nodes.
For example, consider the following code, inspired by \example{tmfmayss}.
\begin{codeexample}[width=6cm]
\DeclareSseqCommand \tower { O{} } {
    \begin{scope}[#1]
    \foreach\i in {1,...,7}{
        \class(\lastx,\lasty+1)
        \structline
    }
    \end{scope}
    \restorestack
}
\DeclareSseqCommand \htwotower { O{} d() } {
    \IfNoValueF{#2}{
        \pushstack(#2)
    }
    \begin{scope}[#1]
    \gettag\thetag(\lastclass)
    \class(\lastx+3,\lasty+1)
    \structline[gray]
    \savestack
    \foreach\i in {1,...,7}{
        \class(\lastx,\lasty+1)
        \structline
        \structline[gray](\lastx-3,\lasty-1,\thetag)
    }
    \restorestack
    \end{scope}
}
\begin{sseqpage}[ y range = {0}{6}, x tick step = 3,
    xscale=0.6, yscale=1.3 ]
\class(0,2) \class(0,3) \class(3,2)
\class[tag = h_0^i](0,0)
\tower[tag = h_0^i]
\class(0,2) \class(0,1)

\htwotower[tag = h_2 h_0^i](0,0)
\htwotower[tag = h_2 h_0^i]
\end{sseqpage}
\end{codeexample}
\end{command}


\subsection{The class stack}
\label{sec:class stack}%
The class stack is a linked list of the classes in the order that they are
produced that \sseqpages\  maintains. Whenever you use the |\class| or
|\replaceclass| command, the class you added is pushed onto the stack.

The following commands are used to access the stack:

\begin{commandlist}{\lastx\opt{\meta{n}},\lasty\opt{\meta{n}},\lastclass\opt{\meta{n}}}%
The commands |\lastx| and |\lasty| evaluate to the |x| and |y| position,
respectively, of the $n$th class on the stack. If $n = 0$ you can leave it off.
The command |\lastclass| evaluates to the coordinate of the most recent class on
the stack. This is useful for writing turtle-style code:
\begin{codeexample}[width=6cm]
\DeclareSseqCommand \etaclass {}{
    \class(\lastx+1,\lasty+1)
    \structline
}
\DeclareSseqCommand \divtwoclass {}{
    \class(\lastx,\lasty-1)
    \structline
}
\begin{sseqpage}
\class(0,0)
\savestack
\foreach \y in { 1,...,5 }{
    \class(0,\y)
    \structline
}
\restorestack
\etaclass\etaclass\etaclass
\divtwoclass\divtwoclass
\end{sseqpage}
\end{codeexample}

You can use |\lastx| and |\lasty| in other contexts than in the body of a
\sseqpages\ command, most notably inside |\SseqParseInt| (they also work
correctly when used inside of |\pgfmathparse| and its siblings). For instance,
consider the following tower command:
\begin{codeexample}[width=6cm]
\DeclareSseqCommand \tower { } {
    \savestack
    \SseqParseInt\numclasses{\ymax-\lasty0}
    \foreach \n in {1,...,\numclasses}{
        \class(\lastx,\lasty+1)
        \structline
    }
    \restorestack
}
\begin{sseqpage}[y range = {0}{5}]
\class(0,0)\tower
\class(1,3)\tower
\class(3,2)\tower
\end{sseqpage}
\end{codeexample}
\end{commandlist}


\begin{command}{\pushstack\pararg{coordinate}}%
This adds a class to the top of the stack. The coordinate is specified using the
same syntax as a coordinate for |\structline| or |\replaceclass|.
\end{command}

\begin{commandlist}{\savestack,\restorestack}%
This saves and reverts the stack. Saves nest. Most frequently, you will want to
use these at the start and end of a command.
\end{commandlist}


\section{Styles}%
The \sseqpages\  package has a large number of styles which control the
appearance of specific components (e.g., classes, differentials, or structure
lines) of a spectral sequence. Each style has two corresponding keys: |classes|
and |change classes|.  Saying |classes = |\marg{keys} adds the keys to the list
of options used to style every future class, whereas%
|change classes = |\marg{keys} only makes sense in a \sseqpageenv\  environment,
and temporarily overwrites the list of options. Note that |change classes| only
applies to classes that existed before the current page, and that even with the
|keep changes| option, the |change classes| options are local to the current
page. Compare:
\begin{codeexample}[width = 8cm]
\begin{sseqdata}[ name = style example ]
\class(0,0)\class(1,1)
\end{sseqdata}
\begin{sseqpage}[ name = style example,
                  classes = { fill, blue },
                  title = change new classes ]
\class(0,1)\class(1,0)
\end{sseqpage}
\quad
\begin{sseqpage}[ name = style example,
                  change classes = { fill, blue },
                  title = change old classes ]
\class(0,1)\class(1,0)
\end{sseqpage}
\end{codeexample}

You can modify these styles outside of a spectral sequence or inside it using
|\sseqset|, you can modify them as options to the \sseqdataenv\  and
\sseqpageenv\  environments, or you can modify them as arguments to the
\scopeenv\  environment.

