Author Topic: SAGE MATH (Read 13069 times)

Holden · « **Reply #30 on:** March 01, 2019, 12:33:20 pm »

Something so fundamental as the fact that mathematics is an axiomatic-deductive system was never taught to me with any degree of clarity in the high school and even back then I almost reached that conclusion on my own.There were no books, no teachers who could have helped me.

I am sick and tired of the human world. It does not interest me. Political positions and women hold not attraction for me.Another thing which attracts me to math is that it is about the only thing I can do all on my own ,without anyone's interference.

Like you say, my brain is made of flesh and blood and does get tired after a while but as long as it is not tired there is very little,in principle, which I find incomprehensible if I really put my mind to it.

Programming? Maybe someday. For now, I am focussing only on mathematics. I must first develop strong foundations.

Holden · « **Reply #31 on:** March 01, 2019, 10:06:00 pm »

What the poet laments then holds for the mathematician, that his works are written with the blood of his heart -Boltzmann

Mad Dog Mike · « **Reply #32 on:** March 02, 2019, 12:12:40 pm »

I found that factoring [quadratic] trinomials, especially using the method of completing the square, was strangley inspirational for me.

I only wished you might become more comfortable compiling programs from the command line since I have a few programs that you could use in conjunction with paper and pencil to kind of check your work. The completing the square program shows each step and can even handle irrational and complex roots. I may have mentioned this already, but quite often, after I have gotten a program to produce correct results, I return to it and build into it "educational" components. This often requires far more work than just producing sensible output. In a real way, such effort is like a gift to my future self should I get a little rusty and need a crash course on these fundamental procedures.

Are you still using the Mac machine? I'm certain that you could install the GNU g++ compilers since Mac uses the UNIX system. I'm not pushing this on you, just leaving links for some rainy day, or a series of rainy days, if you ever catch the codemode bug. Also see How to Install g++ on the Mac.

Of course, if this seems daunting and unnecessary, then I take no offense if you prefer not to bother with it.

Still, I am curious how you feel about factoring trinomials. What methods do you use? Trial and Error? Grouping? Completing the square?

For some reason, this was one of the fundamental procedures which I found very satisfying to go over thoroughly.

Take care. You sound as though you have embraced the reality that this will be a very long process, and I am pleased to witness you keeping your feet on the ground and getting into whatever you study at the moment. Years pass like months when it comes to studying math. It's good that you are not racing, since we are always living only in the present moment.

Holden · « **Reply #33 on:** March 03, 2019, 11:20:19 am »

I have only studied Number systems,Arithmetic Progression,Geometric Progression,Harmonic Progression,Averages,Alligations,Percentages recently so far.So kindly keep your questions confined to these topics. Thanks.

https://www.dailymotion.com/video/xdoj7y

Mad Dog Mike · « **Reply #34 on:** March 03, 2019, 12:31:11 pm »

Quote from: olden

I have only studied Number systems,Arithmetic Progression,Geometric Progression,Harmonic Progression,Averages,Alligations,Percentages recently so far.So kindly keep your questions confined to these topics. Thanks.

I was only suggesting "completing the square" and factoring quadratic trinomials as an area I think would give you some intellectual stimulation, or even a strong dose of satisfaction. I only asked if you were familiar with the method, but did not pose any specific question.

Your request is noted.

As for ideas and concepts related to programming, forgive me if I use this message board as a kind of notebook to highlight some revelations. These posts may be of interest to you or not. I will be posting such things not necessarily directed to anyone in particular, but simply as a means of highlighting certain "aha" moments I may experience, where philosophical terminology is used to describe certain technicalities in programming.

A computer language such as C++ provides a programmer with some built-in types, such as char, int, or double (char representing an alpha-numeric character or symbol, int representing an integer, and double representing a "real number".

Types that are not built-in are called user-defined types, such as classes (data structures).

What are user-defined types good for?

Types are good for directly representing our ideas directly into code.

We want to represent an "idea" or "concept" in code as a data structure plus a set of functions.

Of course, the devil is in the details, the technicalities, but the reason for mentioning this here is to breathe life into these key words: representation and idea.

These are two English words, both used in translating the German concept of Vertretung.

die Vorstellung : imagination, perception, presentation, notion

to represent : darstellen ?

Anyway, I'm in an in between zone (between chapters in two different math textbooks), and I am trying to force myself to focus a little on some technicalities in C++.

Mad Dog Mike · « **Reply #35 on:** March 03, 2019, 07:31:02 pm »

Quote from: Holden

Another thing which attracts me to math is that it is about the only thing I can do all on my own, without anyone's interference.

