2.1.1. Installation of Python

NZMATH requires Python version 3.8 or later. If you do not have Python installed on your machine, please install it. The Python language is a very high level language. It is downloadable from the website. There are also some documents there.

Ensure you can run Python from the command line:

% python --version

(We use '%' for a command line prompt on UNIX/macOS. On Windows, it may be 'C:>' or something. Sometimes, you may need to be a privileged user and the prompt may change to # or so on, but we don't care.)

2.1.2. Installation of NZMATH

% python -m pip --version

% python -m pip install --upgrade pip setuptools wheel

% python -m pip install nzmath

nzmath-x.y.z.tar.gz
nzmath-x.y.z-py3-none-any.whl

% python -m pip install --no-index --find-links=/tmp/dist/ nzmath

% python -m pip install /tmp/dist/nzmath-x.y.z.tar.gz

% python -m pip install /tmp/dist/nzmath-x.y.z-py3-none-any.whl

2.1.3. Installation of IPython

(Optional, but recommended)

IPython is an enhanced interactive Python shell. If you do not have it installed on your system, it is recommended to install it now.

You can get IPython with pip:

% python -m pip install ipython

2.1.4. Installation of mpmath

(Optional, but recommended)

mpmath is a multiple precision floating point arithmetic package for Python. Some modules in NZMATH essentially depend on the availability of mpmath, and some other modules can be more powerful with mpmath.

You can get mpmath with pip:

% python -m pip install mpmath

2.2.1. User Interfaces

NZMATH does not have own interpreter nor graphical interface. Users have to use with the raw Python interpreter (or possibly IPython). Though the interpreters are designed well, of course, they are not specialized for mathematical computation. Please be patient about it.

2.2.2. Sample Session

Start your Python interpreter.

% python
Python 3.8.6 (....................) [....................] on ........
Type "help", "copyright", "credits" or "license" for more information.
>>>

Here, '>>>' is a Python prompt. You are in the Python interpreter until you will type 'exit()'. Then, type

>>> from nzmath import *
>>>

The whole NZMATH stuff is imported.

>>> r = rational.Rational(113, 355)
>>> print(r)
113/355
>>>
....

The session continues until you will stop.

2.2.3. Readline

(Optional)

As you see, class names of NZMATH objects may be boringly long to type. You can use completion feature; if you are using ipython it is presented by default, or if you use default Python you might be able to configure it to use readline. Unfortunately, sometimes Python is built WITHOUT readline module for some license issue. So, the following is for those who are lucky to have readline enabled Python.

Save the following content in your file, pythonrc.py, for example:

try:

import readline

except ImportError:

print("Module readline not available.")

else:

import rlcompleter readline.parse_and_bind("tab: complete")

Then, set environment variable PYTHONSTARTUP pointing to the file.

(Please read Python Library Reference of readline and rlcompleter modules for more detailed explanation.)

4.1.1. Integer

There is an integer data type int (arbitrary precision) in Python. NZMATH has Integer (nzmath.rational.Integer) to give a rational result for division instead of a float.

>>> rational.Integer(3) / 4
Rational(3, 4)
>>> 3 / 4
0.75

Python's int behaves just like C's int type by double slash operator, i.e. floor division.

>>> 3 // 4
0
>>> 8 // 5
1

4.1.2. Rational

NZMATH provides Rational (nzmath.rational.Rational) class representing a rational number, as already appeared in the previous example.

4.1.3. Algebraic number

In NZMATH, algfield module provides algebraic numbers.

4.1.4. floating point number

Python has float data type for it. The mpmath also provides it.

4.2.1. Polynomials

There are several polynomial classes. New users should use poly sub-package.

>>> poly.uniutil.polynomial({0:-1,100:1}, rational.theIntegerRing)
IntegerPolynomial([(0, -1), (100, 1)], IntegerRing())

poly.uniutil.polynomial is the factory function for univariate polynomials.

4.2.2. Matrices

There are several matrix classes. matrix module provides them.

4.3.1. Rings

Integers are in the integer ring, a polynomial in a certain polynomial ring, etc.... They are obtained from elements of them by getRing method. For example, rational.Integer(1).getRing() returns a rational.IntegerRing object.

This is a convention in NZMATH and does not apply to the object provided by Python itself such as int...

4.3.2. Fields

Fields are a part of rings (see Rings).

There are some fields: the field of rational numbers, real numbers, and complex numbers are defined. Finite fields are provided through finitefield module.

4.3.3. Groups

There are some groups in NZMATH: for example, class group of imaginary quadratic fields in quad module, or rational point of elliptic curves over finite fields in elliptic module.

We are not providing general frameworks for them, though.

6.1.1. Mailing List

Your feedbacks are always welcomed. Please consider to join the mailing list.