Over time, I have developed a sense of what I want and am ready to be responsible for my Thinkpad P16 :)

I learned about the process from the official guide and supplemented it with the notes by Michele Gementi, Max Pershin, Abhishek Prakash, quantinium, Daniel Wayne Armstrong, Gentoo and Ubuntu. It took around half-dozen test runs in VirtualBox over the course of a month before performing the actual installation. Here is a documentation to get started with the best operating system.

I will follow the Arch Wiki convention: The numeral or hash sign (#) indicates that the command needs to be run as root, whereas the dollar sign ($) shows that the command should be run as a regular user.

Prepararation

1. Check ArchLinux website status since they are prone to DDoS attacks. I encountered this during my first ever test run of Arch Linux. Also, the services may send an initial connection reset due to the TCP SYN authentication performed by the hosting provider, but subsequent requests should work as expected.
   1. In the case of downtime for archlinux.org:
      1. Mirrors: The mirror list endpoint used in tools like reflector is hosted on this site. Please default to the mirrors listed in the pacman-mirrorlist package during an outage.
      2. ISO: Installation image is available on a lot of the mirrors, for example the DevOps administered geomirrors. Please always verify its integrity.
   2. In the case of downtime for aur.archlinux.org:
      1. Packages: A mirror of AUR packages is maintained on GitHub. You can retrieve a package using:

          $ git clone --branch <package_name> --single-branch https://github.com/archlinux/aur.git <package_name>
         

      2. I will not use any package from AUR in this tutorial. It is similar (but superior) to the third-party repositories like PPA for Ubuntu, COPR for Fedora, and OBS for openSUSE.
2. Download the latest archlinux-YYYY.MM.DD-x86_64.iso, sha256sums.txt, and archlinux-YYYY.MM.DD-x86_64.iso.sig from the nearest mirror like mirror.arizona.edu.
3. Verify the integrity and authenticity of your ISO image using Linux (if Windows, use WSL).
   1. Integrity: Ensure the download image matches the checksum from the sha256sums.txt

       $ sha256sum -c sha256sums.txt
      

      This should output archlinux-YYYY.MM.DD-x86_64.iso: OK. You may see “No such file or directory” for other files which we didn’t download but their checksums also included.

   2. Authenticity: One should never use a GnuPG version just downloaded from internet to check the integrity; instead use an existing, trusted GnuPG installation, e.g., the one provided by your Linux distribution (if Windows, then use WSL).

       $ gpg --auto-key-locate clear,wkd -v --locate-external-key pierre@archlinux.org
       $ gpg --verify archlinux-YYYY.MM.DD-x86_64.iso.sig archlinux-YYYY.MM.DD-x86_64.iso
      

      GPG might give warning This key is not certified with a trusted signature!, but you can verify it here.

4. Create a bootable USB drive using Ventoy; remember to verify the checksum of Ventoy itself.
5. In UEFI, disable secure boot.

From chroot to root

1. Boot from the Live USB drive and select Arch Linux from the systemd-boot greeting screen to get logged in on the first virtual console as the root user, and presented with a Zsh shell prompt.
2. Verify that the boot mode is UEFI by ensuring that the following command returns 64.

    # cat /sys/firmware/efi/fw_platform_size
   

3. Connect to WiFi using iwctl.

    # iwctl
    [iwd]# device list
    [iwd]# station <device-name> scan
    [iwd]# station <device-name> get-networks
    [iwd]# station <device-name> connect <Name of WiFi access point>
    [iwd]# exit
    $ ping -c 5 ping.archlinux.org
   

4. Ensure that the system clock is syncronized via Network Time Protocol (NTP).

    # timedatectl set-ntp true
    # timedatectl
   

5. Use cfdisk to create the following GUID Partition Table (GPT), without hibernation feature (suspend-to-disk).

   Mount point	Parition type	Size	Partition
   /efi	EFI System Partition	1 GiB	/dev/efi_system_partition
   [swap]	Linux swap	6 GiB	/dev/swap_partition
   /	Linux Filesystem	(all of the remaining space )	/dev/root_partition

   Can later get the partition names using fdisk -l.

6. Format the partitions using mkfs.

    # mkfs.fat -F 32 /dev/efi_system_partition
    # mkswap /dev/swap_partition
    # mkfs.btrfs /dev/root_partition
   

7. Create the Btrfs filesystem layout recommended for snapper

    # mount /dev/root_partition /mnt
    # btrfs subvolume create /mnt/@
    # btrfs subvolume create /mnt/@home
    # btrfs subvolume create /mnt/@var_log
    # btrfs subvolume create /mnt/@var_cache
    # btrfs subvolume create /mnt/@var_spool
    # btrfs subvolume create /mnt/@var_tmp
    # btrfs subvolume create /mnt/@snapshots
    # btrfs subvolume list -t /mnt
    # lsblk --fs
    # umount /mnt
   

8. Mount the file systems as we prepare to chroot with Btrfs compression settings optimized for NVMe SSD (Kioxia XG8) and not using Mutt.

    # mount -o noatime,compress=zstd:1,subvol=@ /dev/root_partition /mnt
    # mkdir -p /mnt/{home,.snapshots} /mnt/var/{log,cache,spool,tmp}
    # mount -o noatime,compress=zstd:1,subvol=@home /dev/root_partition /mnt/home
    # mount -o noatime,compress=zstd:1,subvol=@var_log /dev/root_partition /mnt/var/log
    # mount -o noatime,compress=zstd:1,subvol=@var_cache /dev/root_partition /mnt/var/cache
    # mount -o noatime,compress=zstd:1,subvol=@var_spool /dev/root_partition /mnt/var/spool
    # mount -o noatime,compress=zstd:1,subvol=@var_tmp /dev/root_partition /mnt/var/tmp
    # mount -o noatime,compress=zstd:1,subvol=@snapshots /dev/root_partition /mnt/.snapshots
    # mount --mkdir /dev/efi_system_partition /mnt/efi
    # swapon /dev/swap_partition
    # lsblk --fs
   

9. Use pacstrap to create a new system installation from scratch.

    # pacstrap -K /mnt
   

   This installs the base metapackage consisting of basic tools like bash, systemd, and pacman. It also copies the LiveUSB’s mirrorlist /etc/pacman.d/mirrorlist generated using reflector to the new system. During the fifth test run I was bit by a bug in this step.

10. Generate fstab file with startup instructions

    # genfstab -U /mnt >> /mnt/etc/fstab
    

    Check the resulting /mnt/etc/fstab file, and edit it in case of errors and various mount options like discard=async and ssd.

11. Switch to the new system’s environment

    # arch-chroot /mnt
    

    1. Set up the time zone.

        # ls /usr/share/zoneinfo/                                     
        # ls /usr/share/zoneinfo/<Zone>/                              
        # ln -sf /usr/share/zoneinfo/<Zone>/<Subzone> /etc/localtime       
        # hwclock --systohc
       

    2. Configure correct region and language specific formatting.
       1. Install a console text-editors like nano:

          # pacman -S nano
          

       2. Use nano to edit /etc/locale.gen and uncomment en_US.UTF-8 UTF-8.
       3. Generate the locales.

          # locale-gen
          

       4. Use nano to create configuration file /etc/locale.conf and write LANG=en_US.UTF-8 in it.
    3. Network configuration.
       1. Use nano to create /etc/hostname and write <PC-Name> in it.
       2. Use nano to edit /etc/hosts and add the following to it

          127.0.0.1 localhost
          ::1 localhost
          127.0.1.1 <PC-Name> 
          

       3. Install and enable network manager to run on boot.

          # pacman -S networkmanager
          # systemctl enable NetworkManager
          

    4. Create a new initramfs (initial RAM file system)
       1. Install userspace utilities for the Btrfs file system (btrfs-progs) and Linux kernel linux with linux-lts as a fallback option. If presented with options for initramfs, choose mkinitcpio. Note that trying to install kernel without btrfs-progs will lead to error when mkinitcpio runs the fsck hook.
       2. Install kernel firmware (linux-firmware) along with additional firmware for Intel CPU (intel-ucode), Intel iGPU (mesa, vulkan-intel), NVIDIA dGPU (nvidia, nvidia-utils), and Dolby Atmos (pipewire, pipewire-alsa, pipewire-pulse, pipewire-jack, wireplumber). Update (Dec 20, 2025): Use nvidia-open instead of nvidia, see news.
       3. Re-run mkinitcpio to be sure that we have an error free initial ramdisk environment.

          # mkinitcpio -P
          

          Note that every time a kernel is installed or upgraded, a pacman hook automatically generates a preset file saved in /etc/mkinitcpio.d/ and -P option process all presets contained in /etc/mkinitcpio.d.

    5. Set root password using passwd command.
    6. Install a btrfs-friendly bootloader, like GRUB.

        # pacman -S grub efibootmgr
        # grub-install --target=x86_64-efi --efi-directory=/efi --bootloader-id=GRUB
        # grub-mkconfig -o /boot/grub/grub.cfg
       

       Kernel packages are installed under the /usr/lib/modules/ path and subsequently used to copy the vmlinuz executable image to /boot/.

    7. We can use the bootloader to switch between linux and linux-lts kernel. But will set linux as the default option by editing /etc/default/grub:

       GRUB_DISABLE_SUBMENU=y
       GRUB_DEFAULT="Arch Linux, with Linux linux"
       

       Regenerate your configuration file with grub-mkconfig.

    8. Exit the chroot environment by typing exit or pressing Ctrl + d.
12. Manually unmount all the partitions

    # umount -R /mnt
    

13. Reboot (or poweroff) the system and remove the installation media

    # reboot
    

From superuser to user

1. Login into the new system with the root account (superuser).
2. Connect to WiFi using nmtui or nmcli.

    # nmcli device wifi connect <Name of WiFi access point> password <password>
   

3. Pacman configuration to automatically update mirrors and periodically clear out cache.

    # pacman -S pacman-contrib
    # systemctl enable --now paccache.timer
    # pacman -S reflector
    # systemctl enable --now reflector.timer
   

4. Install man to have offline access to Arch Linx documentation.

    # pacman -S man-db
   

5. Create a user and add to administration group (wheel) with sudo access. Note that logging in using root account is disabled for GUI.

     # useradd -mG wheel <user-name>
     # passwd <user-name>
     # pacman -S sudo
     # EDITOR=nano visudo
   

   The last command opens the /etc/sudoers file using nano; look for a line which says something like Uncomment to allow members of group wheel to execute any command and uncomment exactly the line BELOW it, by removing the #. This will grant superuser priviledges to your user.

6. Check NVIDIA configuration by ensuring that the Direct Rendering Manager (DRM) is enabled.

    # cat /sys/module/nvidia_drm/parameters/modeset
   

   This should return Y.

7. Install KDE with Wayland support following advice from the KDE documentation and Arch dependency tree of plasma-desktop. We have consciously excluded discover from KDE because it can lead to partial upgrades which are unsupported in Arch.
   1. base: plasma-{desktop,pa,nm,systemmonitor,firewall}, kscreen, bluedevil, powerdevil, tlp
   2. keyring (PAM): kwalletmanager, kwallet-pam
   3. terminal (otherwise will need to use tty): konsole
   4. file manager: dolphin, dolphin-plugins, kdegraphics-thumbnailers, ffmpegthumbs
   5. XDG Desktop Portal (Wayland and Firefox integration): xdg-desktop-portal-gtk, xdg-desktop-portal-kde
   6. Theme consistency (GTK in Qt): breeze-gtk, kde-gtk-config

       # pacman -S <space separated list of packages>    
      

      You may be prompted to choose between ffmpeg or gstreamer backend for qt6-multimedia. I chose ffmpeg because that seems to be the default.

8. Install Simple Desktop Display Manager (SDDM).

    # pacman -S sddm
    # systemctl enable sddm
    # pacman -S --needed sddm-kcm
   

9. Reboot to finalize installation.

    # reboot
   

Personalization

1. Login using user account in SDDM.
2. Check if any systemd services have failed or errors in the log files located in /var/log/.

