System

Define systems, which compose elements, interactions, and nested systems on a space, in a time.

System(label='system', *, elements=(), interactions=(), systems=(), space=None, time=None)

Bases: BasePart[BaseSpace, SimpleNamespace]

Composition of elements and the interactions between them, with nested systems, on a space, in a time.

A system is defined by its parts and by nothing about how it runs. An interaction refers to an element by its path relative to the system that holds the interaction, so forest/foxes names the element foxes of the nested system forest. Groups and nested systems without a space of their own live on the space of the system.

Attributes:

Name	Type	Description
laws_	Sequence[BasePart]	The laws the system contributes for the namespace of its last run.

Examples:

>>> from typing import Annotated
>>> from types import SimpleNamespace
>>> from sage.all__sagemath_symbolics import var
>>> from skcomplex.core.elements import Element
>>> from skcomplex.core.laws import RateLaw
>>> from skcomplex.specs import StateSpec
>>> from skcomplex.core.system import System
>>> class DecayElement(Element):
...     def __init__(self, label, x: Annotated[float, StateSpec()] = 1.0):
...         super().__init__(label)
...         self.x = x
...
...     def _get_laws(self, namespace):
...         return [RateLaw(namespace.x, -namespace.x)]
>>> system = System(elements=[DecayElement('decay')]).check().prepare()
>>> namespace = SimpleNamespace(decay=SimpleNamespace(x=var('x')))
>>> [type(law).__name__ for law in system.run(namespace).laws_]
['RateLaw']

Parameters:

Name	Type	Description	Default
label	str	The label of the system, which names it when it is nested in another one.	'system'
elements	Sequence[BaseElement]	The elements and groups.	()
interactions	Sequence[BaseInteraction]	The interactions between the elements.	()
systems	Sequence[System]	The nested systems.	()
space	BaseSpace | None	The space the elements live on, which gives vector states their dimension, or None for none.	None
time	BaseTime | None	The time the system evolves in, ContinuousTime, DiscreteTime with its schedule, or StaticTime, or None to infer it from the laws.	None

Source code in src/skcomplex/core/system.py

def __init__(
    self,
    label: str = 'system',
    *,
    elements: Sequence[BaseElement] = (),
    interactions: Sequence[BaseInteraction] = (),
    systems: Sequence[System] = (),
    space: BaseSpace | None = None,
    time: BaseTime | None = None,
) -> None:
    """Store the label and the parts of the system.

    Args:
        label:
            The label of the system, which names it when it is nested in another one.

        elements:
            The elements and groups.

        interactions:
            The interactions between the elements.

        systems:
            The nested systems.

        space:
            The space the elements live on, which gives vector states their dimension, or `None` for none.

        time:
            The time the system evolves in, `ContinuousTime`, `DiscreteTime` with its schedule, or `StaticTime`, or
            `None` to infer it from the laws.
    """
    super().__init__(label)
    self.elements = elements
    self.interactions = interactions
    self.systems = systems
    self.space = space
    self.time = time