I understand this. I would never study the way I do if some other person were insisting that I must.

I can be easily irritated. annoyed, and even overwhelmed unless I am engaging with something by my own volition. As Henry Fool told Simon Grimm, you can't put a fence around a man's soul. We need time to think, and we must be genuinely interested in what we choose to give our attention to.

In fact, when I find I am becoming a little sickened by the complexity of some code I am trying to understand, often the only thing that can calm my anxiety is to work through some math problems with paper and pencil. So, I do not blame you, Holden, not in the least, if your instincts tell you to block out everything other than what is essential to whatever it is you are working on at the moment.

- Brother Mike

Holden · « **Reply #36 on:** March 04, 2019, 12:01:02 am »

Quote

I understand this. I would never study the way I do if some other person were insisting that I must.

-Herr Kaspar

I am sorry but that is not what I meant primarily. I mean that mathematics does not need "team work", you do not have to be a part of a group to do it-its not like one guy solves the first 5 steps and the next guy the following 3 steps. Generally, one guy solves the whole of the question all on his own.Or if he fails to do so then its again all on this own.

Mad Dog Mike · « **Reply #37 on:** October 25, 2020, 11:22:31 am »

footnotes: (1):

table([(i,n(cos(2*i), digits=4), cos(2*i)) for i in [0..2*pi+0.1, step=pi/12]], header_row=["$i$", "$cos(2*i)$", "$rational$"], frame=True)

+----------+------------+--------------+
| $i$ | $cos(2*i)$ | $rational$ |
+==========+============+==============+
| 0 | 1.000 | 1 |
+----------+------------+--------------+
| 1/12*pi | 0.8660 | 1/2*sqrt(3) |
+----------+------------+--------------+
| 1/6*pi | 0.5000 | 1/2 |
+----------+------------+--------------+
| 1/4*pi | 0.0000 | 0 |
+----------+------------+--------------+
| 1/3*pi | -0.5000 | -1/2 |
+----------+------------+--------------+
| 5/12*pi | -0.8660 | -1/2*sqrt(3) |
+----------+------------+--------------+
| 1/2*pi | -1.000 | -1 |
+----------+------------+--------------+
| 7/12*pi | -0.8660 | -1/2*sqrt(3) |
+----------+------------+--------------+
| 2/3*pi | -0.5000 | -1/2 |
+----------+------------+--------------+
| 3/4*pi | 0.0000 | 0 |
+----------+------------+--------------+
| 5/6*pi | 0.5000 | 1/2 |
+----------+------------+--------------+
| 11/12*pi | 0.8660 | 1/2*sqrt(3) |
+----------+------------+--------------+
| pi | 1.000 | 1 |
+----------+------------+--------------+
| 13/12*pi | 0.8660 | 1/2*sqrt(3) |
+----------+------------+--------------+
| 7/6*pi | 0.5000 | 1/2 |
+----------+------------+--------------+
| 5/4*pi | 0.0000 | 0 |
+----------+------------+--------------+
| 4/3*pi | -0.5000 | -1/2 |
+----------+------------+--------------+
| 17/12*pi | -0.8660 | -1/2*sqrt(3) |
+----------+------------+--------------+
| 3/2*pi | -1.000 | -1 |
+----------+------------+--------------+
| 19/12*pi | -0.8660 | -1/2*sqrt(3) |
+----------+------------+--------------+
| 5/3*pi | -0.5000 | -1/2 |
+----------+------------+--------------+
| 7/4*pi | 0.0000 | 0 |
+----------+------------+--------------+
| 11/6*pi | 0.5000 | 1/2 |
+----------+------------+--------------+
| 23/12*pi | 0.8660 | 1/2*sqrt(3) |
+----------+------------+--------------+
| 2*pi | 1.000 | 1 |
+----------+------------+--------------+

To plot:

t = var('t')
polar_plot(cos(2*t), t, 0, 2*pi)

