pycommute.expression

Polynomial expressions involving quantum-mechanical operators and manipulations with them

Index sequence

Note

Indices objects are not the same thing as Python tuples because they follow a different ordering rule. Unlike the Python tuples, two index sequences I1 and I2 always compare as I1 < I2 if len(I1) < len(I2).

class pycommute.expression.Indices

Mixed sequence of integer/string indices

__eq__(self: pycommute.expression.Indices, arg0: pycommute.expression.Indices) → bool

__getitem__(self: pycommute.expression.Indices, arg0: int) → int | str

Individual index access.

__gt__(self: pycommute.expression.Indices, arg0: pycommute.expression.Indices) → bool

__hash__ = None

__init__(self: pycommute.expression.Indices, *args) → None

Construct an index sequence from positional integer/string arguments.

__iter__(self: pycommute.expression.Indices) → Iterator[int | str]

__len__(self: pycommute.expression.Indices) → int

Index sequence length.

__lt__(self: pycommute.expression.Indices, arg0: pycommute.expression.Indices) → bool

__ne__(self: pycommute.expression.Indices, arg0: pycommute.expression.Indices) → bool

__repr__(self: pycommute.expression.Indices) → str

property indices

Index sequence as a list of integers and strings

Algebra ID constants

Fermionic algebra ID

expression.FERMION = -3

Bosonic algebra ID

expression.BOSON = -2

Spin algebra ID

expression.SPIN = -1

Algebra generator objects

class pycommute.expression.Generator

Abstract algebra generator

__eq__(self: pycommute.expression.Generator, g2: pycommute.expression.Generator) → bool

__gt__(self: pycommute.expression.Generator, g2: pycommute.expression.Generator) → bool

__hash__ = None

__lt__(self: pycommute.expression.Generator, g2: pycommute.expression.Generator) → bool

__ne__(self: pycommute.expression.Generator, g2: pycommute.expression.Generator) → bool

__repr__(self: pycommute.expression.Generator) → str

property algebra_id

ID of the algebra this generator belongs to.

property indices

Indices carried by this generator.

class pycommute.expression.GeneratorFermion

Bases: Generator

Generator of the fermionic algebra

__init__(self: pycommute.expression.GeneratorFermion, dagger: bool, indices: pycommute.expression.Indices) → None

Construct a creation or annihilation fermionic operator with given indices.

Parameters:

• dagger – True/False for a creation/annihilation operator respectively.

• indices – Index sequence of the creation/annihilation operator.

property dagger

Is this generator a creation operator?

expression.make_fermion(dagger: bool, *args) → pycommute.expression.GeneratorFermion

Make a creation or annihilation fermionic operator with indices passed as positional arguments.

Parameters:

• dagger – True/False for a creation/annihilation operator respectively.

• *args – Indices of the creation/annihilation operator.

class pycommute.expression.GeneratorBoson

Bases: Generator

Generator of the bosonic algebra

__init__(self: pycommute.expression.GeneratorBoson, dagger: bool, indices: pycommute.expression.Indices) → None

Construct a creation or annihilation bosonic operator with given indices.

Parameters:

• dagger – True/False for a creation/annihilation operator respectively.

• indices – Index sequence of the creation/annihilation operator.

property dagger

Is this generator a creation operator?

expression.make_boson(dagger: bool, *args) → pycommute.expression.GeneratorBoson

Make a creation or annihilation bosonic operator with indices passed as positional arguments.

Parameters:

• dagger – True/False for a creation/annihilation operator respectively.

• *args – Indices of the creation/annihilation operator.

class pycommute.expression.SpinComponent

Enumeration: spin operator component, \(S_+\), \(S_-\) or \(S_z\).

Members:

PLUS : Label for the spin raising operators \(S_+ = S_x + i S_y\)

MINUS : Label for the spin lowering operators \(S_- = S_x - i S_y\)

Z : Label for the 3rd spin projection operators \(S_z\)

class pycommute.expression.GeneratorSpin

Bases: Generator

Generator of the spin algebra

__init__(*args, **kwargs)

Overloaded function.

1. __init__(self: pycommute.expression.GeneratorSpin, c: pycommute.expression.SpinComponent, indices: pycommute.expression.Indices) -> None

Construct a spin-1/2 operator corresponding to a single spin component and carrying given indices.

Parameters:

• c – Which spin component to construct, one of SpinComponent values.

