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V. Urbonaite, S. Winkler, A. Körner:
"Random Generation of Mathematical Examples in Maple T.A.";
Talk: MATHMOD 2012 - 7th Vienna Conference on Mathematical Modelling, Wien; 02-14-2012 - 02-17-2012; in: "Preprints Mathmod 2012 Vienna - Full Paper Volume", F. Breitenecker, I. Troch (ed.); Argesim / Asim, 38 (2012), 415 - 416.

Introduction. Maple T.A. is an online testing, evaluation and grading software powered by Maple. The Vienna
University of Technology uses it to help students preparing to start an intensive education in maths, to refresh basic
mathematical skills from high school and improve success in advanced university mathematics. Although this
system has its own commands and it is possible to call 80% of Maple functions from Maple T.A. . The common
Maple functions are limited in sense of random generation and evaluation of mathematical examples. For this
reason at Vienna University of Technology an appended Maple "Random" library was created, which increased
example creation opportunities and diversity.
Random generation of examples in Maple T.A. A construction of algorithmic variables is the way to randomize
the questions in Maple T.A. These algorithmic variables can use the built-in algorithmic generator in Maple
T.A. or can use any of Maple´s randomization routines. Various functions inside Maple T.A. can be used to create
just simple random variables like integers or real numbers. There are also a wide variety of routines and packages
in Maple that can be used as straight functions or combinations of functions to create more complex algorithmic
variables in this system. But the more complex the objects are, the more complicated Maple T.A. code and creation
of question gets. Such Maple random-routines require longer execution time and that leads to some technical
problems in case of a large number of students working on the same question at the same time. On the Vienna
University of Technology an additional Maple randomization library was developed, which made this process less
difficult and less time-consuming.
The following functions are implemented in "Random" library:
. Random[FromSet](Set, Count)
A given number of random elements (with or without replacement; sorted or not) are selected from a set.
The data types of the set elements are not restricted.
. Random[FromInts]([Min1, Max1], [Min2, Max2], . . . , Count)
For given interval boundaries (minimum and maximum) the function returns a sequence of either a specified
number or all integers between these boundaries.
. Random [FromRats]([Min, Max, MinDenom, MaxDenom], Count)
The function is similar to FromInts. In this case the return values are rational numbers, that are restricted by
some additional parameters for the denominators.
. Random[Vec](Set, Dim, zerocount = k)
For a given dimension this function returns a random vector with user-defined entries. Number of zeros in
the vector can be given.
. Random[Mat](Set, rows = m, cols = n, zerocount = k, shape = s)
The Mat-function generates random matrices. It is possible to define the matrix dimension as well as a
required shape and number of zero entries.
. Random[MatInts](Set, rows = m, cols = n, zerocount = k, rank = r, shape = s)
Just like the vector function, MatInts creates matrices only with integer entries. The rank of the matrix can
be also given.
. Random[MatIntsDef](Max, Pos, Neg, Zero)
This function delivers a random symmetric matrix with integer entries and specified numbers of positive
(pos), negative (neg) and eigenvalues equal zero (zero). The dimension of the matrix is defined by: dim =
pos +neg + zero, and the rank equals pos + neg.