In cases where the same drawing feature is affected by multiple of these styles,
the more specific style takes precedence. For instance, for a class that is the
source or target of a differential on the current page, the precedence order
from lowest to highest goes: |sseq style|, |class style|,%
|transient cycle style|, |this page cycle style|, and then any options from
scopes in the order they appear, and any local options (the options that come
right with the class, e.g., |\class[local options](x,y)|). If you don't want the
options to your scopes to override more specific styles, use |sseq|:
\begin{codeexample}[width = 7cm]
\begin{sseqpage}[ classes = { blue, fill },
   title style = { align = center, text width = 2.4cm },
   title = { everything is orange } ]
\begin{scope}[orange]
\class(0,0) \class(0,1)
\structline(0,0)(0,1)
\end{scope}
\end{sseqpage}

\begin{sseqpage}[ classes = { blue, fill },
   title style = { align = center, text width = 2.4cm },
   title = { only structure line is orange } ]
\begin{scope}[ sseq = orange ]
\class(0,0) \class(0,1)
\structline(0,0)(0,1)
\end{scope}
\end{sseqpage}
\end{codeexample}


Throughout, ``class'' and ``cycle'' are synonyms.
\begin{stylekeylist}{sseqs, change sseqs,sseq,change sseq}%
This passes options to all features in all future spectral sequences in the
current scope. Note that for many global options you can set a default directly
by saying |\sseqset{key = \marg{value}}| and this is in some cases preferable.

\begin{codeexample}[width = 7cm]
% Applies to both of the following sseqs:
\sseqset{ sseqs = { blue, scale = 0.5 } }
\begin{sseqpage}
\foreach \x in {0,1}
\foreach \y in {0,1,2} {
    \class(\x,\y)
}
\end{sseqpage}
\begin{sseqpage}[ Adams grading, classes = fill ]
\foreach \x in {0,1,2}
\foreach \y in {0,1,2} {
    \class(\x,\y)
}
\d2(1,0)
\d2(2,0)
\end{sseqpage}
\end{codeexample}
\end{stylekeylist}

\begin{stylekeylist}{classes, cycles,change classes,change cycles}
\begin{codeexample}[width = 6cm]
\begin{sseqpage}[ classes = { blue, fill, minimum width = 0.5em },
                  scale = 0.5, x tick step = 2, y tick step = 2 ]
\class(0,0)
\class(2,2)
\end{sseqpage}
\end{codeexample}
\end{stylekeylist}


\begin{stylekeylist}{%
    permanent classes, permanent cycles,%
    change permanent classes, change permanent cycles%
}%
These options change the appearance of all permanent cycles (e.g., those classes
which never support or are hit by a differential). For instance, we can circle
the permanent cycles automatically. In the following example, note that because
|permanent cycles| is more specific than |classes|, the%
|permanent cycles = {draw}| command takes precedence over the%
|classes = {draw = none}| command and the permanent cycle nodes are drawn.
\begin{codeexample}[width = 6.5cm]
\begin{sseqpage}[ cohomological Serre grading,
                  classes = { draw = none },
                  permanent cycles = {draw} ]
\foreach \x in {0,2} \foreach \y in {0,1} {
    \class["\mathbb{Z}"](\x,\y)
}
\d2(0,1)
\end{sseqpage}
\end{codeexample}
\end{stylekeylist}

\begin{stylekeylist}{
    transient classes, transient cycles,
    change transient classes,change transient cycles
}%
These options change the appearance of all transient cycles (e.g., those classes
which eventually support or are hit by a differential). Again, this takes
precedence over the |classes| option.
\begin{codeexample}[width = 6.5cm]
\begin{sseqpage}[ cohomological Serre grading,
                  classes = { draw = none },
                  transient cycles = red ]
\foreach \x in {0,2} \foreach \y in {0,1} {
    \class["\mathbb{Z}"](\x,\y)
}
\d2(0,1)
\end{sseqpage}
\end{codeexample}
\end{stylekeylist}

\begin{stylekeylist}{%
    this page classes, this page cycles,%
    change this page classes,change this page cycles%
}%
These options change the appearance of all cycles which support or are hit by a
differential on this page. Any class that is hit on the current page is also a
transient cycle, and so |this page classes| takes precedence over%
|transient cycles|.
\begin{codeexample}[width = 6cm]
\begin{sseqdata}[ name = this page cycles example, Adams grading,
                  transient cycles = { red, fill }, this page cycles = { blue } ]
\class(0,0)
\class(0,2) \class(1,0)
\class(1,3) \class(2,0)
\d2(1,0) \d3(2,0)
\end{sseqdata}
\printpage[ name = this page cycles example, page = 2 ] \qquad
\printpage[ name = this page cycles example, page = 3 ]
\end{codeexample}
\end{stylekeylist}

\begin{stylekeylist}{
    edges, differentials, struct lines, extensions,
    change edges, change differentials, change struct lines, change extensions
}%
The |edges| key applies to both differentials and structure lines. The
|differentials|, |struct lines|, and |extensions| keys take precedence over |edges|.
\end{stylekeylist}

\begin{stylekeylist}{this page struct lines, change this page struct lines}%
This style applies to structure lines whose source or target is hit on the
current page. It takes precedence over |struct lines|.
\end{stylekeylist}

\begin{stylekeylist}{tikz primitives,change tikz primitives}
Applies to all \tikzpkg\  primitives.
\end{stylekeylist}


\begin{stylekeylist}{labels,change labels}%
This style applies to labels on classes, differentials, and structure lines. All
the more specific label styles take precedence over it.
\end{stylekeylist}

\begin{stylekeylist}{
    class labels,inner class labels,outer class labels,
    change class labels,change inner class labels,change outer class labels
}%
Inner class labels specifically applies to class labels that are inside the
node, outer class labels specifically applies to ones outside it:
\begin{codeexample}[]
\begin{sseqpage}[ no axes, classes = { inner sep = 1pt },
    label distance = 2pt,
    outer class labels = { red },
    inner class labels = { blue } ]
\class["a", "b" above](0,0)
\class["a", "c" right](1,0)
\end{sseqpage}
\end{codeexample}
\end{stylekeylist}

\begin{stylekeylist}{
    edge labels,differential labels,struct line labels, extension labels,
    change edge labels,change differential labels,change struct line labels, change extension labels,
}%

