Typed target¶

The documents of sbmlode (typst, LaTeX, markdown) lay out the equations of a model as a page. An application which lays out the equations itself, in its own user interface, needs them as data instead: OdeSystem.typeset returns the system typeset for a dialect as frozen dataclasses, the same data the documents are rendered from.

from sbmlode import OdeSystem

system = OdeSystem.from_sbml("model.xml")
typeset = system.typeset("latex")

for ode in typeset.odes:
    print(ode.lhs, "=", " ".join(ode.lines))

\frac{\mathrm{d} \,\mathrm{PX}}{\mathrm{d} t} = v_{\mathrm{Reaction4}} - v_{\mathrm{Reaction7}}
...

The sections¶

typeset(dialect="latex", symbols="id", wrap=None) returns a TypesetSystem with the sections of a document:

section	content
`odes`	the ODE of every state, `TypesetEquation` with `lhs` the derivative `dX/dt` and `lines` the right hand side written with the rates of the reactions and divided by the volume of a species in concentration, minus the dilution `S/V dV/dt` of a species in concentration in a compartment whose size changes, or the rate rule; `origin` is `reactions`, `rate_rule` or `dilution` (a species diluted alone)
`reactions`	the rate of every reaction, `TypesetReaction` with `symbol` (`v` with the id as subscript), `lines` (the kinetic law), the reaction equation, the modifiers and the local parameters
`assignments`	the assignment rules and the rates of the sizes of the compartments with an assignment rule in the order of their dependencies, `TypesetEquation` with `origin` `assignment_rule` or `size_rate`; the rate of a size with a rate rule is its ODE
`functions`	the function definitions, `TypesetFunction` with `lhs` `f(x, y)` and `rhs`
`initial`	the initial assignments and the initial values which are a conversion between amount and concentration, `TypesetEquation` with `origin` `initial_assignment` or `initial_value`
`events`	the events, `TypesetEvent` with the trigger, delay, priority, flags and the assignments with their effective value
`unsupported`	the constructs the system does not hold, `TypesetUnsupported` with the construct (`algebraic rule`, `delay`, `fast reaction`) and the id of its element
`model`, `units`, `compartments`, `species`, `parameters`, `dilution`	the title and metadata, the tables of a document and whether an ODE has a dilution

The math is LaTeX (which KaTeX and MathJax typeset) or typst, a long sum is split into lines of at most four terms, a line after the first begins with its sign. Text, such as a name, is escaped for the dialect. Every equation carries the Symbol of its left hand side as variable, so that an application knows which element an equation belongs to.

Linking the symbols¶

wrap(symbol, typeset) is called with the Symbol and the typeset symbol of every element the math writes, and its result is written instead. It is called for the symbols the documents make up as well: the rate v_{J0} is called with the symbol of the reaction J0, the rate dV/dt of the size of a compartment with the symbol of the rate (of kind rate), the derivative dS/dt of an ODE wraps the symbol of S inside it.

Symbol.source names the element of the model a symbol stands for: (sid,) for an element of the model, (reaction, id) for a local parameter, which the analysis renames to <reaction>_<id>, and (compartment,) for the rate of the size of a compartment, dV/dt. An application resolves it to its own reference of the element. SBML4Humans wraps every symbol as a link of KaTeX, so that a click on a symbol of an equation opens its element:

def wrap(symbol: Symbol, typeset: str) -> str:
    pk = resolve(symbol.source)  # the element in the report, None if there is none
    return typeset if pk is None else rf"\htmlData{{pk={pk}}}{{{typeset}}}"


typeset = system.typeset("latex", "id", wrap)

The symbols are typeset from the ids (symbols="id"), which are SIds and safe inside such a wrapper; symbols="name" typesets the name of an element where it is a valid symbol.