We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.
We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.
Published online by Cambridge University Press: 11 November 2009
Abstract
This article gives some overview on Singular, a computer algebra system for polynomial computations with special emphasis on the needs of commutative algebra, algebraic geometry and singularity theory, which has been developed under the guidance of G.-M. Greuel, G. Pfister and the second author [31]. We draw the bow from Singular's early years to its latest features. Moreover, we present some explicit calculations, focusing on applications in singularity theory.
Introduction
By the development of effective computer algebra algorithms and of powerful computers, algebraic geometry and singularity theory (like many other disciplines of pure mathematics) have become accessible to experiments. Computer algebra may help
to discover unexpected mathematical evidence, leading to new conjectures or theorems, later proven by traditional means,
to construct interesting objects and determine their structure (in particular, to find counter-examples to conjectures),
to verify negative results such as the non-existence of certain objects with prescribed invariants,
to verify theorems whose proof is reduced to straightforward but tedious calculations,
to solve enumerative problems, and
to create data bases.
In fact, in the last decades, there is a growing number of research articles in algebraic geometry and singularity theory originating from explicit computations (such as [1] and [46] in this volume).
What abilities of a computer algebra system are needed to become a valuable tool for algebraic geometry and, in particular, for singularity theory? First of all, the system needs an efficient representation of polynomials with exact coefficients.
To save this book to your Kindle, first ensure [email protected] is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.
Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.
Find out more about the Kindle Personal Document Service.
To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Dropbox.
To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.