\end{stylekeylist}


\subsection{Style-like options}
The options are not styles, but can be modified in the same set of places
(namely, anywhere):

\begin{keylist}{label distance = \meta{dimension}}%
This sets the default distance from a class to an outer label. There are also
variants like |above label distance| corresponding to |above|, |below|, |left|,
|right|, |above left|, |above right|, |below left|, and |below right|.
\begin{codeexample}[width = 6cm]
\begin{sseqpage}[ label distance = 0.3em,
                  right label distance = 0em,
                  no axes, yscale = 1.25 ]
\class["a" above](0,0)
\class["b" above right](0,1)
\class["c" right](1,0)
\class["c" {right = 1em}](1,1)
\end{sseqpage}
\end{codeexample}
\end{keylist}

\begin{keylist}{run off = \meta{start tip}--\meta{end tip},
    run off differentials = \meta{start tip}--\meta{end tip} (initially {...--...}),
    run off struct lines = \meta{start tip}--\meta{end tip}  (initially {...--...}),
    run off extensions = \meta{start tip}--\meta{end tip} (initially {...--...}),}%
Change the default behavior of run off edges for either all edges, just
differentials, just structure lines, or just extensions respectively. Local
arrowhead options override this.

If an edge runs off the edge of the clipping, \sseqpages\ automatically add an
arrowhead to indicate that the edge continues. This option controls which arrow
head is added if the start or end of an edge runs off the page.
\begin{codeexample}[width = 6cm]
\begin{sseqpage}[ x range = {0}{2}, y range = {0}{2},
                  draw orphan edges, run off = &gt;-stealth ]
\class(0,0)
\class(3,0) \class(0,3)
\structline(0,0)(3,0)
\structline[red](0,0)(0,3)
\structline[blue](3,0)(0,3)
\end{sseqpage}
\end{codeexample}
\end{keylist}

\begin{key}{class label handler = \meta{function}}
\declarecustomhandler{class label handler}{\codehandler}%
The value of |class label handler| is a function that is applied to all labels
before displaying them. It should put its output into |\result|. This is
intended to help with code reusability. Because these handlers may crash or have
annoying side-effects on some input, you may want to toggle the value of this
command on and off. To turn this off for the rest of the current spectral
sequence you can say |\sseqset{class label handler = {}}|. You can also use the
|class label handler| key in a \scopeenv.

The main function \sseqpages\ provides for use here is
|\SseqNormalizeMonomial{#1}|. This makes it convenient to translate expressions
with polynomial labels. You can write your own handlers if your \TeX\
programming skills are sufficient. Let me know if there are any other functions
that you want here, and if you implement them yourself, please send me your
implementation. Here is an example of a function that evaluates an arithmetic
expression:
\begin{codeexample}[width=6cm]
\begin{sseqpage}[
    class label handler = { \SseqParseInt\result{#1} }
]
\class["1+1"](0,0)
\class["1+2*(1+3*(4-1))"](1,1)
\end{sseqpage}
\end{codeexample}
Here's an example using |\SseqNormalizeMonomial|:
\begin{codeexample}[width = 6cm]
\NewSseqGroup \test {m} {
    \class["1#1"](0,0)
    \class["\alpha#1"](0,1)
    \class["y#1"](1,0)
    \class["\alpha y#1"](1,1)
}
\begin{sseqpage}[
    class label handler = { \SseqNormalizeMonomial{#1} },
    classes = { draw = none }, class labels = { font = \small } ]
\test{}
\test[red](2,0){y^2}
\test[orange](2,2){\alpha^2y^2}
\test[blue](0,2){\alpha^2}
\end{sseqpage}
\end{codeexample}

Here is another example which demonstrates a useful idiom for drawing Serre
spectral sequences. For a more complete example, see \example{KF3n}. Note the
use of braces in |{Sq^1\iota_2}|. Without braces, |\SseqNormalizeMonomial| will
simplify |Sq^1xSq^2x| into $S^2q^3x^2$, which is obviously undesirable, so the
correct way to input this is |{Sq^1x}{Sq^2x}|. Unfortunately, |\foreach| strips
a pair of braces from its arguments, so you need to put two pairs of braces.
%\pgfmanualpdflabel{normalizemonomialex-labels}
\begin{codeexample}[width=8cm]
\begin{sseqpage}[
  xscale = 1.4,
  classes = { draw = none },
  class label handler = {\SseqNormalizeMonomial{#1}} ]

\foreach \x/\xlabel in
  { 0/1, 2/\iota_2, 3/{{Sq^1\iota_2}}, 4/\iota_2^2 }
\foreach \y/\ylabel in
  { 0/1, 1/\alpha, 2/x, 3/\alpha x, 4/x^2 }
{
    \class["\ylabel\xlabel"] (\x,\y)
}
\end{sseqpage}
\end{codeexample}
\end{key}