    $ systemctl --failed
    $ journalctl -b -p 3
   

3. Go to Settings → Colors & Themes → Login Screen (SDDM) → Breeze → Change Background → Apply.
4. Install essential software using the package manager.
   1. Browser: firefox (along with extensions: uBlock Origin, Privacy Badger, Decentraleyes, ClearURLs, and password manager)
   2. Document viewer: okular, ebook-tools, kdegraphics-mobipocket, unarchiver
   3. Image viewer: gwenview, kimageformats, qt6-imageformats
   4. Video player (mpv and yt-dlp based): haruna, yt-dlp
   5. Archiving tool: ark, 7zip
   6. Screenshot tool: spectacle
   7. Calculator: kalk
   8. Text editor: kate
   9. File searching tool: kfind
   10. Messaging: signal-desktop
   11. GPU manager (NVIDIA): nvidia-settings
   12. Webcam controls (LogiTune): cameractrls
   13. Wireless mouse (LogiBolt): solaar
   14. IDE: emacs-wayland
5. Battery care configuration using tlp.

   $ sudo systemctl enable --now tlp.service
   $ sudo tlp-stat -s
   $ sudo tlp-stat -b
   

   We can configure tlp by editing battery care settings in /etc/tlp.conf.

6. Configure Git and GitHub.

    $ sudo pacman -S git openssh
   

   1. Set the name and email for git commits. Also set default editor and push behavior.

      $ git config --global user.name  "Your Name"
      $ git config --global user.email "your.email@github.com"
      $ git config --global core.editor "nano -w"
      $ git config --global push.default simple
      

   2. Configure SSH for GitHub interaction:
      1. Generate a new public and private SSH key pair using OpenSSH.
      2. Add SSH public key to the GitHub account.
7. Configure rclone for Google Drive backup.

    $ sudo pacman -S rclone
   

   1. Create your own Google Drive OAuth2 client ID for rclone:
      1. Log into the Google API Console with your Google account. It doesn’t matter what Google account you use. (It need not be the same account as the Google Drive you want to access.
      2. Select a project or create a new project.
      3. Under “ENABLE APIS AND SERVICES” search for “Drive”, and enable the “Google Drive API”.
      4. Click “Oauth Consent Screen” in the left panel and select user type “External”. Then add Application name (anything you want) and save.
      5. Click “Credentials” in the left panel. Then click on “+ CREATE CREDENTIALS” button at the top of the screen, then select “OAuth client ID”. Select Application type as “Desktop app”, enter whaever client anme you want and click create.
      6. It will show you a client ID and client secret. Use these values in rclone config.
   2. Now configure rclone for Google Drive via Terminal: rclone config and follow the steps. Remember to use the Client ID and client secret we created above. Since we created this API for personal use, we won’t be submitting it for verfication. Hence don’t be alarmed by the very scary confirmation screen shown when we connect via your browser for rclone to be able to get its token-id. Also, if you want to fetch Google Docs as links (instead of converting them to .odt etc) from Google Drive, in “advance-config” set “export-formats” to “link.html”.
   3. Sync files using “copy” and NOT “sync”: rclone copy source:path dest:path [flags]. For example, to sync all files from “New Folder” Google Drive (named: Drive) to PC (folder: home) and view the progress, type: rclone copy Drive:"New Folder" /home -P. Google Drive tend to have duplicate files since it allows same names files in same folder, in that case use dedupe to delete all duplicate files.
8. Configure snapper for automatic / snapshots per the Wiki.

    $ sudo su
    # pacman -S snapper
   

   1. Unmount /.snapshots

      # btrfs subvolume list -t /
      # lsblk --fs
      # umount /.snapshots
      # rm -r /.snapshots
      

   2. Create a new snapper configuration named root for the Btrfs subvolume at /.

       # snapper -c root create-config /
       # btrfs subvolume list -t /
       # btrfs subvolume delete /.snapshots
       # mkdir /.snapshots
       # mount -o noatime,compress=zstd:1,subvol=@snapshots /dev/root_partition /.snapshots
      

      This will create a configuration file at /etc/snapper/configs/root. When you delete config file, then also delete its entry from /etc/conf.d/snapper to read SNAPPER_CONFIGS="".

   3. Make this mount permanent by adding an entry to fstab.

       # btrfs subvolume list -t /
       # lsblk --fs
       # blkid
       # nano /etc/fstab
       # mount -a
       # chmod 750 /.snapshots
       # chown :wheel /.snapshots
      

   4. Use systemd timer units for automatic timeline snapshots and cleanup.

       # systemctl enable --now snapper-timeline.timer
       # systemctl enable --now snapper-cleanup.timer
       # systemctl edit --full snapper-timeline.timer
       # systemctl edit --full snapper-cleanup.timer
      

      For taking snapshots use realtime timer OnCalendar=hourly in snapper-timeline.timer unit and for cleanup use monotomic timer OnBootSec=10m and OnUnitActiveSec=1h in snapper-cleanup.timer unit. Unlike Timeshift, we will not use cron job.

   5. Set snapshot limits by editing /etc/snapper/configs/root

      # limit for number cleanup
      NUMBER_MIN_AGE="1800"
      NUMBER_LIMIT="10"
      NUMBER_LIMIT_IMPORTANT="5"
      
      # limits for timeline cleanup
      TIMELINE_MIN_AGE="1800"
      TIMELINE_LIMIT_HOURLY="5"
      TIMELINE_LIMIT_DAILY="7"
      TIMELINE_LIMIT_WEEKLY="0"
      TIMELINE_LIMIT_MONTHLY="0"
      TIMELINE_LIMIT_YEARLY="0"
      
      # limits for empty pre-post-pair cleanup
      EMPTY_PRE_POST_MIN_AGE="1800"
      

      Here 1800 seconds = 30 min.

   6. We can use the grub-btrfs daemon to automatically update GRUB upon snapshot creation or deletion, and avoid dependency on LiveUSB for restoring snapshots.

      # pacman -S grub-btrfs inotify-tools
      # systemctl enable --now grub-btrfsd
      

      Then enable booting into read-only snapshots using overlay filesystem by adding grub-btrfs-overlayfs to the end of the HOOKS array in /etc/mkinitcpio.conf and regenerating the initramfs.

      # nano /etc/mkinitcpio.conf
      # mkinitcpio -P
      

      If you try to boot from these read-only snapshots available in GRUB menu, the following warning/error might appear:

      ********************* WARNING *********************
      * The root device is not configured to be mounted *
      * read-write! It may be fsck'd again later.       *
      ***************************************************
      [FAILED] Failed to start Remount Root and Kernel File Systems.
      

      Here the WARNING just confirms that our snapshot is read-only and [FAILED] confirms that systemd failed to mount the underlying read-only root filesystem. Despite this “failure” message, the boot process should continue using OverlayFS’s temporary read-write upper layer, leaving the original Btrfs snapshot untouched.

   7. Use snap-pac to make pacman automatically use snapper to create pre/post snapshots.

      # pacman -S snap-pac
      

   8. Testing snapshots by installing inxi.

      # pacman -S inxi
      # inxi -Fxz
      # snapper -c root list
      

9. Reboot and check if things if the things are as expected.

Maintainance

1. Must subscribe to the mailing list is for official announcements and check that before updating.
2. When refreshing the package database, always do a full upgrade.

   # pacman -Syu
   

3. Uninstall pacakge along with its dependecies.

   # pacman -Rs <package>
   

4. Recursively remove orphaned packages that were installed as a dependency but now, no other packages depend on them.

   # pacman -Qdtq | pacman -Rns -
   

5. Check list all foreign packages that are no longer be in the remote repositories, but still on your local system.

   # use pacman -Qm.
   

   This list will also include packages that have been installed manually (e.g., from the AUR).

6. Use nvme to probe the health of SSD.

   # pacman -S nvme-cli 
   # nvme smart-log /dev/root_partition
   

7. To view a list of snapshots under root configurations.

   # snapper -c root list
   

8. If GUI fails then can use LiveUSB arch-chroot or Desktop environment’s tty.
9. To restore / using one of snapper’s snapshots, we need access to OverlayFS (either via LiveUSB or grub-btrfs) and follow these steps.
   1. Mount the toplevel subvolume.

      # fdisk -l
      # mount /dev/root_partition /mnt
      # lsblk --fs
      # btrfs subvolume list -t /mnt
      

   2. Move @ to another location (e.g. /@.broken) to save a copy of the current system.

      # mv /mnt/@ /mnt/@.broken
      # btrfs subvolume list -t /mnt
      

   3. Find the number of the snapshot that you want to recover:

      # grep -r '<date>' /mnt/@snapshots/*/info.xml
      

   4. Create a read-write snapshot of the read-only snapshot snapper took:

      # btrfs subvolume snapshot /mnt/@snapshots/<number>/snapshot /mnt/@
      

   5. Check fstab is correct.

      # cat /mnt/etc/fstab
      

   6. Unmount the top-level subvolume (ID=5), then mount @ to /mnt and your ESP or boot partition to the appropriate mount point.

      # umount /mnt
      # mount -o noatime,compress=zstd:1,subvol=@ /dev/root_partition /mnt
      # mount /dev/efi_system_partition /mnt/efi
      

   7. If using LiveUSB then Change root to your restored snapshot before regenerating initramfs image.

      # arch-chroot /mnt     
      # mkinitcpio -P
      # exit
      # reboot
      

   8. If everything is as expected then delete the broken snapshot.

      # btrfs subvolume delete /@.broken
      

10. Vendor firmware updates (like UEFI)

       # pacman -S fwupd udisks2
       # fwupdmgr get-devices
    

The past

In the past, I have dabbled in programming using different languages:

Unfortunately, I never spent time honing my programming skills. Therefore, at the beginning of my graduate school, I thought of properly learning programming in Python. However, most of the study materials I found were more about “writing code to solve data science problems” rather than “learning to solve problems using programming.”

The present

I spent one year learning the basics of computer science following the advice from UArizona Computer Science department students and professors. None of the textbooks were read cover to cover.

During this one-year journey, I got the opportunity to practice programming in different languages:

I also learned regular expression usage in AWK (Frequency Analysis) and Python (Lexical Analysis).

The future

Next, I would like to improve my programming skills by

• using Python to solve the exercises from Project Euler, id0-rsa, Cryptopals, CrytoHack, and other CTFs;
• using C++ to solve competitive programming problems from Advent of Code and popular online judges (eg. UVa, Kattis, Codeforces, Sphere, AtCoder, Timus, DMOJ, Marisa, …);
• contributing to Open Source projects, especially SageMath;

However, there are many more programming languages to choose from. For example, the following are some of the main programming languages developed before the Internet age (source: Programming Languages - Principles and Practice, by Louden & Lambert, 3rd ed)

Eventually, I would also like to learn Rust and contribute to modern computer security projects.

The Nexus 7 is one of the best piece of hardware I ever owned, but it lacked good quality acccesories. Moreover, in my opinion, Samsung Galaxy Tab S6 Lite is a modified version of Samsung Google Nexus 10 with added Wacom drawing tablet functionality, reduced screen resolution, and removed camera-flash (full comparison). On the other hand, Samsung Galaxy Tab S series in general have filled the void left by Google Pixel C after Google dumped Android in favor of ChromeOS tablet Google Pixel Slate which supported Pixelbook Pen (Wacom’s AAAA-battery AES pen).

Initially, since reading was the main purpose of the tablet, I tried replacing my older tablet with Kindle Paperwhite (3rd generation). However, its small screen made it impossible to quickly jump between the pages of the large documents. Moreover, to be able to read pdf/DjVu files properly, one first has to optimize them for viewing using k2pdfopt or jailbreak kindle (complicated). Another adavantage of using a tablet PC instead of an e-reader is that nowadays there are many open source online textbooks available, like The Stacks project and nLab.

Review

Took some time to get used to writing on bigger screen than Nexus 7.

Settings > Display > Navigation bar > Swipe gestures > Swipe from sides and bottom

Also, enable “Block gestures with S Pen” and in Xodo app enable “Stylus as Pen”

Cons: low resolution, speakers position only good for landscape viewing, front camera is only good for portrait use.

The free rein of proprietary softwares

In the world of (abstract) mathematical computations, proprietary softwares tend to be more advanced than the open source alternatives. This is mainly because of the lack of industrial support, i.e. nobody can make money by having a better abstract math computation system (see DLMF and NumFOCUS list). Following is the list of current market leaders and their open-source competitors/clones:

However, closed-source projects tend to die in a decade or two (see the comments by Tim Daly). For up-to-date information, check out ISSAC (SIGSAM), Computeralgebra-Rundbrief, ICMS, JSS, and swMATH.