• indices – Index sequence of the spin component operator.

2. __init__(self: pycommute.expression.GeneratorSpin, spin: float, c: pycommute.expression.SpinComponent, indices: pycommute.expression.Indices) -> None

Construct an operator for a general spin \(S\) corresponding to a single spin component and carrying given indices.

Parameters:

• spin – Integer or half-integer value of spin \(S\).

• c – Which spin component to construct, one of SpinComponent values.

• indices – Index sequence of the spin component operator.

property component

Whether this generator \(S_+\), \(S_-\) or \(S_z\)?

property multiplicity

Multiplicity \(2S+1\) of the spin algebra this generator belongs to.

property spin

Spin \(S\) of the algebra this generator belongs to.

expression.make_spin(*args, **kwargs)

Overloaded function.

1. make_spin(c: pycommute.expression.SpinComponent, *args) -> pycommute.expression.GeneratorSpin

Make a spin-1/2 operator corresponding to a single spin component and carrying indices passed as positional arguments.

Parameters:

• c – Which spin component to construct, one of SpinComponent values.

• *args – Indices of the operator.

2. make_spin(spin: float, c: pycommute.expression.SpinComponent, *args) -> pycommute.expression.GeneratorSpin

Make an operator for a general spin \(S\) corresponding to a single spin component and carrying indices passed as positional arguments.

Parameters:

• spin – Integer or half-integer value of spin \(S\).

• c – Which spin component to construct, one of SpinComponent values.

• *args – Indices of the operator.

Monomial object

class pycommute.expression.Monomial

Monomial: a product of algebra generators

__contains__(self: pycommute.expression.Monomial, arg0: pycommute.expression.Generator) → bool

__copy__(self: pycommute.expression.Monomial) → pycommute.expression.Monomial

__deepcopy__(self: pycommute.expression.Monomial, memo: dict) → pycommute.expression.Monomial

__eq__(self: pycommute.expression.Monomial, arg0: pycommute.expression.Monomial) → bool

__getitem__(*args, **kwargs)

Overloaded function.

1. __getitem__(self: pycommute.expression.Monomial, arg0: int) -> pycommute.expression.Generator

Get a generator in the monomial by its index.

2. __getitem__(self: pycommute.expression.Monomial, arg0: slice) -> pycommute.expression.Monomial

Get a slice of the monomial.

__gt__(self: pycommute.expression.Monomial, arg0: pycommute.expression.Monomial) → bool

__hash__ = None

__init__(*args, **kwargs)

Overloaded function.

1. __init__(self: pycommute.expression.Monomial) -> None

Construct an identity monomial (a product of zero generators).

2. __init__(self: pycommute.expression.Monomial, arg0: list[pycommute.expression.Generator]) -> None

Construct from a list of algebra generators.

__iter__(self: pycommute.expression.Monomial) → Iterator[pycommute.expression.Generator]

__len__(self: pycommute.expression.Monomial) → int

Number of generators in this monomial.

__lt__(self: pycommute.expression.Monomial, arg0: pycommute.expression.Monomial) → bool

__mul__(*args, **kwargs)

Overloaded function.

1. __mul__(self: pycommute.expression.Monomial, arg0: pycommute.expression.Generator) -> pycommute.expression.Monomial

2. __mul__(self: pycommute.expression.Monomial, arg0: pycommute.expression.Monomial) -> pycommute.expression.Monomial

__ne__(self: pycommute.expression.Monomial, arg0: pycommute.expression.Monomial) → bool

__repr__(self: pycommute.expression.Monomial) → str

__reverse__(self: pycommute.expression.Monomial) → Iterator[pycommute.expression.Generator]

__rmul__(self: pycommute.expression.Monomial, arg0: pycommute.expression.Generator) → pycommute.expression.Monomial

property is_ordered

Is this monomial canonically ordered?

swap_generators(self: pycommute.expression.Monomial, n1: int, n2: int) → None

Swap two generators at given positions within the monomial.

Parameters:

• n1 – Position of the first generator to be swapped.

• n2 – Position of the second generator to be swapped.

Expression objects

class pycommute.expression.ExpressionR

Polynomial in quantum-mechanical operators with real coefficients

__add__(*args, **kwargs)

Overloaded function.

