Algebraic device and methods of use thereof

摘要

This invention provides a novel affordance to algebra. It combines the immediacy of a manipulative with the power of a computer algebra system. Operations are executed in-place on a mutable expression, by direct manipulation of its terms by the user.;Terms, whether simple or complex, can be selected by the user and dragged from one location in the expression to another. The equivalence of the expression is maintained by changes to the moving term and other terms in the expression. A highly interactive interface illuminates to the user the range of potential actions.;The beneficiaries of this technology are students, who have a new avenue for exploratory learning and technologists, who have a new tool for symbolic reasoning.

主权项

1. A method of generating an expression of algebra consistent with an existing expression on an output means, comprising:
a. providing a memory which is able to store said existing expression in said memory, b. providing an output means which is operatively connected to said memory for displaying said expression stored in said memory, c. providing an input means which a human operator can use to select one or more terms within said expression displayed by said output, d. providing an input means which a human operator can use to maneuver said selected term or terms to one or more loci, e. providing a computer algebra system operatively connected to said memory for manipulating said existing expression stored in said memory, f. providing an object program which will:
i. load an expression into said memory, andii. display said expression on said output means, andiii. register a human operator's selection of one or more terms within said expression via said input means, andiv. display on said output means a representation of the currently selected term as said human operator manipulates said currently selected term, and v. respond to said human operator using said input means to interact with said loci and thus drive said computer algebra system to create a modified version of said expression in said memory, andvi. display said modified expression on said output means as the result of an edit-in-place operation, andvii. repeat steps iv through vi until said human operator signals via the input means that the manipulation is complete,whereby said output means will display said modified expression in the place of said existing expression, and a human operator can manipulate an electronic representation of an algebraic expression.