I must point out that RStudio is the only open-source alternative that has been able to overtake the proprietary alternatives, mainly because statistical computations can help you make money. Moreover, though the Anaconda distribution has become the standard open-source alternative to all proprietary computational softwares, there still isn’t any Python library for “structural computations” (Galois representations, isomorphisms, counting points on varieties, etc.). I believe that this is because SageMath’s motto “building the car instead of reinventing the wheel” turned it into bloatware since they integrated other well-developed open source programs like R, FriCAS, Maxima, and SymPy using Python (the glue language of scientific computing), instead of just building the Python libraries (like CyPari2) which would act as an alternative to Magma, fulfilling the original motto “Software for Arithmetic Geometry Experimentation”. To overcome this failure, SageMath evolved into a cloud-based subscription service called CoCalc to generate revenue for funding the massive project. However, the main contributions seem to come from the developments related to the LMFDB project. It might also be useful to look at the ANTS proceedings.

Mix and match

Open-source softwares has been a lifesaver for students in countries like India, where our universities couldn’t afford the proprietary softwares. I learned numerical analysis on GNU Octave and number theory on SageMath. Note that, there exist computer algebra systems that follow the philosophy of accepting a given general-purpose programming language and extending it by a set of algebraic capabilities:

That is, people have tried achieving a full-fledged CAS in many other programming languages, but all of them are half-baked due to the lack of contributors. In fact, using GiNaC we can get a symbolic extension for GNU Octave (nowadays can also use SymPy) and its fork Pynac provides the backend for symbolic expressions in SageMath (before that Maxima was used). Moreover, SymEngine is planned to be used as an optional fast symbolic core for SymPy since it is much faster than Pynac and a bit faster than GiNaC. However, for doing computational experiments in higher arithmetic we will have to learn multiple languages:

Any mathematician who is serious about doing extensive computational work in algebraic number theory and arithmetic geometry is strongly urged to become familiar with all three systems [Sage, Pari, and Magma] since they all have their pros and cons. Pari is sleek and small, Magma has much unique functionality for computations in arithmetic geometry, and Sage has a wide range of functionality in most areas of mathematics, a large developer community, and much unique new code. – SageMath October 2008 Bordeaux meeting

There is similar advice from Andrew Sutherland and John Voight in this blog post by Frank Calegari.

Python: General-purpose programming language (open-source)

During my undergraduate studies, I had the perception that C++ is “the langauge” for scientific computations (see the table above). In fact, the C/C++ libraries like GMP, MPFR, and GNU MPC serve as the foundations for various other higher arithmetic computation libraries. However, with the advent of Cython (not to be confused with CPython, which is the original Python implementation), Python has become “the new langauge” for scientific computations. The key advantage of Python over C++ is that Python provides better code readability than C++ (like using whitespaces instead of curly braces). In fact, all these C/C++ libraries can now be accessed via SageMath using Python-based syntax. For example, in 2016, Robert J. Lemke Oliver used SageMath and C++ to verify the observations by Kannan Soundarajan, leading to the famous discovery of biases in the distribution of consecutive primes.

To begin the Python journey, we will need the following packages:

*Note that Fedora will automatically install the required dependecies like mpmath, Cython, matplotlib etc.

**Requires the actual PARI/GP package and the PARI library development package.

If you want GUI version of Python development environment then can get IDLE by installing the package python3-idle. We will use Vim as the text editor for writing Python scripts. Note that we don’t need to add a file extension, however for proper syntax highlighting we will use the file extension .py. Therefore, it would be helpful to install the python-mode plugin (instructions). Following are some the key mappings for some of the python-mode commands (documentation):

Note that the text-wrap is disabled by default, with the maximum line length of 79 characters. Moreover, it uses pylint to check code at every save. I couldn’t figureout how to use code completion via rope.

One can learn the basics by going through Hands-on Python Tutorial by Andrew N. Harrington or skimming through the tutorial available in the official documentation. If you prefer video lectures, then the MIT OCW Introduction to Computer Science and Programming in Python is a good option (many other free tutorials are also there on YouTube).

Python is a multi-paradigm, call by object, statically scoped, both dynamically and strongly typed programming language.

Therefore, though Python is an object-oriented language, it doesn’t imply that it doesn’t support other programming paradigms (wikipedia). Also, it would be wise to keep in mind the floating point arithmetic limitations that these general purpose programming languages. For example, if using Python as a calculator, we will get “wrong” answers when using decimals:

# Python3 examples
>>> 3.3 - 1.1  # Do not depend on the exactness of floating point arithmetic, even for apparently simple expressions! 
2.1999999999999997
>>> 0.1+0.2  # so here 0.3 is not equal to 0.1 + 0.2
0.30000000000000004
>>> format(.1, '.20f')  # 0.1 does not has exact representation in binary floating point
'0.10000000000000000555'

To familiarize yourself with the useful maths libraries in Python (for example, mpmath provides support for arbitrary-precision floating point arithmetic, one can use the notes for the Maths with Python course at the University of Southampton or Fundamentals of Computer Programming course by Clinton Bradford at Purdue University. If you prefer video lectures, then the MIT OCW Introduction to Computational Thinking and Data Science is a good option. For example, we can get “correct” answers for float arithmetic by using decimal module:

# trying to bypass float arithmetic problem
>>> from decimal import *
>>> Decimal('3.3') - Decimal('1.1')
Decimal('2.2')
>>> Decimal('0.1') + Decimal('0.2')
Decimal('0.3')
>>> Decimal('0.1') == 0.1
False
>>> Decimal('3.5') == 3.5
True

Examples

For elementary numer theory examples, you can use either the course notes for this (very) short course in Number Theory by Robert Campbell at the University of Maryland, Baltimore County (course website) or the the companion website for the book “An Illustrated Theory of Numbers” by Martin H. Weissman. However, here we will take some examples from SageMath and solve them using Python libraries.

• Plotting elliptic curves over affine plane

  • SageMath script and output

     p=plot(EllipticCurve([0,0,0,3,0]), gridlines='true', color=hue(0.7),xmin=-4, xmax=4, ymin=-3, ymax=3, legend_label='$y^2=x^3+3x$')
     p+=plot(EllipticCurve([0,0,0,2,0]), gridlines='true', color='cornflowerblue',xmin=-4, xmax=4, ymin=-3, ymax=3, legend_label='$y^2=x^3+2x$')
     p+=plot(EllipticCurve([0,0,0,1,0]), gridlines='true', color='red',xmin=-4, xmax=4, ymin=-3, ymax=3, legend_label='$y^2=x^3+x$')
     p+=plot(EllipticCurve([0,0,0,-1,0]), gridlines='true', color='orange',xmin=-4, xmax=4, ymin=-3, ymax=3)
     p+=plot(EllipticCurve([0,0,0,-2,0]), gridlines='true', color=hue(0.2),xmin=-4, xmax=4, ymin=-3, ymax=3, legend_label='$y^2=x^3-2x$')
     p+=plot(EllipticCurve([0,0,0,-3,0]), gridlines='true', color=hue(0.3),xmin=-4, xmax=4, ymin=-3, ymax=3, legend_label='$y^2=x^3-3x$')
     p.set_legend_options(shadow=False, loc=2)
     show(p)
     p.axes_labels(['$x$','$y$'])
     p.save('ec.pdf')
    

    

  • Python script and output

  to-do

• Plotting elliptic curve modulo prime

  • SageMath script and output

    E=EllipticCurve(GF(1021),[0,-1,-1,0,0])
    A=E.plot()
    show(A)
    A.save('v1.pdf')
  

  

  • Python script and output

  to-do

• Comparing the prime counting functions

  • SageMath script and output

   P = plot(Li(x), (x,2,10000), linestyle="--", thickness=2, rgbcolor=(0,0,0), legend_label='$\\mathrm{Li}(x)$')
   Q = plot(prime_pi(x), (x,2,10000),thickness=2, rgbcolor=(0,0,0), legend_label='$\\pi(x)$')
   R = plot(x/log(x), (x,2,10000), linestyle=":", thickness=3, rgbcolor=(0,0,0), legend_label='$x/\\log(x)$')
   (P+Q+R)
  

  

  • Python script and output

  to-do

• Plotting Riemann zeta function for real inputs (trivial zeros)

  • SageMath script and output

    p=plot(zeta(x), (x,-13,-1), legend_label='$\\zeta(x)$')
    show(p)
  

  

  • Python script and output

  to-do

• Plotting the real and imaginary parts of the Riemann zeta function $\zeta(1/2 + it)$ for $0 < t < 30$

  • SageMath script and output

    i = CDF.gen()
    v = [zeta(0.5 + n/10 * i) for n in range(300)]
    L = [(z.real(), z.imag()) for z in v]
    line(L)
  

  

• Comparing the argument and absolute values of Riemann zeta function $\zeta(1/2 + it)$ for $0 \leq t \leq 50$

  • SageMath script and output

    i = CDF.0
    p1 = plot(lambda t:  arg(zeta(0.5+t*i)), 1, 50,linestyle="--", rgbcolor=(0,0,0), legend_label='$\\mathrm{arg}(\\zeta(0.5+it))$')
    p2 = plot(lambda t:  abs(zeta(0.5+t*i)), 1, 50, rgbcolor=(0,0,0), legend_label='$|\\zeta(0.5+it)|$')
    p1+p2
  

  

• Plotting complex valued functions

  • SageMath script and output

    complex_plot(x^4-1,(-5,5),(-5,5))
  

  

• Ideal factorization

  • SageMath script and output

    K.<a>=NumberField(x^3-19)
    I = K.ideal(3)
    F = I.factor()
    F
  

    (Fractional ideal (3, 1/3*a^2 + 1/3*a + 1/3))^2 * (Fractional ideal (3, 1/3*a^2 + 1/3*a - 2/3))
  

  • Python script and output

  to-do

  to-do

Magma: Domain-specific programming language (proprietary)

There exist individual C/C++ libraries, like FLINT and m4ri, which are much more efficient than Magma. In fact, Magma itself uses some of the C/C++ libraries like ATLAS, GMP, GMP-ECM, MPC, and MPFR. However, there aren’t enough libraries available to enable SageMath completely replace Magma.

In the USA, because of the Simons Foundation Agreement, you can get access to Magma for free by contacting your department’s IT support staff. You should be able to access its full-version on your department’s computer clusters and student-version on your personal computer (installation steps). Note that the student-version is available only for the outdated 32-bit architecture, therefore you might also need to install additonal packages like glibc.i686 in Fedora (details) or ia32-libs-multiarch in Ubuntu (details).

We will use Vim as the text editor for writing Magma scripts. Note that, just like for Python scripts, we don’t need to add any specific filename extensions to the text files in order to be able to “load them” in Magma (details). However, one can use filename extension .m to get Objective-C syntax highlighting (objc.vim) and to be consistent with the extension used for magma package files (details). Moreover, we can run the code without having to leave the text editor by adding the following to .vimrc file (source):

map <F2> :w<CR>:!magma %<CR> "once you press <F2> in normal mode, it first saves your file and then run the file with magma.
imap <F2> <Esc>:w<CR>:!magma %<CR> "once you press <F2> in insert mode, it first leaves insert mode, then saves the file and then run the file with magma.

One can learn the basics by going through the “First Steps in Magma” or skimming through the first chapter of the “Handbook of Magma Functions”, you will be ready to start using Magma for solving math problems. Note that Magma supports the old-school procedural programming paradigm with an ability to implement functional style.

Magma is an imperative, call by value, statically scoped, dynamically typed programming language, with an essentially functional subset.

Examples

For some elementary numer theory examples, see the Micro introduction into Magma available on the legacy website of Harvard University’s Department of Mathematics. However, we will take some examples from SageMath and solve them using Magma. Note that, unlike SageMath, Magma doesn’t have access to any plotting library like matplotlib. Therefore, we can’t reproduce the graphical examples we saw above.

• Ideal factorization

  • SageMath script and output (doc)

    K.<a>=NumberField(x^3-19)
    I = K.ideal(3)
    F = I.factor()
    F
  

    (Fractional ideal (3, 1/3*a^2 + 1/3*a + 1/3))^2 * (Fractional ideal (3, 1/3*a^2 + 1/3*a - 2/3))
  

  • Magma script and output

    R<x>:=PolynomialRing(Integers());
    f:=x^3 - 19;
    K<y>:=NumberField(f);
    O:=MaximalOrder(K);
    I:=3*O;
    Factorization(I);
  

    [
    <Prime Ideal of O
    Two element generators:
        [3, 0, 0]
        [2, 0, 2], 1>,
    <Prime Ideal of O
    Two element generators:
        [3, 0, 0]
        [0, 2, 1], 2>
    ]
  

Conclusion

William Stein has played a key role in starting this open-source mathematical software revolution. For example, there exist free online textbooks which use SageMath to teach elementary number theory, linear algebra, abstract algebra, graph theory, and game theory. However, it would have been great if the academic community could understand the value of open-source Python-based Magma.