sage: table([(i,n(cos(2*i), digits=4), cos(2*i)) for i in [0..2*pi+0.1, step=pi/8]], header_row=["$i$", "$cos(2*i)$", "$rational$"], frame=True)
+---------+------------+--------------+
| $i$ | $cos(2*i)$ | $rational$ |
+=========+============+==============+
| 0 | 1.000 | 1 |
+---------+------------+--------------+
| 1/8*pi | 0.7071 | 1/2*sqrt(2) |
+---------+------------+--------------+
| 1/4*pi | 0.0000 | 0 |
+---------+------------+--------------+
| 3/8*pi | -0.7071 | -1/2*sqrt(2) |
+---------+------------+--------------+
| 1/2*pi | -1.000 | -1 |
+---------+------------+--------------+
| 5/8*pi | -0.7071 | -1/2*sqrt(2) |
+---------+------------+--------------+
| 3/4*pi | 0.0000 | 0 |
+---------+------------+--------------+
| 7/8*pi | 0.7071 | 1/2*sqrt(2) |
+---------+------------+--------------+
| pi | 1.000 | 1 |
+---------+------------+--------------+
| 9/8*pi | 0.7071 | 1/2*sqrt(2) |
+---------+------------+--------------+
| 5/4*pi | 0.0000 | 0 |
+---------+------------+--------------+
| 11/8*pi | -0.7071 | -1/2*sqrt(2) |
+---------+------------+--------------+
| 3/2*pi | -1.000 | -1 |
+---------+------------+--------------+
| 13/8*pi | -0.7071 | -1/2*sqrt(2) |
+---------+------------+--------------+
| 7/4*pi | 0.0000 | 0 |
+---------+------------+--------------+
| 15/8*pi | 0.7071 | 1/2*sqrt(2) |
+---------+------------+--------------+
| 2*pi | 1.000 | 1 |
+---------+------------+--------------+

sage: table([(i,n(sin(2*i), digits=4), sin(2*i)) for i in [0..2*pi+0.1, step=pi/8]], header_row=["$i$", "$sin(2*i)$", "$rational$"], frame=True)
+---------+------------+--------------+
| $i$ | $sin(2*i)$ | $rational$ |
+=========+============+==============+
| 0 | 0.0000 | 0 |
+---------+------------+--------------+
| 1/8*pi | 0.7071 | 1/2*sqrt(2) |
+---------+------------+--------------+
| 1/4*pi | 1.000 | 1 |
+---------+------------+--------------+
| 3/8*pi | 0.7071 | 1/2*sqrt(2) |
+---------+------------+--------------+
| 1/2*pi | 0.0000 | 0 |
+---------+------------+--------------+
| 5/8*pi | -0.7071 | -1/2*sqrt(2) |
+---------+------------+--------------+
| 3/4*pi | -1.000 | -1 |
+---------+------------+--------------+
| 7/8*pi | -0.7071 | -1/2*sqrt(2) |
+---------+------------+--------------+
| pi | 0.0000 | 0 |
+---------+------------+--------------+
| 9/8*pi | 0.7071 | 1/2*sqrt(2) |
+---------+------------+--------------+
| 5/4*pi | 1.000 | 1 |
+---------+------------+--------------+
| 11/8*pi | 0.7071 | 1/2*sqrt(2) |
+---------+------------+--------------+
| 3/2*pi | 0.0000 | 0 |
+---------+------------+--------------+
| 13/8*pi | -0.7071 | -1/2*sqrt(2) |
+---------+------------+--------------+
| 7/4*pi | -1.000 | -1 |
+---------+------------+--------------+
| 15/8*pi | -0.7071 | -1/2*sqrt(2) |
+---------+------------+--------------+
| 2*pi | 0.0000 | 0 |
+---------+------------+--------------+
___________________________________________________________
(2):

How tables can be generated in Sage to help plot polar graphs. Now you can copy and paste it into http://sagecell.sagemath.org to see what I mean:

table([(i,n(cos(2*i), digits=4), cos(2*i)) for i in [0..2*pi+0.1, step=pi/12]], header_row=["$i$", "$cos(2*i)$", "$rational$"], frame=True)

___________________________________________________
t = var('t')
p1 = polar_plot(cos(2*t), t, 0, 2*pi)
p2 = polar_plot(sin(2*t), t, 0, 2*pi, linestyle="--")
show(p1 + p2)
_____________________________________________
table([(i,n(cos(2*i), digits=4), cos(2*i)) for i in [0..2*pi+0.1, step=pi/8]], header_row=["$i$", "$cos(2*i)$", "$rational$"], frame=True)

Mad Dog Mike · « **Reply #38 on:** September 30, 2025, 09:20:13 am »

For quite some time, binaries to install computer algebra system, SageMath, in Microsoft Windows have been discontinued.

I will be looking a few guides before committing to what approach I will take, since I am leaving computers with Linux and multiple operating systems menus in storage for protection.

I am using an older notebook with smaller hard-drive with much taken up by a partition of data, so I want C:\ drive to have breathing room for "Microsoft Windows 10" (the machine is not capable of running Windows 11.

I had used Sandy Scott's Web Spot to install on other machines back in 2023 when I rented a room in Asbury Park.

I am looking at a more clear guide by a Will Hoffer where he installed Sage on a Windows system and configured it to work using VSCode for convenient editing.

