Total

Total[list]

gives the total of the elements in list.

Total[list,n]

totals all elements down to level n.

Total[list,{n}]

totals elements at level n.

Total[list,{n1,n2}]

totals elements at levels n1 through n2.

Details and Options

Examples

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Basic Examples  (1)

Total the values in a list:

Scope  (6)

Use exact arithmetic to total the values:

Use machine arithmetic:

Use 47-digit precision arithmetic:

Total the columns of a matrix:

Total the rows:

Total all the elements:

Total by adding parts in the first dimension:

Total in the last dimension only:

Total in the last two dimensions:

Total all but the last dimension:

Total all the elements:

Total the last dimension in a ragged array:

Total all the elements:

You cannot total in the first dimension because the lists have incompatible lengths:

Total the columns in a sparse matrix:

Total the rows:

Total several sparse vectors:

Total all the elements in all the vectors:

Options  (2)

Method  (1)

Use Method->"CompensatedSummation" to reduce accumulated errors in a sum:

Without compensated summation, small errors may accumulate with each term:

AllowedHeads  (1)

Total[expr,AllowedHeads->Inherited] works with any head:

Find the total derivative order:

Applications  (3)

Form a polynomial from monomials:

Show that the trace of a matrix is equal to the total of its eigenvalues:

Search for "perfect" numbers equal to the sum of their divisors:

Properties & Relations  (2)

Total[list] is equivalent to Apply[Plus,list]:

Total[list,k] is equivalent to Total[Flatten[list,k-1]]:

Introduced in 2003
 (5.0)
 |
Updated in 2007
 (6.0)
2019
 (12.0)