Singular

D.2.3.16 sum

Usage:

sum(id[,v]); id ideal/vector/module/matrix/intvec/intmat/list, v intvec (default: v=1..number of entries of id)

Assume:

list members can be added.

Return:

The sum of all entries of id [with index given by v] of type depending on the entries of id.

Note:

If id is not a list, id is treated as a list of polys resp. integers. A module m is identified with the corresponding matrix M (columns of M generate m).
If v is outside the range of id, we have the empty sum and the result will be 0 (of type int).

LIB "general.lib";
ring r1 = 0,(x,y,z),dp;
vector pv = [xy,xz,yz,x2,y2,z2];
sum(pv);
==> x2+xy+y2+xz+yz+z2
sum(pv,2..5);
==> x2+y2+xz+yz
matrix M[2][3] = 1,x,2,y,3,z;
intvec w=2,4,6;
sum(M,w);
==> x+y+z
intvec iv = 1,2,3,4,5,6,7,8,9;
sum(iv,2..4);
==> 9
iv = intvec(1..100);
sum(iv);
==> 5050
ring r2 = 0,(x(1..10)),dp;
sum(x(3..7),intvec(1,3,5));
==> x(3)+x(5)+x(7)