sum

sum(array: PolyArray[_Dim], axis: None = None) → Poly
sum(array: PolyArray[_Dim], axis: int | tuple[int, ...]) → Poly | PolyArray[Dim]
sum(arg: Sequence[Poly | float] | Iterator[Poly | float]) → Poly
sum(
arg: Sequence[Constraint | ConstraintList] | Iterator[Constraint | ConstraintList],
) → ConstraintList
sum(stop: int, func: Callable[[int], Poly]) → Poly
sum(start: int, stop: int, func: Callable[[int], Poly]) → Poly
sum(start: int, stop: int, step: int, func: Callable[[int], Poly]) → Poly
sum(sequence: Sequence[_T], func: Callable[[_T], Poly]) → Poly
sum(iterable: Iterable[_T], func: Callable[[_T], Poly]) → Poly
sum(iterator: Iterator[_T], func: Callable[[_T], Poly]) → Poly
sum(iterable: Iterable, /, start: object = 0) → Any

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

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, sequence, or iterator whose elements the function adds.

  • axis (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[_Dim]): Array, sequence, or iterator whose elements the function adds.

  • 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 3.

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 4.

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 5.

Args:

  • stop (int)

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

Returns:

amplify.Poly:

Overload 6.

Args:

  • start (int)

  • stop (int)

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

Returns:

amplify.Poly:

Overload 7.

Args:

  • start (int)

  • stop (int)

  • step (int)

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

Returns:

amplify.Poly:

Overload 8.

Args:

  • sequence (collections.abc.Sequence[_T]): Sequence or iterator of elements to map and sum.

  • func (collections.abc.Callable[[_T], Poly]): Mapping function applied to each element.

Returns:

amplify.Poly: Sum of mapped elements.

Overload 9.

Args:

  • iterable (collections.abc.Iterable[_T]): Sequence or iterator of elements to map and sum.

  • func (collections.abc.Callable[[_T], Poly]): Mapping function applied to each element.

Returns:

amplify.Poly: Sum of mapped elements.

Overload 10.

Args:

  • iterator (collections.abc.Iterator[_T]): Sequence or iterator of elements to map and sum.

  • func (collections.abc.Callable[[_T], Poly]): Mapping function applied to each element.

Returns:

amplify.Poly: Sum of mapped elements.

Overload 11.

Args:

  • iterable (Iterable)

  • start (object): Defaults to 0.

Returns:

typing.Any: