Method for live symbolic calculations in a mathematical document editor

Claim 1

A computer-based method for performing live symbolic mathematical operations in a mathematical document editor, said mathematical document editor capable of editing and processing a mathematical document and controlled by a computer having a screen capable of displaying the mathematical document, the method comprising the steps of: placing mathematical expressions in standard mathematical form at any position on the mathematical document, a subset of the mathematical expressions comprising a symbolic evaluation operator; maintaining a dependency graph so that the dependency graph continuously represents mathematical dependencies between the mathematical expressions in the mathematical document; symbolically evaluating each mathematical expression in the mathematical document that includes the symbolic evaluation operator, said step of symbolically evaluating including performing, for each mathematical expression that includes the symbolic evaluation operator, the substeps of (i) utilizing the dependency graph to ascertain all mathematical expressions on which the mathematical expression that includes the symbolic evaluation operator directly and indirectly depend, and (ii) passing the mathematical expression that includes the symbolic evaluation operator and the mathematical expressions ascertained at substep (i) to a symbolic algebra engine for symbolic evaluation; displaying in the mathematical document results of the symbolic evaluation of each mathematical expression evaluated at the previous step; editing a mathematical expression in the mathematical document; and automatically updating the mathematical document whenever a mathematical expression is edited by utilizing the dependency graph to take into account all mathematical dependencies in the mathematical document so that all mathematical expressions comprising the symbolic evaluation operator are consistent with all antecedent mathematical expressions upon which said mathematical expressions comprising the symbolic evaluation operator depend, said step of automatically updating including the substeps of (a) utilizing the dependency graph to ascertain if a mathematical expression that includes the symbolic evaluation operator depends upon the edited mathematical expression, (b) utilizing the dependency graph to determine all mathematical expressions on which the mathematical expression that includes the symbolic evaluation operator ascertained at substep (a) depends, and (c) passing the edited mathematical expression, the mathematical expression that includes the symbolic evaluation operator ascertained at substep (a) and the mathematical expressions determined at substep (b) to the symbolic algebra engine for symbolic evaluation.