SageMath, SINGULAR, Macaulay2

VMP
List of computer algebra systems
Journal of Software for Algebra and Geometry

Macaulay2
Macaulay2Doc — Macaulay2 documentation
Function — the class of all functions
mathematical examples
Computations in algebraic geometry with Macaulay 2
M2SingularBook — Macaulay2 examples for the Singular book M2SingularBook consists of Macaulay2 translations of the examples in the book A Singular introduction to commutative algebra
A Singular Introduction to Commutative Algebra
Elementary uses of Groebner bases

Downloads Macaulay2
Macaulay2 Ubuntu
Ubuntu under Windows
Problems when installing Macaulay2 in Ubuntu 18.04
Macaulay2 for ‘Linux subsystem for Windows’, with GUI
GitHub Location of WSL rootfs filesystem for post – Fall Creator’s Update installations
VS Code extension for Macaulay2
Linux-разработка в Windows с WSL и Visual Studio Code Remote

using Macaulay2 with emacs
editing Macaulay2 code with emacs

Macaulay2 GitHub
Interactive Shell – a Web App for Macaulay2
Packages included with Macaulay2 version 1.15
macaulay2-jupyter-kernel 0.6.7
Macaulay2-Jupyter-Kernel demo
SageMath Interface to Macaulay2
Computations in algebraic geometry with macaulay2

WiKi Macaulay2
Computations in algebraic geometry with macaulay2 pdf


Macaulay 2 Tutorial

Singular is a computer algebra system for polynomial computations
Singular Online Manual
A Singular Introduction to Commutative Algebra
Interfaces GP/PARI, GAP, Singular, Maxima
Interface to Singular

CoCoA (Computations in Commutative Algebra)[

SageMath
Sagemath GitHub
Intermediate Python
SymPy
The Python Package Index
Welcome to the Sage Tutorial!
SageMath Help and Support
Sage Quick Reference Cards
SageMath Library

These software packages are used by SageMath
quickref-ru.pdf Краткое Руководство по Sage Уильям Стайн 2014
quickref-linalg.pdf
quickref-calc.pdf
quickref-algebra.pdf
Interface to Singular
Interfaces GP/PARI, GAP, Singular, Maxima
SageMath Interface to Macaulay2
The Elliptic Curve Factorization Method
GMP-ECM (Elliptic Curve Method for Integer Factorization)
Interface to Magma
Interface to Maple
Interface to Mathematica
Interface to MATLAB

Interpreter Interfaces

r = singular.ring(0, ‘(x,y,z)’, ‘dp’)
s1 = singular.poly(‘x2’);
s2 = singular.poly(‘y3’);
s3 = singular.poly(‘z’);
i = singular.ideal(s1, s2-s1, 0,s2*s3, s3^4);
i
output>
x^2,
y^3-x^2,
0,
y^3*z,
z^4

f = singular(‘9*y^8 – 9*x^2*y^7 – 18*x^3*y^6 – 18*x^5*y^6 +’
‘9*x^6*y^4 + 18*x^7*y^5 + 36*x^8*y^4 + 9*x^10*y^4 – 18*x^11*y^2 -‘
‘9*x^12*y^3 – 18*x^13*y^2 + 9*x^16’)
f
>9*x^16-18*x^13*y^2-9*x^12*y^3+9*x^10*y^4-18*x^11*y^2+36*x^8*y^4+18*x^7*y^5-18*x^5*y^6+9*x^6*y^4-18*x^3*y^6-9*x^2*y^7+9*y^8
F = f.factorize(); F
>[1]:
_[1]=9
_[2]=x^6-2*x^3*y^2-x^2*y^3+y^4
_[3]=-x^5+y^2
[2]:
1,1,2
F[1][2]
> x^6-2*x^3*y^2-x^2*y^3+y^4

Singular is a computer algebra system for polynomial computations
DOWNLOAD SINGULAR

Singular Online Manual
Singular A.3 Commutative Algebra
Singular A.4 Singularity Theory


Singular is a computer algebra system for polynomial computations
Singular Online Manual
A Singular Introduction to Commutative Algebra

A Singular Introduction to Commutative Algebra 0

The Stacks project AlgGeo
GitHub stacks-project
an open source textbook and reference work on algebraic geometry

Jupyter Notebook Using Singular in Jupyter
PySingular Python module which can execute Singular commands
Installation of Singular for the bundled extension
Building Singular from source
FLINT: Fast Library for Number Theory
A Tour of NTL: Using NTL with GMP
A Tour of NTL: Obtaining and Installing NTL for UNIX
Download NTL
Cygwin: Введение


Using Singular in Jupyter
Welcome to Singular online!

Macaulay2
Interactive Shell – a Web App for Macaulay2

WiKi Macaulay2
Build web apps for interactive command-line tools http://web.macaulay2.com
Macaulay2 is a software system devoted to supporting research in algebraic geometry and commutative algebra, whose creation has been funded by the National Science Foundation since 1992.
BeginningMacaulay2 — Mathematicians’ Introduction to Macaulay2

Examples
A.1 Programming procedures and libraries, formatting output, etc.
A.2 Computing Groebner and Standard Bases GB conversion, slim GB
A.3 Commutative Algebra saturation, elimination, free resolution, factorization, primary decomposition, normalization, etc.
A.4 Singularity Theory singular and critical points, invariants of hypersurface singularities, classification, resolution of singularities, etc.
A.5 Invariant Theory G_a-invariants, invariants of finite groups
A.6 Geometric Invariant Theory
A.7 Non-commutative Algebra Groebner bases and applications in G-algebras
A.8 Applications Solving systems of polynomial equations, AG codes

Install Singular 4-x-x on a Microsoft Windows Platform
Installing Singular 3-0-3 on a Microsoft Windows platform
Installing SINGULAR Windows

Singular is a computer algebra system for polynomial computations, with special emphasis on commutative and non-commutative algebra, algebraic geometry, and singularity theory. It is free and open-source under the GNU General Public Licence. Singular provides highly efficient core algorithms, a multitude of advanced algorithms in the above fields, an intuitive, C-like programming language, easy ways to make it user-extendible through libraries, and a comprehensive online manual and help function. Its main computational objects are ideals, modules and matrices over a large number of baserings. These include polynomial rings over various ground fields and some rings (including the integers), localizations of the above, a general class of non-commutative algebras (including the exterior algebra and the Weyl algebra), quotient rings of the above, tensor products of the above. Singular’s core algorithms handle Gröbner resp. standard bases and free resolutions, polynomial factorization, resultants, characteristic sets, and numerical root finding. Its advanced algorithms, contained in currently more than 90 libraries, address topics such as absolute factorization, algebraic D-modules, classification of singularities, deformation theory, Gauss-Manin systems, Hamburger-Noether (Puiseux) development, invariant theory, (non-) commutative homological algebra, normalization, primary decomposition, resolution of singularities, and sheaf cohomology. Further functionality is obtained by combining Singular with third-party software linked to SINGULAR. This includes tools for convex geometry, tropical geometry, and visualization.

Linux-разработка в Windows с WSL и Visual Studio Code Remote

Visual Studio Code Remote – WSL

Developing on Windows with WSL2 (Subsystem for Linux), VS Code, Docker, and the Terminal


What’s a Tensor?

How to compute S-pairs in Macaulay2?
Macaulay2