1. __add__(self: pycommute.expression.ExpressionR, arg0: pycommute.expression.ExpressionR) -> pycommute.expression.ExpressionR

2. __add__(self: pycommute.expression.ExpressionR, arg0: float) -> pycommute.expression.ExpressionR

3. __add__(self: pycommute.expression.ExpressionR, arg0: pycommute.expression.ExpressionC) -> pycommute.expression.ExpressionC

4. __add__(self: pycommute.expression.ExpressionR, arg0: complex) -> pycommute.expression.ExpressionC

__copy__(self: pycommute.expression.ExpressionR) → pycommute.expression.ExpressionR

__deepcopy__(self: pycommute.expression.ExpressionR, memo: dict) → pycommute.expression.ExpressionR

__eq__(self: pycommute.expression.ExpressionR, arg0: pycommute.expression.ExpressionR) → bool

__hash__ = None

__iadd__(*args, **kwargs)

Overloaded function.

1. __iadd__(self: pycommute.expression.ExpressionR, arg0: pycommute.expression.ExpressionR) -> pycommute.expression.ExpressionR

2. __iadd__(self: pycommute.expression.ExpressionR, arg0: float) -> pycommute.expression.ExpressionR

__imul__(*args, **kwargs)

Overloaded function.

1. __imul__(self: pycommute.expression.ExpressionR, arg0: pycommute.expression.ExpressionR) -> pycommute.expression.ExpressionR

2. __imul__(self: pycommute.expression.ExpressionR, arg0: float) -> pycommute.expression.ExpressionR

__init__(*args, **kwargs)

Overloaded function.

1. __init__(self: pycommute.expression.ExpressionR) -> None

Construct a zero expression.

2. __init__(self: pycommute.expression.ExpressionR, x: float) -> None

Construct a constant expression equal to \(x\).

Parameters:

x – Constant \(x\).

3. __init__(self: pycommute.expression.ExpressionR, x: float, m: pycommute.expression.Monomial) -> None

Construct an expression with one monomial, \(x \cdot m\).

Parameters:

• x – Coefficient \(x\).

• m – Monomial \(m\).

__isub__(*args, **kwargs)

Overloaded function.

1. __isub__(self: pycommute.expression.ExpressionR, arg0: pycommute.expression.ExpressionR) -> pycommute.expression.ExpressionR

2. __isub__(self: pycommute.expression.ExpressionR, arg0: float) -> pycommute.expression.ExpressionR

__iter__(self: pycommute.expression.ExpressionR) → Iterator[tuple[pycommute.expression.Monomial, float]]

__len__(self: pycommute.expression.ExpressionR) → int

Number of monomials in this expression.

__mul__(*args, **kwargs)

Overloaded function.

1. __mul__(self: pycommute.expression.ExpressionR, arg0: pycommute.expression.ExpressionR) -> pycommute.expression.ExpressionR

2. __mul__(self: pycommute.expression.ExpressionR, arg0: float) -> pycommute.expression.ExpressionR

3. __mul__(self: pycommute.expression.ExpressionR, arg0: pycommute.expression.ExpressionC) -> pycommute.expression.ExpressionC

4. __mul__(self: pycommute.expression.ExpressionR, arg0: complex) -> pycommute.expression.ExpressionC

__ne__(self: pycommute.expression.ExpressionR, arg0: pycommute.expression.ExpressionR) → bool

__neg__(self: pycommute.expression.ExpressionR) → pycommute.expression.ExpressionR

__radd__(*args, **kwargs)

Overloaded function.

1. __radd__(self: pycommute.expression.ExpressionR, arg0: float) -> pycommute.expression.ExpressionR

2. __radd__(self: pycommute.expression.ExpressionR, arg0: complex) -> pycommute.expression.ExpressionC

__repr__(self: pycommute.expression.ExpressionR) → str

__rmul__(*args, **kwargs)

Overloaded function.

1. __rmul__(self: pycommute.expression.ExpressionR, arg0: float) -> pycommute.expression.ExpressionR

2. __rmul__(self: pycommute.expression.ExpressionR, arg0: complex) -> pycommute.expression.ExpressionC

__rsub__(*args, **kwargs)

Overloaded function.

1. __rsub__(self: pycommute.expression.ExpressionR, arg0: float) -> pycommute.expression.ExpressionR

2. __rsub__(self: pycommute.expression.ExpressionR, arg0: complex) -> pycommute.expression.ExpressionC

__sub__(*args, **kwargs)

Overloaded function.

