# Source code for qutip.core.dimensions

    """
    Internal use module for manipulating dims specifications.
    """
    # Required for Sphinx to follow autodoc_type_aliases
    from __future__ import annotations

    import numpy as np
    import numbers
    from operator import getitem
    from functools import partial
    from typing import Literal
    from qutip.settings import settings
    from qutip.typing import SpaceLike, DimensionLike

    __all__ = ["to_tensor_rep", "from_tensor_rep", "Space", "Dimensions"]

    def flatten(l):
        """Flattens a list of lists to the first level.

        Given a list containing a mix of scalars and lists or a dimension object,
        flattens it down to a list of the scalars within the original list.

        Parameters
        ----------
        l : scalar, list, Space, Dimension
            Object to flatten.

        Examples
        --------

        >>> flatten([[[0], 1], 2]) # doctest: +SKIP
        [0, 1, 2]

        Notes
        -----
        Any scalar will be returned wrapped in a list: ``flaten(1) == [1]``.
        A non-list iterable will not be treated as a list by flatten. For example, flatten would treat a tuple
        as a scalar.
        """
        if isinstance(l, (Space, Dimensions)):
            l = l.as_list()
        if not isinstance(l, list):
            return [l]
        else:
            return sum(map(flatten, l), [])

    def deep_remove(l, *what):
        """Removes scalars from all levels of a nested list.

        Given a list containing a mix of scalars and lists,
        returns a list of the same structure, but where one or
        more scalars have been removed.

        Examples
        --------

        >>> deep_remove([[[[0, 1, 2]], [3, 4], [5], [6, 7]]], 0, 5) # doctest: +SKIP
        [[[[1, 2]], [3, 4], [], [6, 7]]]

        """
        if isinstance(l, list):
            # Make a shallow copy at this level.
            l = l[:]
            for to_remove in what:
                if to_remove in l:
                    l.remove(to_remove)
                else:
                    l = [deep_remove(elem, to_remove) for elem in l]
        return l

    def unflatten(l, idxs):
        """Unflattens a list by a given structure.

        Given a list of scalars and a deep list of indices
        as produced by `flatten`, returns an "unflattened"
        form of the list. This perfectly inverts `flatten`.

        Examples
        --------

        >>> l = [[[10, 20, 30], [40, 50, 60]], [[70, 80, 90], [100, 110, 120]]] # doctest: +SKIP
        >>> idxs = enumerate_flat(l) # doctest: +SKIP
        >>> unflatten(flatten(l), idxs) == l # doctest: +SKIP
        True

        """
        acc = []
        for idx in idxs:
            if isinstance(idx, list):
                acc.append(unflatten(l, idx))
            else:
                acc.append(l[idx])
        return acc

    def _enumerate_flat(l, idx=0):
        if not isinstance(l, list):
            # Found a scalar, so return and increment.
            return idx, idx + 1
        else:
            # Found a list, so append all the scalars
            # from it and recurse to keep the increment
            # correct.
            acc = []
            for elem in l:
                labels, idx = _enumerate_flat(elem, idx)
                acc.append(labels)
            return acc, idx

    def _collapse_composite_index(dims):
        """
        Given the dimensions specification for a composite index
        (e.g.: [2, 3] for the right index of a ket with dims [[1], [2, 3]]),
        returns a dimensions specification for an index of the same shape,
        but collapsed to a single "leg." In the previous example, [2, 3]
        would collapse to [6].
        """
        return [np.prod(dims)]

    def _collapse_dims_to_level(dims, level=1):
        """
        Recursively collapses all indices in a dimensions specification
        appearing at a given level, such that the returned dimensions
        specification does not represent any composite systems.
        """
        if level == 0:
            return _collapse_composite_index(dims)
        return [_collapse_dims_to_level(index, level=level - 1) for index in dims]

    def collapse_dims_oper(dims):
        """
        Given the dimensions specifications for a ket-, bra- or oper-type
        Qobj, returns a dimensions specification describing the same shape
        by collapsing all composite systems. For instance, the bra-type
        dimensions specification ``[[2, 3], [1]]`` collapses to
        ``[[6], [1]]``.

        Parameters
        ----------

        dims : list of lists of ints
            Dimensions specifications to be collapsed.