Fortunately, the OSCAR project, supported by the German Research Foundation (DFG) since January 2017, has the potential of becoming an open-source Julia-based Magma. I believe that unlike SageMath, OSCAR will be able to replace Magma, since like Magma is maintained by the Computational Algebra Group at the University of Sydney, OSCAR is maintained by the Algebra, Geometry and Computer Algebra group at TU Kaiserslautern (usecase example). Moreover, Julia has simple syntax like Python (Python equivalent is CPython: interpreted language for fast software development), is as fast as C++ (Python equivalent is Cython: compiled language for fast computations) and uses a LLVM just-in-time (JIT) compiler similar to the JVM JIT compiler of Java (Python equivalent is PyPy, similar to LuaJIT: dynamic language for fast computations).

In my opinion, the research papers funded by public taxes should be freely available (like free beer) and the softwares needed to do tax-funded research should also be freely available (like free speech). Recently, there has been a surge in researchers using SageMath or Python for doing computations in higher arithmetic. For example, this arithmetic geometry paper uses Python for computations.

\usepackage{graphicx} %add images
\graphicspath{ {./figures/} } %images are kept in a folder under the directory of the main document.
\usepackage{subcaption} %to add multiple subfigures.

However, for better integration into the pdf document we should be using vector graphics and it can be done with the help of following programs/packages:

Graphs

pgfplots

For including 2D and 3D plots, we can use the pgfplots package. Read the documentation. First include the following in the preamble:

\usepackage{pgfplots} %draws function plots using pgf/tikz
\pgfplotsset{compat=1.16} %running latest version of pgfplots
\usepgfplotslibrary{external} %avoid recompiling unchanged graphs
\tikzexternalize[prefix=./figures/] %images will be stored in a folder under the working directory to avoid recompling unchanged files

For example, we can plot 3D surfaces by following methods:

\begin{tikzpicture} %https://tex.stackexchange.com/a/359914/
\begin{axis}[title=$f^{-1}(-1)$: Hyperboloid of 1 sheet,axis equal]
\addplot3[surf,domain=0:360,y domain=-2:2] ({cosh(y)*cos(x)},{cosh(y)*sin(x)},{sinh(y)});
\end{axis}
\end{tikzpicture}

  \begin{tikzpicture}%https://tex.stackexchange.com/a/28775/
  \begin{axis}[title=$f^{-1}(0)$: Double cone, domain=0:5, y domain=0:2*pi,xmin=-10, xmax=10, ymin=-10, ymax=10, samples=20]
  \addplot3 [surf,z buffer=sort] ({x*cos(deg(y))}, {x*sin(deg(y))}, {x});
  \addplot3 [surf,z buffer=sort] ({x*cos(deg(y))}, {x*sin(deg(y))}, {-x});
  \end{axis}
  \end{tikzpicture}

The downside of this method is that it will increase the compliation time if prefix option is not used (since pdfLaTeX is limited to single CPU thread). We can also use contour gnuplot and \addplot gnuplot to extend the built-in capabilities of pgfplots by means of gnuplot’s math library, although their use is optional.

Matplotlib

Another way of including 2D and 3D plots is to use the Python library Matplotlib. Read this guide. I will illustrate the steps involved by the following plotting the 2D vector field $X=-y\frac{\partial}{\partial x} + x\frac{\partial}{\partial y} and its flow lines:

1. Save and run the following Python scripts in the “figures” subfolder inside the folder containg the main LaTeX file (source1, source2):

import numpy as np
import matplotlib.pyplot as plt

#use quiver plot to plot the vector field
x,y = np.meshgrid(np.linspace(-5,5,10),np.linspace(-5,5,10))
u = -y
v = x
plt.quiver(x,y,u,v)

#save as pdf and pgf
plt.savefig('field.pdf')
plt.savefig('field.pgf')

import numpy as np
import matplotlib.pyplot as plt

#use stream plot to create the flow lines
x,y = np.meshgrid(np.linspace(-5,5,10),np.linspace(-5,5,10))
u = -y
v = x
plt.streamplot(x,y,u,v)

#save as pdf and pgf
plt.savefig('flow.pdf')
plt.savefig('flow.pgf')

1. Add the following lines in the preamble of the main LaTeX file:

\usepackage{pgf}
\usepackage{import} %import images from different folder 

1. Finally, to include pgf version of these plots in the document, use:

\resizebox{0.75\textwidth}{!}{\import{./figures/}{field.pgf}}

\resizebox{0.75\textwidth}{!}{\import{./figures/}{flow.pgf}}

You can also use figure or center environment as per your needs.

1. We will get the following plots with proper font and resolution:

Alternatively, you can insert the pdf file by following this guide.

Diagrams

PGF/TikZ

Manually

Apart from all these tools, one can directly use TikZ package to manually draw things like flowcharts. Read the documentation for details. For example, we can add the following to the preamble:

\usepackage{tikz}
\usetikzlibrary{shapes,arrows, chains, matrix, calc, trees, positioning, fit}
\usetikzlibrary{external}
\tikzexternalize[prefix=./figures/] %images will be stored in a folder under the working directory

Then we can draw function mapping:

\begin{tikzpicture}[line width=1pt,>=latex]
			\node (a1) {$\mathbb{Q}_p(\sqrt{u}) \ \bullet$};
			\node[below=of a1] (a2) {$\mathbb{Q}_p(\sqrt{-p})\ \bullet$} ;
			\node[below=of a2] (a3) {$\mathbb{Q}_p(\sqrt{-p\cdot u})\ \bullet$};

			\node[right=4cm of a1] (b1) {$ \bullet \ \mu_p$};
			\node[right=4cm of a2] (b2) {$ \bullet \ \lambda_p$};
			\node[right=4cm of a3] (b3) {$ \bullet \ \mu_p\lambda_p$};

			\node[shape=ellipse, draw, minimum size=3cm,fit={(a1) (a3)}] {};
			\node[shape=ellipse, draw, minimum size=3cm,fit={(b1) (b3)}] {};

			\node[below=1cm of a3] {$\mathcal{E}$};
			\node[below=1cm of b3] {$\mathcal{Q}$};

			\draw[->] (a1) -- (b1);
			\draw[->] (a2) -- (b2);
			\draw[->] (a3) -- (b3);
\end{tikzpicture}

and flowcharts

\begin{tikzpicture}[>=latex']
\node[left] at (0,0) (input) {$p$};
\node[block] at (4,0) (block) [text=white]{\textbf{Reciprocity Law}};
\node at (9,0) (output) {$\chi_\tau(\Frob_p)$};
\draw[very thick, ->] (input) -- (block);
\draw[very thick, ->] (block) -- (output);
\end{tikzpicture}

Using GeoGebra Classic

The easiest way to include simple diagrams is to use GeoGebra, since it gives us the option of exporting the Graphics View as PGF/TikZ code. Installing GeoGebra Classic 6 is a dependency hell (ex1 and ex2). Therefore, we will just use the online version: https://www.geogebra.org/classic For example, add the following to the preamble:

\usepackage{pgf,tikz}
\usetikzlibrary{arrows}%you can see what extra packages are needed by going through the exported tex file

Then draw the following diagram in GeoGebra

And add the following corresponding code in the tex file:

\begin{tikzpicture}[line cap=round,line join=round,>=triangle 45,x=2.1cm,y=2.1cm]
\clip(1.5,-0.5) rectangle (10,3);
\draw (2,0)-- (4.83,0);
\draw (2,0)-- (3.41,1.41);
\draw (3.41,1.41)-- (4.83,0);
\draw (2,0.91) node[anchor=north west] {\scriptsize{$\overline{CA} \, = \, 2$}};
\draw (4.15,0.92) node[anchor=north west] {\scriptsize{$\overline{CB} \, = \, 2$}};
\draw (3.18,0) node[anchor=north west] {\scriptsize{$\overline{AB} \, = \, 2.83$}};
\draw (6,0)-- (6,1);
\draw (6,1)-- (7,1);
\draw (7,1)-- (7,0);
\draw (7,0)-- (6,0);
\draw (5.35,0.66) node[anchor=north west] {\scriptsize{$\overline{DE} \, = \, 1$}};
\draw (6.25,1.25) node[anchor=north west] {\scriptsize{$\overline{EF} \, = \, 1$}};
\draw (7.04,0.66) node[anchor=north west] {\scriptsize{$\overline{FG} \, = \, 1$}};
\draw (6.34,0) node[anchor=north west] {\scriptsize{$\overline{GD} \, = \, 1$}};
\draw (4.5,1.5)-- (5.5,1.5);
\draw (5.5,1.5)-- (5.5,2.5);
\draw (5.5,2.5)-- (4.5,1.5);
\draw (4.86,1.52) node[anchor=north west] {\scriptsize{$\overline{HI} \, = \, 1$}};
\draw (5.54,2.19) node[anchor=north west] {\scriptsize{$\overline{IJ} \, = \, 1$}};
\draw (4.25,2.2) node[anchor=north west] {\scriptsize{$\overline{JH} \, = \, 1.41$}};
\draw (7.5,1.5)-- (8.5,1.5);
\draw (8.5,1.5)-- (9.5,2.5);
\draw (9.5,2.5)-- (8.5,2.5);
\draw (8.5,2.5)-- (7.5,1.5);
\draw (8.7,2.73) node[anchor=north west] {\scriptsize{$\overline{NM} \, = \, 1$}};
\draw (9,2.08) node[anchor=north west] {\scriptsize{$\overline{ML} \, = \, 1.41$}};
\draw (7.83,1.5) node[anchor=north west] {\scriptsize{$\overline{LK} \, = \, 1$}};
\draw (7.2,2.22) node[anchor=north west] {\scriptsize{$\overline{KN} \, = \, 1.41$}};
\draw (1.94,2.51)-- (2.94,1.51);
\draw (2.94,1.51)-- (3.94,2.51);
\draw (3.94,2.51)-- (1.94,2.51);
\draw (2.8,2.76) node[anchor=north west] {\scriptsize{$\overline{OQ} \, = \, 2$}};
\draw (3.3,2) node[anchor=north west] {\scriptsize{$\overline{QP} \, = \, 1.41$}};
\draw (1.75,2) node[anchor=north west] {\scriptsize{$\overline{PO} \, = \, 1.41$}};
\begin{scriptsize}
\fill [color=black] (2,0) circle (1.5pt);
\draw[color=black] (1.9,-0.08) node {$A$};
\fill [color=black] (4.83,0) circle (1.5pt);
\draw[color=black] (4.88,-0.08) node {$B$};
\fill [color=black] (3.41,1.41) circle (1.5pt);
\draw[color=black] (3.46,1.5) node {$C$};
\fill [color=black] (6,0) circle (1.5pt);
\draw[color=black] (6.05,-0.08) node {$D$};
\fill [color=black] (6,1) circle (1.5pt);
\draw[color=black] (6.05,1.09) node {$E$};
\fill [color=black] (7,1) circle (1.5pt);
\draw[color=black] (7.04,1.09) node {$F$};
\fill [color=black] (7,0) circle (1.5pt);
\draw[color=black] (7.05,-0.08) node {$G$};
\fill [color=black] (4.5,1.5) circle (1.5pt);
\draw[color=black] (4.4,1.4) node {$H$};
\fill [color=black] (5.5,1.5) circle (1.5pt);
\draw[color=black] (5.63,1.4) node {$I$};
\fill [color=black] (5.5,2.5) circle (1.5pt);
\draw[color=black] (5.53,2.6) node {$J$};
\fill [color=black] (7.5,1.5) circle (1.5pt);
\draw[color=black] (7.45,1.4) node {$K$};
\fill [color=black] (8.5,1.5) circle (1.5pt);
\draw[color=black] (8.65,1.4) node {$L$};
\fill [color=black] (9.5,2.5) circle (1.5pt);
\draw[color=black] (9.6,2.58) node {$M$};
\fill [color=black] (8.5,2.5) circle (1.5pt);
\draw[color=black] (8.45,2.58) node {$N$};
\fill [color=black] (1.99,2.51) circle (1.5pt);
\draw[color=black] (1.99,2.59) node {$O$};
\fill [color=black] (2.94,1.51) circle (1.5pt);
\draw[color=black] (2.99,1.45) node {$P$};
\fill [color=black] (3.94,2.51) circle (1.5pt);
\draw[color=black] (3.99,2.59) node {$Q$};
\fill [color=black] (2.94,2.51) circle (1.5pt);
\fill [color=black] (2.71,0.71) circle (1.5pt);
\fill [color=black] (4.12,0.71) circle (1.5pt);
\fill [color=black] (3.41,0) circle (1.5pt);
\end{scriptsize}
\end{tikzpicture}