1. __sub__(self: pycommute.expression.ExpressionR, arg0: pycommute.expression.ExpressionR) -> pycommute.expression.ExpressionR

2. __sub__(self: pycommute.expression.ExpressionR, arg0: float) -> pycommute.expression.ExpressionR

3. __sub__(self: pycommute.expression.ExpressionR, arg0: pycommute.expression.ExpressionC) -> pycommute.expression.ExpressionC

4. __sub__(self: pycommute.expression.ExpressionR, arg0: complex) -> pycommute.expression.ExpressionC

clear(self: pycommute.expression.ExpressionR) → None

Reset expression to zero.

class pycommute.expression.ExpressionC

Polynomial in quantum-mechanical operators with complex coefficients

__add__(*args, **kwargs)

Overloaded function.

1. __add__(self: pycommute.expression.ExpressionC, arg0: pycommute.expression.ExpressionC) -> pycommute.expression.ExpressionC

2. __add__(self: pycommute.expression.ExpressionC, arg0: complex) -> pycommute.expression.ExpressionC

3. __add__(self: pycommute.expression.ExpressionC, arg0: pycommute.expression.ExpressionR) -> pycommute.expression.ExpressionC

4. __add__(self: pycommute.expression.ExpressionC, arg0: float) -> pycommute.expression.ExpressionC

__copy__(self: pycommute.expression.ExpressionC) → pycommute.expression.ExpressionC

__deepcopy__(self: pycommute.expression.ExpressionC, memo: dict) → pycommute.expression.ExpressionC

__eq__(self: pycommute.expression.ExpressionC, arg0: pycommute.expression.ExpressionC) → bool

__hash__ = None

__iadd__(*args, **kwargs)

Overloaded function.

1. __iadd__(self: pycommute.expression.ExpressionC, arg0: pycommute.expression.ExpressionC) -> pycommute.expression.ExpressionC

2. __iadd__(self: pycommute.expression.ExpressionC, arg0: complex) -> pycommute.expression.ExpressionC

3. __iadd__(self: pycommute.expression.ExpressionC, arg0: pycommute.expression.ExpressionR) -> pycommute.expression.ExpressionC

4. __iadd__(self: pycommute.expression.ExpressionC, arg0: float) -> pycommute.expression.ExpressionC

__imul__(*args, **kwargs)

Overloaded function.

1. __imul__(self: pycommute.expression.ExpressionC, arg0: pycommute.expression.ExpressionC) -> pycommute.expression.ExpressionC

2. __imul__(self: pycommute.expression.ExpressionC, arg0: complex) -> pycommute.expression.ExpressionC

3. __imul__(self: pycommute.expression.ExpressionC, arg0: pycommute.expression.ExpressionR) -> pycommute.expression.ExpressionC

4. __imul__(self: pycommute.expression.ExpressionC, arg0: float) -> pycommute.expression.ExpressionC

__init__(*args, **kwargs)

Overloaded function.

1. __init__(self: pycommute.expression.ExpressionC) -> None

Construct a zero expression.

2. __init__(self: pycommute.expression.ExpressionC, x: complex) -> None

Construct a constant expression equal to \(x\).

Parameters:

x – Constant \(x\).

3. __init__(self: pycommute.expression.ExpressionC, x: complex, m: pycommute.expression.Monomial) -> None

Construct an expression with one monomial, \(x \cdot m\).

Parameters:

• x – Coefficient \(x\).

• m – Monomial \(m\).

4. __init__(self: pycommute.expression.ExpressionC, expr: pycommute.expression.ExpressionR) -> None

Construct from a real expression by complexifying its coefficients.

__isub__(*args, **kwargs)

Overloaded function.

1. __isub__(self: pycommute.expression.ExpressionC, arg0: pycommute.expression.ExpressionC) -> pycommute.expression.ExpressionC

2. __isub__(self: pycommute.expression.ExpressionC, arg0: complex) -> pycommute.expression.ExpressionC

3. __isub__(self: pycommute.expression.ExpressionC, arg0: pycommute.expression.ExpressionR) -> pycommute.expression.ExpressionC

4. __isub__(self: pycommute.expression.ExpressionC, arg0: float) -> pycommute.expression.ExpressionC

__iter__(self: pycommute.expression.ExpressionC) → Iterator[tuple[pycommute.expression.Monomial, complex]]

__len__(self: pycommute.expression.ExpressionC) → int

Number of monomials in this expression.