        Returns
        -------

        collapsed_dims : list of lists of ints
            Collapsed dimensions specification describing the same shape
            such that ``len(collapsed_dims[0]) == len(collapsed_dims[1]) == 1``.
        """
        return _collapse_dims_to_level(dims, 1)

    def collapse_dims_super(dims):
        """
        Given the dimensions specifications for an operator-ket-, operator-bra- or
        super-type Qobj, returns a dimensions specification describing the same
        shape by collapsing all composite systems. For instance, the super-type
        dimensions specification ``[[[2, 3], [2, 3]], [[2, 3], [2, 3]]]`` collapses
        to ``[[[6], [6]], [[6], [6]]]``.

        Parameters
        ----------

        dims : list of lists of ints
            Dimensions specifications to be collapsed.

        Returns
        -------

        collapsed_dims : list of lists of ints
            Collapsed dimensions specification describing the same shape
            such that ``len(collapsed_dims[i][j]) == 1`` for ``i`` and ``j``
            in ``range(2)``.
        """
        return _collapse_dims_to_level(dims, 2)

    def enumerate_flat(l):
        """Labels the indices at which scalars occur in a flattened list.

        Given a list containing a mix of scalars and lists,
        returns a list of the same structure, where each scalar
        has been replaced by an index into the flattened list.

        Examples
        --------

        >>> print(enumerate_flat([[[10], [20, 30]], 40])) # doctest: +SKIP
        [[[0], [1, 2]], 3]

        """
        return _enumerate_flat(l)[0]

    def deep_map(fn, collection, over=(tuple, list)):
        if isinstance(collection, over):
            return type(collection)(deep_map(fn, el, over) for el in collection)
        else:
            return fn(collection)

    def dims_to_tensor_perm(dims):
        """
        Given the dims of a Qobj instance, returns a list representing
        a permutation from the flattening of that dims specification to
        the corresponding tensor indices.

        Parameters
        ----------

        dims : list, Dimensions
            Dimensions specification for a Qobj.

        Returns
        -------

        perm : list
            A list such that ``data[flatten(dims)[idx]]`` gives the
            index of the tensor ``data`` corresponding to the ``idx``th
            dimension of ``dims``.
        """
        if isinstance(dims, list):
            dims = Dimensions(dims)
        return dims._get_tensor_perm()

    def dims_to_tensor_shape(dims):
        """
        Given the dims of a Qobj instance, returns the shape of the
        corresponding tensor. This helps, for instance, resolve the
        column-stacking convention for superoperators.

        Parameters
        ----------

        dims : list, Dimensions
            Dimensions specification for a Qobj.

        Returns
        -------

        tensor_shape : tuple
            NumPy shape of the corresponding tensor.
        """
        perm = np.argsort(dims_to_tensor_perm(dims))
        dims = flatten(dims)
        return tuple(map(partial(getitem, dims), perm))

    def dims_idxs_to_tensor_idxs(dims, indices):
        """
        Given the dims of a Qobj instance, and some indices into
        dims, returns the corresponding tensor indices. This helps
        resolve, for instance, that column-stacking for superoperators,
        oper-ket and oper-bra implies that the input and output tensor
        indices are reversed from their order in dims.

        Parameters
        ----------

        dims : list, Dimensions
            Dimensions specification for a Qobj.

        indices : int, list or tuple
            Indices to convert to tensor indices. Can be specified
            as a single index, or as a collection of indices.
            In the latter case, this can be nested arbitrarily
            deep. For instance, [0, [0, (2, 3)]].

        Returns
        -------

        tens_indices : int, list or tuple
            Container of the same structure as indices containing
            the tensor indices for each element of indices.
        """
        perm = dims_to_tensor_perm(dims)
        return deep_map(partial(getitem, perm), indices)

    def to_tensor_rep(q_oper):
        """
        Transform a ``Qobj`` to a numpy array whose shape is the flattened
        dimensions.

        Parameters
        ----------
        q_oper: Qobj
            Object to reshape

        Returns
        -------
        ndarray:
            Numpy array with one dimension for each index in dims.

