Dear all, This discussion on the level of detail to include in the mathematical definitions raises some very important points centering on usability.
1. The exercise here should be primarily of choosing a "usable" default definition. The MathML3 work has greatly improved the mechanism and precision with which definitions and overrides can be specified, but most of the time it should not be necessary to use the mechanism. The default definitions remain usable right up to the point where the differences between the defaults and your useage interfere with or become the focus of the mathematical point you are trying to present. For example, in most K-14 mathematical discussions around trigonometric functions, the exact choice of branch cuts, etc. doesn't matter. If you were asked what a specific function is, you would most likely refer the person to a "standard reference". Those are the definitions people expect, and the ones that should be used. That way you only need to reference an alternative definition when you are working on the fringe cases. 2. Whereever possible the default mathematical functions should be close to those used by common computational systems such as matlab, mathematica, maple, and others. For "ordinary computational uses" (whatever that means) it should not be necessary to override the default defintion. The author should only need to override the default definition when it is important to the mathematical discussion. (for example, a document that discusses the differences in how the three systems above handle a specific function.) Note that is is analogous to how the systems are used in practice. The boundary cases are sometimes important, but most of the time have no bearing on the discussion. Their definitions are also derived from standard references. Again, by refering to a standard definition, the only time you need to refer to a "different" definition is when the mathematical discourse / computation strays into the areas where the system in use differs from such a standard reference. 3. A final point. The technical details of a specific function do not really change whether it is being used by a new student, or an advanced mathematician - only the amount / type of detail that the user is aware of or focussed on. ---- This suggests to me that it is perfectly okay to define functions (for example) by reference to definitions from Abromovitz and Stegun, but provide a K-14 accessible summary. In both cases, this approach minimizes the number of times an author needs to point out their readers that the function they are using is different. Stan Devitt _______________________________________________ Om3 mailing list [email protected] http://openmath.org/mailman/listinfo/om3
