Abstract: A method for document extraction includes receiving, from a user device associated with a user, an annotated document that includes one or more fields. Each respective field of the one or more fields of the annotated document is labeled by a respective annotation. The method includes clustering, using a template matching algorithm, the annotated document into a cluster and inducing, using the annotated document, a document template for the cluster. The method includes receiving, from the user device, an unannotated document including the one or more fields. The method includes clustering, using the template matching algorithm, the unannotated document into the cluster and, in response to clustering the unannotated document into the cluster, extracting, using the document template, the one or more fields.

Abstract: Described is a technology, such as implemented in a computational software program, by which a minimal polynomial is efficiently determined for a radical expression over the ring Z of integer numbers or the ring Q of rational numbers. The levels of the radical are grouped into a level permutation group that is used to find a level permutation set. An annihilation polynomial is found based upon the level permutation set. The annihilation polynomial is factored, and a selection mechanism selects the minimal polynomial based upon the annihilation polynomial's factors.

Abstract: Described is a technology, such as implemented in a computational software program, by which a minimal polynomial is efficiently determined for a radical expression over the ring Z of integer numbers or the ring Q of rational numbers. The levels of the radical are grouped into a level permutation group that is used to find a level permutation set. An annihilation polynomial is found based upon the level permutation set. The annihilation polynomial is factored, and a selection mechanism selects the minimal polynomial based upon the annihilation polynomial's factors.

Abstract: Described is a technology, such as implemented in a computational software program, by which a minimal polynomial is efficiently determined for a radical expression based upon its structure of the radical expression. An annihilation polynomial is found based upon levels of the radical to obtain roots of the radical. A numerical method performs a zero test or multiple zero tests to find the minimal polynomial. In one implementation, the set of roots corresponding to a radical expression is found. The annihilation polynomial is computed by grouping roots of the set according to their conjugation relationship and multiplying factor polynomials level by level. A selection mechanism selects the minimal polynomial based upon the annihilation polynomial's factors.