Reference Guide

1-26 RPL Programming

Using Summations Instead of Loops

For certain calculations that involve summations, you can use the Σ function instead of loops. You can use Σ with

stack syntax or with algebraic syntax. Σ automatically repeats the addition for the specified range of the index

variable — without using a loop structure.

Example:

The following programs take an integer upper limit n from the stack, then find the summation. One

program uses a FOR … NEXT loop — the other uses Σ.

Program: Comments:

0 1 ROT

Initializes the summation and puts

the limits in place.

FOR j

j SQ +

Loops through the calculation.

Program: Comments:

→ n

'Σ(j=1,n,j^2)'

Uses Σ to calculate the summation.

Example:

The following program uses

LIST to calculate the summation of all elements of a vector or matrix.

The program takes from the stack an array or a name that evaluates to an array, and returns the summation.

Program: Comments:

OBJ→

Finds the dimensions of the array and

leaves it in a list on level 1.

Adds 1 to the list. (If the array is a vector,

the list on level 1 has only one element.

ΠLIST will error if the list has fewer than

two elements.)

œLIST

Multiplies all of the list elements together.

→LIST

ΣLIST

Converts the array elements into a list, and

sums them.

j 1=

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