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Total—Wolfram Language Documentation

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  • Plus
  • Accumulate
  • Tr
  • Mean
  • Count
  • Norm
  • Sum
  • Max
  • SparseArray
• Related Guides
  • Math & Counting Operations on Lists
  • Arithmetic Functions
  • Computation with Structured Datasets
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  • Basic Statistics

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.

• Total[list] is equivalent to Apply[Plus,list]. »
• Total[list,Infinity] totals all elements at any level in list. »
• For a 2D array or matrix: »
• Total[list] or Total[list,{1}] totals for each column Total[list,{2}] totals for each row Total[list,2] overall total of all elements
• By default, Total only adds up elements inside List, Association and special array representations like SparseArray, SymmetrizedArray and QuantityArray. Total[…,AllowedHeads->heads] will add up elements inside other expressions. Possible settings for heads include:
• Automatic add up elements inside List, Association and special array representations Inherited add up elements inside Head[expr] All add up elements inside any normal expression Association add up the values in Association List adds up elements in lists h add up elements inside h {h₁,…} add up elements inside any of h₁,…
• Total[list,Method->"CompensatedSummation"] uses compensated summation to reduce numerical error in the result. »
• Total works with SparseArray objects. »

Total the values in a list:

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:

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

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

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:

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