Modern Computer Algebra
Joachim von zur Gathen and Jürgen Gerhard.
Textbook, 3rd edition, Cambridge University Press 2013 (publisher site).
ISBN 978-1107039032.
808 pages, 55 b/w illustrations, 53 colour illustrations, 40 tables, 560 exercises.
(Second edition 2003: ISBN 978-0521826464.)
(First edition 1999: ISBN 0521641764.)
MCA gallery: elliptic curves
The elliptic curve y^2=x^3-x over the real numbers (left diagram), and the elliptic curves y^2=x^3-x+b for b=0, 1/10, 2/10, 3/10, 4/10, 5/10.
Adding two points P with x=-0.9 (red) and Q with x=-0.5 (green) on the elliptic curve y^2=x^3-x. The point R=P+Q (blue) is the negative of the intersection point S (black) of the two lines with the curve.
© Joachim von zur Gathen and Jürgen Gerhard, last change: 7 May 1999