\begin{key}{class name handler = \meta{function}}
\declarecustomhandler{class name handler}{\codehandler}%
The value of |class name handler| is a function that is applied to all names
before using them. It should put its output into |\result|. The main functions
intended for use here are |\SseqAHSSNameHandler| and |\SseqNormalizeMonomial|,
though you can make your own. This is applied both when you name the class, as
in \codeverb|\class[name=a](\meta{coordinate})| and when you refer to a class by
name, as in |\structline(a)(b)|. One advantage if you are using
|\SseqNormalizeMonomial| is that you can ensure that |xy| and |yx| refer to the
same class:
\begin{codeexample}[]
\SseqNormalizeMonomialSetVariables{xy}
\begin{sseqpage}[ class name handler = \SseqNormalizeMonomial,
                  classes = {show name = {right,pin}} ]
\class[name = xy](0,0)
\class[name = yxy](0,1)
\class(1,0)
\structline(yx)(yyx)
\end{sseqpage}
\end{codeexample}
The next page is an example drawing the Atiyah Hirzebruch spectral sequence
computing $KO^*\mathbb{R}P^{8}$.
% Have to load from file so that \afterpage doesn't cause trouble with verbatim reading.
\afterpage{%
    An AHSS using \scantokens{|class name handler = \SseqAHSSNameHandler|:}
    \par
    \codeexample[from file=KORP8,vbox]
    \newpage
}
\end{key}

\begin{keylist}{class name prefix = \meta{prefix}, class name postfix = \meta{postfix}}%
These keys add respectively a prefix or a postfix to all names of all classes in
the scope. This is applied both when you name the class, as in
\codeverb|\class[name=a](\meta{coordinate})| and when you refer to a class by
name, as in |\structline(a)(b)|. The prefix and postfix are added to the command
before the |class name handler| is applied, so if you say |name=\meta{the name}|
then the name actually given to the class is the value of |\result| after saying
\begin{center}
|\classnamehander{\meta{name prefix}\meta{the name}\meta{name postfix}}|
\end{center}
\end{keylist}

\section{Global Options}
These options can only be set at the beginning of a \sseqdataenv\  or
\sseqpageenv\  environment. When it makes sense, you can also set a default
value using |\sseqset|. Generally, these options either modify the plot style or
the logic for the spectral sequence.
\begin{key}{name = \meta{sseq name}}%
This option must be used with the \sseqdataenv\  environment where it indicates
the name of the spectral sequence, which will be used with the \sseqpageenv\
environment or |\printpage| command to draw the spectral sequence. The name used
in a \sseqdataenv\  environment must be new unless the environment is used with
the |update existing| key in which case the \sseqdataenv\  environment will add
to the existing spectral sequence. It is optional when used with \sseqpageenv\ ,
and if included the name given must be the name of an existing spectral
sequence.
\end{key}

\begin{key}{page = \meta{page number}\opt{--\meta{page max} (initially 0)}}%
This key is for \sseqpageenv\  and |\printpage|. It specifies which page of the
spectral sequence is to be printed. On page r, all |\class|es that are not hit
by differentials on pages less than r will be printed, as well as all
|\structline|s whose source and target classes are both printed on page r, and
all differentials of length exactly r. The special value |page = 0| prints all
classes, differentials, and structure lines but no extensions. The special value
|page=\infty| will draw the infinity page with extensions.

If you use this key with a range, e.g., |page=2--5|, then all differentials in
that range of lengths will be drawn, so in the example differentials of length
greater than or equal to 2 and less than or equal to 5 are drawn. The larger
number only changes which differentials are drawn, classes and structlines are
drawn as if the page was the small endpoint of the range. If you use 0 for the
\meta{page max}, then all differentials longer than \meta{page number} will be
drawn, e.g., |page=5---0| draws all differentials of length at least 5, but no
extensions. Using |page=5---\infty| will draw all differentials of length at
least 5 and also all extensions whose endpoint classes are in the
final generation on page 5.
\end{key}

\begin{keylist}{%
    degree = \marg{x degree}\marg{y degree},%
    cohomological Serre grading,%
    homological Serre grading,%
    Adams grading%
}%
Specifies the degree of differentials. The \meta{x degree} and \meta{y degree}
should both be mathematical expressions in one variable |#1| that evaluate to
integers on any input. They specify the $\mathtt{x}$ and $\mathtt{y}$
displacement of a page $\mathtt{\#1}$ differential. In practice, they will be
linear expressions with |#1| coefficient 1, -1, or 0.

The |degree| option must be given before placing any differentials. It can be
specified at the beginning of the \sseqdataenv\  environment, at the beginning
of the \sseqpageenv\  environment if it is being used as a standalone page, or
as a default by saying |\sseqset{degree = \marg{x degree}\marg{y degree}}| or
|\sseqset{Adams grading}| outside of the \sseqdataenv\  and \sseqpages\
environments.

You can make a named grading convention by saying \codeverb|\sseqset{my
grading/.sseq grading = \marg{x degree}\marg{y degree}}|. Then later passing%
|my grading| to a spectral sequence is equivalent to saying%
|degree = \marg{x degree}\marg{y degree}|. The following grading conventions
exist by default:
\begin{codeexample}[width = 6cm]
% equivalent to degree = {#1}{1-#1}:
\begin{sseqpage}[ cohomological Serre grading ]
\class(0,1)
\class(2,0)
\d2(0,1)
\end{sseqpage}
\end{codeexample}
\begin{codeexample}[width = 6cm]
% equivalent to degree = {-#1}{#1-1}:
\begin{sseqpage}[ homological Serre grading ]
\class(0,1)
\class(2,0)
\d2(2,0)
\end{sseqpage}
\end{codeexample}
\begin{codeexample}[width = 6cm]
% equivalent to degree = {-1}{#1}:
\begin{sseqpage}[ Adams grading ]
\class(0,2)
\class(1,0)
\d2(1,0)
\end{sseqpage}
\end{codeexample}
\end{keylist}

