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From: 中村 憲 <nak...@tm...> - 2025-12-05 16:38:19
|
Dear All,
We are releasing the new version of NZMATH 3.0.3 .
You can use the newest NZMATH immediately by typing:
% python -m pip install -U nzmath
from the command line on your machine. You can also
get the NZMATH language notebook for "Lectures on
Elementary Number Theory" (Teiji Takagi), enttakagi,
from the following site:
https://sourceforge.net/projects/nzmath/files/nzmath-enttakagi/
You can then unzip the compressed file and run
enttakagi from the command line, for example，by
% cd enttakagi; python sect1.py
The purpose of this release is to improve NZMATH by our
notes on the prime number table and index table (discrete
logarithm table) at the end of our textbook. In particular,
we are creating modules related to primes table, primitive
roots of primes, and index table of primitive roots. Our idea
is to consider not only the tables themselves but also
the software used to create them as tables in a broad sense.
Also, we have included traditional tablles "primitive root
of p < 1,000,000" and "primitive root index of p < 2,000".
In conjunction with these updates, enttakagi has also been
rewritten to reference NZMATH more frequently in some
sections. Beginners in algorithmic number theory can kill
three birds with one stone by simultaneously learning
"Elementary Number Theory", "Python Programming", "English
for Mathematics". Take advantage of NZMATH, convenient
"Calculator on Number Theory ."
See the following release note in detail.
------------------------------------
NZMATH development group
Chief developer: "TANAKA, Satoru" <st...@me...>
Advisor: "NAKAMULA, Ken" <nak...@tm...>
------------------------------------
------------------------------------
News
====
NZMATH 3.0.3 is released
------------------------
We are pleased to announce that NZMATH 3.0.3 is
available. The highlight of new feature is here:
The purpose of this release is to improve NZMATH on
the prime number table and the index table (discrete
log table) at the end of our textbook, using our
notebook. Our idea is to consider not only the tables
themselves but also the software used to create them
as tables in a broad sense.
* essential idea on primitive roots modulo odd
primes [enttakagi/sec11.py]
* explain on tables of primitive roots modulo
primes [enttakagi/sect1.py]
* explain on tables of primitive root index
(discrete log) of primes [enttakagi/sect2.py]
------------------------------------
File
====
You can download the full distribution from SourceForge.net:
https://sourceforge.net/projects/nzmath/files/nzmath/
The following source distribution and built distribution are available:
nzmath-3.0.3.tar.gz
nzmath-3.0.3-py3-none-any.whl
You can also find the same files at PyPI:
https://pypi.org/project/nzmath/
To keep all, the sdist nzmath-3.0.3.tar.gz include everything.
------------------------
The notebook "enttakagi" from TAKAGI, Teiji's book is here:
https://sourceforge.net/projects/nzmath/files/nzmath-enttakagi/
enttakagi-0.0.5 feachers
sec11.py (Table of Primitive Roots), (Existence of Primitive Roots)
Example, Theorem 1.27 ((Z/p)* == {1. r, ..., r**(p-2)})
Remark (the exponent of r**k), (Compare Several Methods)
(generalize the computation of the textbook as a program)
(Table of Index for Primitive Roots), Example
Theorem 1.28 (Isomorphism via Index), Examples 1, 2, 3
Problems 1, 2 (key point for small size table)
Problem 3 (base change of Ind), Problem 4, Problem 5 (Wilson)
power residue and non residue
sect1.py (1) detailed explanation of type 1: p < 100, sec04d.py
type 2: p < N, nzmath.prime.eratosthenes(N)
type 2: p < N, nzmath.prime.generator_eratosthenes_(N)
type 2: p < N, nzmath.prime.generator_eratosthenes(N)
(2) type 1: r of p < 1000 (our textbook)
(3) r: the least positive
(i) type 2: nzmath.residue.primitiveRoots(N=1000)
type 2: nzmath.residue.primitiveRoots2(N=1000)
(ii) type 1: r of p < 1000000, DATADIR/primitiveRoots.csv
sect2.py (1) (previous) type 1: Jacobi-Cunningham p < 1000, sec11.py
(2) index Ind(N) by r**Ind(N) == N (mod p) (N in range(1,p))
index table IX = [Ind(N) for N in range(1,p)]
(3) IX type 1: full p < 50, part 50 < p < 100 (our textbook)
(4) power Pow(I) == r**I (mod p) (I in range(p-1))
essential part PW = [Pow(I) for I in range(p-1)]
(i) PW type 2: nzmath.primitiveRoot0PW(p, r)
(ii) PW type 1: [p,r] + PW_ of p < 2000, where
PW_ = [PW[I] for I in range((p-1)>>1)] (half size)
collect them to DATADIR/primitiveRootPW_.csv
------------------------
There also is an archive of test programs for NZMATH itself:
https://sourceforge.net/projects/nzmath/files/nzmath-test/
------------------------------------
Change
======
Other news from CHANGES.txt are as follows.