        Examples
        --------
        >>> ket.dims
        [[2, 3], [1]]
        >>> to_tensor_rep(ket).shape
        (2, 3, 1)

        >>> oper.dims
        [[2, 3], [2, 3]]
        >>> to_tensor_rep(oper).shape
        (2, 3, 2, 3)

        >>> super_oper.dims
        [[[2, 3], [2, 3]], [[2, 3], [2, 3]]]
        >>> to_tensor_rep(super_oper).shape
        (2, 3, 2, 3, 2, 3, 2, 3)
        """
        dims = q_oper._dims
        data = q_oper.full().reshape(dims._get_tensor_shape())
        return data.transpose(dims._get_tensor_perm())

    def from_tensor_rep(tensorrep, dims):
        """
        Reverse operator of :func:`to_tensor_rep`.
        Create a Qobj From a N-dimensions numpy array and dimensions with N
        indices.

        Parameters
        ----------
        tensorrep: ndarray
            Numpy array with one dimension for each index in dims.

        dims: list of list, Dimensions
            Dimensions of the Qobj.

        Returns
        -------
        Qobj
            Re constructed Qobj
        """
        from . import Qobj
        dims = Dimensions(dims)
        data = tensorrep.transpose(np.argsort(dims._get_tensor_perm()))
        return Qobj(data.reshape(dims.shape), dims=dims)

    def _frozen(*args, **kwargs):
        raise RuntimeError("Dimension cannot be modified.")

    def einsum(subscripts, *operands):
        """
        Implementation of numpy.einsum for Qobj.
        Evaluates the Einstein summation convention on the operands.
        Parameters
        ----------
        subscripts: str
            Specifies the subscripts for summation as comma
            separated list of subscript labels.
        operands: list of array_like
            These are the arrays for the operation.

        Returns
        -------
        Qobj (numpy.complex128)
            Result of einsum as Qobj (numpy.complex128 if result is scalar)
        """
        operands_array = [to_tensor_rep(op) for op in operands]
        result = np.einsum(subscripts, *operands_array)
        if result.shape == ():
            return result
        dims = [
            [d for d in result.shape[:result.ndim // 2]],
            [d for d in result.shape[result.ndim // 2:]]
        ]
        return from_tensor_rep(result, dims)

    class MetaSpace(type):
        def __call__(cls, *args: SpaceLike, rep: str = None) -> "Space":
            """
            Select which subclass is instantiated.
            """
            if cls is Space and len(args) == 1 and isinstance(args[0], list):
                # From a list of int.
                return cls.from_list(args[0], rep=rep)
            elif len(args) == 1 and isinstance(args[0], Space):
                # Already a Space
                return args[0]

            if cls is Space:
                if len(args) == 0:
                    # Empty space: a Field.
                    cls = Field
                elif len(args) == 1 and args[0] == 1:
                    # Space(1): a Field.
                    cls = Field
                elif len(args) == 1 and isinstance(args[0], Dimensions):
                    # Making a Space out of a Dimensions object: Super Operator.
                    cls = SuperSpace
                elif len(args) > 1 and all(isinstance(arg, Space) for arg in args):
                    # list of space: tensor product space.
                    cls = Compound

            if settings.core['auto_tidyup_dims']:
                if cls is Compound and all(arg.size == 1 for arg in args):
                    cls = Field
                elif cls is SuperSpace and args[0].type == 'scalar':
                    cls = Field

            args = tuple([
                tuple(arg) if isinstance(arg, list) else arg
                for arg in args
            ])

            if cls is Field:
                return cls.field_instance

            if cls is SuperSpace:
                args = (*args, rep or 'super')

            if args not in cls._stored_dims:
                instance = cls.__new__(cls)
                instance.__init__(*args)
                cls._stored_dims[args] = instance
            return cls._stored_dims[args]

        def from_list(
            cls,
            list_dims: list[int] | list[list[int]],
            rep: str = None
        ) -> "Space":
            if len(list_dims) == 0:
                raise ValueError("Empty list can't be used as dims.")
            elif (
                sum(isinstance(entry, list) for entry in list_dims)
                not in [0, len(list_dims)]
            ):
                raise ValueError(f"Format dims not understood {list_dims}.")
            elif not isinstance(list_dims[0], list):
                # Tensor
                spaces = [Space(size) for size in list_dims]
            elif len(list_dims) == 1:
                # [[2, 3]]: tensor with an extra layer of list.
                spaces = [Space(size) for size in list_dims[0]]
            elif len(list_dims) % 2 == 0:
                # Superoperators or tensor of Superoperators
                spaces = [
                    Space(Dimensions(
                        Space(list_dims[i+1]),
                        Space(list_dims[i])
                    ), rep=rep)
                    for i in range(0, len(list_dims), 2)
                ]
            else:
                raise ValueError(f'Format not understood {list_dims}')

