Math Formulas - Constants, Variables, Operators

For entering mathematical formulas there are several special variables and constants, most of which are directly connected to the contents or indices of the data matrix:

Identifier	Type		Explanation
NCol	const	R/O	Number of columns of the data matrix
NRow	const	R/O	Number of rows of the data matrix
Pi	const	R/O	The number Pi (3.14159...)
Cx	var	R/W	Data in column x (x = 1..NCol)
Rx	var	R/W	Data in row x (x =1..NRow)
Cx:Cy	var	R/W	Data in columns x to y (x,y = 1..NCol)
Rx:Ry	var	R/W	Data in rows x to y (x,y = 1..NRow)
CuRv:CxRy	var	R/W	Data in a rectangular area of the data matrix which is bounded by the columns Cu and Cx and the rows Rv and Ry.
All	var	W/O	All data of the data matrix; the identifier "All" is only allowed in the left part of an equation.
°	var	R/O	Current reference cell. This symbol indicates the value of the currently referenced cell when iterating through a range of cells.
Marked	var	W/O	All marked cells of the data matrix; the identifier "Marked" is only allowed in the left part of an equation.
Rix	var	R/O	Row index of the data matrix
Cix	var	R/O	Column index of the data matrix

The following operators are currently available for mathematical transformations:

Operator	Function	Explanation	Example
+	summation	x+y	c1+c2+c7 calculates the sum of the columns 1, 2, and 7
-	subtraction	x-y	r5-r7 computes the difference between row 5 and 7
*	multiplication	x*y
/	division	x/y
#	modulo	x#y, the modulo function returns the remainder of integer division of round(x)/round(y)	c3#5 returns the values in column 3 modulo 5
^	exponentiation	x^y , x,y..any real values
()	parenthesis	parenthesis can be used to change operator precedence	(c1+c2)*(c3+c4) is different from c1+c2*c3+c4
ABS	absolute value	abs(x), x..any real number
ARCCOS	inverse cosine	arccos(x)
ARCSIN	inverse sine	arcsin(x)
ARCTAN	inverse tangens	arctan(x)
COS	cosine	cos(x), x..angle in radians	cos(c1) returns the cosine of the values in column 1 (assuming that the column contains angles measured in radians)
EXP	exponent	exp(x)
FRAC	decimal part of a real number	frac(x)	frac(-3.822) returns the value -0.822
GAUSS	random number	generates normally distributed random numbers with zero mean and unit standard deviation	c1:=0.2*gauss+6.5 fills the column 1 with normally distributed random numbers having a mean of 6.5 and a standard deviation of 0.2
INT	integer part of a real number	int(x)
LG	decadic logarithm	lg(x)
LN	natural logarithm	ln(x)
MAX	returns the maximum of a list of columns or rows	max(list), the list contains a list of columns or rows separated by commas; a range of neighboring columns/rows may be abbreviated by the ':' sign. The list may contain constant values, as well.	max(c3,c5,100) calculates the maximum of the columns 3 and 5 and the value 100 (i.e. whenever both the column 3 and the column 5 contain a value below 100 the function returns a value of 100).
MEAN	returns the mean of a list of columns or rows	mean(list), the list contains a list of columns or rows separated by commas; a range of neighboring columns/rows may be abbreviated by the ':' sign. The list may contain constant values, as well.	mean(r8:10,r5) calculates the mean of the rows 5, 8, 9, and 10.
MIN	returns the minimum of a list of columns or rows	min(list), the list contains a list of columns or rows separated by commas; a range of neighboring columns/rows may be abbreviated by the ':' sign. The list may contain constant values, as well.	min(c2:4,c7) calculates the minimum of the columns 2, 3, 4 and 7.
NDDENS	density y of the standard normal distribution at the position x	nddens(x)
NDINT	integral of the standard normal distribution from -infinity to x	ndint(x)
NDQUANT	quantile of the standard normal distribution for a probability p	ndquant(p)
RAND	uniformly distributed random numbers	random(x), x..amplitude of noise (mean = 0.0)	rand(8) creates uniformly distributed random numbers in the range of -4 to +4
ROUND	rounding to integer	round(x)
SIGN	returns the sign of variable x	sign(x)
SIN	sine	sin(x), x..angle in radians	sin(c1+pi/2) returns the sine of the values in column 1 plus pi/2 (assuming that the column contains angles measured in radians)
SQR	square	sqr(x)
SQRT	square root	sqrt(x), with x >= 0. Negative numbers generate an error message
SUM	returns the sum of a list of columns or rows	sum(list), the list contains a list of columns or rows separated by commas; a range of neighboring columns/rows may be abbreviated by the ':' sign. The list may contain constant values, as well.	sum(c2,c8:11) calculates the sum of the columns 2, 8, 9, 10, and 11.
TAN	tangens	tan(x), x..angle in radians	tan(c4) returns the tangens of the values in column 4 (assuming the column contains angles measured in radians)
VAR	returns the variance of a list of columns or rows	var(list), the list contains a list of columns or rows separated by commas; a range of neighboring columns/rows may be abbreviated by the ':' sign. The list may contain constant values, as well.	var(c1:4,c7,c9) calculates the variance of the columns 1, 2, 3, 4, 7, and 9.

Hint:

You should seriously consider to use the programming capabilities instead of the pocket calculator. The programming of DataLab provides much more flexibility (see section DLabPascal Scripts for more). Please note, that the identifiers and functions described above are solely valid for the pocket calculator, DLabPascal has its own (much larger) set of identifiers and functions.