diff --git a/books/bookvol10.1.pamphlet b/books/bookvol10.1.pamphlet index ad4fc73..803ce2b 100644 --- a/books/bookvol10.1.pamphlet +++ b/books/bookvol10.1.pamphlet @@ -2415,6 +2415,17 @@ are the same. We are trying to predict patterns of how words occur in documents instead of trying to predict patterns of how players score on holes. \chapter{Quaternions} +from\cite{1}: +\begin{quotation} +Quaternions are inextricably linked to rotations. +Rotations, however, are an accident of three-dimensional space. +In spaces of any other dimensions, the fundamental operations are +reflections (mirrors). The quaternion algebra is, in fact, merely a +sub-algebra of the Clifford algebra of order three. If the quaternion +algebra might be labelled the algebra of rotations, then the Clifford +algebra is the algebra of mirrors and it is thus vastly more general +than quaternion algebra. +\end{quotation} \begin{center} \bigskip \large Peter Guthrie Tait, Robert S. Sutor, Timothy Daly @@ -7595,106 +7606,108 @@ Gaussian Elimination \chapter{Diophantine Equations} Diophantine Equations \begin{thebibliography}{99} -\bibitem{1} Laurent Bertrand. Computing a hyperelliptic integral using +\bibitem{1} Altmann, Simon L. Rotations, Quaternions, and Double Groups +Dover Publications, Inc. 2005 ISBN 0-486-44518-6 +\bibitem{2} Laurent Bertrand. Computing a hyperelliptic integral using arithmetic in the jacobian of the curve. {\sl Applicable Algebra in Engineering, Communication and Computing}, 6:275-298, 1995 -\bibitem{2} M. Bronstein. On the integration of elementary functions. +\bibitem{3} M. Bronstein. On the integration of elementary functions. {\sl Journal of Symbolic Computation} 9(2):117-173, February 1990 -\bibitem{3} M. Bronstein. The Risch differential equation on an +\bibitem{4} M. Bronstein. The Risch differential equation on an algebraic curve. In S.Watt, editor, {\sl Proceedings of ISSAC'91}, pages 241-246, ACM Press, 1991. -\bibitem{4} M. Bronstein. {\sl Symbolic Integration I--Transcendental +\bibitem{5} M. Bronstein. {\sl Symbolic Integration I--Transcendental Functions.} Springer, Heidelberg, 1997 -\bibitem{5} M. Bronstein. The lazy hermite reduction. Rapport de +\bibitem{6} M. Bronstein. The lazy hermite reduction. Rapport de Recherche RR-3562, INRIA, 1998 -\bibitem{6} E. Hermite. Sur l'int\'{e}gration des fractions +\bibitem{7} E. Hermite. Sur l'int\'{e}gration des fractions rationelles. {\sl Nouvelles Annales de Math\'{e}matiques} ($2^{eme}$ s\'{e}rie), 11:145-148, 1872 -\bibitem{7} Daniel Lazard and Renaud Rioboo. Integration of rational +\bibitem{8} Daniel Lazard and Renaud Rioboo. Integration of rational functions: Rational coputation of the logarithmic part {\sl Journal of Symbolic Computation}, 9:113-116:1990 -\bibitem{8} Joseph Liouville. Premier m\'{e}moire sur la +\bibitem{9} Joseph Liouville. Premier m\'{e}moire sur la d\'{e}termination des int\'{e}grales dont la valeur est alg\'{e}brique. {\sl Journal de l'Ecole Polytechnique}, 14:124-148, 1833 -\bibitem{9} Joseph Liouville. Second m\'{e}moire sur la +\bibitem{10} Joseph Liouville. Second m\'{e}moire sur la d\'{e}termination des int\'{e}grales dont la valeur est alg\'{e}brique. {\sl Journal de l'Ecole Polytechnique}, 14:149-193, 