* to satisfy the above 3 purposes, add new functions primitiveRoots,
primitiveRoots2, primitiveRootPW_, primitiveRootPW,
primitiveRoot0PW, primitiveRootIX, primitiveRootGet,
primitiveRootPWGet (nzmath.residue.py)
* put table primitiveRoots.csv of primitive roots of primes p < 1000000
* put table primitiveRootPW_.csv of indices of primes p < 2000
* comment (least exponent)==(multiplicative order) (enttakagi/sec10{,a}.py)
* change style of Eratosthenes sieve (enttakagi/sec04d.py, nzmath/prime.py)
* put nzmathconf.py.example to our home page to introduce by "tutorial"
* on presentation of enttakagi, start using boldface by enttakagi/utils.py
Thank you for looking forward to release. Have fun!
------------------------------------
|
|
From: 中村 憲 <nak...@tm...> - 2025-02-28 12:09:37
|
Dear All,
We are releasing the new version of NZMATH 3.0.2 .
You can use the newest NZMATH immediately by typing:
% python -m pip install -U nzmath
from the command line on your machine. You can also
get the NZMATH language notebook for "Lectures on
Elementary Number Theory" (Teiji Takagi), enttakagi,
from the following site:
https://sourceforge.net/projects/nzmath/files/nzmath-enttakagi/
You can then unzip the compressed file and run
enttakagi from the command line, for example，by
% cd enttakagi; python sec11.py
The purpose of this release is to fully reflect the
improvements and overcoming of weaknesses in NZMATH
that have been clarified and corrected through the
execution of enttakagi. In particular, the modules
related to the Chinese Remainder Theorem, solving
congruence equations, cyclotomic polynomials, and
primitive roots are being corrected. There are also
other improvements to the prime factorization method.
In conjunction with these updates, enttakagi has
progressed to §11 and has been rewritten to reference
NZMATH more. Please make use of NZMATH, a convenient
"calculator on number theory" that is a three-birds-one
learning material for beginners of algorithmic number
theory to learn number theory, programming, and English
for mathematics at the same time.
See the following release note in detail.
------------------------------------
NZMATH development group
Chief developer: "TANAKA, Satoru" <st...@me...>
Advisor: "NAKAMULA, Ken" <nak...@tm...>
------------------------------------
News
====
NZMATH 3.0.2 is released
------------------------
We are pleased to announce that NZMATH 3.0.2 is
available. The highlight of new feature is here:
This version 3.0.2 has made several trial to fully
reflect the improvements and overcoming of weaknesses
in NZMATH that have been clarified and corrected through
the execution of enttakagi:
* add new function arith1.CRT_Gauss
* add equation.{e2_Fp,liftup_ZpnZ,allroots_ZnZ}
* add new modules "residue" for functions primRootDef
and primRootTakagi
* add new modules "cyclotomic" for functions cycloPoly
and cycloMoebius
* add perfect power test at the beginings of factor.mpqs
and factor.ecm
------------------------------------
File
====
You can download the full distribution from SourceForge.net:
https://sourceforge.net/projects/nzmath/files/nzmath/
The following source distribution and built distribution are available:
nzmath-3.0.2.tar.gz
nzmath-3.0.2-py3-none-any.whl
You can also find the same files at PyPI:
https://pypi.org/project/nzmath/
To keep all, the sdist nzmath-3.0.2.tar.gz include everything.