\begin{keylist}{strict degree, lax degree}
If the degree is strict, then \LaTeX will throw an error if you try to specify a
differential that doesn't have the proper grading. The degree is strict by
default.
\begin{codeexample}[code only]
\begin{sseqdata}[ name = laxdegree, Adams grading ]
\class(0,2)
\class(1,0)
\d3(1,0)(0,2) % Error: differential does not respect grading.
              % Target should be in position (0,3) but instead it is (0,2)...
\end{sseqdata}
\end{codeexample}

\begin{codeexample}[]
\begin{sseqdata}[ name = laxdegree, Adams grading, lax degree, yscale = 0.6 ]
\class(0,2)
\class(1,0)
\d3(1,0)(0,2) % No error because degree checking is off
\end{sseqdata}
\printpage[ name = laxdegree, page = 3 ]
\end{codeexample}
\end{keylist}

\begin{key}{update existing}
This key is only for the \sseqdataenv\  environment. It specifies that the
current \sseqdataenv\  environment is adding data to an existing spectral
sequence. If you don't pass this key, then giving a \sseqdataenv\  environment
the same |name| as a different \sseqdataenv\  environment will cause an error.
This is intended to help you avoid accidentally reusing the same name.
\end{key}


\begin{key}{keep changes =\meta{boolean} (default true)(initially false)}%
This option is only for the \sseqpageenv\  environment, and only works when a
|name| is provided. This option specifies that all of the commands in the
current \sseqpageenv\  environment should be carried forward to future pages of
the same named spectral sequence. For example:
\begin{codeexample}[]
\begin{sseqdata}[ name = keep changes example, Adams grading, y range = {0}{3} ]
\class(0,0)
\class(1,0)
\end{sseqdata}

\begin{sseqpage}[ name = keep changes example, sseq = orange ]
\class(0,2)
\class(1,2)
\classoptions[orange](1,0)
\d2(1,0)
\end{sseqpage} \qquad

\printpage[ name = keep changes example, page = 2 ] \qquad

\begin{sseqpage}[ name = keep changes example, sseq = blue, keep changes ]
\class(0,3)
\class(1,3)
\classoptions[blue](1,0)
\d3(1,0)
\end{sseqpage} \qquad

\printpage[ name = keep changes example, page = 3 ]
\end{codeexample}
Note that the orange classes and differential do not persist because the
|keep changes| option is not set in the first \sseqpageenv\  environment, but the blue
classes and differential do, since the |keep changes| option is set in the
second \sseqpageenv\  environment.
\end{key}


\begin{keylist}{no differentials,draw differentials}
The option |no differentials| suppresses all of the differentials on the current
page, whereas |draw differentials| causes the page appropriate differentials to
be drawn. This is useful for explaining how the computation of a spectral
sequence goes, or if you want to display one of the edges of the spectral
sequence, like in \example{KF3n}.
\end{keylist}

\begin{keylist}{no struct lines,draw struct lines}
The option |no struct lines| suppresses all of the structure lines on the
current page, whereas the option |draw struct lines| causes the page appropriate
structure lines to be drawn.
\end{keylist}

\begin{keylist}{no orphan edges,draw orphan edges}
An edge is an ``orphan'' if both its source and target lie off the page. By
default these are drawn, but with the option |no orphan edges| they are not. If
the option |no orphan edges| has been set, |draw orphan edges| undoes it.
\begin{codeexample}[width = 9cm]
\begin{sseqdata}[
    name = orphan edges example,
    cohomological Serre grading,
    x range = {0}{2}, y range = {0}{2} ]
\class(0,3) \class(3,1)
\d3(0,3)
\class(2,1) \class(4,0)
\d2(2,1)
\end{sseqdata}
\printpage[ name = orphan edges example ]
\quad
\printpage[ name = orphan edges example,
            no orphan edges ]
\end{codeexample}
\end{keylist}


\begin{key}{class pattern = \meta{class pattern name} (initially standard)}%
This key specifies the arrangement of multiple classes at the same coordinate.
The default value is |standard|.
\begin{codeexample}[width = 5cm]
\begin{sseqdata}[ name = class pattern example, no axes, ymirror ]
\class(0,0)
\class(1,0) \class(1,0)
\class(0,1) \class(0,1) \class(0,1)
\class(1,1) \class(1,1) \class(1,1) \class(1,1)
\class(0,2) \class(0,2) \class(0,2) \class(0,2) \class(0,2)
\class(1,2) \class(1,2) \class(1,2) \class(1,2) \class(1,2) \class(1,2)
\end{sseqdata}

\printpage[ name = class pattern example, class pattern = standard ]
\printpage[ name = class pattern example, change classes = blue,
    class pattern = linear, class placement transform = { rotate = 45 } ]
\end{codeexample}

You can add new class patterns using |\SseqNewClassPattern|:
\begin{command}{\SseqNewClassPattern\marg{class pattern name}\marg{offsets}}
Creates a new class pattern. For example, the |linear| class pattern is created
using the command:
\begin{codeexample}[code only]
\SseqNewClassPattern{linear}{
    (0,0);
    (-0.13,0)(0.13,0);
    (-0.2,0)(0,0)(0.2,0);
    (-0.3,0)(-0.1,0)(0.1,0)(0.3,0);
    (-0.4,0)(-0.2,0)(0,0)(0.2,0)(0.4,0);
    (-0.5,0)(-0.3,0)(-0.1,0)(0.1,0)(0.3,0)(0.5,0);
}
\end{codeexample}
For instance the third row indicates that if there are three classes at the
position |(x,y)| they should be printed at |(x-0.2,y)|, |(x,y)|, and
|(x+0.2,y)|. You can give as many rows as you like; \sseqpages\  will throw an
error if there are more classes in any position than the maximum number that
your class pattern can handle -- for instance, the |linear| class pattern can
handle up to six classes based on this definition.
\end{command}
\end{key}


