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The complexity of a mathematical expression is a measure that can be used to compare the expression with other mathematical expressions and judge which one is simpler. In the paper, we analyze three effect factors for the complexity of a mathematical expression: representational length, computational time, and intelligibility. Mainly, the paper introduces a binary-lambda-calculus based calculation method for representational complexity and a rule based calculation method for algebraic computation complexity. In the process of calculating the representation complexity of mathematical expressions, we transform the de bruijn notation into the binary lambda calculus of mathematical expressions that is inspired by compressing symmetry strings in Kolmogorov complexity theorem. Furthermore, the application of complexity of mathematical expressions in MACP, a mathematics answer checking protocol, is also addressed. MACP can be used in a computer aided assessment system in order to compute correct answers, verify equivalence of expressions, check user answers whether in a simplification form, and give automatic partial grades.

The ability for users online creating and editing mathematical expressions is very important for Science Computing Systems, Science Communication Systems, and Web-based Mathematics Education Systems. Lanzhou university/China and Kent University/USA are jointly developing a mathematical expression editor. The editor MathEdit, implemented in JavaScript and MathML, is a web-based visual interactive editor for mathematical expressions. Figure 1 shows the end-user view of the MathEdit architecture. In MathEdit the MathML Content code is the core code of being edited mathematical expression. User actions, inserting, deleting and editing sub-expressions by mouse clicks and keyboard input, are treated as commands. The commands will invoke JavaScript functions in the command processing module to modify the MathML content code by revising DOM tree of expression. The MathML Content will synchronously convert to MathML Presentation code and Math Infix code. The user will intuitively see the changed math expression displayed by MathML Presentation.