------------------------
The notebook "enttakagi" from TAKAGI, Teiji's book is here:
https://sourceforge.net/projects/nzmath/files/nzmath-enttakagi/
enttakagi-0.0.4 feachers
sec11.py (Table of Primitive Roots), (Existence of Primitive Roots)
((Z/p)* == 1. r, ..., r**(p-2), (the exponent of r**k)
(Compare Several Methods)
(generalize the computation of the textbook as a program)
(Table of Index for Primitive Roots), (Isomorphism via Index)
------------------------
There also is an archive of test programs for NZMATH itself:
https://sourceforge.net/projects/nzmath/files/nzmath-test/
------------------------------------
Change
======
Other news from CHANGES.txt are as follows.
* fix class factor.misc.FactoredInteger
* add prime.LucasLehmer, gcd.part_frac,
algorithm.digital_method_func
* poly.uniutil.IntegerPolynomial.reduce
* modify ../nzmath/all.py for Python3.12
ModuleNotFoundError: No module 'imp'
* Solved most of ../test/*.py for Python3.12
(RuntimeError: dictionary changed size during iteration)
* put data of our Home Page to independent directory ../www/
Thank you for looking forward to release. Have fun!
------------------------------------
|
|
From: 中村 憲 <nak...@tm...> - 2024-12-01 13:08:57
|
Dear All, We are releasing the new version 0.0.3 of 'enttakagi', a Python- NZMATH program notebook for Takagi's "Lectures on Elementary Number Theory": https://sourceforge.net/projects/nzmath/files/nzmath-enttakagi/ This time new is Sections 8--10, "Euler's Function, Roots of Unity, Fermat's Theorem". Get the appropriate zipped file nzmath-enttakagi-0.0.2.tar.gz etc. from the above site. On the command line, change directory to the unzipped folder 'enttakagi', and run the notebook with % python sec08.py etc. Note that '%' is the command line prompt. To run the notebook, you need the Python package NZMATH version 3.0.1 or higher: https://nzmath.sourceforge.io/ If you do not have necessary NZMATH, you can immediately install NZMATH 3.0.1.1 by typing % python -m pip install nzmath on your own machine. You will be able to use it. This notebook 'enttakagi' for beginners on algorithmic number theory is used for parallel self-study of number theory, programming, and English for mathematics by the "calculator on number theory" NZMATH. See the following release note in detail. ------------------------------------ enttakagi 0.0.3 is released --------------------------- We are pleased to announce that enttakagi 0.0.3 is available. The highlight of new feature of enttakagi version 0.0.3 is here: This version 0.0.3 newly contains Sections 8--10, "Euler's Function, Roots of Unity, Fermat's Theorem". Highlight is Theorem (There are infinitely many primes of the form m*t + 1.) at the end of Section 10, which solves a special case of the classical prime number theorem in arithmetic progression by elementary method applying cyclotomic polynomials. Other topics (coefficients of cyclotomic polynomials) and (irreducible proper fraction and purely repeating decimal) are also interesting. ------------------------------------ New features ============= sec08.py (phi(n) == euler(n) in terms of factored n) (phi(n) is multiplicative, reduced system of residues) (generalize phi to Phi over floating real) (sum(phi(d)for d|n)==n)(Moebius function) (Moebius inversion formula, mu(n) == moebius(n)) sec09.py (Z/nZ: k (mod n) <--> exp(2j*pi*k/n): n-th roots of 1) (n n-th roots of 1 and phi(n) primitive ones) (cyclotomic polynomials, interesting coefficients set) (simple efficient algorithm) (norm and trace of primitive root) (isomorphic Z/nZ residue classes <--> n-th roots of 1) (direct sum Z/aZ + Z/bZ == Z/abZ if GCD(a, b) == 1) sec10.py (primarity test full_euler by Fermat's Theorem) (exponent of reduced residue) (primes of arithmetic progression 4*n + 1) (There are infinitely many primes of the form m*t + 1.) sec10a.py (irreducible proper fraction = purely repeating decimal) Ver.0.0.2 features ================== sec01.py (divmod) sec02.py (lcm)(gcd, Eucledean Algorithm == GCD) (gcd_, general GCD by modl)(lcm_, by gcd_) sec03.py (gcd_of_list, general extended GCD) (general extended GCD by extgcd_gen) sec04.py (prime factorization) sec04a.py (tau function)(sigma function)(multiplicative function) (perfect number)(Mersenne