HeldExpression

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

HeldExpression

HeldExpression()

Methods

Name Description
__add__ Add this transformer to other, returning the result.
__call__ Execute a bound transformer
__eq__ Compare two transformers.
__ge__ Compare two transformers
__gt__ Compare two transformers
__le__ Compare two transformers
__lt__ Compare two transformers
__mul__ Add this transformer to other, returning the result.
__neg__ Negate the current transformer, returning the result.
__neq__ Compare two transformers.
__pow__ Take self to power exp, returning the result.
__radd__ Add this transformer to other, returning the result.
__rmul__ Add this transformer to other, returning the result.
__rpow__ Take base to power self, returning the result.
__rsub__ Subtract this transformer from other, returning the result.
__rtruediv__ Divide other by this transformer, returning the result.
__rxor__ Returns a warning that ** should be used instead of ^ for taking a power.
__sub__ Subtract other from this transformer, returning the result.
__truediv__ Divide this transformer by other, returning the result.
__xor__ Returns a warning that ** should be used instead of ^ for taking a power.
contains Create a transformer that checks if the expression contains the given element.
is_type Test if the transformed expression is of a certain type.
matches Create a transformer that tests whether the pattern is found in the expression

__add__

HeldExpression.__add__(other: HeldExpression | Expression | int | float | complex | Decimal) -> HeldExpression

Related type: Expression

Add this transformer to other, returning the result.

Parameters

  • other (HeldExpression | Expression | int | float | complex | Decimal) The other operand to combine or compare with.

__call__

HeldExpression.__call__() -> Expression

Execute a bound transformer. If the transformer is unbound, you can call it with an expression as an argument.

Examples

from symbolica import *
x = S('x')
e = (x+1)**5
e = e.hold(T().expand())()
print(e)

__eq__

HeldExpression.__eq__(other: HeldExpression | Expression | int | float | complex | Decimal) -> Condition

Related types: Expression, Condition

Compare two transformers.

Parameters

  • other (HeldExpression | Expression | int | float | complex | Decimal) The other operand to combine or compare with.

__ge__

HeldExpression.__ge__(other: HeldExpression | Expression | int | float | complex | Decimal) -> Condition

Related types: Expression, Condition

Compare two transformers. If any of the two expressions is not a rational number, an interal ordering is used.

Parameters

  • other (HeldExpression | Expression | int | float | complex | Decimal) The other operand to combine or compare with.

__gt__

HeldExpression.__gt__(other: HeldExpression | Expression | int | float | complex | Decimal) -> Condition

Related types: Expression, Condition

Compare two transformers. If any of the two expressions is not a rational number, an interal ordering is used.

Parameters

  • other (HeldExpression | Expression | int | float | complex | Decimal) The other operand to combine or compare with.

__le__

HeldExpression.__le__(other: HeldExpression | Expression | int | float | complex | Decimal) -> Condition

Related types: Expression, Condition

Compare two transformers. If any of the two expressions is not a rational number, an interal ordering is used.

Parameters

  • other (HeldExpression | Expression | int | float | complex | Decimal) The other operand to combine or compare with.

__lt__

HeldExpression.__lt__(other: HeldExpression | Expression | int | float | complex | Decimal) -> Condition

Related types: Expression, Condition

Compare two transformers. If any of the two expressions is not a rational number, an interal ordering is used.

Parameters

  • other (HeldExpression | Expression | int | float | complex | Decimal) The other operand to combine or compare with.

__mul__

HeldExpression.__mul__(other: HeldExpression | Expression | int | float | complex | Decimal) -> HeldExpression

Related type: Expression

Add this transformer to other, returning the result.

Parameters

  • other (HeldExpression | Expression | int | float | complex | Decimal) The other operand to combine or compare with.

__neg__

HeldExpression.__neg__() -> HeldExpression

Negate the current transformer, returning the result.

__neq__

HeldExpression.__neq__(other: HeldExpression | Expression | int | float | complex | Decimal) -> Condition

Related types: Expression, Condition

Compare two transformers.

Parameters

  • other (HeldExpression | Expression | int | float | complex | Decimal) The other operand to combine or compare with.

__pow__

HeldExpression.__pow__(exp: HeldExpression | Expression | int | float | complex | Decimal) -> HeldExpression

Related type: Expression

Take self to power exp, returning the result.

Parameters

  • exp (HeldExpression | Expression | int | float | complex | Decimal) The exponent.

