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Modern Computer Algebra

Modern Computer Algebra, Cover 2nd editionJoachim von zur Gathen and J├╝rgen 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: Musical scales

Part of a piano keyboard

Diophantine approximations with denominator n to the logarithms of the six "pleasant" musical intervals r_1=2/1 (octave), r_2=3/2 (fifth), r_3=4/3 (fourth), r_4=5/4 (major third), r_5=6/5 (minor third), and r_6=9/8 (whole tone), and the quality of the nth approximation (lower diagram).

© Joachim von zur Gathen and Jürgen Gerhard, last change: 7 May 1999

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