number, Lucas-Lehmer test) sec04b.py (FactoredInteger plays important role) sec04c.py (binomial coefficients, partial fraction decomposition) sec04d.py (eratosthenes sieve)(Tschebyschef, nextPrime)(twin prime) (primes of arithmetic progression 4*n-1)(prime.generator) (Goldbach conjecture) sec05.py (fundamental arithmetic of congruence) (congruence arithmetic by digital criterion) sec06.py (e1_ZnZ, extended GCD) sec06a.py (CRT_, Chinese Remainder Theorem) (CRT_Gauss by moduli symmetric) (partial fraction decomposition) sec06b.py (CRT of moduli m, n, GCD(m, n) > 1) (CRT of general non-coprime moduli) sec07.py (allroots_Fp, cyclicity of Fp*) (digital method, Karatsuba) (lift up prime power modulus, Hensel lift) sec07a.py (allroots_ZnZ, complete solutions modulo n) (allroots_Fp, liftup_ZpnZ, CRT_, allroots_ZnZ) Thank you for looking forward to release. Have fun! ----- NZMATH development group Chief developer: "TANAKA, Satoru" <st...@me...> Advisor: "NAKAMULA, Ken" <nak...@tm...> ------------------------------------ |
|
From: 中村 憲 <nak...@tm...> - 2024-08-08 07:30:28
|
Dear All, We are releasing the new version 0.0.2 of 'enttakagi', a Python- NZMATH program notebook for Takagi's "Lectures on Elementary Number Theory": https://sourceforge.net/projects/nzmath/files/nzmath-enttakagi/ The previous version 0.0.1 was about Sections 1--4, "Divisors, Multiples, Prime Factorization, Prime Numbers", but this time new is Sections 5--7, "Solving Polynomial Congruences". Get the appropriate zipped file NZMATH-enttakagi-0.0.2.tar.gz etc. from the above site. On the command line, change directory to the unzipped folder 'enttakagi', and run the notebook with % python sec05.py etc. Note that '%' is the command line prompt. To run the notebook, you need the Python package NZMATH version 3.0.1 or higher: https://nzmath.sourceforge.io/ If you do not have necessary NZMATH, you can immediately install NZMATH 3.0.1.1 by typing % python -m pip install nzmath on your own machine. You will be able to use it. This notebook 'enttakagi' for beginners on algorithmic number theory is used for parallel self-study of number theory, programming, and English for mathematics by the "calculator on number theory" NZMATH. See the following release note in detail. ------------------------------------ We are pleased to announce that enttakagi 0.0.2 is available. The highlight of new feature of enttakagi version 0.0.2 is here: This version 0.0.2 newly contains Sections 5--7, "Solving Polynomial Congruences". Highlight is Theorem 1.17, which solves f(x) == 0 (mod m) for any integer coefficient polynomial f of one variable and any positive integer m . The process summarizes Sections 5--7 and is defined as a function allroots_ZnZ(f, m) in fix_nzmath.py . ------------------------------------ New features ============= sec05.py (fundamental arithmetic of congruence) (congruence arithmetic by digital criterion) sec06.py (e1_ZnZ, extended GCD) sec06a.py (CRT_, Chinese Remainder Theorem) (CRT_Gauss by moduli symmetric) (partial fraction decomposition) sec06b.py (CRT of moduli m, n, GCD(m, n) > 1) (CRT of general non-coprime moduli) sec07.py (allroots_Fp, cyclicity of Fp*) (digital method, Horner) (lift up prime power modulus, Hensel lift) sec07a.py (allroots_ZnZ, complete solutions modulo n) (allroots_Fp, liftup_ZpnZ, CRT_, allroots_ZnZ) Ver.0.0.1 features ================== sec01.py (divmod) sec02.py (lcm)(gcd, Eucledean Algorithm == GCD) (gcd_, general GCD by modl)(lcm_, by gcd_) sec03.py (gcd_of_list, general extended GCD) (general extended GCD by extgcd_gen) sec04.py (prime factorization) sec04a.py (tau function)(sigma function)(multiplicative function) (perfect number)(Mersenne number, Lucas-Lehmer test) sec04b.py (FactoredInteger plays important role) sec04c.py (binomial coefficients, partial fraction decomposition) sec04d.py (eratosthenes sieve)(primes of arithmetic progression) (prime.generator)(Tschebyschef, nextPrime)(twin prime) (Goldbach conjecture) Thank you for looking forward to release. Have fun! ----- NZMATH development group Chief developer: "TANAKA, Satoru" <st...@me...> Supervisor: "NAKAMULA, Ken" <nak...@tm...> |
|
From: 中村 憲 <nak...@tm...> - 2024-07-11 06:25:00
|
Dear All,
We release new version of NZMATH 3.0.1.1 .