Another example, where this approach makes the job easy is the following:

Just add this code generated by GeoGebra:

\begin{tikzpicture}[line cap=round,line join=round,>=triangle 45,x=0.75cm,y=0.75cm]
\clip(2.5,-5.5) rectangle (13.5,5.5);
\draw [shift={(8,0)},fill=black,fill opacity=0.1] (0,0) -- (0:1.2) arc (0:289.87:1.2) -- cycle;
\draw [shift={(8,0)},fill=black,fill opacity=0.1] (0,0) -- (0:0.7) arc (0:197.97:0.7) -- cycle;
\draw(8,0) circle (3.75cm);
\draw(6,0) circle (1.95cm);
\draw (8,0)-- (3.24,-1.54);
\draw (3.24,-1.54)-- (9.7,-4.7);
\draw (9.7,-4.7)-- (8,0);
\draw [dash pattern=on 3pt off 3pt] (6,0)-- (4.93,-2.37);
\draw [dash pattern=on 3pt off 3pt] (6,0)-- (13,0);
\draw [shift={(8,0)},->] (0:1.2) arc (0:289.87:1.2);
\draw [shift={(8,0)},->] (0:0.7) arc (0:197.97:0.7);
\begin{scriptsize}
\fill [color=black] (8,0) circle (1.5pt);
\draw[color=black] (7.8,-0.2) node {$O$};
\fill [color=black] (13,0) circle (1.5pt);
\draw[color=black] (13.18,-0.12) node {$B$};
\fill [color=black] (6,0) circle (1.5pt);
\draw[color=black] (5.98,0.25) node {$O'$};
\fill [color=black] (8.6,-0.08) circle (1.5pt);
\draw[color=black] (8.74,-0.22) node {$D$};
\fill [color=black] (3.24,-1.54) circle (1.5pt);
\draw[color=black] (2.94,-1.4) node {$E'$};
\fill [color=black] (9.7,-4.7) circle (1.5pt);
\draw[color=black] (9.84,-4.44) node {$E_1'$};
\fill [color=black] (4.93,-2.37) circle (1.5pt);
\draw[color=black] (4.82,-2.08) node {$G'$};
\draw[color=black] (7.5,0.8) node {$2\theta_1'$};
\draw[color=black] (8.1,0.4) node {$2\theta_0'$};
\end{scriptsize}
\end{tikzpicture}

tikz-cd

Manually

We can draw commutative diagrams using tikz-cd package. Read its documentation for details. Firstly you will have to add the following to the preamble:

\usepackage{tikz-cd}

%%homebrewcommands

\newcommand{\delbar}{\overline{\partial}}
\newcommand{\Om}{\Omega}
\newcommand{\mz}{\mathcal{Z}}

\DeclareMathOperator{\ceco}{\check{H}}

Then add the following code:

\[\begin{tikzcd}[column sep = 1.5em]
0\arrow{r} & \mz^{p,\ell}(M) \arrow[hookrightarrow]{r} & \Om^{p,\ell}(M) \arrow{r}{\delbar} & \mz^{p,\ell+1}(M) \arrow{r}{\Delta} & \ceco^1(M,\mz^{p,\ell}) \arrow{r} & 0 \arrow{r} & \ceco^1(M,\mz^{p,\ell+1}) \arrow{d}{\Delta}\\
& \cdots & 0\arrow{l} & \ceco^3(M,\mz^{p,\ell}) \arrow{l}& \ceco^2(M,\mz^{p,\ell+1})\arrow{l}[swap]{\Delta} & 0 \arrow{l} & \ceco^2(M,\mz^{p,\ell})\arrow{l}
\end{tikzcd}\]

to get

Using quiver app

The easiest way to include commutative diagrams is by using quiver app available online at https://q.uiver.app/ For example, add the following to the preamble:

\usepackage{tikz-cd}

Then draw the following diagram using quiver app

And add the corresponding exported code in the tex file:

\[\begin{tikzcd}
	&& {Z} \\
	\\
	&& {X\times_S Y} \\
	\\
	{X} &&&& {Y} \\
	\\
	&& {S}
	\arrow[from=1-3, to=5-1]
	\arrow[from=1-3, to=5-5]
	\arrow["{f}"', from=5-1, to=7-3]
	\arrow["{g}", from=5-5, to=7-3]
	\arrow[from=3-3, to=7-3]
	\arrow["{\exists !}", from=1-3, to=3-3, dashed]
	\arrow["{\pi_X}", from=3-3, to=5-1]
	\arrow["{\pi_Y}"', from=3-3, to=5-5]
\end{tikzcd}\]

Inkscape

The easiest way to include diagrams as vector graphics is by using Inkscape as follows:

1. Draw the desired diagram in Inkscape, and enclose mathematical symbols in $...$. If you don’t know how to use Inkscape then just go to Help > Tutorials > Inkscape: Basic and you will be ready to use.
2. Create a folder called “pictures” inside the folder containg the main tex file and save the diagram as svg so that you can edit it in the future if needed. Then also save PDF+LaTeX output to the same “pictures” folder: File > Save As... > Select PDF from the drop-down menu > Click Save > Choose the following options

You can also use command-line to achieve the same result:

inkscape mySVGinputFile.svg --export-area-drawing --batch-process --export-type=pdf --export-filename=output.pdf

1. Add the following code to the preamble of your main tex file (source1 and source2):

\usepackage{import} % it will enable us to access images without keeping them in the document's directory
\usepackage{calc} % enable usage of \svgscale
\usepackage{graphicx} % for inserting images
\usepackage{xcolor} % for adding colors
\usepackage{transparent} % enables usage of separate color stack for transparency

1. Now we can add “image.svg” in one of the following ways (source1 and source2):

\begin{figure}[h]
\centering
\resizebox{75mm}{!}{\import{./figures/}{image.pdf_tex}}
\caption{Your figure}
\label{figure:example}
\end{figure}


\begin{figure}[h]
 \centering
\def\svgwidth{0.75\columnwidth}                 %Using \def\svgwidth{desired width} instead of \resizebox will preserve the font size
\import{./figures/}{image.pdf_tex}
\caption{Your figure}
\label{figure:example}
\end{figure}


\begin{figure}[h]
\centering
\def\svgscale{0.75}
\import{./figures/}{image.pdf_tex}
\caption{Your figure}
\label{figure:example}
\end{figure}

You can also write scripts to make this process easier. The main advantage of Inkscape is that there’s hardly any command or action that is impossible to do from keyboard. Linux users may not get the expected results with the key combinations starting with Alt key if the Window Manager catches those key events before they reach the inkscape application. One solution would be to change the WM’s configuration accordingly.

Preparation

The plan is to use Vim as the text-editor and MuPDF as the pdf-viewer since both can be accessed solely via keyboard, while keeping all the desired features from other LaTex editor like “live pdf preview” and “compile using latexmk” from GTK based Gummi and “forward and backward search to switch between the sources and the PDF” and “detailed compilation errors” from Qt based TexMaker.

We will need the following packages to begin with:

If you want GUI version of Vim then can get gVim by installing the package vim-X11. For gVim you will have to modify these steps accordingly.

Vim configuration

Once you finish learning basics using vimtutor, you are ready to start configuring Vim as per your requirements.

.vimrc file creation

To start Vim with all the favorite option settings and mappings, one writes them in what is called the vimrc file. The vimrc file can contain all the commands that you type after a colon. Vim executes the commands in this file when it starts up. Read the documentation for more details. Note that Vim 8.0 onwards, if Vim is started normally and no user vimrc file is found, the defaults.vim script is loaded. This will set ‘compatible’ off, switch on syntax highlighting and a few more things. See this reddit post for a discussion about this. To disable loading of defaults.vim completely add let skip_defaults_vim=1 to /etc/vimrc (see this).

Since vimrc is something personal that evolves over times as per one’s usage requirements, it’s not recommended to blindly copy it from the internet. I used this example as reference for creating the following ~/.vimrc

set nocompatible               " get rid of Vi compatibility mode. 
filetype plugin indent on      " filetype detection[ON] plugin[ON] auto-indent[ON] depending on filetype
set t_Co=256                   " enable 256-color mode.
syntax enable                  " enable syntax highlighting (can also use syntax on).
colorscheme morning            " I am using it with solarized (dark) color pallet in xfce4-terminal.
set hidden                     " allows you to re-use the same window without saving it first and keep an undo history for all the files using the same window.
set number                     " show line numbers to the left
set ruler                      " Always show cursor position.
set laststatus=2               " always display the status line so that you can see the current mode, file name, file status, ruler, etc. 
filetype indent on             " activates indenting for files
set hlsearch                   " highlight searched phrases.
set ignorecase                 " Make searches case-insensitive.
set smartcase                  " Make search case-sesitive when using capital letters
set autoindent                 " When opening a new line and no filetype-specific indenting is enabled, keep " the same indent as the line you're currently on.
set backspace=indent,eol,start " Allow backspacing over autoindent, line breaks and start of insert action
set tabstop=8                  " sets tab stops to 8 characters wide
set softtabstop=4              " makes the Tab key intent by 4 spaces
set shiftwidth=4               " width of autointents set to 4 spaces
set expandtab                  " converts tabs to white space
set mouse=a                    " Enable use of the mouse for all modes
set wrap linebreak nolist      " Soft wrapping text. To move the cursor up and down within wrapped line use the commands gk and gj.

You can use this guide to create a backup of your vimrc file using GitHub so that you can easily configure Vim on any other computer (how to find git folder). You can follow the official guide to set-up GitHub for this purpose.

vimtex plugin installation and configuration

You can install vimtex manually or using a plugin manager (see this guide). We will use the vim-plug plugin manager to install vimtex. Firstly, we will download plug.vim and put it in the ~/.vim/autoload directory using following code:

curl -fLo ~/.vim/autoload/plug.vim --create-dirs \
    https://raw.githubusercontent.com/junegunn/vim-plug/master/plug.vim

Next we will enable vimtex by adding the following section to the ~/.vimrc file:

call plug#begin('~/.vim/plugged')  " Specify the directory ~/.vim/plugged for plugins. Avoid using standard Vim directory names like ~/.vim/plugin
Plug 'lervag/vimtex'               " Shorthand notation for fetching the vimtex plugin from https://github.com/lervag/vimtex
call plug#end()                    " To update &runtimepath and initialize plugin system

Once the vimrc is properly configured, restart Vim or reload the vimrc file (make sure that git is installed for this to work). Finally, run the :PlugInstall command to start the installation of vimtex plugin. Vim-plug will download all the packages directly from GitHub and put them into the ~/.vim/plugged directory and load them whenever Vim is loaded. To update plugins use :PlugUpdate command and to remove them use :PlugClean command. Also, to update vim-plug itself, use :PlugUpgrade command.

Now we will set it up following the official documentation of vimtex, and adding the following to ~/.vimrc:

let g:tex_flavor = 'latex'           " Vim ships with some support for plain TeX, ConTeXt, and LaTeX files. This means that the `.tex` extension is ambiguous. Vimtex is only activated for LaTeX files with 'filetype' set to `tex`.
let g:vimtex_view_method = 'mupdf'   "  Set the pdf viewer. MuPDF supports forward and backward search via xdotool. For backward search use :VimtexRSearch command. Forward search will only take you to the correct page.  Backward search will take you to the line in Vim that corresponds to the first line of the current page in MuPDF.
let g:vimtex_compiler_latexmk= {'options' : ['-pdf', '-shell-escape', '-verbose', '-file-line-error', '-synctex=1', '-interaction=nonstopmode',],} " we need to enable -shell-escape to be able to use externalization library for avioiding recompiling unchanged diagrams/graphs created using tikz/pgfplots

Note that by default the following desired options are already there:

• latexmk is the compiler which does compilation as soon as you save the file (continous compilation, better than live preview)
• auto-completion is enabled,
• BibTex is used for bib files,
• fold types are enabled,
• intentation in both tex and bib are enabled,
• vimtex will open the pdf viewer automatically after compilation
• forward search is enabled, i.e. it will perform a forward search to the current cursor position when the first invocation of the pdf viewer happens. It uses SyncTex and requires xdotool to work with MuPDF (also prevents opening multiple instances of pdf).