__radd__

HeldExpression.__radd__(other: HeldExpression | Expression | int | float | complex | Decimal) -> HeldExpression

Related type: Expression

Add this transformer to other, returning the result.

Parameters

  • other (HeldExpression | Expression | int | float | complex | Decimal) The other operand to combine or compare with.

__rmul__

HeldExpression.__rmul__(other: HeldExpression | Expression | int | float | complex | Decimal) -> HeldExpression

Related type: Expression

Add this transformer to other, returning the result.

Parameters

  • other (HeldExpression | Expression | int | float | complex | Decimal) The other operand to combine or compare with.

__rpow__

HeldExpression.__rpow__(base: HeldExpression | Expression | int | float | complex | Decimal) -> HeldExpression

Related type: Expression

Take base to power self, returning the result.

Parameters

  • base (HeldExpression | Expression | int | float | complex | Decimal) The base expression.

__rsub__

HeldExpression.__rsub__(other: HeldExpression | Expression | int | float | complex | Decimal) -> HeldExpression

Related type: Expression

Subtract this transformer from other, returning the result.

Parameters

  • other (HeldExpression | Expression | int | float | complex | Decimal) The other operand to combine or compare with.

__rtruediv__

HeldExpression.__rtruediv__(other: HeldExpression | Expression | int | float | complex | Decimal) -> HeldExpression

Related type: Expression

Divide other by this transformer, returning the result.

Parameters

  • other (HeldExpression | Expression | int | float | complex | Decimal) The other operand to combine or compare with.

__rxor__

HeldExpression.__rxor__(a: Any) -> HeldExpression

Returns a warning that ** should be used instead of ^ for taking a power.

Parameters

  • a (Any) The operand passed with ^; use ** for exponentiation instead.

__sub__

HeldExpression.__sub__(other: HeldExpression | Expression | int | float | complex | Decimal) -> HeldExpression

Related type: Expression

Subtract other from this transformer, returning the result.

Parameters

  • other (HeldExpression | Expression | int | float | complex | Decimal) The other operand to combine or compare with.

__truediv__

HeldExpression.__truediv__(other: HeldExpression | Expression | int | float | complex | Decimal) -> HeldExpression

Related type: Expression

Divide this transformer by other, returning the result.

Parameters

  • other (HeldExpression | Expression | int | float | complex | Decimal) The other operand to combine or compare with.

__xor__

HeldExpression.__xor__(a: Any) -> HeldExpression

Returns a warning that ** should be used instead of ^ for taking a power.

Parameters

  • a (Any) The operand passed with ^; use ** for exponentiation instead.

contains

HeldExpression.contains(element: HeldExpression | Expression | int | float | complex | Decimal) -> Condition

Related types: Expression, Condition

Create a transformer that checks if the expression contains the given element.

Parameters

  • element (HeldExpression | Expression | int | float | complex | Decimal) The element that should be contained in the expression.

is_type

HeldExpression.is_type(atom_type: AtomType) -> Condition

Related types: AtomType, Condition

Test if the transformed expression is of a certain type.

Parameters

  • atom_type (AtomType) The atom type to test or require.

matches

HeldExpression.matches(
    lhs: Expression | int | float | complex | Decimal,
    cond: PatternRestriction | Condition | None = None,
    min_level: int = 0,
    max_level: int | None = None,
    level_range: tuple[int, int | None] | None = None,
    level_is_tree_depth: bool = False,
    partial: bool = True,
    allow_new_wildcards_on_rhs: bool = False,
) -> Condition

Related types: Expression, PatternRestriction, Condition

Create a transformer that tests whether the pattern is found in the expression. Restrictions on the pattern can be supplied through cond.

Parameters

  • lhs (Expression | int | float | complex | Decimal) The expression to match against.
  • cond (PatternRestriction | Condition | None) An additional restriction that a match or replacement must satisfy.
  • min_level (int) The minimum level at which a match is allowed.
  • max_level (int | None) The maximum level at which a match is allowed.
  • level_range (tuple[int, int | None] | None) The (min_level, max_level) range in which matches are allowed.
  • level_is_tree_depth (bool) Whether levels should be measured by tree depth instead of function nesting.
  • partial (bool) Whether matches are allowed inside larger expressions instead of only at the top level.
  • allow_new_wildcards_on_rhs (bool) Whether wildcards that appear only on the right-hand side are allowed.