Solution

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

`Solution`

Solution()

One equality-solution branch: Expression assignments and validity conditions.

Index or iterate over the mapping to read assigned variables and their values. Use free_variables() for the family’s free coordinates and variables for all requested unknowns. All assignments hold simultaneously, subject to conditions(), which includes the parent set’s coverage guard.

Examples

from symbolica import Expression, S
x, y = S("x", "y")
branch = Expression.solve(x + y - 1, [x, y])[0]
branch[x] == 1 - y
True
dict(branch) == {x: 1-y}
True
branch.free_variables() == [y]
True
y in branch
False

Attributes

Name	Description
`domain`	The allowed domain of this branch’s unknowns.
`variables`	All requested unknowns in coordinate order, including free variables.

`domain`

Solution.domain: SolveDomain

The allowed domain of this branch’s unknowns.

`variables`

Solution.variables: list[Expression]

All requested unknowns in coordinate order, including free variables.

Methods

Name	Description
`__contains__`	Check whether a variable has an assignment in this branch.
`__getitem__`	Retrieve an assigned Expression; raise KeyError for a free or absent variable.
`__iter__`
`__len__`	Count assignments, excluding free variables.
`__repr__`
`__str__`
`_repr_html_`
`_repr_pretty_`	Display the assignments in IPython.
`as_dict`	Return assigned variables mapped directly to Expressions
`codimension`	Return the number of unknowns minus the dimension, or None if unknown.
`conditions`	Return additional conditions that must hold for this branch to be valid.
`dimension`	Return the number of independent coordinates in this branch, or None if unknown.
`free_variables`	Return the unknowns that remain free within this branch.
`get`	Return an assigned Expression, or None for a free or absent variable.
`is_conditional`	Return whether this branch has additional validity conditions.
`is_point`	Return whether all unknowns have assigned expressions, possibly subject to conditions.
`items`	Return (variable, Expression) pairs, omitting free variables.
`keys`	Return the assigned variables in coordinate order; free variables are omitted.
`values`	Return the assigned Expressions in the same order as `keys()`.

`contains`

Solution.__contains__(variable: Expression) -> bool

Check whether a variable has an assignment in this branch.

Parameters

variable (Expression) Variable to look up; free variables are not mapping keys.

`getitem`

Solution.__getitem__(variable: Expression) -> Expression

Retrieve an assigned Expression; raise KeyError for a free or absent variable.

Parameters

variable (Expression) Variable whose assignment to retrieve.

`iter`

Solution.__iter__() -> Iterator[Expression]

`len`

Solution.__len__() -> int

Count assignments, excluding free variables.

`repr`

Solution.__repr__() -> str

`str`

Solution.__str__() -> str

`_repr_html_`

Solution._repr_html_() -> str

`_repr_pretty_`

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

Display the assignments in IPython.

Parameters

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

`as_dict`

Solution.as_dict() -> dict[Expression, Expression]

Return assigned variables mapped directly to Expressions.

Use free_variables() for free coordinates and conditions() for the restrictions under which these assignments are valid.

`codimension`

Solution.codimension() -> int | None

Return the number of unknowns minus the dimension, or None if unknown.

`conditions`

Solution.conditions() -> list[SolutionCondition]

Return additional conditions that must hold for this branch to be valid.

`dimension`

Solution.dimension() -> int | None

Return the number of independent coordinates in this branch, or None if unknown.

`free_variables`

Solution.free_variables() -> list[Expression]

Return the unknowns that remain free within this branch.

`get`

Solution.get(variable: Expression) -> Expression | None

Return an assigned Expression, or None for a free or absent variable.

Parameters

variable (Expression) Variable whose assignment to retrieve. branch[variable] raises KeyError when the variable is free or absent.

`is_conditional`

Solution.is_conditional() -> bool

Return whether this branch has additional validity conditions.

`is_point`

Solution.is_point() -> bool

Return whether all unknowns have assigned expressions, possibly subject to conditions.

`items`

Solution.items() -> list[tuple[Expression, Expression]]

Return (variable, Expression) pairs, omitting free variables.

`keys`

Solution.keys() -> list[Expression]

Return the assigned variables in coordinate order; free variables are omitted.

`values`

Solution.values() -> list[Expression]

Return the assigned Expressions in the same order as keys().