You can further customize by adding snippets as demonstrated in various blog posts (ex1, ex2, ex3 and ex4).

Usage instructions

Following are the useful key mappings for the various vimtex commands:

We have many other shorthand keymaps like:

Note that vimtex supports most multi-file documents. The main method uses a recursive search algorithm that should find the main LaTeX file in most cases. Read the documentation for more details.

Update (Aug 30, 2023): I have moved to Windows 11 with WSL. We have Microsoft Windows supporters like SUSE (openSUSE), Ubuntu (Debian Sid), and RedHat/Oracle Linux (Fedora) for WSL, Azure,… and competitors like Apple macOS (UNIX) and Google chromeOS (ChromiumOS).

Open-source software is better

Open-source softwares are great because they have scope for technical superiority by allowing transparency. In fact, this is good enough incentive for many big corporations like Intel (server processors), IBM (Red Hat Enterprise Linux), Microsoft (Azure), Google (Chrome), Novell (SUSE Linux), etc. and smaller companies like Canonical (Ubuntu), etc. to sponsor Linux Foundation and other commmunity-driven Linux projects like GNOME (with major contributions coming from Red Hat), KDE (with major contributions coming from SUSE), and Debian (with major contributions coming from Canonical). However, there are still some popular Linux related projects like Arch Linux, Gentoo, Cinnamon DE and Xfce that are being developed by the community at a steady pace without any corporate funding. Though these community-only projects are really powerful and allow the user to create a custom workflow, they tend to attract only the ones with considerable knowledge of Linux and a desire to contribute.

For normal consumer products like desktops and laptops, Microsoft Windows has the monopoly because it comes pre-installed for free and is supported by all softwares (games) and the latest hardware. However, in the enterprise world where mainframe computers and servers need to be really secure, Linux distributions like Ubuntu, RHEL, CentOS, SUSE, and Debian tend to be more popular. Among these, Debian is the only one which is not owned by any specific company, but companies can directly fund the long-term-support. Ubuntu, which derives its source from Debian Sid, is quite popular among tech start-ups because of its freemium kind of business model where anyone can download it for free and one only needs to pay for extended service (similar to the extreme popularity of the free-to-play games like Fortnite and PUBG). In fact, it was marketed so well that it is the most popular Linux distribution among people who just wants a better OS than Windows but can’t afford to be a part of the Mac ecosystem.

Ubuntu’s major contribution has been the LightDM display manager. However, neither Ubuntu nor Debian is the market leader because they lack fast-paced innovation. RHEL has been the market leader for enterprise linux for a long time, mainly because it has invested a lot in innovation. Following is a rough representation of how it works in present:

Update: CentOS development was stopped on Dec 08, 2020 after being bought by IBM. However, the development of Rocky Linux has started.

The second most popular enterprise Linux distro is SUSE, it is the oldest commercial Linux distro. In recent years, it has also reorganized itself by starting community driven openSUSE project similar to the successful Fedora project to speed up innovation:

This new Tumbleweed was a result of the ‘merger’ of Old Tumbleweed and Factory in November 2014. Recently, AMD to complement its great technological advancements have started making significant contributions to the Linux kernel. In fact, it is also one of the primary sponsors of openSUSE project. In my opinion, openSUSE Tumbleweed is a good comeptitor for Fedora since it strives to provide access to latest packages using rolling release instead of short lived point release. On the other hand, openSUSE Leap is a good competitor for Ubuntu LTS since it gives an option for upgrading to much superior SUSE enterprise.

I especially like the open-source softwares like these, which let individual users access them for free while charging big corporations for techincal support. Some other examples are, Anaconda by Travis Oliphant (it also helps fund development of NumPy etc. via NumFOCUS) and MySQL by Oracle Corp.

Mix and Match

Now a days there are many emerging comeptitors like Manjaro and Solus competing with Ubuntu and its forks for the non-technical users. I was introduced to linux as a non-techincal user in 2006 when I ran Ubuntu in a virtual box on my Windows XP desktop PC, thanks to the free CD I got with the PC World magazine I had bought during summer vacations. I have been using Ubuntu-based distros (I replaced Windows 7 with Lubuntu on my Netbook) since Windows XP died in 2014, and it has been a nice journey. Whenever I ran into some trouble, I just copy-pasted codes from some blog/forum and ignored issues as long as work got done. For example, I chose not to use WiFi over using Windows 8 when Realtek drivers were breaking on Ubuntu (had no idea it has to do something with Linux Kernel). But now since I have built my own PC for the first time, I have a much better knowledge of the hardware and find it difficult to just shrug shoulders as long as system boots. Theorefore, Ubuntu can no more fulfill my needs and I will have to move to a little less stable distro.

The main use of my new PC is to write documents in LaTeX, hence I would really like to have easy access to the latest version of texlive and text-editor (like Vim, though you will always get some version of vim-minimal pre-installed). However, stable distros like Ubuntu LTS and openSUSE Leap tend to have outdated repositories of both of these and Ubuntu tries to mitigate this with untrusted PPAs, unstable Snaps and useless Flatpaks. Moreover, compiling them from sources can be a bit tricky (eg: installing TexLive and Vim). Hence I felt the need to migrate to a distro which can give easy access to latest version of these programs. But I don’t have enough time and knowledge to be able to maintain the stability and security of rolling-release distros like Arch, openSUSE TW and Gentoo. Therefore, since I don’t need any proprietary drivers for my PC, I decided to take a middle ground and move to the pseudo-rolling/stable-release distro Fedora (13 month life cycle, new release every 6 months) which is the upstream source of the commercial Red Hat Enterprise Linux distribution. Another reason for choosing Fedora was that its community is more knowledgebable (RedHat is one of the biggest contributer to Linux kernel) and the bugs acutally get resolved (for Ubuntu there can exist an year old bugs like the initramfs bug with temporary solution in forums). One bug that has followed me in Ubuntu and Linux Mint is the momentary blackout of screen when some pop-up menu opens in applications like Google Chrome and TexMaker Settings, however I have no hope of it getting solved since there is this similar three years old bug report in the forums.

For the desktop environment I decided to go with Xfce because most of my applications use GTK (hence not KDE or LXQt), didn’t want to waste RAM for customizability (hence not GNOME 3 or MATE which are resource heavy but still lack simple in-built customization options like desktop wallpaper slideshow, requires separate pacakges like GNOME Tweaks and GNOME Extensions) and needed stability (hence not Cinnamon which lacks proper documentation and bug resolving mechanism, eg: this an year old zombie-windows bug which requires restarting cinnamon to troubleshoot, moreover most appearance tweaks depend on themes and applets created by volunteers which are not guaranteed to be actively maintained). Cinnamon is an attempt to mimic Xfce while staying close to GNOME, however its lack of documentation ability to tweak easily is a big negative. One thing I miss in Xfce is the absence of dock (using Plank is fissible but not ideal). However, it can easily be mitigated by setting up keyboard shortcuts for the frequently used applications.

I installed Fedora Xfce using Server Netinstall instead of the official Spins since they tend to be bloated and will have to install lots of updates afterwards. Fedora comes with Ubuntu’s LightDM display manager which manages the login screen, in the case of Xfce Fedora uses the Xubuntu’s LightDM GTK+ Greeter.

Update (June 22, 2021): My university changed their wired internet connection protocol and now it requires unsername and password. Hence can’t use this Netinstall method anymore. Back to using the livecd image.

Differences between Ubuntu and Fedora

Most of my Linux experience is based on Ubuntu. Following are some differences that I experienced:

Administrator vs. User

Users have the option of setting a root password in when installing a non-GNOME Fedora, but it is not required if the user creates an initial user account and selects the option to add it to the wheel group. If root password is set, then the root account is the account for the system admin. This account is disabled in Ubuntu. In Ubuntu, one performs actions that require root privileges using sudo, while in a Fedora spin, sudo is not the default method of gaining administrative permissions. Therefore, in Fedora Xfce spin with root password, root access can only be gained with su. su will ask for the root password, not the regular user password. After logging in successfully as root, one has administrative rights until terminal is closed or logged out with exit. However, for GNOME Fedora, it’s just like Ubuntu i,e. no root password set by default and user account is handled by gnome-initial-setup. Having a root password is not useful for nontechnical users.

Package management

Fedora uses different tools for package management to Debian. Here is a quick overview of how to accomplish common tasks in Fedora: (source)

In older versions, apt-get in Ubuntu corresponded to yum in Fedora. To know if a reboot is needed after doing a dnf update use either tracer or needs-restarting plugin. Unlike Debian/ubuntu, I don’t need to remeber to use autoremove after removing some package.

Moreover, like in Ubuntu we use dpkg for installing .deb files, we can use rpm in Fedora for installing .rpm files. Following is a comparison of commands:

You can also use dnf instead of rpm, just like we can use apt instead of dpkg. You can find an outdate but more extensive list in Ubuntu Wiki.

Finding packages using GUI

Fedora’s equivalent to Debian’s Synaptic package manager is dnfdragora which uses the widget abstraction library written by SUSE. Unfortuately it’s nowhere as good as Synaptic. Moreover it is extremely RAM hungry. However, in GNOME edition of Fedora there is GNOME Software Centre which makes things smoother, but requires PC reboot for installing updates. In the RPM world opeSUSE has YaST as a worthy competitor of Synaptic (but that feels too nosey, it is much more than just a package manager).

Installing packages not in repository

The equivalent of the Ubuntu restricted and multiverse repositories, that include patented and closed-source technologies and programs, is the RPMFusion repository. free is the equivalent of universe and contains potentially patent-encumbered software like gstreamer-plugins-bad or the VLC media player, while nonfree includes non-free software like proprietary 3D graphics drivers.

These repositories can easily be enabled by typing (as root):

dnf install https://download1.rpmfusion.org/free/fedora/rpmfusion-free-release-$(rpm -E %fedora).noarch.rpm
dnf install https://download1.rpmfusion.org/nonfree/fedora/rpmfusion-nonfree-release-$(rpm -E %fedora).noarch.rpm

Moreover, the equivalent of the PPAs in Ubuntu is Copr. This repository can be added with

dnf copr enable user/project.

Note that just like Ubuntu PPA and Arch AUR, there is no way to verify that a package in Copr does not contain anything malicious unless you review the source code.

Linux Security Modules

Ubuntu uses AppArmor (which was earlier developed by SUSE), whereas Fedora uses SELinux. AppAromor is said to be easier to maintain than SELinux.

Installing Fedora

Firstly download and verify the iso file. Then make a bootable pendrive using the Qt app Fedora Media Writer, unfortunately it requires KDE so will install that also. I decided to use ext4 file system, which is the current default file system for Workstation and Spins, instead of the dfault file system xfs for Server/Netinstall (there are benchmarks claiming either xfs is better or ext4 is better). I followed Fedora’s recommended partitioning scheme and created the following GUID partition table:

Note that modern Linux OS don’t require separate partitions for both /boot and /boot/efi (EFI System Partition) directories. The only requirement for suing GRUB2 boot loader is that /boot directory must be on a plain ext4 or xfs partition and /boot/efi directory must be on a plain vfat partition. If one wants to install Fedora with only two paritions / and /boot then it is recommended to use systemd-boot boot loader instead. However, since we were following Fedora’s recommended partitoning scheme we created separate /boot and /home paritions with standard ext4 format instead of leaving them with /. Also, I alloted thrice the recommended size for 20 GB for / because I plan to use Timeshift which saves snapshots in root directory itself and works only with GRUB2 (very important tool, was fixed later).

Select Xfce Fedora without any extra software programs, we will manually install the ones we want. To bypass creating root password in netinstall mode, just create a user account and mark it as administrator. After installing, the first think we will do is set-up drop-down terminal following this guide. Also consider changing first day of week to Monday by following this guide.

Free and open source softwares

Vim, PulseAudio Volume Control and dnfdragora are already installed.

Note that Firefox also lets you use streaming services like Netflix which require h264/mp3/aac and widevine. Also, you can remove “Pocket” from Firefox following these steps.

Unfortunately, Signal doesn’t have an official Fedora repo, however it can be installed using Copr.

To find more softwares, use: dnfdragora > Groups > Xfce desktop option.

Finally, if you need Windows to access applications like OneNote instead of Xournal++ then you can install it by running Win 10 virtual machine, by using virtIO drivers along with virtualization, that is choose i440FX chipset, UEFI without secure boot, QXL video and virtio for Virtual Disk and Virtual Network Interface (make sure to update all the missing Windows drivers using the virtIO iso file). Alternatively, dual-boot Fedora with Windows following this guide and remember to disable HDCP support overrride in Display settings of AMD Radeon driver if not using HDMI port.

