# sum(List) -- sum the elements of a list

## Synopsis

• Function: sum

## Description

sum v yields the sum of the elements in the list v.

 i1 : sum {1,2,3,4,5} o1 = 15

The sum of an empty list is the integer 0.

 i2 : sum {} o2 = 0 i3 : class oo o3 = ZZ o3 : Ring

When summing a possibly empty list of elements from a ring, one may use promote to ensure the result is always in the same ring.

 i4 : R = QQ[x_1 .. x_10]; i5 : f = n -> sum for i from 1 to n list x_i; i6 : f 4 o6 = x + x + x + x 1 2 3 4 o6 : R i7 : f 0 o7 = 0 i8 : class oo o8 = ZZ o8 : Ring i9 : g = n -> promote(sum for i from 1 to n list x_i, R); i10 : g 10 o10 = x + x + x + x + x + x + x + x + x + x 1 2 3 4 5 6 7 8 9 10 o10 : R i11 : g 0 o11 = 0 o11 : R i12 : class oo o12 = R o12 : PolynomialRing