Quote

Install Windows Subsystem for Linux (WSL2)

In Debian, I received errors when issuing command, "sudo apt update" then used:

wget --no-check-certificate https://deb.freexian.com/extended-lts/pool/main/f/freexian-archive-keyring/freexian-archive-keyring_2022.06.08_all.deb && sudo dpkg -i freexian-a
rchive-keyring_2022.06.08_all.deb

source

Still errors since so many of the URL's have changed.

https://unix.stackexchange.com/questions/744401/security-repo-for-debian-stretch-not-working-anymore

I may try to make kali-linux my default Linux distro rather than Debiam. I would hate to have to use Ubunu, the Microsoft of the Linux World.

Bad News for Kali-Linux users also according to https://www.kali.org/blog/new-kali-archive-signing-key/

Missing key 827C8569F2518CC677FECA1AED65462EC8D5E4C5, which is needed to verify signature.

They had to roll a new signing key for the Kali repository. You need to download and install the new key manually, here’s the one-liner (issued within instance of Kali-Linux:

sudo wget https://archive.kali.org/archive-keyring.gpg -O /usr/share/keyrings/kali-archive-keyring.gpg

After this, I was able to "sudo apt update" in wsl Kali-Linux/.

This is the output:

Quote
wolf@coyote2:~$ sudo wget https://archive.kali.org/archive-keyring.gpg -O /usr/share/keyrings/kali-archive-keyring.gpg
--2025-09-30 10:44:24-- https://archive.kali.org/archive-keyring.gpg
Resolving archive.kali.org (archive.kali.org)... 148.113.211.220, 2607:5300:214:dc00::
Connecting to archive.kali.org (archive.kali.org)|148.113.211.220|:443... connected.
HTTP request sent, awaiting response... 200 OK
Length: 3464 (3.4K) [text/plain]
Saving to: ‘/usr/share/keyrings/kali-archive-keyring.gpg’

/usr/share/keyr 100%[======>] 3.38K --.-KB/s in 0s

2025-09-30 10:44:25 (28.5 MB/s) - ‘/usr/share/keyrings/kali-archive-keyring.gpg’ saved [3464/3464]

wolf@coyote2:~$ sudo apt update
Get:1 http://kali.download/kali kali-rolling InRelease [34.0 kB]
Get:2 http://kali.download/kali kali-rolling/main amd64 Packages [21.1 MB]
Get:3 http://kali.download/kali kali-rolling/non-free amd64 Packages [201 kB]
Get:4 http://kali.download/kali kali-rolling/contrib amd64 Packages [118 kB]
Fetched 21.4 MB in 9s (2,414 kB/s)
Reading package lists... Done
Building dependency tree
Reading state information... Done
160 packages can be upgraded. Run 'apt list --upgradable' to see them.
wolf@coyote2:~$ apt list --upgradable

Then I issued command: sudo apt upgrade
______________________________________________________
Install Sage though WSL

sudo apt install sagemath

Configue WSL on VSCode[/size]

Will Hoffer found the official sagemath documentation lacking in several key steps and containing redundant or outdated information that made the overall process less clear..

I am going into codemode to distract my mind from "suicidal ideations" --- kind of the way Betrand Russell became obsessed with mathematics as a young man, as an alternative to suicide.

Mad Dog Mike · « **Reply #39 on:** September 30, 2025, 09:20:43 pm »

SAGE MATH in Windows update

After installing Ubuntu 24.94.1 LTS (Long Term Support) distro in WSL2, and trying without success to install sagemath, I next installed Arch Linux:

wsl --install -d archlinux

as "root" without even creating a user, I issued:

pacman -Syu

then issued: pacman -S sagemath

It did not take too long to install, then I just typed sage at the prompt:

[root@coyote2 ~]# sage
┌────────────────────────────────────────────────────────────────────┐
│ SageMath version 10.7, Release Date: 2025-08-09 │
│ Using Python 3.13.7. Type "help()" for help. │
└────────────────────────────────────────────────────────────────────┘
sage:

Philosophers in Rags :: We dive deeper, and come up muddier.

News:

Author Topic: SAGE MATH (Read 13069 times)

Holden

Re: SAGE MATH

Holden

Re: SAGE MATH

Mad Dog Mike

Re: SAGE MATH

Holden

Re: SAGE MATH

Mad Dog Mike

Re: SAGE MATH

Mad Dog Mike

Re: SAGE MATH

Holden

Re: SAGE MATH

Mad Dog Mike

footnote: simple example of table generated by sage command

Mad Dog Mike

Re: SAGE MATH

Mad Dog Mike

Re: SAGE MATH