Restricted softwares

Note that Google Chrome poorly integrates with the Linux. For example, if you change the default DPI of 96 or font scaling for the display then Google Chrome text and images get blurred and you have to fix it yourself (possible solution 1 and solution 2).

/usr/bin/google-chrome-stable --force-device-scale-factor=1 %U

It also poorly integrates with Xfce since it attempts to creat its own default keyring for password encryption, so either you will have to create another password or disable it.

DNF plugins

We will install the following two plugins:

Xfce panel plugins appearance

Few panel plugins like Datetime, Places, PulseAudio and ScreenShooter are already installed.

Note that the weather plugin has known bugs, like using inaccurate data from Meteorologisk institutt instead of actual data from OpenWeatherMap and co-ordinating day/night icon with UTC instead of local time. None of these bugs are there in Cinnamon’s weather plugin.

Appearance: Themes and Wallpapers

We will install the following themes and wallpapers:

To apply this theme select “Numix” in

• Settings Manager > Window Manager > Style
• Settings Manager > Appearance > Style
• Settings Manager > Appearance > Icons
• Settings Manager > LightDM GTK+ Greeter settings > Appearance

Note that the default appearance editor can only edit GTK2 themes/icons. Therefore, to edit GTK3 themes/icons either edit the ~/.config/gtk-3.0/settings.ini or use the LXDE appearance editor lxappearance. You might also have to make changes in Settings Manager > Windows Manager Tweaks > Accessibility.

Finally, to change background use “Settings Manager > Desktop > Background” and select the folder /usr/share/backgrounds/f32/extras/.

Introspection

The plan is to upgrade to next version of Fedora three months after its release so that maximum bugs can be avoided (eg: initial release of Fedora 32 had a bug which has been corrected later using system updates). Hence I will get a system wide update twice a year. Fedora is going to change to btrfs as default filesystem in the next release of Fedora 33 (something default in SUSE but abandoned by Red Hat). One annoying thing is that I have to install lots of updates everyday since Fedora pushes bug fixes as soon as they are found, irrespective of how important they are. Moreover, the supported releases are updated to the latest stable version of the Linux kernel, increasing the chances of unstability.

Though Xfce is highly customizable and has a great documentation, it lacks GUI for basic things like system info viewer, individual CPU core usage, user login picture manager (though Fedora has Whisker menu plugin, it lacks the required Mugshot package) and tablet pen-pressure settings (which can also be done in GNOME 3, Cinnamon and KDE). However, these can easily be done using manually via Terminal:

• For system info we have CLI tools like inxi (doc), neofetch and lshw.

• To view system usage information we can use tool like top in terminal, and get individual core usage by top 1 (doc).

• We can manually edit the profile picture configuration

$ sudo mkdir /var/lib/AccountsService/icons/<your_user_name>
$ sudo cp ~/home/<my_picture_of_size_96x96>.png /var/lib/AccountsService/icons/<your_user_name>

$ sudo mousepad /var/lib/AccountsService/users/<your_user_name>

Add the line: Icon=/var/lib/AccountsService/icons/<your_user_name>/<my_picture_of_size_96x96>.png.

• For Wacom tablet pen-pressure on X Window System we can use xsetwacom (doc)

xsetwacom set "Wacom One by Wacom S Pen stylus" PressureCurve 0 50 50 100

However, any setting changed by xsetwacom will be reset to default (or a statically configured setting) whenever the device is unplugged, disabled or the X Server is restarted. One can make Linux run the command automatically when hot-plugging the device by entering the above command to Settings Manager > Removable Drives and Media > Input Devices > Automatically run this command when a tablet is connected. Note that, these CLI methods won’t work when using Wayland instead of Xorg. I could’t make CLI work in Cinnamon, only GUI settings worked and provided the following options:

  0  75   25  100  # very soft
  0  50   50  100  # soft
  0  25   75  100  # little soft
  0   0  100  100  # default
 25   0  100   75  # little firm
 50 100  100   50  # firm
 75   0  100   25  # very firm

Though main advantage of Fedora is that it is much more customizable. However, the following three errors were still logged:

1. AMD-Vi: Most likely this is a false alarm from the Linux kernel. However, turning off IOMMU in BIOS is not an option (which somehow is suggested in forums) since it is needed for HSA used by AMD for making GPU and CPU work together in its APUs. If I end up with black-screen during boot then I will consider updating AGESA drivers in the BIOS.

2. Watchdog: Another AMD Ryzen related bug in Linux Kernel. We can just silence it. If I end up with black-screen during boot then I will consider updating AGESA drivers in the BIOS.

3. GNOME key-ring: Issue originating from GNOME which have crept into LightDM.

Epilogue

After one year of using Fedora 32 and 33 with Xfce 4.14, in June 2021, I moved to OpenSUSE Leap 15.3 with KDE 5.18 instead of Fedora 34 with Xfce/GNOME. It was mainly because of the issues with Xfce 4.16 (unable to control power settings for idle time) and Linux kernel 5.12 (messing with swap partition, hanging since not freeing the RAM). I was also annoyed by the large number of updates I received everyday on Fedora (but stuck with TexLive 2017, which was always up-to-date in Fedora). However, I do miss the package information system and documentation of Fedora. Other than that, OpenSUSE and KDE have worked great out of the box (DON’T ENCRYPT THE HARD DRIVE, disable secureboot and disable NVRAM). I had to install OpenSUSE in virtual machine first, in order to make the installation USB using SUSE Studio Image Writer (moreover, change in college internet connection policy made it impossible to use netinstall). Another option would be to use Ventoy.

After installing, I used windows to reformat the USB stick to exFAT format. Then to access USB stick in openSUSE, install fuse-exfat package.

If Konsole starts in super user mode, then go to Settings > Manage Profiles > Edit profile > General it is important that in ‘Command’ it does not say su- but /bin/bash.

Disable automatic screen locking: System Settings > Workspace behavior > screen locking

Adjust screen off time: System Settings > Power management > energy saving

Disable the auto-updater PackageKit since it can interfere with the manual software installation: Configure System Tray > Software Updates > Disabled.

Replace Firefox’s Extended Support Release (ESR) with the latest version from the Mozilla repository using YaST or terminal:

> sudo zypper ar -f http://download.opensuse.org/repositories/mozilla/openSUSE_Leap_15.3/ mozilla
> sudo zypper ref
> zypper up --from mozilla

Unfortunately, the fonts don’t render properly sometimes due to KDE integration limitations. Also install Plasma integration add-on. Then, to watch Netflix, also install the KDE multimedia codecs from Packman using 1-click. Somehow, vlc-lang package didn’t swtich the repository so had to do it manually.

> sudo zypper up --allow-vendor-change
Loading repository data...
Reading installed packages...

The following package is going to be upgraded:
  vlc-lang

The following package is going to change vendor:
  vlc-lang  openSUSE -> http://packman.links2linux.de

Also, had to build SageMath from the source, took 4 hours (for reference: 6000+ packages of texlive-scheme-full take 1 hour to download and install)

> sudo zypper install gcc gcc-c++ make m4 binutils perl tar python3 dvipng ffmpeg texlive-scheme-full

> ./configure
# we will skip installing the suggested packages, openSUSE Leap has a limted collection of packages.
# will rather build everything from source, hence the long build time.

> make
-----
[2021-07-14 22:12:09] SageMath version 9.3, Release Date: 2021-05-09
Yes, Sage starts.

real    225m36.799s
user    229m31.133s
sys     13m38.360s
Sage build/upgrade complete!
-----

> ./sage --testall

> sudo ln -s /path/to/sage-x.y/sage /usr/local/bin/sage

There is color-scheme bug. Ceate a file called 50-color.ipy in .sage/ipython-X.Y.Z/profile_default/startup with the following content:

%colors Linux

Also, KDE icon can be created using the folliwing command for launching in Applications tab:

konsole -T "sage" -e /path/to/sage-x.y/sage

Performance

Following is the comparison of my PC with the best laptop available in the market in May 2020 for USD 650 (before tax):

This will certainly an upgrade from the desktop computer I used a decade ago with Intel Pentium 4 CPU and 512MB RAM (no idea what graphics card was there in that machine). Moreover, though on paper Intel Core i7 4702MQ (my old Thinkpad) is not much worse than AMD Ryzen 3 3200G in terms of CPU performance, the AMD iGPU much better. For instance, with the best graphic settings of SuperTuxKart (for 60FPS/1080p required to have min AMD Radeon RX 460 with 1 GB VRAM), AMD gives about 30 fps on an average whereas Intel only gives 10 fps.

Cloud Backup Setup for Linux PC (tested in Linux Mint and Ubuntu)

I am using rclone to sync files between my PC and Google Drive. Following are the steps one can follow to set it up:

1. Create your own Google Drive OAuth2 client ID for rclone:

   a) Log into the Google API Console with your Google account. It doesn’t matter what Google account you use. (It need not be the same account as the Google Drive you want to access.

   b) Select a project or create a new project.

   c) Under “ENABLE APIS AND SERVICES” search for “Drive”, and enable the “Google Drive API”.

   d) Click “Oauth Consent Screen” in the left panel and select user type “External”. Then add Application name (anything you want) and save.

   e) Click “Credentials” in the left panel. Then click on “+ CREATE CREDENTIALS” button at the top of the screen, then select “OAuth client ID”. Select Application type as “Desktop app”, enter whaever client anme you want and click create.

   f) It will show you a client ID and client secret. Use these values in rclone config.

2. Install the latest version of rclone via Terminal: curl https://rclone.org/install.sh | sudo bash
3. Now configure rclone for Google Drive via Terminal: rclone config and follow the steps. Remember to use the Client ID and client secret we created above. Since we created this API for personal use, we won’t be submitting it for verfication. Hence don’t be alarmed by the very scary confirmation screen shown when we connect via your browser for rclone to be able to get its token-id. Also, if you want to fetch Google Docs as links (instead of converting them to .odt etc) from Google Drive, in “advance-config” set “export-formats” to “link.html”.
4. Sync files using “copy” and NOT “sync”: rclone copy source:path dest:path [flags]. For example, to sync all files from “New Folder” Google Drive (named: Drive) to PC (folder: home) and view the progress, type: rclone copy Drive:"New Folder" /home -P. Google Drive tend to have duplicate files since it allows same names files in same folder, in that case use dedupe to delete all duplicate files.

5. Set-up auto update for rclone program (can see the latest version here):

   a) Open the bash file using a text editor like gedit/xed/vim: ~/.bashrc

   b) Add the following code to the file and save it: rclone() { if [[ $@ == "-U" ]]; then command curl https://rclone.org/install.sh | sudo bash; else command rclone "$@"; fi; }

   c) To update to the latest version run this in the Terminal: rclone -U and enter the PC password.

In case you wish to remove rclone, run the following commands in terminal which will delete the files containing information about rclone:

sudo rm /usr/bin/rclone
sudo rm /usr/local/share/man/man1/rclone.1

Build Details

All the system part recommendations were from PC-Part-Picker forums and Build-a-PC subreddit hence were biased towards gaming performance.

I also bought IKEA Micke (Black-Brown) computer desk for kids (had to remove the bigger drawer to accomodate my legs) and IKEA Flintan+Nominell office chair (USD 80 + USD 100).

Introspection

The original plan was to use Ubuntu 20.04 GNOME as the OS since I wanted a stable system (hence not the rolling release distros like Arch/Manjaro, Solus and openSUSE TW) with Linux kernel greater than 4.20 for AMD Ryzen Picasso APUs (hence not Debian and CentOS) and large software repository (hence not enterprise focused distros like OpenSUSE Leap and Fedora). But Ubuntu turned out to be RAM hungry, since it required extra softwares like GNOME extensions and Variety for customization, and depended on the unstable Snap store. While trying to fix these issues I was able to brick my system thrice and hence decided to shift to Linux Mint 20 Cinnamon which provides out-of-the-box support for Flatpak(needed for Xournal++) and blocks Snap while providing better customizability and the same 5 year support (unlike official Ubuntu flavours which give only 3 years support). Though the appearance and RAM usage became much better with Linux Mint, it still inherited many boot errors like:

1. IOMMU: Most likely this is a false alarm from the Linux kernel. However, turning off IOMMU in BIOS is not an option (which somehow is suggested in forums) since it is needed for HSA used by AMD for making GPU and CPU work together in its APUs. If I end up with black-screen during boot then I will consider updating AGESA drivers in the BIOS.

