# Ideals, varieties, and algorithms: an introduction to computational algebraic geometry and commutative algebra By **David A. Cox & John Little & Donal O’Shea** book pdf

Author : **David A. Cox & John Little & Donal O’Shea**

Years : **2007**

Edition : **3rd ed**

Series : *Undergraduate texts in mathematics*

Pages : **565**

ISBN : **9780387356518, 0387356509, 9780387356501, 0387356517**

Language : **English**

**Algebraic Geometry** is the study of systems of **polynomial equations** in one or more variables, asking such questions as: Does the system have finitely many solutions, and if so how can one find them? And if there are infinitely many solutions, how can they be described and manipulated?

**The solutions of a system of polynomial equations** form a **geometric** object called a variety; the corresponding **algebraic** object is an ideal. There is a close relationship between ideals and varieties which reveals the intimate link between **algebra and geometry**. Written at a level appropriate to undergraduates, this **book Ideals, varieties, and algorithms: an introduction to computational algebraic geometry and commutative algebra pdf** covers such topics as the **Hilbert Basis Theorem**, the Nullstellensatz, **invariant theory**, **projective geometry**, and **dimension theory**.

The **algorithms** to answer questions such as those posed above are an important part of **algebraic geometry**. Although the **algorithmic roots of algebraic geometry** are old, it is only in the last forty years that computational methods have regained their earlier prominence. New **algorithms**, coupled with the power of fast computers, have led to both theoretical advances and interesting applications, for example in robotics and in **geometric theorem** proving.

In addition to enhancing the text of the second edition, with over 200 pages reflecting changes to enhance clarity and correctness, this third edition of Ideals, **Varieties and Algorithms** includes: A significantly updated section on Maple in Appendix C; Updated information on **AXIOM**, **CoCoA**, **Macaulay 2**, **Magma**, **Mathematica** and **SINGULAR**; A shorter proof of the Extension Theorem presented in Section 6 of Chapter 3. From the 2nd Edition:

“I consider the **book** to be wonderful. … The exposition is very clear, there are many helpful pictures, and there are a great many instructive exercises, some quite challenging … offers the heart and soul of modern commutative and algebraic geometry.” –**The American Mathematical** Monthly

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