--- capa/capa51/pProj/Changes	2000/02/09 22:10:24	1.2
+++ capa/capa51/pProj/Changes	2000/08/30 15:02:30	1.3
@@ -1,4 +1,96 @@
 
+
+New functions
+
+
+array_min(array_name)
+array_max(array_name)
+
+will calculate the min or max value from the 
+array given by array_name. All elements in 
+array array_name should be of numerical type, 
+if there is one element assigned a string value, 
+then array_min() and array_max() will give an
+error, indicating that it could not calculate 
+the min or max value for strings.
+
+/LET arr[123]=123
+/LET arr[456]=456
+/LET arr[1]=1
+/LET arr[34]=34
+/LET arr[56]=56
+/LET arr[78]=78
+/LET arr[12]=12
+/LET arr[4]=4
+/LET arr["124"]=124
+/LET arr[1.2]=1.01234567
+/LET max = array_max(arr)
+/LET min = array_min(arr)
+
+The results of max will be 456 and min will be 1.
+
+
+array_moments(result_array, input_array)
+
+
+/LET elements = array_moments(result_array, data_array)
+
+The input array is data_array and the calculated results will be placed in a newly
+created array named result_array. This resulting array contains exactly five elements, 
+result_array[0]  = number of elements in input array
+result_array[1]  = mean value of elements in input array
+result_array[2]  = variance of elements in input array
+result_array[3]  = skewness of elements in input array
+result_array[4]  = Kurtosis value of elements in input array
+
+Suppose all values in array data_array is denoted by $X$, 
+the $i$-th element in the array is denoted by $x_i$, and 
+the number of elements in the array is denoted by $n$.
+The formula of mean value is given by $\Sigma_{i=0}^{n-1} x_i / n$.
+Let $\mu$ represents the mean value of the array. 
+The variance is defined as  $\frac{\Sigma_{i=0}^{n-1}(x_i - \mu)^2}{n-1}$. 
+The standard deviation of the array can be calculated by taking the square root
+of variance. Let $\sigma$ denotes the standard deviation of the array. 
+Skewness is calculated from $\frac{\Sigma_{x=0}^{n-1}((x_i - \mu)/\sigma)^3}{n}$
+The Kurtosis value is from the formula 
+\frac{\Sigma_{i=0}^{n-1}(x_i - \mu)/\sigma)^4}{n} - 3$
+The constant $3$ is used to make the normal distribution appear to have a zero Kurtosis.
+
+
+Formula answer
+
+As of CAPA 5.1, a new type of answer can be used by the instructor. 
+A formula as an answer to a problem. That is, the instructor defines a string of 
+formula and ask the students to enter the formula, as long as the entered formula
+is equivalent to the answer formula, the CAPA system will check and 
+issue correctness or incorrectness based on their equivalence. 
+The underlying mechanism behind this type of answer is that besides the formula string, 
+two additional pieces of informations have to be provided 
+by the instructor, (1) the list of variables used in the answer string and 
+(2) the values of these variables to be used in evaluating formula equivalence.
+Those two pieces of information are given within a pair of angle brackets appearing
+as the right hand side of the keywork "eval =". 
+
+The list of variables is entered as a string or a variable containing a 
+string value. Within that string, each variable is separated by a comma. 
+The symbol '@' then follows. 
+Two forms of variable values can be used. A string with comma separated numerical values
+or two comma separated numerical values divided by a ':' symbol and followed by
+a '#' symbol and an integer indicating the number of values to be 
+interpolated within the two values given previously. Both form can be replaced by
+a variable containing the proper string value. 
+
+Tolerence can be given to allow the instructor fine tune the results
+of acceptable values when checking the equivalence of two formulae. 
+
+
+/LET f="x^2+y*y^(2)"
+/LET vlist = "x,y"
+/LET pts = "1,4:4,5#5"
+
+/ANS(f,str=FML ,eval = <"x,y" @ "-1.0,-1.0":"1,1"#4, pts, "0.0,0.0"> ,tol=1e-9) 
+
+--
 Fixed rad != 1/s  in capaUnit.c
 add   init_array() function to the user