With this release, you can use NZMATH immediately by typing
% python -m pip install nzmath
from the command line on your machine.
Before explaining the contents, we would like to make a
correction and apology. NZMATH announced that it was
possible to implement version 3.0.0 on 2023/08/31 and
version 3.0.1 on 2024/04/29 using pip, but this was
incomplete. If you have implemented these versions using
pip, please delete them with the following command
% python -m pip uninstall nzmath
However, if these versions have been implemented by the
previous methods not relying on pip, there is no problem.
Also, older releases than these will continue to be valid.
We apologize for the inconvenience.
The purpose of this release is to unify the installation
of NZMATH to the pip method. Ver.3.0.1.1 is completely
identical to Ver.3.0.1, except for the installation method.
Old Ver.3.0.1 had various installation methods and four
types of files for installation to choose from, but with new
Ver.3.0.1.1 you don't even need to be aware of the files.
This is a review, but the common main contents are as follows.
* Notes on "Lectures on elementary number theory"
(Teiji Takagi) enttakagi Sections 1 to 4
https://sourceforge.net/projects/nzmath/files/nzmath-enttakagi/
* Improvements to modules such as gcd and factor by enttakagi
NZMATH is a nice "Calculator on Number Theory" that allows beginners
to learn number theory, programming, and scientific English at a time.
See the following release note in detail.
------------------------------------
NZMATH 3.0.1.1 is released
--------------------------
We are pleased to announce that NZMATH 3.0.1.1 is available.
The highlight of new feature of NZMATH version 3.0.1.1 is here:
This version 3.0.1.1 is the first to unify the NZMATH installation
to the pip method. In previous versions, the implementation method
differed depending on the user's machine, and different files had to
be downloaded in advance for each implementation method. With this
latest revision, anyone can use NZMATH on any machine with Python
installed by simply typing
% python -m pip install nzmath
from the command line. This revision resulted in major changes to
the distribution files and distribution locations.
The code of NZMATH is almost completely the same as version 3.0.1
except non-essential expressions.
------------------------------------
Download
========
You can download the full distribution from SourceForge.net:
https://sourceforge.net/projects/nzmath/files/nzmath/
The following source distribution and built distribution are available:
nzmath-3.0.1.1.tar.gz
nzmath-3.0.1.1-py3-none-any.whl
You can also find the same files at PyPI:
https://pypi.org/project/nzmath/
The notebook "enttakagi" from TAKAGI, Teiji's book is here:
https://sourceforge.net/projects/nzmath/files/nzmath-enttakagi/
There also is an archive of test programs for NZMATH itself:
https://sourceforge.net/projects/nzmath/files/nzmath-test/
To keep all, the sdist nzmath-3.0.1.1.tar.gz include everything.
Changes
=======
Other news from CHANGES.txt are as follows.
version 3.0.1 to 3.0.1.1
------------------------
* stop 'python setup.py install' start 'python -m pip install nzmath'
* put Japanese manual to our HP
Thank you for looking forward to release. Have fun!
