## About the TU Wien Maple Library for Möbius

The TU Wien Maple Library is a collection of custom Maple commands we created in order to streamline and advance the process of developing and grading examples in Möbius. It is divided into four main modules:

• Grade - Provides a range of options for evaluating Maple-graded question types.
• Random - Allows for the randomization of various mathematical objects.
• MatTools - Assists with practical handling of matrices.
• Print - Allows for the display of mathematical expressions using MathML.

The library is continually under development and adopts to the (new) needs in designing Möbius examples.

## Input in Möbius

To make input in Möbius easier, we use a modified syntax that differs from Maple in some aspects. The goal of this syntax is to keep the syntactic requirements on the students as low as possible and not restrict the input options to the data types supported by Maple.

## Current Developments

The TU Wien Maple Library is an ongoing project, and we are constantly working to improve and expand it. This section will provide updates on developments and new features that have been added to the library. Please note that the updates may not be as frequent as the ongoing work.

• Grading of General Solution of Linear System. This command allows for the evaluation of the general solution of systems of linear equations with partial credit. The form of the solution is not revealed to the student (it is entered in a single input field) and the choice of free variables is left up to the student. The answer can be provided either as a single vector or as a linear combination of vectors, and partial credit is possible in both cases.
• Grading of Orthonormal Bases for a Given Vector Space with partial credit.
• Grading and Calculation of real Integrals. These commands allow for evasion of the default Maple assumption that the integration variable is complex.

• Generation of Randomized Integer Matrices with Integer Eigenvalues. This command allows for the generation of matrices with randomly chosen integer values and integer eigenvalues. It is a Maple Implementation of the approach published in the paper by Towse and Campbell (2016) titled 'Constructing integer matrices with integer eigenvalues'.
• Displaystyle Mode. Allows for the display of mathematical expressions in a larger, more visually appealing format.