\begin{keylist}{%
    class placement transform = \marg{transform keys},%
    add class placement transform = \marg{transform keys}%
}%
\declareasstyle{class placement transform}\declareasstyle{add class placement transform}%
The option |class placement transform| allows the user to specify a \tikzpkg\
coordinate transform to adjust the relative position of multiple nodes in the
same $\mathtt{(x,y)}$ position. The |class placement transform| key overrides
the previous value of transformations, the |add class placement transform| just
adds the new transformation to the end of the list. This coordinate transform
can only involve rotation and scaling, no translation. Specifying a scaling
factor helps if the nodes are too large and overlap. In some cases a rotation
makes it easier to see which class is the target of a differential.
\begin{codeexample}[width = 5cm]
\begin{sseqpage}[ class placement transform = { xscale = 1.5 },
                  class pattern = linear,
                  classes = { draw = none },
                  xscale = 2, x axis extend end = 0.7cm ]
\class["\mathbb{Z}"](0,0)
\class["\mathbb{Z}/2"](1,1)
\class["\mathbb{Z}/3"](1,1)
\end{sseqpage}
\end{codeexample}
\begin{codeexample}[width = 5cm]
\begin{sseqpage}[ class placement transform = { rotate = 40 },
                  cohomological Serre grading, scale = 0.65,
                  classes = fill, differentials = blue ]
\class(0,0)
\class(0,2)\class(0,2)
\class[red](3,0)\class[green](3,0)\class[blue](3,0)

\d3(0,2,1,2)
\d3(0,2,-1,-1)
\draw[-&gt;,red](3,0,1)--(0,0);
\end{sseqpage}
\end{codeexample}
With multiple large class labels, the best option is to arrange the classes
vertically:
\begin{codeexample}[width = 5.5cm]
\begin{sseqpage}[ classes = {draw = none }, xscale = 2, yscale=1.55,
    class pattern = linear,
    class placement transform = { scale = 1.5, rotate = 90 },
    right clip padding = 20pt, top clip padding = 20pt,
    x axis gap = 30pt, y axis gap = 20pt ]
\class["\iota_3\beta\iota_3"](7,0)
\class["P^1\iota_3"](7,0)

\class["\iota_2\iota_3\beta\iota_3"](7,2)
\class["\iota_2P^1\iota_3"](7,2)

\class["(\beta\iota_3)^2"](8,0)
\class["P^1\beta\iota_3"](8,0)
\class["\beta P^1\iota_3"](8,0)

\class["\iota_2(\beta\iota_3)^2"](8,2)
\class["\iota_2P^1\beta\iota_3"](8,2)
\class["\iota_2\beta P^1\iota_3"](8,2)
\end{sseqpage}
\end{codeexample}
\end{keylist}

\begin{key}{math nodes = \meta{boolean} (default true)(initially true)}%
This key instructs \sseqpages\  to put all labels in math mode automatically.
\end{key}



\subsection{Global coordinate transformations}
Of the normal \tikzpkg\ coordinate transformations, only the following can be
applied to a \sseqpages\  chart:
\begin{keylist}{scale = \meta{factor},xscale = \meta{factor}, yscale = \meta{factor}, xmirror, ymirror}%
Scale the chart by \meta{factor}. Under normal circumstances, you can tell
\tikzpkg\ to mirror a chart by saying, for instance, |xscale = -1|, but
\sseqpages\  needs to be aware that the chart has been mirrored in order to draw
the axes correctly. Thus, if you want to mirror a spectral sequence, use the
|xmirror| and |ymirror| options as appropriate.
\end{keylist}

\begin{key}{rotate = \meta{angle}}
It probably won't look great if you pick an angle that isn't a multiple of 90 degrees.
\end{key}

\subsection{Plot options and axes style}
\begin{keylist}{x range = \marg{x min}\marg{x max},y range = \marg{y min}\marg{y
max}} These options set the x range (respectively y range) to be a specific
interval. By default, if no range is specified then the range is chosen to fit
all the classes. If an x range is specified but no y range, then the y range is
chosen to fit all the classes that lie inside the specified x range, and vice
versa. The values must be integers -- if you want to extend the x axis a
noninteger amount, try using |x axis start extend| or |x axis end extend|.
\end{keylist}

\begin{commandlist}{
    \SseqOrientationNormal,\SseqOrientationSideways,\SseqOrientationToggle
}
By default, the \sseqpageenv\ environment will try to check whether the chart
fits onto the page (without causing overfull boxes). Environments like the
\env{sideways} environment rotate the content by 90 degrees. The range checker
needs to be aware of this. |\SseqOrientationNormal| indicates that the content is
normal (not rotated). |\SseqOrientationSideways| indicates that the content is
rotated 90 degrees (it doesn't matter in which direction). |\SseqOrientationToggle|
swaps between |\SseqOrientationNormal| and |\SseqOrientationSideways|.

\sseqpages\ will automatically detect the chart is being printed inside of a
sideways environment or not. This can be arranged for other environments with
|\AtBeginEnvironment{my-sideways}{\SseqOrientationToggle}|.
\end{commandlist}
\begin{keylist}{range check on (default), range check off, range check standard, range check sideways}
These options control the range checking behavior.

By default \sseqpages\ will try to compute whether the chart fits onto the page
(without causing overfull boxes). The computation isn't perfectly accurate and
it assumes that the entire page is available for the chart to use up, so for
instance if the chart is indented because of |\textindent| or not at the top of
the page, this might give overly large values. Also, the values computed aren't
perfectly accurate.

