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[Axiom-math] First about Sage published

From: Bill Page
Subject: [Axiom-math] First about Sage published
Date: Wed, 21 Feb 2007 10:31:43 -0500

Althought this is not directly about Axiom, it might be of interest
to note that Sage does include an interface to Axiom as well as
several other computer algebra systems. I think it is remarkable
that a system that is less than two years old is already the basis
of a new book - even if the author of the book is also the (primary)
author of the system.

Modular Forms, a Computational Approach
William Stein

The leading expert in computations with modular forms demystifies
this process with practical algorithms . free software is available
to assist with exercises .



This marvellous and highly original book fills a significant gap in
the extensive literature on classical modular forms. This is not
just yet another introductory text to this theory, though it could
certainly be used as such in conjunction with more traditional
treatments. Its novelty lies in its computational emphasis
throughout: Stein not only defines what modular forms are, but shows
in illuminating detail how one can compute everything about them in
practice. This is illustrated throughout the book with examples from
his own (entirely free) software package SAGE, which really bring the
subject to life while not detracting in any way from its theoretical
beauty. The author is the leading expert in computations with modular
forms, and what he says on this subject is all tried and tested and
based on his extensive experience. As well as being an invaluable
companion to those learning the theory in a more traditional way,
this book will be a great help to those who wish to use modular forms
in applications, such as in the explicit solution of Diophantine
equations. There is also a useful Appendix by Gunnells on extensions
to more general modular forms, which has enough in it to inspire many
PhD theses for years to come. While the book's main readership will
be graduate students in number theory, it will also be accessible to
advanced undergraduates and useful to both specialists and non-
specialists in number theory.

--John E. Cremona, University of Nottingham

William Stein is an associate professor of mathematics at the
University of Washington at Seattle. He earned a PhD in mathematics
from UC Berkeley and has held positions at Harvard University and
UC San Diego. His current research interests lie in modular forms,
elliptic curves, and computational mathematics.


Oh, for the "glory days" of Axiom when Axiom might have been the
tool of choice for this type of work!

Bill Page.

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