            if len(spaces) == 1:
                return spaces[0]
            elif len(spaces) >= 2:
                return Space(*spaces)
            else:
                raise ValueError(f'Format not understood {list_dims}')

    class Space(metaclass=MetaSpace):
        _stored_dims = {}

        def __init__(self, dims):
            idims = int(dims)
            if idims <= 0 or idims != dims:
                raise ValueError("Dimensions must be integers > 0")
            # Size of the hilbert space
            self.size = dims
            self.issuper = False
            # Super representation, should be an empty string except for SuperSpace
            self.superrep = None
            # Does the size and dims match directly: size == prod(dims)
            self._pure_dims = True
            self.__setitem__ = _frozen

        def __eq__(self, other) -> bool:
            return self is other or (
                type(other) is type(self)
                and other.size == self.size
            )

        def __hash__(self):
            return hash(self.size)

        def __repr__(self) -> str:
            return f"Space({self.size})"

        def as_list(self) -> list[int]:
            return [self.size]

        def __str__(self) -> str:
            return str(self.as_list())

        def dims2idx(self, dims: list[int]) -> int:
            """
            Transform dimensions indices to full array indices.
            """
            if not isinstance(dims, list) or len(dims) != 1:
                raise ValueError("Dimensions must be a list of one element")
            if not (0 <= dims[0] < self.size):
                raise IndexError("Dimensions out of range")
            if not isinstance(dims[0], numbers.Integral):
                raise TypeError("Dimensions must be integers")
            return dims[0]

        def idx2dims(self, idx: int) -> list[int]:
            """
            Transform full array indices to dimensions indices.
            """
            if not (0 <= idx < self.size):
                raise IndexError("Index out of range")
            return [idx]

        def step(self) -> list[int]:
            """
            Get the step in the array between for each dimensions index.

            If element ``[i, j, k]`` is ``ket.full()[m, 0]`` then element
            ``[i, j+1, k]`` is ``ket.full()[m + ket._dims.step()[1], 0]``.
            """
            return [1]

        def flat(self) -> list[int]:
            """ Dimensions as a flat list. """
            return [self.size]

        def replace_superrep(self, super_rep: str) -> "Space":
            return self

        def scalar_like(self) -> "Space":
            return Field()

    class Field(Space):
        field_instance = None

        def __init__(self):
            self.size = 1
            self.issuper = False
            self.superrep = None
            self._pure_dims = True
            self.__setitem__ = _frozen

        def __eq__(self, other) -> bool:
            return type(other) is Field

        def __hash__(self):
            return hash(0)

        def __repr__(self) -> str:
            return "Field()"

        def as_list(self) -> list[int]:
            return [1]

        def step(self) -> list[int]:
            return [1]

        def flat(self) -> list[int]:
            return [1]

    Field.field_instance = Field.__new__(Field)
    Field.field_instance.__init__()

    class Compound(Space):
        _stored_dims = {}

        def __init__(self, *spaces: Space):
            spaces_ = []
            if len(spaces) <= 1:
                raise ValueError("Compound need multiple space to join.")
            for space in spaces:
                if isinstance(space, Compound):
                    spaces_ += space.spaces
                else:
                    spaces_ += [space]
            self.spaces = tuple(spaces_)
            self.size = np.prod([space.size for space in self.spaces])
            self.issuper = all(space.issuper for space in self.spaces)
            if not self.issuper and any(space.issuper for space in self.spaces):
                raise TypeError(
                    "Cannot create compound space of super and non super."
                )
            self._pure_dims = all(space._pure_dims for space in self.spaces)
            superrep = [space.superrep for space in self.spaces]
            if all(superrep[0] == rep for rep in superrep):
                self.superrep = superrep[0]
            else:
                raise TypeError(
                    "Cannot create compound space of of super operators "
                    "with different representation."
                )
            self.__setitem__ = _frozen

        def __eq__(self, other) -> bool:
            return self is other or (
                type(other) is type(self) and
                self.spaces == other.spaces
            )

        def __hash__(self):
            return hash(self.spaces)

        def __repr__(self) -> str:
            parts_rep = ", ".join(repr(space) for space in self.spaces)
            return f"Compound({parts_rep})"

        def as_list(self) -> list[int]:
            return sum([space.as_list() for space in self.spaces], [])