1833 -\bibitem{10} Thom Mulders. A note on subresultants and a correction to +\bibitem{11} Thom Mulders. A note on subresultants and a correction to the lazard/rioboo/trager formula in rational function integration {\sl Journal of Symbolic Computation}, 24(1):45-50, 1997 -\bibitem{11} M.W. Ostrogradsky. De l'int\'{e}gration des fractions +\bibitem{12} M.W. Ostrogradsky. De l'int\'{e}gration des fractions rationelles. {\sl Bulletin de la Classe Physico-Math\'{e}matiques de l'Acae\'{e}mie Imp\'{e}riale des Sciences de St. P\'{e}tersbourg,} IV:145-167,286-300, 1845 -\bibitem{12} Robert Risch. On the integration of elementary functions +\bibitem{13} Robert Risch. On the integration of elementary functions which are built up using algebraic operations. Research Report SP-2801/002/00, System Development Corporation, Santa Monica, CA, USA, 1968 -\bibitem{13} Robert Risch. Further results on elementary +\bibitem{14} Robert Risch. Further results on elementary functions. Research Report RC-2042, IBM Research, Yorktown Heights, NY, USA, 1969 -\bibitem{14} Robert Risch, The problem of integration in finite +\bibitem{15} Robert Risch, The problem of integration in finite terms. {\sl Transactions of the American Mathematical Society} 139:167-189, 1969 -\bibitem{15} Robert Risch. The solution of problem of integration in +\bibitem{16} Robert Risch. The solution of problem of integration in finite terms. {\sl Transactions of the American Mathematical Society} 76:605-608, 1970 -\bibitem{16} Robert Risch. Algebraic properties of the elementary +\bibitem{17} Robert Risch. Algebraic properties of the elementary functions of analysis. {\sl American Journal of Mathematics}, 101:743-759, 1979 -\bibitem{17} Maxwell Rosenlicht. Integration in finite terms. {\sl +\bibitem{18} Maxwell Rosenlicht. Integration in finite terms. {\sl American Mathematical Monthly}, 79:963-972, 1972 -\bibitem{18} Michael Rothstein. A new algorithm for the integration of +\bibitem{19} Michael Rothstein. A new algorithm for the integration of exponential and logarithmic functions. In {\sl Proceedings of the 1977 MACSYMA Users Conference}, pages 263-274. NASA Pub CP-2012, 1977 -\bibitem{19} Barry Trager. Algebraic factoring and rational function +\bibitem{20} Barry Trager. Algebraic factoring and rational function integration. In {Proceedings of SYMSAC'76} pages 219-226, 1976 -\bibitem{20} Barry Trager {\sl On the integration of algebraic +\bibitem{21} Barry Trager {\sl On the integration of algebraic functions}, PhD thesis, MIT, Computer Science, 1984 -\bibitem{21} M. van Hoeij. An algorithm for computing an integral +\bibitem{22} M. van Hoeij. An algorithm for computing an integral basis in an algebraic function field. {\sl J. Symbolic Computation} 18(4):353-364, October 1994 -\bibitem{22} Andr\'{e} Weil, {\sl Courbes alg\'{e}briques et +\bibitem{23} Andr\'{e} Weil, {\sl Courbes alg\'{e}briques et vari\'{e}t\'{e}s Abeliennes} Hermann, Paris, 1971 -\bibitem{23} D.Y.Y. Yun. On square-free decomposition algorithms. In +\bibitem{24} D.Y.Y. Yun. On square-free decomposition algorithms. In {\sl Proceedings of SYMSAC'76} pages 26-35, 1976 -\bibitem{24} Bronstein, Manuel "Symbolic Integration Tutorial" +\bibitem{25} Bronstein, Manuel "Symbolic Integration Tutorial" INRIA Sophia Antipolis ISSAC 1998 Rostock -\bibitem{25} Jenks, R.J. and Sutor, R.S. +\bibitem{26} Jenks, R.J. and Sutor, R.S. ``Axiom -- The Scientific Computation System'' Springer-Verlag New York (1992) ISBN 0-387-97855-0 -\bibitem{26} Knuth, Donald E., ``Literate Programming'' +\bibitem{27} Knuth, Donald E., ``Literate Programming'' Center for the Study of Language and Information ISBN 0-937073-81-4 Stanford CA (1992) -\bibitem{27} Daly, Timothy, ``The Axiom Wiki Website''\\ +\bibitem{28} Daly, Timothy, ``The Axiom Wiki Website''\\ {\bf http://axiom.axiom-developer.org} -\bibitem{28} Watt, Stephen, ``Aldor'',\\ +\bibitem{29} Watt, Stephen, ``Aldor'',\\ {\bf http://www.aldor.org} -\bibitem{29} Lamport, Leslie, ``Latex -- A Document Preparation System'', +\bibitem{30} Lamport, Leslie, ``Latex -- A Document Preparation System'', Addison-Wesley, New York ISBN 0-201-52983-1 -\bibitem{30} Ramsey, Norman ``Noweb -- A Simple, Extensible Tool for +\bibitem{31} Ramsey, Norman ``Noweb -- A Simple, Extensible Tool for Literate Programming''\\ {\bf http://www.eecs.harvard.edu/ $\tilde{}$nr/noweb} -\bibitem{31} Daly, Timothy, "The Axiom Literate Documentation"\\ +\bibitem{32} Daly, Timothy, "The Axiom Literate Documentation"\\ {\bf http://axiom.axiom-developer.org/axiom-website/documentation.html} -\bibitem{32} {\bf http://www.puffinwarellc.com/p3a.htm} -\bibitem{33} Tait, P.G., +\bibitem{33} {\bf http://www.puffinwarellc.com/p3a.htm} +\bibitem{34} Tait, P.G., {\it An Elementary Treatise on Quaternions} \\ C.J. Clay and Sons, Cambridge University Press Warehouse, Ave Maria Lane 1890 -\bibitem{34} Knuth, Donald, {\it The \TeX{}book} \\ +\bibitem{35} Knuth, Donald, {\it The \TeX{}book} \\ Reading, Massachusetts, Addison-Wesley Publishing Company, Inc., 1984. ISBN 0-201-13448-9 -\bibitem{35} Hathway, Arthur S., "A Primer Of Quaternions" (1896) -\bibitem{36} Conway, John H. and Smith, Derek, A., +\bibitem{36} Hathway, Arthur S., "A Primer Of Quaternions" (1896) +\bibitem{37} Conway, John H. and Smith, Derek, A., "On Quaternions and Octonions", A.K Peters, Natick, MA. (2003) ISBN 1-56881-134-9 -\bibitem{37} http://mathworld.wolfram.com/Quaternion.html +\bibitem{38} http://mathworld.wolfram.com/Quaternion.html \end{thebibliography} \end{document} diff --git a/changelog b/changelog index 02990d7..e6dd95f 100644 --- a/changelog +++ b/changelog @@ -1,4 +1,6 @@ -20100209 tpd src/axiom-website/patches.html 20100212.01.tpd.patch +20100212 tpd src/axiom-website/patches.html 20100212.02.tpd.patch +20100212 tpd books/bookvol10.1 add quaternion quote from Altmann +20100212 tpd src/axiom-website/patches.html 20100212.01.tpd.patch 20100212 tpd src/interp/pf2sex.lisp removed 20100212 tpd src/interp/Makefile remove pf2sex 20100212 tpd books/bookvol5 merge and remove pf2sex diff --git a/src/axiom-website/patches.html b/src/axiom-website/patches.html index 63f1439..a5ad61d 100644 --- a/src/axiom-website/patches.html +++ b/src/axiom-website/patches.html @@ -2449,5 +2449,7 @@ books/bookvol5 treeshake ptrees, pf2sex
books/bookvol5 treeshake ptrees, pf2sex
20100212.01.tpd.patch books/bookvol5 merge and remove pf2sex
+20100212.02.tpd.patch +books/bookvol10.1 add quaternion quote from Altmann