-----
NZMATH development group
Chief developer: "TANAKA, Satoru" <st...@me...>
Supervisor: "NAKAMULA, Ken" <nak...@tm...>
|
|
From: 田中 覚 <st...@me...> - 2024-05-06 23:42:48
|
Dear members, We are pleased to announce that NZMATH 3.0.1 is now available by pip. To install NZMATH for python version 3.4 or above, you can only do it simple command: ~~~ % pip install nzmath ~~~ Thank you for looking forward to release. Have fun! -- Tanaka Satoru, NZMATH development group. (Chief developer: TANAKA, Satoru / Supervisor: NAKAMULA, Ken) |
|
From: 中村 憲 <nak...@tm...> - 2024-03-28 07:00:28
|
Dear All, We release new version of NZMATH 3.0.1 . https://nzmath.sourceforge.io/ A notebook for "Elementary Number Theory Lecture" (TAKAGI, Teiji) in NZMATH language is also released together: https://sourceforge.net/projects/nzmath/files/nzmath-enttakagi/ Please utilize NZMATH as a handy practical calculator on number theory. See the following release note in detail. ------------------------------------ NZMATH 3.0.1 is released ------------------------ We are pleased to announce that NZMATH 3.0.1 is available. Some of the highlights of new feature of NZMATH version 3.0.1 are here: This version 3.0.1 contains several program corrections/additions by the "notebook" of the book 'Elementary Number Theory Lecture' (TAKAGI, Teiji) in Python-NZMATH language. On the other hand, the "notebook" itself is available as an archive NZMATH-enttakagi-0.0.1.tar.gz at https://sourceforge.net/projects/nzmath/files/nzmath-enttakagi/ . The "notebook" is designed for beginning students on algorithmic number theory to self-study Number Theory, Programming and scientific English together all at a time. ------------------------------------ Download ======== You can download it from SourceForge.net: http://downloads.sourceforge.net/nzmath/ Several distribution files for installation are available. There also is an archive of test programs for NZMATH itself. Other news from CHANGES.txt are as follows. version 3.0.0 to 3.0.1 ---------------------- * remove bigrange.range (User Request #10) * rewrite bigrange.multilange (User Request #11) * alias bigrandom.randrange to random.randrange (User Request #14) * rewrite sequence.fibonacci (User Request #15) * remove prime.properDivisors (use FactoredInteger.proper_divisors instead) * remove configurations for using psyco (python 3 is not supported) * remove network access from ecpp.hilbert (since hilbert-class-polynomial-hrd GAE will be ceased. use mpmath instead) * add gcd.{divmodl,gcd_,modl,lcm_,extgcd_,extgcd_gen} by enttakagi * add factor.misc.{countDivisors,sumDivisors} by enttakagi * improve factor.{find,methods}.{pmom,rhomethod} by enttakagi * improve factor.misc.{allDivisors,primeDivisors,squarePart} by enttakagi * improve {gcd.{gcd,gcd_of_list},multiplicative.sigma} by enttakagi * fix {combinatorial.binomial,factor.mpqs.mpqsfind,gcd.lcm} by enttakagi Thank you for looking forward to release. Have fun! ----- NZMATH development group Chief developer: "TANAKA, Satoru" <st...@me...> Supervisor: "NAKAMULA, Ken" <nak...@tm...> |
|
From: 田中 覚 <st...@me...> - 2023-09-14 07:06:18
|
Dear members, We are pleased to announce that NZMATH 3.0.0 is now available by pip. To install NZMATH for python version 3.4 or above, you can only do it simple command: ~~~ % pip install nzmath ~~~ Thank you for looking forward to release. Have fun! -- Tanaka Satoru, NZMATH development group. (Chief developer: TANAKA, Satoru / Supervisor: NAKAMULA, Ken) |
|
From: NAKAMULA, K. <nak...@tm...> - 2022-04-05 06:01:51
|
Dear All, We release new version of NZMATH based on Python 3 . https://nzmath.sourceforge.io/ There are two motivations. One is the sunset of Python 2 https://www.python.org/doc/sunset-python-2/ and the other is the recent high popularity of Python https://www.tiobe.com/tiobe-index/ NZMATH is a handy and practical "calculator on number theory." We would like to continue using it on Python 3 also. See the following release note in detail. ------------------------------------ NZMATH 3.0.0 is released We are pleased to announce that NZMATH 3.0.0 is available. Download ======== You can download it from SourceForge.net: http://downloads.sourceforge.net/nzmath/ Several distribution files for installation are available. There also is an archive of test programs for NZMATH itself. What's new ========== Some of the highlights of new feature of NZMATH version 3.0.0 are here: - the first of series based on Python 3 - mailing list nzmath-user is opened https://lists.sourceforge.net/lists/listinfo/nzmath-user - NZMATH web site is opened https://nzmath.sourceforge.io/ Other news from CHANGES.txt are as follows. version 1.2.0 to 3.0.0 ------------------------ * port Python 2 code to Python 3 for all modules. * add Japanese manual (incomplete). Thank you for looking forward to release. Have fun! ----- NZMATH development group Chief developer: "TANAKA, Satoru" <st...@me...> Supervisor: "NAKAMULA, Ken" <nak...@tm...> |
