Abstract: An information retrieval system that deals with the problems of synonymy, polysemy, and retrieval by concept by allowing for a wide margin of uncertainty in the initial choice of keywords in a query. For each input query vector and an information matrix, the disclosed system solves an optimization problem which maximizes the stability of a solution at a given level of misfit. The disclosed system may include a decomposition of the information matrix in terms of orthogonal basis functions. Each basis encodes groups of conceptually related keywords. The bases are arranged in order of decreasing statistical relevance to a query. The disclosed search engine approximates the input query with a weighted sum of the first few bases. Other commercial applications than the disclosed search engine can also be built on the disclosed techniques.

Abstract: A method and system for locking a defined portion of the live mathematical document. A live mathematical document program, executed on a computer processor, allows a user to edit a live mathematical document and also processes the document. The user can enter mathematical expressions in any position in the live mathematical document. The program automatically updates the live mathematical document to ensure that all expressions are consistent with all expressions upon which they depend. The user can position a first boundary line and a second boundary line in the live mathematical document. The program locks an area on the live mathematical document, the locked area being the area between the first boundary line and the second boundary line. An editor allows editing of expressions in the live mathematical document, and ascertains whether an edit is within the locked area and disallows such edits.

Abstract: A method and system for encoding nested matrices and vectors. The system can be used in a live mathematical document program executed on a computer processor. The mathematical document program stores elements of matrices in contiguous memory locations in a primary memory as floating point numbers. Each scalar element is stored as a floating point number. Each matrix element is stored as a two part combination such that the two part combination occupies no more memory space than each scalar element, The first part of the two part combination including a code to indicate that the entry is a symbolic entity and the second part of the two part combination includes a pointer to a memory location storing elements of the matrix element. The scalar elements and the two part combinations are stored in contiguous memory locations in primary memory.

Abstract: A mathematical document editor that can perform live symbolic calculations. The mathematical document editor is capable of placing mathematical expressions at any position on a computer screen, that represents a printed document. A symbolic dependency graph is maintained such that it always reflects the mathematical dependencies on the computer screen. Any expression which includes a symbolic evaluation operator is evaluated by a symbolic algebra engine, taking into account all the definitions and constraints upon which the expression depends. If an expression is modified, introduced or deleted, the symbolic dependency graph is used to determine which expression containing the symbolic evaluation operator need to be modified. The present invention ensures that the document is `up to date` in the sense that all expressions, including those requiring symbolic calculations, are consistent with all antecedent expressions upon which they depend.

Abstract: A mathematical document editor that can perform live symbolic calculations. The mathematical document editor is capable of placing mathematical expressions at any position on a computer screen, that represents a printed document. A symbolic dependency graph is maintained such that it always reflects the mathematical dependencies on the computer screen. Any expression which includes a symbolic evaluation operator is evaluated by a symbolic algebra engine, taking into account all the definitions and constraints upon which the expression depends. If an expression is modified, introduced or deleted, the symbolic dependency graph is used to determine which expression containing the symbolic evaluation operator need to be modified. The present invention ensures that the document is `up to date` in the sense that all expressions, including those requiring symbolic calculations, are consistent with all antecedent expressions upon which they depend.