Computational Mathematics with SageMath

Co m pu ta tio na lM at he m at ic s w ith Sa ge M at h or Sage for short, is an open-source mathematical system based on the Python language. Sage is developed by an international community of hundreds of teachers and researchers, whose aim is to provide an alternative to the commercial products Magma, Maple, Mathematica and Matlab. To reach this goal, Sage relies on many open-source programs, including GAP, Maxima, PARI and various scientific libraries for Python, to which thousands of new functions are added. Sage is freely available and is supported by all modern operating systems.

[1]  J. Edmonds Paths, Trees, and Flowers , 1965, Canadian Journal of Mathematics.

[2]  David Goldberg What Every Computer Scientist Should Know About Floating-Point Arithmetic , 1992 .

[3]  Nicholas J. Higham,et al.  The Accuracy of Floating Point Summation , 1993, SIAM J. Sci. Comput..

[4]  Henri Cohen,et al.  A course in computational algebraic number theory , 1993, Graduate texts in mathematics.

[5]  Doron Zeilberger,et al.  Proof of the alternating sign matrix conjecture , 1994, Electron. J. Comb..

[6]  Joachim von zur Gathen,et al.  Modern Computer Algebra , 1998 .

[7]  Uri M. Ascher,et al.  Computer methods for ordinary differential equations and differential-algebraic equations , 1998 .

[8]  A. Storjohann Algorithms for matrix canonical forms , 2000 .

[9]  M. Schatzman,et al.  Numerical Analysis: A Mathematical Introduction , 2002 .

[10]  Kazuo Murota,et al.  Numerical indefinite integration by double exponential sinc method , 2004, Math. Comput..

[11]  M. Mori Discovery of the Double Exponential Transformation and Its Developments , 2005 .

[12]  Fabrice Rouillier,et al.  Motivations for an Arbitrary Precision Interval Arithmetic and the MPFI Library , 2005, Reliab. Comput..

[13]  Philippe Flajolet,et al.  Analytic Combinatorics , 2009 .

[14]  Richard P. Brent,et al.  Modern Computer Arithmetic , 2010 .

[15]  Warwick Tucker,et al.  Validated Numerics: A Short Introduction to Rigorous Computations , 2011 .

[16]  Fredrik Johansson,et al.  Arb: a C library for ball arithmetic , 2014, ACCA.