        def dims2idx(self, dims: list[int]) -> int:
            if len(dims) != len(self.spaces):
                raise ValueError("Length of supplied dims does not match the number of subspaces.")
            pos = 0
            step = 1
            for space, dim in zip(self.spaces[::-1], dims[::-1]):
                pos += space.dims2idx([dim]) * step
                step *= space.size
            return pos

        def idx2dims(self, idx: int) -> list[int]:
            dims = []
            for space in self.spaces[::-1]:
                idx, dim = divmod(idx, space.size)
                dims = space.idx2dims(dim) + dims
            return dims

        def step(self) -> list[int]:
            steps = []
            step = 1
            for space in self.spaces[::-1]:
                steps = [step * N for N in space.step()] + steps
                step *= space.size
            return steps

        def flat(self) -> list[int]:
            return sum([space.flat() for space in self.spaces], [])

        def replace_superrep(self, super_rep: str) -> Space:
            return Compound(
                *[space.replace_superrep(super_rep) for space in self.spaces]
            )

        def scalar_like(self) -> Space:
            return Space([space.scalar_like() for space in self.spaces])

    class SuperSpace(Space):
        _stored_dims = {}

        def __init__(self, oper: "Dimensions", rep: str = 'super'):
            self.oper = oper
            self.superrep = rep
            self.size = oper.shape[0] * oper.shape[1]
            self.issuper = True
            self._pure_dims = oper._pure_dims
            self.__setitem__ = _frozen

        def __eq__(self, other) -> bool:
            return (
                self is other
                or self.oper == other
                or (
                    type(other) is type(self)
                    and self.oper == other.oper
                    and self.superrep == other.superrep
                )
            )

        def __hash__(self):
            return hash((self.oper, self.superrep))

        def __repr__(self) -> str:
            return f"Super({repr(self.oper)}, rep={self.superrep})"

        def as_list(self) -> list[list[int]]:
            return self.oper.as_list()

        def dims2idx(self, dims: list[int]) -> int:
            posl, posr = self.oper.dims2idx(dims)
            return posl + posr * self.oper.shape[0]

        def idx2dims(self, idx: int) -> list[int]:
            posl = idx % self.oper.shape[0]
            posr = idx // self.oper.shape[0]
            return self.oper.idx2dims(posl, posr)

        def step(self) -> list[int]:
            stepl, stepr = self.oper.step()
            step = self.oper.shape[0]
            return stepl + [step * N for N in stepr]

        def flat(self) -> list[int]:
            return sum(self.oper.flat(), [])

        def replace_superrep(self, super_rep: str) -> Space:
            return SuperSpace(self.oper, rep=super_rep)

        def scalar_like(self) -> Space:
            return SuperSpace(self.oper.scalar_like(), rep=self.superrep)

    class MetaDims(type):
        def __call__(cls, *args: DimensionLike, rep: str = None) -> "Dimensions":
            if len(args) == 1 and isinstance(args[0], Dimensions):
                return args[0]
            elif len(args) == 1 and len(args[0]) == 2:
                args = (
                    Space(args[0][1], rep=rep),
                    Space(args[0][0], rep=rep)
                )
            elif len(args) != 2:
                raise NotImplementedError('No Dual, Ket, Bra...', args)

            if args not in cls._stored_dims:
                instance = cls.__new__(cls)
                instance.__init__(*args)
                cls._stored_dims[args] = instance
            return cls._stored_dims[args]

    class Dimensions(metaclass=MetaDims):
        _stored_dims = {}
        _type: str = None

        def __init__(self, from_: Space, to_: Space):
            self.from_ = from_
            self.to_ = to_
            self.shape = to_.size, from_.size
            self.issuper = from_.issuper
            self._pure_dims = from_._pure_dims and to_._pure_dims
            self.issquare = False
            if self.from_.size == 1 and self.to_.size == 1:
                self.type = 'scalar'
                self.issquare = True
                self.superrep = None
            elif self.from_.size == 1:
                self.issuper = self.to_.issuper
                self.type = 'operator-ket' if self.issuper else 'ket'
                self.superrep = self.to_.superrep
            elif self.to_.size == 1:
                self.issuper = self.from_.issuper
                self.type = 'operator-bra' if self.issuper else 'bra'
                self.superrep = self.from_.superrep
            elif self.from_ == self.to_:
                self.issuper = self.from_.issuper
                self.type = 'super' if self.issuper else 'oper'
                self.superrep = self.from_.superrep
                self.issquare = True
            else:
                if from_.issuper != to_.issuper:
                    raise NotImplementedError(
                        "Operator with both space and superspace dimensions are "
                        "not supported. Please open an issue if you have an use "
                        f"case for these: {from_}, {to_}]"
                    )
                self.type = 'super' if self.from_.issuper else 'oper'
                if self.from_.superrep == self.to_.superrep:
                    self.superrep = self.from_.superrep
                else:
                    self.superrep = 'mixed'
            self.__setitem__ = _frozen