__mul__(*args, **kwargs)

Overloaded function.

1. __mul__(self: pycommute.expression.ExpressionC, arg0: pycommute.expression.ExpressionC) -> pycommute.expression.ExpressionC

2. __mul__(self: pycommute.expression.ExpressionC, arg0: complex) -> pycommute.expression.ExpressionC

3. __mul__(self: pycommute.expression.ExpressionC, arg0: pycommute.expression.ExpressionR) -> pycommute.expression.ExpressionC

4. __mul__(self: pycommute.expression.ExpressionC, arg0: float) -> pycommute.expression.ExpressionC

__ne__(self: pycommute.expression.ExpressionC, arg0: pycommute.expression.ExpressionC) → bool

__neg__(self: pycommute.expression.ExpressionC) → pycommute.expression.ExpressionC

__radd__(*args, **kwargs)

Overloaded function.

1. __radd__(self: pycommute.expression.ExpressionC, arg0: complex) -> pycommute.expression.ExpressionC

2. __radd__(self: pycommute.expression.ExpressionC, arg0: float) -> pycommute.expression.ExpressionC

__repr__(self: pycommute.expression.ExpressionC) → str

__rmul__(*args, **kwargs)

Overloaded function.

1. __rmul__(self: pycommute.expression.ExpressionC, arg0: complex) -> pycommute.expression.ExpressionC

2. __rmul__(self: pycommute.expression.ExpressionC, arg0: float) -> pycommute.expression.ExpressionC

__rsub__(*args, **kwargs)

Overloaded function.

1. __rsub__(self: pycommute.expression.ExpressionC, arg0: complex) -> pycommute.expression.ExpressionC

2. __rsub__(self: pycommute.expression.ExpressionC, arg0: float) -> pycommute.expression.ExpressionC

__sub__(*args, **kwargs)

Overloaded function.

1. __sub__(self: pycommute.expression.ExpressionC, arg0: pycommute.expression.ExpressionC) -> pycommute.expression.ExpressionC

2. __sub__(self: pycommute.expression.ExpressionC, arg0: complex) -> pycommute.expression.ExpressionC

3. __sub__(self: pycommute.expression.ExpressionC, arg0: pycommute.expression.ExpressionR) -> pycommute.expression.ExpressionC

4. __sub__(self: pycommute.expression.ExpressionC, arg0: float) -> pycommute.expression.ExpressionC

clear(self: pycommute.expression.ExpressionC) → None

Reset expression to zero.

expression.conj(*args, **kwargs)

Overloaded function.

1. conj(expr: pycommute.expression.ExpressionR) -> pycommute.expression.ExpressionR

Hermitian conjugate.

Parameters:

expr – Expression to conjugate.

2. conj(expr: pycommute.expression.ExpressionC) -> pycommute.expression.ExpressionC

Hermitian conjugate.

Parameters:

expr – Expression to conjugate.

expression.transform(*args, **kwargs)

Overloaded function.

1. transform(expr: pycommute.expression.ExpressionR, f: Callable[[pycommute.expression.Monomial, float], float]) -> pycommute.expression.ExpressionR

Apply a given function to all monomial/coefficient pairs and replace the coefficients with values returned by the function. Zero return values will result in respective monomials being discarded.

Parameters:

• expr – Expression to be transformed.

• f – Transformation function. It must take two arguments, one of type Monomial and one float argument.

2. transform(expr: pycommute.expression.ExpressionC, f: Callable[[pycommute.expression.Monomial, complex], complex]) -> pycommute.expression.ExpressionC

Apply a given function to all monomial/coefficient pairs and replace the coefficients with values returned by the function. Zero return values will result in respective monomials being discarded.

Parameters:

• expr – Expression to be transformed.

• f – Transformation function. It must take two arguments, one of type Monomial and one complex argument.

3. transform(expr: pycommute.expression.ExpressionR, f: Callable[[pycommute.expression.Monomial, float], complex]) -> pycommute.expression.ExpressionC

Apply a given function to all monomial/coefficient pairs and replace the coefficients with values returned by the function. Zero return values will result in respective monomials being discarded.

Parameters:

• expr – Expression to be transformed.

• f – Transformation function. It must take two arguments, one of type Monomial and one float argument.