If the range check is not desirable, you can use |range check off|.

The options |range check standard| and |range check sideways| only work for the
\sseqpageenv\ environment. |range check standard| is equivalent to |range check on| 
and |\SseqOrientationNormal|. |range check sideways| is equivalent to |range check on| 
and |\SseqOrientationSideways|.
\end{keylist}

\begin{keylist}{
    grid = \meta{grid type},
    grid color = \meta{color},
    grid step = \meta{positive integer},
    x grid step = \meta{positive integer},
    y grid step = \meta{positive integer}
}%
Makes \sseqpages\  draw a grid. The grid types and a significant part of the
code that produces them were stolen from the \sseqpkg\ package.
\begin{codeexample}[vbox]
\begin{sseqdata}[ name = grid example, scale = 0.8 ]
\class(0,0)
\class(3,0)
\class(2,1)\class(2,1)
\class(1,2)\class(1,2)\class(1,2)
\class(0,3)
\class(3,3)
\end{sseqdata}
\hbox{
\printpage[ name = grid example, grid = chess, title=chess ]
\qquad
\printpage[ name = grid example, grid = crossword, title=crossword ]
}
\vskip20pt
\hbox{
\printpage[ name = grid example, grid = go, title=go ]
\qquad
\printpage[ name = grid example, grid = none ]
}
\end{codeexample}
It is possible to make your own grid type by defining the command
|\sseq@grid@yourgridname| to draw a grid.

It is a known problem that acrobat reader displays grids very dark and thick.
This is caused by the enhance thin lines ``feature'' of Acrobat reader. You can
turn it off globally by going into the acrobat reader preferences window and
unchecking the ``Enhance thin lines'' checkbox in the ``Rendering'' section.
Unfortunately, there is no way to instruct Acrobat Reader to not apply this
feature to a particular document. This has apparently been annoying graphic
designers for over a decade.

The grid color option changes the color of the grid; the default value is |gray|.
The grid step keys change the grid step.
\end{keylist}

\begin{keylist}{%
    title = \meta{text},%
    title style = \meta{keys},%
    x label = \meta{text},%
    y label = \meta{text},%
    x label style = \meta{keys},%
    y label style = \meta{keys},%
    label style = \meta{keys}%
}
\declareasstyle{title style}
\declareasstyle{x label style}
\declareasstyle{y label style}
\declareasstyle{label style}
This make chart labels.
\begin{codeexample}[width = 6cm]
\begin{sseqpage}[ title = { An example }, yscale = 0.5,
    x label = { x axis label },
    y label = { y axis label },
    label style = { blue, font = \small },
    x label style = { yshift = 5pt },
    ]
\class(0,0)
\class(2,2)
\end{sseqpage}
\end{codeexample}
Note that if you make multiple versions of the same chart and some of the charts
have labels and others don't, they might not align the way you want. An easy
solution to this is to use |\path[background] (min x, min y) -- (max x, max y);|
where the coordinates are below and to the left, respectively above and to the
right, of everything else drawn in any picture. This makes the bounding boxes
for all of the pictures the same size, so that they line up even if the exact
collection of things drawn changes. See the example at the end of the
|background| key for an illustration of this.
\end{keylist}

\needspace{5\baselineskip}
\begin{keylist}{no title, draw title, no x label, no y label, no labels, draw x label, draw y label, draw labels}
Suppress or unsuppress the title, x label, y label, or both x and y labels,
respectively.
\end{keylist}


\begin{keylist}{no x ticks, no y ticks, no ticks, draw x ticks, draw y ticks, draw ticks}
Suppress axes ticks (the numbers next to the axes). Only matters if axes are
drawn. You can make your own ticks using \tikzpkg\  inside a \scopeenv\
environment with the |background| key. For instance, you might want to label the
axes as 0, $n$, $2n$, \ldots You can achieve this as follows: (you can also use
|x tick handler|).
\begin{codeexample}[width = 5.7cm]
\begin{sseqpage}[ no x ticks, x range = {0}{3} ]
\begin{scope}[ background ]
    \node at (0,\ymin - 1) {0};
    % \vphantom is fragile so we have to throw in an extra \protect
    \node at (1,\ymin - 1) {\protect\vphantom{2}n};
\foreach \n in {2,..., \xmax}{
    \node at (\n,\ymin - 1) {\n n};
}
\end{scope}
\class(0,0)
\class(3,2)
\end{sseqpage}
\end{codeexample}
\end{keylist}


\begin{keylist}{x tick step = \meta{positive integer} (initially 1),y tick step = \meta{positive integer} (initially 1),tick step = \meta{positive integer} (initially 1)}
Sets the interval between labels.
\end{keylist}

\begin{keylist}{x tick offset = \meta{integer} (initially 0),y tick offset = \meta{integer} (initially 0),tick offset = \meta{integer} (initially 0)}%
Sets the label offset -- by default the ticks will always be the set of numbers
that are 0 mod \meta{tick step}. Change it so that the ticks are the set of
numbers that are \meta{tick offset} mod \meta{tick step}.
\end{keylist}

\begin{keylist}{
    x major tick step = \meta{nonnegative integer} (initially 0),
    y major tick step = \meta{nonnegative integer} (initially 0),
    major tick step = \meta{nonnegative integer},
    x minor tick step = \meta{nonnegative integer} (initially 0),
    y minor tick step = \meta{nonnegative integer} (initially 0),
    minor tick step = \meta{nonnegative integer}%
}%
If these are nonzero, they control the placement of tick marks on the axes. The
value 0 prevents tick marks from being drawn. Uses |x tick offset| as an offset.
\begin{codeexample}[width=7cm]
\begin{sseqpage}[
    tick step = 5,
    major tick step = 5,
    minor tick step = 1,
    scale = 0.4,
    axes type = frame
]
\class(0,0)
\class(10,10)
\end{sseqpage}
\end{codeexample}
\end{keylist}

