SolutionSet

Symbolica documentation for getting started, symbolic expressions, numerical evaluation, pattern matching, and APIs in Python and Rust.

`SolutionSet`

SolutionSet()

Exact solutions returned by Expression.solve.

Iterate or index this set to get Solution branches. Each branch describes an alternative: a point, or a family of points with free variables. len(result) counts branches, so a set of length one can still contain infinitely many points. Branch order is not guaranteed.

For a generic result, the assignments apply where coverage_guard is true. Solve again after substituting parameter values outside that guard. Use dict(result[i]) or result[i].as_dict() to extract assignments. Use branch.free_variables() and branch.conditions() to inspect a family’s free coordinates and validity restrictions.

Printing a set shows each branch’s assignments and restrictions; notebooks display them as aligned equations. A branch with an empty mapping describes a family in which all requested variables are free.

Examples

from symbolica import Expression, S, Reals
x = S("x")
result = Expression.solve(x.eq(2), [x], domain=Reals)
print(result)
[0] {x = 2}
dict(result[0]) == {x: 2}
True
bool(Expression.solve(x**2 + 1, [x], domain=Reals))
False

Attributes

Name	Description
`coverage`	Whether the represented solutions are complete or generic.
`coverage_guard`	The condition under which the coverage claim applies.
`domain`	The solve domain, also used as the default domain of external parameters.
`parameters`	Symbols treated as fixed parameters during the solve.
`variables`	The unknowns requested in the solve, in the original input order.

`coverage`

SolutionSet.coverage: Literal['complete', 'generic']

Whether the represented solutions are complete or generic.

`coverage_guard`

SolutionSet.coverage_guard: Condition

The condition under which the coverage claim applies.

`domain`

SolutionSet.domain: SolveDomain

The solve domain, also used as the default domain of external parameters.

`parameters`

SolutionSet.parameters: list[Expression]

Symbols treated as fixed parameters during the solve.

`variables`

SolutionSet.variables: list[Expression]

The unknowns requested in the solve, in the original input order.

Methods

Name	Description
`__bool__`
`__getitem__`
`__iter__`
`__len__`
`__repr__`
`__str__`
`_repr_html_`
`_repr_pretty_`	Display assignments using IPython’s pretty printer.
`dimension`	Return the largest branch dimension for fixed external parameter values
`is_empty`	Return whether there are no solutions

`bool`

SolutionSet.__bool__() -> bool

`getitem`

SolutionSet.__getitem__(index: int) -> Solution

`iter`

SolutionSet.__iter__() -> Iterator[Solution]

`len`

SolutionSet.__len__() -> int

`repr`

SolutionSet.__repr__() -> str

`str`

SolutionSet.__str__() -> str

`_repr_html_`

SolutionSet._repr_html_() -> str

`_repr_pretty_`

SolutionSet._repr_pretty_(pretty: Any, cycle: bool) -> None

Display assignments using IPython’s pretty printer.

Parameters

pretty (Any) IPython’s pretty printer.
cycle (bool) Whether this object is already being displayed.

`dimension`

SolutionSet.dimension() -> int | None

Return the largest branch dimension for fixed external parameter values.

A finite nonempty collection of points has dimension zero; a free line has dimension one. Returns -1 for a complete empty set, or None if unknown.

`is_empty`

SolutionSet.is_empty() -> bool

Return whether there are no solutions.

Raises IncompleteCoverage if completeness is not established or emptiness depends on unresolved branch conditions. bool(result) is the opposite of this check; use len(result) to count represented branches.