4. transform(expr: pycommute.expression.ExpressionC, f: Callable[[pycommute.expression.Monomial, complex], float]) -> pycommute.expression.ExpressionR

Apply a given function to all monomial/coefficient pairs and replace the coefficients with values returned by the function. Zero return values will result in respective monomials being discarded.

Parameters:

• expr – Expression to be transformed.

• f – Transformation function. It must take two arguments, one of type Monomial and one complex argument.

Expression factory functions

expression.c_dag(*args) → pycommute.expression.ExpressionR

Returns a fermionic creation operator with indices passed as positional arguments.

Parameters:

*args – Indices of the operator.

expression.c(*args) → pycommute.expression.ExpressionR

Returns a fermionic annihilation operator with indices passed as positional arguments.

Parameters:

*args – Indices of the operator.

expression.n(*args) → pycommute.expression.ExpressionR

Returns a fermionic particle number operator with indices passed as positional arguments.

Parameters:

*args – Indices of the operator.

expression.a_dag(*args) → pycommute.expression.ExpressionR

Returns a bosonic creation operator with indices passed as positional arguments.

Parameters:

*args – Indices of the operator.

expression.a(*args) → pycommute.expression.ExpressionR

Returns a bosonic annihilation operator with indices passed as positional arguments.

Parameters:

*args – Indices of the operator.

expression.S_p(*args, **kwargs)

Overloaded function.

1. S_p(*args) -> pycommute.expression.ExpressionR

Returns a spin-1/2 raising operator \(S_+\) with indices passed as positional arguments.

Parameters:

*args – Indices of the operator.

2. S_p(*args, **kwargs) -> pycommute.expression.ExpressionR

Returns a general spin raising operator \(S_+\) with indices passed as positional arguments.

Parameters:

• spin – Spin \(S\).

• *args – Indices of the operator.

expression.S_m(*args, **kwargs)

Overloaded function.

1. S_m(*args) -> pycommute.expression.ExpressionR

Returns a spin-1/2 lowering operator \(S_-\) with indices passed as positional arguments.

Parameters:

*args – Indices of the operator.

2. S_m(*args, **kwargs) -> pycommute.expression.ExpressionR

Returns a general spin lowering operator \(S_-\) with indices passed as positional arguments.

Parameters:

• spin – Spin \(S\).

• *args – Indices of the operator.

expression.S_x(*args, **kwargs)

Overloaded function.

1. S_x(*args) -> pycommute.expression.ExpressionC

Returns a spin-1/2 x-projection operator \(S_x\) with indices passed as positional arguments.

Parameters:

*args – Indices of the operator.

2. S_x(*args, **kwargs) -> pycommute.expression.ExpressionC

Returns a general spin \(S\) x-projection operator \(S_x\) with indices passed as positional arguments.

Parameters:

• spin – Spin \(S\).

• *args – Indices of the operator.

expression.S_y(*args, **kwargs)

Overloaded function.

1. S_y(*args) -> pycommute.expression.ExpressionC

Returns a spin-1/2 y-projection operator \(S_y\) with indices passed as positional arguments.

Parameters:

*args – Indices of the operator.

2. S_y(*args, **kwargs) -> pycommute.expression.ExpressionC

Returns a general spin \(S\) y-projection operator \(S_y\) with indices passed as positional arguments.

Parameters:

• spin – Spin \(S\).

• *args – Indices of the operator.

expression.S_z(*args, **kwargs)

Overloaded function.

1. S_z(*args) -> pycommute.expression.ExpressionR

Returns a spin-1/2 z-projection operator \(S_z\) with indices passed as positional arguments.

Parameters:

*args – Indices of the operator.

2. S_z(*args, **kwargs) -> pycommute.expression.ExpressionR

Returns a general spin \(S\) z-projection operator \(S_z\) with indices passed as positional arguments.

Parameters:

• spin – Spin \(S\).

• *args – Indices of the operator.

expression.make_complex(expr: pycommute.expression.ExpressionR) → pycommute.expression.ExpressionC

Make a complex expression out of a real one.

Parameters:

expr – Real expression to be complexified.

Hermitian conjugate placeholder

class pycommute.expression.HC

A placeholder type that adds/subtracts the Hermitian conjugate to/from an expression. There is a module-level constant of this type called hc, which allows to mimic the \(\pm H.c.\) notation in expressions.

expression.hc = <pycommute.expression.HC object>