\begin{stylekeylist}{x tick style,y tick style,tick style}
Change the tick style:
\begin{codeexample}[width = 7cm]
\begin{sseqpage}[ tick style = { blue, font = \tiny } ]
\class(0,0) \class(2,1)
\end{sseqpage}
\end{codeexample}
\end{stylekeylist}

\begin{keylist}{%
    x tick handler = \meta{function} (initially \#1),%
    y tick handler = \meta{function} (initially \#1),%
    tick handler = \meta{function} (initially \#1)%
}
\declarecustomhandler{x tick handler}{\codehandler}
\declarecustomhandler{y tick handler}{\codehandler}
\declarecustomhandler{tick handler}{\codehandler}
The value for |x tick handler| should be a function that takes in the current
$\mathtt{x}$ value and outputs the appropriate tick. Correspondingly with%
|y tick handler|. The |tick handler| key sets both.
\begin{codeexample}[width = 7cm]
\begin{sseqpage}[ x range = {0}{4}, yscale = 1.78,
    x tick handler = {
        \ifnum#1 = 0\relax
            0
        \else
            \ifnum#1 = 1\relax
                % \vphantom is fragile so we \protect it
                \protect\vphantom{2}n
            \else
                #1n
            \fi
        \fi
    }
]
\class(0,0)
\class(4,2)
\end{sseqpage}
\end{codeexample}
\end{keylist}

\subsection{Layout}
\begin{keylist}{%
    x axis type = \meta{type} (initially border),%
    y axis type = \meta{type} (initially border),%
    axes type = \meta{type} (initially border),%
    no x axis,%
    no y axis,%
    no axes%
}%
The \meta{type} is either |border|, |center|, |frame|, or |none|. |no axes| is a
shorthand for |axes type=none|. The |border| type is the default and puts the
axes on the bottom and left of the picture. The |center| type by default places
the axes to pass through $(0,0)$; this can be modified using the |x axis origin|
and |y axis origin| keys. See \example{KRAHSS} and \example{KUHFPSS} for
examples where this is used. The |frame| type draws a frame around the entire
chart:

\begin{codeexample}[width=6cm]
\begin{sseqpage}[ axes type = frame ]
\class(0,0)
\class(3,2)
\end{sseqpage}
\end{codeexample}
\end{keylist}

\parskip=0pt
\begin{keylist}{%
    x axis origin = \meta{x value} (initially 0),%
    y axis origin = \meta{y value} (initially 0)%
}%
If you use |axes type = center|, these keys change the position of the axes.
Otherwise, they are ignored.
\end{keylist}
%
\begin{keylist}{%
    x axis gap = \meta{dimension} (initially 0.5cm),%
    y axis gap = \meta{dimension} (initially 0.5cm),%
    axes gap = \meta{dimension} (initially 0.5cm)%
}%
%
\end{keylist}
%
\begin{keylist}{%
    x tick gap = \meta{dimension} (initially 0.5cm),%
    y tick gap = \meta{dimension} (initially 0.5cm)%
}
%
\end{keylist}
%
\begin{keylist}{%
    x axis extend start = \meta{dimension} (initially 0.5cm),%
    y axis extend start = \meta{dimension} (initially 0.5cm),%
    x axis extend end = \meta{dimension} (initially 0.5cm),%
    y axis extend end = \meta{dimension} (initially 0.5cm),%
    x axis tail = \meta{dimension} (initially 0.9cm),%
    y axis tail = \meta{dimension} (initially 0.9cm)%
}
\end{keylist}
%
\begin{keylist}{%
    x axis clip padding = \meta{dimension} (initially 0.1cm),%
    y axis clip padding = \meta{dimension} (initially 0.1cm)%
}
\end{keylist}
%
\begin{keylist}{%
    right clip padding = \meta{dimension} (initially 0.1cm),%
    left clip padding = \meta{dimension} (initially 0.1cm),%
    top clip padding = \meta{dimension} (initially 0.1cm),%
    bottom clip padding = \meta{dimension} (initially 0.1cm)%
}
\end{keylist}

\afterpage{
\begin{center}
\input spectralsequencesmanual-layoutcharts
\end{center}
}


\parskip=10pt
\begin{key}{custom clip = \meta{clip path}}%
Give a custom clipping. The clipping specified must be in the form of a valid
\tikzpkg\ path, for instance |\clip (0,0) rectangle (10,10);|. This clipping is
also applied to any grid and is used to draw ellipses on appropriate
differentials or structure lines that go out of bounds and to determine whether
a differential or structure line is an ``orphan''. It is not applied to any
background elements, which is important because these are often used for axes
labels and such that should lie outside of the clipping region. Weird things can
happen with out of range edges if you provide an oddly shaped path.
\end{key}

\begin{key}{clip = \meta{boolean} (default true)(initially true)}%
If this is false the spectral sequence chart won't be clipped. I'm not really
sure why you would want that, but there might be some use case. Setting this to
be false is not fully supported, and it's possible that weird things will happen
with some of the edges that go out of range.
\end{key}


\begin{key}{rotate labels = \meta{boolean} (default true)(initially false)}%
If you use |rotate = 90| but also want the labels rotated (so that the whole
chart is sideways) use this key.
\end{key}
\end{document}
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