These are a particular example of the principle that purely abstract or intellectual methods are not patentable. For example, an abstract shortcut method of division would be excluded from patentability by Art. 52(2)(a) and Art. 52(3). However, a calculating machine constructed to operate accordingly (e.g. by executing a program designed to carry out the method) would not be excluded. Electrical filters designed according to a particular mathematical method would also not be excluded.
Furthermore, a method for analysing the cyclical behaviour of a curve relating two parameters, which are not further specified, to one another is a mathematical method as such, excluded from patentability by Art. 52(2)(a) and Art. 52(3), unless it uses technical means, for example, if it is computer-implemented.
A claim directed to a technical process in which a mathematical method is used, thus being restricted to a particular application of the mathematical method in a technical field, does not seek protection for the mathematical method as such. For instance, a method of encoding audio information in a communication system may aim to reduce distortion induced by channel noise. Although the idea underlying such a method may be considered to reside in a mathematical method, the encoding method as a whole is not a mathematical method as such, and hence is not excluded from patentability by Art. 52(2)(a) and Art. 52(3). Similarly, a method of encrypting/decrypting or signing electronic communications may be regarded as a technical method, even if it is essentially based on a mathematical method (see T 1326/06).
A procedural step (e.g. a mathematical algorithm) may contribute to the technical character of a claimed method only if it serves an adequately defined technical purpose of the method. In particular, specific technical applications of computer-implemented simulation methods, even if involving mathematical formulae, are to be regarded as modern technical methods which form an essential part of the fabrication process. Such simulation methods cannot be denied a technical effect merely on the ground that they do not yet incorporate the physical end product. However, the meta-specification of an undefined technical purpose (for example, the simulation of a "technical system"), could not be considered adequate (T 1227/05).
In a mathematical method for processing data, although defining the origin of the data records, i.e. what the data represents, may imply technical aspects, it does not necessarily confer technical character upon the method. For example, in a mathematical method for classifying data records, the classification algorithm would not derive a technical character from specifying that the data records are assembled from events in a telecommunications network if the classification is not performed for a technical purpose. What is also decisive is whether a technical effect is achieved by the functional nature of the data irrespective of its cognitive content (see T 1194/97, T 1161/04). For example, a mathematical method for processing data representing an image stored as an electric signal by a computer-implemented method and providing as its result a certain change in the image (e.g. restoring the image if it is distorted) is considered as being used in a technical process (T 208/84 and T 1161/04).
The increased speed or efficiency of a method based on improved algorithms is not sufficient on its own to establish a technical character of the method (see T 1227/05). Characteristics such as speed and efficiency are inherent in both technical and non-technical methods. For example, if a sequence of auction steps leads to price determination more quickly than some other auction method, that does not necessarily imply that the auction steps contribute to the technical character of the method (see T 258/03).