Abstract
This book draft gives the theory of a new method for p dimensional adaptive integration by repeated 2^p subdivision of simplexes and hypercubes. A new method of constructing high order integration routines for these geometries permits adjustable samplings of the integration region controlled by user supplied parameters. An outline of the programs and use instructions are also included in the draft. The fortran programs are not included, but will be published with this draft as a book.
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