        def __eq__(self, other: "Dimensions") -> bool:
            if isinstance(other, Dimensions):
                return (
                    self is other
                    or (
                        self.to_ == other.to_
                        and self.from_ == other.from_
                    )
                )
            return NotImplemented

        def __ne__(self, other: "Dimensions") -> bool:
            if isinstance(other, Dimensions):
                return not (
                    self is other
                    or (
                        self.to_ == other.to_
                        and self.from_ == other.from_
                    )
                )
            return NotImplemented

        def __matmul__(self, other: "Dimensions") -> "Dimensions":
            if self.from_ != other.to_:
                raise TypeError(f"incompatible dimensions {self} and {other}")
            args = other.from_, self.to_
            if args in Dimensions._stored_dims:
                return Dimensions._stored_dims[args]
            return Dimensions(*args)

        def __hash__(self):
            return hash((self.to_, self.from_))

        def __repr__(self) -> str:
            return f"Dimensions({repr(self.from_)}, {repr(self.to_)})"

        def __str__(self) -> str:
            return str(self.as_list())

        def as_list(self) -> list:
            """
            Return the list representation of the Dimensions object.
            """
            return [self.to_.as_list(), self.from_.as_list()]

        def __getitem__(self, key: Literal[0, 1]) -> Space:
            if key == 0:
                return self.to_
            elif key == 1:
                return self.from_
            raise IndexError("Dimensions index out of range")

        def dims2idx(self, dims):
            """
            Transform dimensions indices to full array indices.
            """
            return self.to_.dims2idx(dims[0]), self.from_.dims2idx(dims[1])

        def idx2dims(self, idxl, idxr):
            """
            Transform full array indices to dimensions indices.
            """
            return [self.to_.idx2dims(idxl), self.from_.idx2dims(idxr)]

        def step(self) -> list[list[int]]:
            """
            Get the step in the array between for each dimensions index.

            If element ``[i, j, k]`` is ``ket.full()[m, 0]`` then element
            ``[i, j+1, k]`` is ``ket.full()[m + ket._dims.step()[1], 0]``.
            """
            return [self.to_.step(), self.from_.step()]

        def flat(self) -> list[list[int]]:
            """ Dimensions as a flat list. """
            return [self.to_.flat(), self.from_.flat()]

        def _get_tensor_shape(self):
            """
            Get the shape to of the Nd tensor with one dimensions for each
            Dimension index. The order of the space values are not in the order of
            the Dimension index.
            """
            # dims_to_tensor_shape
            stepl = self.to_.step()
            flatl = self.to_.flat()
            stepr = self.from_.step()
            flatr = self.from_.flat()
            return tuple(np.concatenate([
                np.array(flatl)[np.argsort(stepl)[::-1]],
                np.array(flatr)[np.argsort(stepr)[::-1]],
            ]))

        def _get_tensor_perm(self):
            """
            Get the permutation of a tensor created using ``_get_tensor_shape`` to
            reorder the tensor dimensions with those of the Dimensions object.
            """
            # dims_to_tensor_perm
            stepl = self.to_.step()
            stepr = self.from_.step()
            return list(np.argsort(np.concatenate([
                np.argsort(stepl)[::-1],
                np.argsort(stepr)[::-1] + len(stepl)
            ])))

        def replace_superrep(self, super_rep: str) -> "Dimensions":
            if not self.issuper and super_rep is not None:
                raise TypeError("Can't set a superrep of a non super object.")
            return Dimensions(
                self.from_.replace_superrep(super_rep),
                self.to_.replace_superrep(super_rep)
            )

        def scalar_like(self) -> "Dimensions":
            return Dimensions([self.to_.scalar_like(), self.from_.scalar_like()])