CellML Specification Overview Entire Specification Introduction Fundamentals Model Structure Mathematics Units Grouping Reactions Metadata Framework |
## 4 Mathematics## 4.1 IntroductionModel components may contain mathematical expressions that manipulate the values of variables that belong to the current component. These expressions are also free to use (but not change) the values of any other variables declared in the current component. Mathematical expressions must be defined using Mathematical Markup Language (MathML), an XML-based language that encodes the underlying structure of an expression. If it is not possible to describe a particular mathematical expression in MathML or if a model specifically prescribes a certain algorithm, model authors may make use of ECMAScript (formerly Netscape's Javascript) to encode algorithms. The first version of MathML reached recommendation status at the World Wide Web Consortium (W3C) in April 1998. A second version was released in February 2001. CellML uses the content markup element set from MathML 2.0, which extends the functionality of MathML 1.0 in many key areas. The MathML 2.0 recommendation also deprecates the use of some MathML 1.0 elements. However, CellML processing software is expected to maintain compatibility with equations defined using MathML 1.0. ECMA is an international industry association that develops standards in information and communication for the European union. ECMA took the scripting language that Netscape developed for adding interactive content to its web browser and developed the formal language specification ECMA-262 (ECMAScript Language Specification). ## 4.2 Basic Structure## 4.2.1 Allowed locations of mathematical expressions
All mathematical expressions defined using MathML must be placed inside a
The CellML syntax for defining scripts using ECMAScript has yet to be determined. It is anticipated that this will involve a Mathematical expressions and scripts may manipulate the variables belonging to the component in which they are defined and may use (but not change) the value of variables belonging to other components if necessary. The declaration of variables in CellML is specified in Section 3. ## 4.2.2 Allowed mathematical expressionsAt the present time, all models defined in CellML consist solely of algebraic equations and ordinary differential equations. However, MathML can specify a wide-range of mathematics, not all of which will necessarily be interpretable by every CellML processor. To encourage interoperability of models created using different processors, the CellML development team intends to define groups of mathematical functionality. CellML processing software could then publish which groups of mathematical functionality it supports. ## 4.2.3 Definition of scriptsScripts will be defined using ECMAScript. The CellML development team is still determining how best to incorporate these scripts into CellML. The use of scripts in CellML is strongly discouraged. CellML is aimed at specifying a model in terms of its most basic governing equations. Wherever possible, mathematical equations should be used to specify the changing behaviour of a model's state variables.
When scripts are used, they are assumed to execute ## 4.3 Examples
The CellML fragment in Figure 6 demonstrates how MathML can be employed within CellML to define mathematical expressions. This fragment is part of the definition of a component that represents the behaviour of the 0.01(V + 10.0) alpha_n = -------------------------- exp(0.1(V + 10.0)) - 1.0
All of the
The ## 4.4 Rules for CellML Documents## 4.4.1 The
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