Sigma

sigma allows you to perform the sum of a series of numeric expressions and the concatenation of a series of expressions returning strings. These expressions depend on an index value that varies between two values with a step of 1.

Syntax

(1) sigma(VAR_NAME = START_INDEX, END_INDEX, EXPRESSION)(2) sigma(START_INDEX, END_INDEX, EXPRESSION)

• VAR_NAME is the name of the variable, optionally prefixed by a class identifier [CLASS].
• START_INDEX is a numeric expression that returns the starting value for the addition loop.
• END_INDEX is a numeric expression that returns the ending value for the addition loop.
• EXPRESSION is an expression that usually includes VAR_NAME (syntax 1) or indcum (syntax 2), system variable used by default as current index for the loop.

Examples

 # Let's compute the latin alphabet (uppercase)ALPHABET = sigma(I=1,26,chr$(64+I))# At the end of the loop, the value of I is 27# Let's create a random string containing uppercase letters (in this case, non indcum is used!) RANDOM_STRING=sigma(1,MAXL,chr$(65+int(rnd(25))))# Let's compute the sum of the squares from 1 to NSQUARE_SUM = sigma(I=1,N,I*I)# The same function with indcumSQUARE_SUM = sigma(1,N,indcum*indcum )# The same result without sigma...SQUARE_SUM = N*(N+1)*(N+2)/6# Double sumDOUBLE_SUM = sigma(I=1,N, sigma(J=1,I,J*J))# Can be written with the following statements (but it is less effective)DOUBLE_CUM=0For I=1 To NFor J=1 To IDOUBLE_CUM+=J*JNext JNext I

Description

sigma allows you to calculate the sum of an expression that depends on an index varying by steps of one between two values. This function works also on character strings, where the summation is performed as a string concatenation.

If the index interval is such that no loop is performed (for example, sigma(I=1,0,I)), the result returned is 0, even if the expression is a string expression.

The type of result depends on the type of arguments:

• If the expression is a string, the type of result is:
  • Char if the length is 255 or less,
  • Clbfile otherwise.
• If the expression is numeric, the type of result is:
  • Integer if only integers are cumulated and if the total does not exceed the range of integer values.
  • Double if a floating point expression is used,
  • Decimal otherwise.

Comment

indcum is an integer variable: thus it is usable only if it varies in an integer interval (between -2^31 and 2^31-1). If sigma expressions need to be nested, it is necessary to use an index variable that is not indcum.

If the variable loop given does not exist, it is created with the Decimal data type.

The final value for the index variable corresponds to the first value that comes out of the range of the loop.

Associated errors

See also

sum, indcum, For, Next, Step.