CAMA(ID:7047/cam016)Michigan interactive maths systemfor Computer-Aided Mathematical Analysis Mathematical conversational computing system developed at Michigan as part of the ConComp project Related languages
References: The graphical, interactive nature of CAMA makes algebraic manipulations more practical than in older system There is distinct advantage in being able to see mathematical symbols as they usually appear in the mathematical literature as opposed to seeing them as rather obscure mnemonics. As an idea is easily lost after a delay of 15 seconds, the immediate viewing of the results of an algebraic manipulation is far superior. At present, the CAMA system has only a limited algebraic capability, but is growing as it is used. All the algebraic operations are based on a group of primitive operations. These include identifying an entity, moving an entity, substituting an expression, applying the associative law of addition or multiplication or the inverse, applying the commutative law of addition or multiplication, applying the distributive law, and the combining of like adjacent terms. Upon these primitive operations more complex operations are built. For example, the gathering of like terms from a long expression is accomplished by identifying one term as an entity, searching for identical entities, moving the entity to an adjacent position, and combining terms. The inverse operation is also available and is sometimes useful. Many operations are currently defined for one- dimensional expressions, that is, expressions in which only the X positions of the symbols are significant. However, a limited but growing set of two-dimensional operations is also available. There are many problems associated with the ambiguous interpretation of two-dimensional expressions which have not been entirely resolved. Many of these problems are easily bypassed, however, because the user can watch the progress of the manipulation and interject the correct interpretation if the programmed interpretation is incorrect. Inasmuch as the algebraic operations are defined in terms of primitives, and since any user can include or delete any operation at will, the ultimate capability in terms of different algebras is great. For example, it was relatively easy to include many operations of matrix algebra and calculus and physical vector algebra and calculus in this system. Tensor algebra and calculus is now being included. Although we have not pursued it to any extent, it seems possible to define algebras to manipulate physical entities such as machine parts, structural elements, or picture elements. |