Sum elements of a polynomial array, sequence, or iterator. sum sum sum sum sum sum sum sum sum sum sum sum Sum a sequence or iterator efficiently. Sum a sequence or iterator of constraints. Deprecated overload of sum(). sum sum Map each element and sum the mapped values. sum sum sum

When the argument is a PolyArray, this function is equivalent to the sum() method of PolyArray. If axis is None, all elements are summed and a Poly is returned. If axis is specified, reduction is applied along that axis and a PolyArray or Poly is returned depending on the result shape.

When the argument elements are Poly, Constraint, or ConstraintList, this function behaves like Python’s built-in sum() but uses an algorithm that reduces intermediate growth during accumulation. In this context, built-in sum() can show \(O(n^2)\)-like behavior, while this function is typically closer to \(O(n)\). Here, \(n\) denotes the total number of terms in a Poly or the total number of elements in a ConstraintList.

The overload that takes start, stop, func has been deprecated since Amplify v1.0.0 and will be removed in a future release. Use amplify.sum(iterable, func) instead.

If a sequence (iterable or iterator) and a function are provided, this function maps each element to a polynomial and sums the mapped polynomials.

Overload 1.

Args:

array (amplify.PolyArray[_Dim]): array
axis (typing.Literal[None]): Axis or axes to reduce. If None, sum all elements. Defaults to None.

Returns:

amplify.Poly: Summed polynomial or polynomial array.

Raises:

ValueError: If axis is out of bounds or invalid.

Overload 2.

Args:

array (amplify.PolyArray[Dim1])
axis (int | tuple[int])

Returns:

amplify.Poly:

Overload 3.

Args:

array (amplify.PolyArray[Dim2])
axis (tuple[int, int])

Returns:

amplify.Poly:

Overload 4.

Args:

array (amplify.PolyArray[Dim2])
axis (int | tuple[int])

Returns:

amplify.PolyArray[Dim1]:

Overload 5.

Args:

array (amplify.PolyArray[Dim3])
axis (tuple[int, int, int])

Returns:

amplify.Poly:

Overload 6.

Args:

array (amplify.PolyArray[Dim3])
axis (tuple[int, int])

Returns:

amplify.PolyArray[Dim1]:

Overload 7.

Args:

array (amplify.PolyArray[Dim3])
axis (int | tuple[int])

Returns:

amplify.PolyArray[Dim2]:

Overload 8.

Args:

array (amplify.PolyArray[Dim4])
axis (tuple[int, int, int, int])

Returns:

amplify.Poly:

Overload 9.

Args:

array (amplify.PolyArray[Dim4])
axis (tuple[int, int, int])

Returns:

amplify.PolyArray[Dim1]:

Overload 10.

Args:

array (amplify.PolyArray[Dim4])
axis (tuple[int, int])

Returns:

amplify.PolyArray[Dim2]:

Overload 11.

Args:

array (amplify.PolyArray[Dim4])
axis (int | tuple[int])

Returns:

amplify.PolyArray[Dim3]:

Overload 12.

Args:

array (amplify.PolyArray[_Dim])
axis (tuple[()])

Returns:

amplify.PolyArray[_Dim]:

Overload 13.

Args:

array (amplify.PolyArray[Dim]): array
axis (int | tuple[int, …]): Axis or axes to reduce. If None, sum all elements.

Returns:

amplify.Poly | amplify.PolyArray[Dim]: Summed polynomial or polynomial array.

Raises:

ValueError: If axis is out of bounds or invalid.

Overload 14.

Args:

arg (collections.abc.Sequence[amplify.Poly | float] | collections.abc.Iterator[amplify.Poly | float]): Input sequence or iterator to sum.

Returns:

amplify.Poly: Summed result.

Overload 15.

Args:

arg (collections.abc.Sequence[amplify.Constraint | amplify.ConstraintList] | collections.abc.Iterator[amplify.Constraint | amplify.ConstraintList]): Input sequence or iterator to sum.

Returns:

amplify.ConstraintList: Sum of all elements.

Overload 16.

Args:

stop (int)
func (collections.abc.Callable[[int], amplify.Poly])

Returns:

amplify.Poly:

Overload 17.

Args:

start (int)
stop (int)
func (collections.abc.Callable[[int], amplify.Poly])

Returns:

amplify.Poly:

Overload 18.

Args:

start (int)
stop (int)
step (int)
func (collections.abc.Callable[[int], amplify.Poly])

Returns:

amplify.Poly:

Overload 19.

Args:

sequence (Sequence[_T]): Sequence or iterator of elements to map and sum.
func (Callable[[_T], Poly]): Mapping function applied to each element.

Returns:

amplify.Poly: Sum of mapped elements.

Overload 20.

Args:

iterable (Iterable[_T]): Sequence or iterator of elements to map and sum.
func (Callable[[_T], Poly]): Mapping function applied to each element.

Returns:

amplify.Poly: Sum of mapped elements.

Overload 21.

Args:

iterator (Iterator[_T]): Sequence or iterator of elements to map and sum.
func (Callable[[_T], Poly]): Mapping function applied to each element.

Returns:

amplify.Poly: Sum of mapped elements.

Overload 22.

Args:

iterable (Iterable)
start (object): Defaults to 0.

Returns:

typing.Any: