SymbolicCoeffs¶

class zixy.container.coeffs.SymbolicCoeffs(data=None, indexer=slice(None, None, None))[source]¶

Bases: Coeffs[Expr]

A collection of Expr.

A resizable vector-like container of coefficients that may be an owning instance referencing a contiguous Rust-bound data object, or a view on a slice of the elements in another collection.

__eq__(other: object) → bool[source]¶: Return whether self and other are equal.

__getitem__(indexer: int | slice) → CoeffT | Self¶

Overloads:

self, indexer (int) → CoeffT
self, indexer (builtins.slice) → Self

Get the element or elements selected by indexer.

Parameters:: indexer – Index or slice selecting the coefficient(s) to return.
Returns:: Coefficient or slice selected by indexer.

Multiply self by rhs in-place.

Raises:: ValueError – If the result of the multiplication cannot be represented by the type of self.

__init__(data=None, indexer=slice(None, None, None))¶

Initialize the coefficient vector.

Parameters:

data – Rust-bound object storing a vector of coefficients. If None, an empty vector of the appropriate type is initialized.
indexer – Slice over which the data is to be viewed.

__iter__() → Iterator[T]¶: Iterate over the elements of self.

__len__() → int¶: Get the number of elements in self.

__neg__() → Self¶: Return the negation of self.

__pos__() → Self¶: Return self.

__repr__() → str¶: Return a string representation of self.

__setitem__(indexer: int | slice, source: CoeffT | Coeffs[CoeffT] | None = None) → None¶

Set the indexed element(s) to the given value(s).

Parameters:

indexer – Index or slice of coefficient(s) within self to assign.
source – Value(s) specifying the coefficient(s) to assign.

allclose(other: Coeffs[Any], rtol: float = 1e-05, atol: float = 1e-08) → bool¶

Check whether self and other are within a certain tolerance.

Parameters:

other – Other instance to compare to.
rtol – Relative tolerance.
atol – Absolute tolerance.

Returns:

Whether self and other are within the given tolerances of each other.

Note

This method operates by comparing the NumPy arrays returned by np_array.

append(value: CoeffT) → None¶

Append value to the end of self.

Parameters:: value – Value to append.

Note

This method operates in-place.

append_n(n: int, value: CoeffT) → None¶

Append value to the end of self n times.

Parameters:

n – Number of times to repeatedly append value.
value – Value to append.

Note

This method operates in-place.

as_view() → Self¶

Return a view of self.

Returns:: If self is owning, a new view on the same underlying data, otherwise self.

clone() → Self¶: Return a deep copy of self.

coeff_type¶: alias of Expr

coeffs_type¶: alias of ExprListWrapper

count(value) → integer -- return number of occurrences of value¶

diff(variable: Symbol | str) → SymbolicCoeffs[source]¶

Differentiate partially with respect to variable out of place.

Parameters:: variable – Symbol or name of symbol by which to differentiate the viewed symbolic expressions.
Returns:: A new contiguously stored instance with the differentiation applied.

extend(other: Self) → None[source]¶

Append the elements of other to the end of self.

Parameters:: other – Other instance whose elements are appended to self.

Note

This method operates in-place.

fill(coeff: CoeffT) → None¶

Set all the coefficients in the vector to the given value.

Parameters:: coeff – Coefficient value to which to set all coefficients in the vector.

property free_symbols: set[Symbol]¶

Get the set of free (unsubstituted) symbols in self.

Returns:: Union of the sets of free symbols across all coefficients in self.

classmethod from_scalar(coeff: CoeffT, n: int = 1) → Self¶

Get a new instance of cls with the given scalar repeated n times.

Parameters:

coeff – Coefficient value.
n – Number of times to repeat coeff.

Returns:

New instance with coeff repeated n times.

classmethod from_sequence(source: Sequence[CoeffT]) → Self¶

Get a new instance from a sequence of coefficients.

Parameters:: source – Sequence of coefficients.
Returns:: New instance with elements set according to source.

classmethod from_size(n: int) → Self¶

Create a new instance of cls with the given size.

Parameters:: n – The size of the new instance.
Returns:: An instance of cls with the given size.

classmethod from_view(source: Self) → Self¶

Create a new instance of cls from a view.

Parameters:: source – View to clone into the new instance.
Returns:: An owning clone of source.

idiff(variable: Symbol | str) → None[source]¶

Differentiate partially with respect to variable in-place.

Parameters:: variable – Symbol or name of symbol by which to differentiate the viewed symbolic expressions.

Note

This method operates in-place.

into(t: type[OutT]) → OutT¶

Clone self into a new related container of type t.

Parameters:: t – Type of the new container to create.
Returns:: A new instance of t containing the same data as self.

is_owning() → bool¶: Check if self is owning (i.e. not a view).

isubs(values: dict[Symbol | str, int | float | complex | Expr]) → None[source]¶

Apply a partial substitution of the symbols in-place.

Parameters:: values – Map from a symbol or symbol name to its new expression or numeric value.

Note

This method operates in-place.

map_index(index: int) → int¶

Map an index in self to an index in the underlying data.

Parameters:: index – Index in self.
Returns:: Corresponding index in the underlying data.

property np_array: NDArray[float64 | complex128]¶

Get the contents of self copied as a flat NumPy array.

Returns:: NumPy array containing all elements of self.

classmethod parse(source: str) → Self[source]¶

Construct an instance of cls from a string representation.

Parameters:: source – The string to read from.
Returns:: An instance of cls represented by source.

reordered(inds: Sequence[int]) → Self¶

Get a new instance with the elements of self in a new order.

Parameters:: inds – Sequence of indices defining the new order. Should be a permutation of range(len(self)).
Returns:: A new instance with the reordered elements.

resize(n: int) → Self¶

Resize the underlying container.

Parameters:: n – The new size of the container.

Note

This method operates in-place.

Raises:: ValueError – If the container is a view.

Scale all elements by a given factor.

Parameters:: scalar – Scalar factor by which to scale all elements.

Note

This method operates in-place.

set(source: Iterable[CoeffT]) → None¶

Assign the viewed coefficients according to the values yielded by the given iterable.

Parameters:: source – Iterable containing the values to be assigned to the viewed coefficients of self.

subs(values: dict[Symbol | str, int | float | complex | Expr]) → SymbolicCoeffs[source]¶

Apply a partial substitution of the symbols out of place.

Parameters:: values – Map from a symbol or symbol name to its new expression or numeric value.
Returns:: A new contiguously stored instance with the substitution applied.

swap_remove(index: int) → None¶

Set the element at index to the final element, then delete the final element.

Parameters:: index – Element index to remove.

Note

This method operates in-place.

to_tuple() → tuple[CoeffT, ...]¶: Get a tuple of clones of the elements of self.

try_to_complex() → ComplexCoeffs[source]¶

Try to evaluate self as a vector of complex coefficients.

Returns:: An instance of ComplexCoeffs with the evaluated coefficients.
Raises:: TypeError – A coefficient is not representable as complex or there are free symbols.

try_to_real() → RealCoeffs[source]¶

Try to evaluate self as a vector of real coefficients.

Returns:: An instance of RealCoeffs with the evaluated coefficients.
Raises:: TypeError – A coefficient is not representable as real or there are free symbols.