Introduction to the SageMath software
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1 Introduction to the SageMath software ( slides available at June 1st 2017, Mini-course HSE Moscow by Vincent Delecroix, CNRS researcher at LaBRI Bordeaux (France) V. Delecroix (LaBRI) 1 / 9
2 Why do you want (good) math softwares? V. Delecroix (LaBRI) 2 / 9
3 Why do you want (good) math softwares? verify your small computations, V. Delecroix (LaBRI) 2 / 9
4 Why do you want (good) math softwares? verify your small computations, make nice illustrations, V. Delecroix (LaBRI) 2 / 9
5 Why do you want (good) math softwares? verify your small computations, make nice illustrations, make huge computations, test conjectures, V. Delecroix (LaBRI) 2 / 9
6 Why do you want (good) math softwares? verify your small computations, make nice illustrations, make huge computations, test conjectures, develop new algorithms, V. Delecroix (LaBRI) 2 / 9
7 Why do you want (good) math softwares? verify your small computations, make nice illustrations, make huge computations, test conjectures, develop new algorithms, experimental physics or mathematics, make conjectures. V. Delecroix (LaBRI) 2 / 9
8 Why SageMath Four commercial softwares are dominating the field of mathematical computations : Mathematica, Maple, Matlab, Magma... V. Delecroix (LaBRI) 3 / 9
9 Why SageMath Four commercial softwares are dominating the field of mathematical computations : Mathematica, Maple, Matlab, Magma... These softwares are expensive. V. Delecroix (LaBRI) 3 / 9
10 Why SageMath Four commercial softwares are dominating the field of mathematical computations : Mathematica, Maple, Matlab, Magma... These softwares are expensive. No way to verify how they work. V. Delecroix (LaBRI) 3 / 9
11 Why SageMath Four commercial softwares are dominating the field of mathematical computations : Mathematica, Maple, Matlab, Magma... These softwares are expensive. No way to verify how they work. Sometimes impossible to get bugs corrected. V. Delecroix (LaBRI) 3 / 9
12 Why SageMath Four commercial softwares are dominating the field of mathematical computations : Mathematica, Maple, Matlab, Magma... These softwares are expensive. No way to verify how they work. Sometimes impossible to get bugs corrected. They can disappear. V. Delecroix (LaBRI) 3 / 9
13 Why SageMath Four commercial softwares are dominating the field of mathematical computations : Mathematica, Maple, Matlab, Magma... These softwares are expensive. No way to verify how they work. Sometimes impossible to get bugs corrected. They can disappear. Free mathematical softwares exists since the 80 s like GAP, R, Maxima, PARI/GP. Each of them is specialized. SageMath is an international project started in 2005 and aims to cover a large range of mathematics. V. Delecroix (LaBRI) 3 / 9
14 The developer map V. Delecroix (LaBRI) 4 / 9
15 The developer map One contributor from Russia!? (Alexey U. Gudchenko, contributed 6 years ago) V. Delecroix (LaBRI) 4 / 9
16 Four important ingredients open source license V. Delecroix (LaBRI) 5 / 9
17 Four important ingredients open source license popular programming language V. Delecroix (LaBRI) 5 / 9
18 Four important ingredients open source license popular programming language generic notebook interface V. Delecroix (LaBRI) 5 / 9
19 Four important ingredients open source license popular programming language generic notebook interface on the shoulders of hundreds of free mathematical libraries V. Delecroix (LaBRI) 5 / 9
20 SageMath is free. Can be downloaded from internet Source code at Contributions open to anyone V. Delecroix (LaBRI) 6 / 9
21 SageMath is free. Can be downloaded from internet Source code at Contributions open to anyone Freeness will remain forever and is guaranteed by the GNU GPL license. V. Delecroix (LaBRI) 6 / 9
22 Python is a very popular programming language that is easy to learn and close to mathematical notation. V. Delecroix (LaBRI) 7 / 9
23 Python is a very popular programming language that is easy to learn and close to mathematical notation. The set can be constructed in Sage as {x {1,..., 20} : 2x 2 1 is prime} [x for x in [1..20] if is_prime(2*xˆ2-1)] V. Delecroix (LaBRI) 7 / 9
24 Python is a very popular programming language that is easy to learn and close to mathematical notation. The set can be constructed in Sage as {x {1,..., 20} : 2x 2 1 is prime} [x for x in [1..20] if is_prime(2*xˆ2-1)] Python is used for many other purposes : web programming, script language, biology, data analysis, etc V. Delecroix (LaBRI) 7 / 9
25 Jupyter is a generic web interface for programming language. It can be used with many different languages and softwares : Sage, PARI/GP, C, C++, etc. The list of kernels can be found at jupyter/wiki/jupyter-kernels V. Delecroix (LaBRI) 8 / 9
26 Sage is built on top of hundreds of scientific libraries and softwares. GMP or MPIR : C library for arbitrary precision integers flint : a C library for algebra linbox : C++ library for exact linear algebra PARI/GP : a CAS for number theory GAP : a CAS for group computations complete list at V. Delecroix (LaBRI) 9 / 9
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