2. Time Stamp Counter: Another Ryzen APU compatibility issue with Linux kernel.

3. Kwallet: KWallet is supposed to be with KDE and not Cinnamon/GNOME.

4. GNOME key-ring: Issue with GNOME.

5. Pulseaudio+BlueZ: due to unavailability of Bluetooth in my computer and presence of Pulseaudio and BlueZ 5.53 in Ubuntu 20.04.

6. initramfs: Boot speed improvements through changing the default kernel compression algorithm to lz4 (in Ubuntu 19.10) on most architectures, and changing the default initramfs compression algorithm to lz4 on all architectures. Somehow doesn’t work well for my PC. I switched to gzip compression to avoid this bug.

7. UVC driver/Alsa: I think that the audio driver of Webcam leading to error during boot.

Out of these 1 and 4 are logged consistently during each boot, 2 and 7 are logged some times, and the remaining could be fixed if they ever occur again. Since I am running LTS distro, I won’t have to worry much about losing compaibility of my hardware or learning about latest softwares. Though there are only non-fatal boot errors, since everything is working as intended, it might be best to just shrug sholders.

Also, if you are using NVMe SSD then consider installing the NVMe tool as discussed here (might lead to logging of boot errors). Once you install any linux OS I would recommend running following commands and checking is everything is running as expected:

inxi -Fxz #system information google to learn more about inxi

lscpu #can also see lspci, lshw

sudo nvme smart-log /dev/nvme0n1" #NVMe info

journalctl -b -p 3 #error log messages

dmesg -l emerg,alert,crit,err

Also, in case things get out of hand, to access GRUB Menu press right Shift if system boots using BIOS or press Esc if system boots using UEFI. Remeber that if you press Esc multiple times then you will enter GRUB command prompt instead.

The current AMD budget processors provide a much superior iGPU performance than their Intel counterparts. For example:

• We can compare the entry level quad-core desktop processors from last year: Intel Core i3-9100 (MSRP USD 120) has better CPU but worse iGPU than AMD Ryzen 3 3200g (MSRP USD 100) (benchmark).
• We can compare the pro level mobile processors from this year: Intel Core i7-10710U with 6-physical cores and hyperthreading, is not better than AMD Ryzen 7 4700U with 8-physical cores but no hyperthreading (comparison).

I decided not to spend extra USD 20 for i3-9100 since the ability of 3200g to allow light gaming would be more than enough for my daily usage. Moreover, since neither of them have hyperthereading/multithreading, I won’t expect much improvement in multitasking. However, Intel being more popular has better support for various hardware (for example, I couldn’t run my monitor via HDMI due to compatibility issue between the motherboard and monitor). Luckily, this time the Realtek ethernet drivers didn’t cause headache with Ubuntu.

We can’t deny the fact that, Intel Core i3 9100 would have been a better choice in terms of processing power. Even after the launch of 10th gen CPUs that build would have costed about USD 20 more since though the RAM will be really cheap as only 2400 MHz is supported by i3 (- USD 10), the CPU and motherboard (H310) will remain a little more expensive than the AMD counterparts (+ USD 30). however, by buying HP VH240a instead of Asus VA229HR, I could have saved USD 30, hence keeping the total cost of build USD 650 even with i3 9100. That said, I am happy with my AMD PC since it allows me to do some light gaming as a bonus (which was not the purpose of this PC). AMD build is clearly better than Intel if one plans to play even a single racing/shooting game with an option for overclocking by buying a better motherboard.

Fortunately, the university gives free unlimited high-speed WiFi which makes Chromebook a viable option. The best Chromebook available in terms of build quality was the USD 650 Google Pixel Go (m3-8100Y processor) but spending so much money on a chromebook was out of question since ChromeOS is a handicapped version of Linux with limited hardware and software support (just like I had to abandon my lovely Google/Asus Nexus 7 2nd gen tablet because Android stopped getting updates). So I searched for something with specs similar to Pixelbook Go but at lower price (i.e. lower build quality). While searching I stumbled upon Asus Chromebook C425 and bought it without putting much though since it fit my budget of USD 350-400.

Performance

Following is the comparison of tech specs of my new laptop (USD 375 + taxes in Jan 2020) with the older laptop (USD 916 + taxes in Oct 2014) :

I considered this as an upgrade since it offered better mobility and screen. Moreover, before getting the Thinkpad as a gift, I was using the netbook HP Mini 1103 (10.1-inch screen with a single-core 1.66-GHz Intel Atom N455 CPU and 1GB of RAM) with Windows 7 replaced with Lubuntu 14.04. I learned LaTeX on that small computer. Note that hyperthreading might be disabled by default, so you will have to enable it by going to chrome://flags/#scheduler-configuration and changing the option to “Enables Hyper-Threading on relevant CPUs”. You might need to repeat this process after each bi-weekly system update.

The thing which I don’t like about the Chromebook is that the browser uses majority of the available RAM irrespective of how many tabs are open or the total RAM the computer has. Also, one wrong browser extension can lead to random crashes. And the stupidest thing is the lack of local trash/recycle-bin folder just like Android, so deleted files can’t be recovered (i.e. make a Downloads folder on Google Drive instead of using the local drive folder).

LaTeX Setup in Chromebook

I will use the Qt based LaTeX editor TexMaker. Most other LaTeX editors don’t work because they are not allowed to save newly compiled files by replacing the existing ones. The Chrome browser is sufficient for opening other pdf files. I tried using Evince, but it used to crash a lot.

1. Turn on Linux (Beta) by following these steps.
2. Check that the sandbox (Penguin container/Crostini) is up-to-date. In your browser, go to chrome://components. Under cros-termina, select “Check for update”. If you download an update, you might need to restart your Chromebook.
3. Open Crostini and make sure that “cros.list” and “sources.list” have the following content (make sure it is “http” and not “https”, otherwise you can get HTTP proxy issues).

   $ cat /etc/apt/sources.list.d/cros.list
   deb http://storage.googleapis.com/cros-packages/83 buster main
   
   $ cat /etc/apt/sources.list
   # Generated by distrobuilder
   deb http://deb.debian.org/debian buster main
   deb http://deb.debian.org/debian-security buster/updates main

Here “buster” should correspond to the version of Debian installed in Crostini. If it’s not the same, then use the pre-installed version of Vim to edit. If you are not familiar with Vim, run the command vimtutor first and also have a look at this brief intro.

1. Update the packages: sudo apt update && sudo apt dist-upgrade (there won’t be any password prompts).
2. Install the basic version of TeX Live: sudo apt install texlive
3. Install TexMaker: sudo apt install texmaker. Note that the screen resolution might be messed up due to different in system and crostini resolution, however it can be fixed.
4. Right click on the folder where you want to create the tex files and choose “Share with Linux” and “Available offline”. The folder can also be accessed via cd /mnt/chromeos/GoogleDrive/MyDrive/"PathOfSharedFolderInYourGoogleDrive".

You might get gibberish text when using Linux, in that case you will have to disable GPU-acceleration for the sandbox, this can be done by going to chrome://flags/#crostini-gpu-support and changing the option to “disabled”.

Though ChromeOS gives you an option of making a backup of Chrostini, I would recommend removing Linux before system restart for the version updates (not needed for smaller updates) and then reinstall everything. Many times Linux breaks after system updates and new features are introduced in each version.

The pdfLatex process in this Chromebook can be as slow as in the old netbook (HP Mini 1103) since the Debian runs in a virtual machine and might get limited access to resources due to sandbox restrictions. In particular, hyperthreading for Crostini sometimes get disabled after ChromeOS update, i.e. only 2 cores instead of 4 are available (discussion thread). Therefore, in Crostini the Intel Core m3-8100Y might sometimes perform like Intel Atom N455. However, the most frustrating thing is when the virtual machine starts utilising 200% or more of the CPU (i.e. approximately 100% of more than one of the available cores) even after you have closed it, in which case you will have to go to Task Manager (Search + Esc) and end it there (discussion thread). Best way to deal with these issues is to report bugs and keep system updated.

Build Quality

From what I had read about Chromebook’s lack of basic capabilities (can’t run most softwares, can’t format flash drive to desired format, don’t have SSD, and no compatible with many hardwares like drawing tablet), for USD 400 I expected the build quality of a USD 800 windows laptop. However, just like the Linux capabilities, the build quality was also disappointing.

Introspection

For Linux access, Crostini runs Debian stable which tends to have outdated packages. However, one can easily get the latest version of software by adding Debian Testing to the source list /etc/apt/sources.list using Vim:

deb http://deb.debian.org/debian testing main

Also mark stable release as default by using the following command in terminal:

echo 'APT::Default-Release "stable";' | sudo tee -a /etc/apt/apt.conf.d/00local`

Then one can install the latest package like texlive using

sudo apt -t testing install texlive 

Somethings that I overlooked because of the Intel branding is that m3 uses DDR3 RAM, whereas even the modern Intel Pentium, Intel Celeron and AMD A4 use DDR4. Moreover, though getting rid of fan makes the system lighter and quiter, it also bottlenecks the capabilities of the processor. One problem with buying Chromebooks (or other computer poarts) is that their price fluctuates a lot, hence if it wasn’t an emergency I would have waited for better price on alternatives. If mobility was not a concern, then 15” windows laptops with Core i3 or Ryzen 3 dual core processors and SSD, like Acer Aspire 5, Asus VivoBook 15, Dell Inspiron and Lenovo Ideapad were good options. If I knew that we will be teaching for home then Apple iPad Mini would have been a better option.

I will end by quoting the reviews I read before buying this chromebook and ignored the warnings:

I’m not a plastic hater, but there are price brackets I equate to plastics being used, and at MSRP USD 499, I don’t expect a mostly-plastic build. While there isn’t a ton of flex and wobbliness with this chassis, there’s no getting around the way plastic feels under your palms as you actually use a Chromebook. —- Chrome Unboxed

Personally, I don’t mind a plastic bottom. In fact, there are advantages to having a plastic bottom, as plastic is lighter and less heat-conductive than metal. However, a plastic main-deck might be enough of a reason to pay extra for the C434. I mean, the plastic on the C425 is not the poor-quality we’ve used to see on entry-level laptops in the past, but it’s still plastic nonetheless, and doesn’t feel as nice or as sturdy as metal….. That being said, I think there’s better value in the USD 550 Chromebook C434 than in this USD 399 ChromeBook C425, even with less RAM. And if you’re on a tight budget, perhaps consider that ChromeBook C302 first, see if you can live with a smaller screen, but without compromising on the build and the screen. The C425 comes as a third option, if those other two failed to meet your mark due to their higher price or smaller display. —- UltrabookReview.com

The C425’s plastic body has more flex and suffers from a duller-looking, non-touch screen, but the keyboard and trackpad are responsive, the screen is fine for documents and spreadsheets, and it has enough battery life to last a full day of work or classes. —- NY Times- Wirecutter

Find the area of that part of the surface of the cylinder $x^2+y^2=a^2$ which is cut out by the cylinder $x^2+z^2=a^2$.

Here we need to find the surface area $S$ of the part of cylinder $C_1: x^2+y^2=a^2$ which lies inside the cylinder $C_2: x^2+z^2=a^2$. That is, the surface $S$ is bounded by the curve $\Gamma$ traced at the intersection of the two curves.

The projection of $\Gamma$ in the $xz$-plane gvies us the domain $D: \{x^2+z^2\leq a^2\}$. Next we consider the part of desired surface in the first octant, and use the following surface area formula:

$ \displaystyle{\frac{1}{8}S = \iint_{D'} \sqrt{1+\left(\frac{\partial f}{\partial x}\right)^2 + \left(\frac{\partial f}{\partial z}\right)^2}dz dx}$

where $f(x,z)= y = \sqrt{a^2-x^2}$ and $D’ = \{(x,z)\in D : x,z\geq 0\} $. Therefore, we have

$\displaystyle{\frac{1}{8}S = \int_{0}^a \int_{0}^{\sqrt{a^2-x^2}}\sqrt{1+ \left(-\frac{x}{\sqrt{a^2-x^2}}\right)^2 + \left(0\right)^2}dz dx }$

$\displaystyle{= \int_{0}^a \int_{0}^{\sqrt{a^2-x^2}}\frac{a}{\sqrt{a^2-x^2}}dz dx = a \int_0^a \left[\frac{z}{\sqrt{a^2-x^2}}\right]_0^{\sqrt{a^2-x^2}}dx}$

$\displaystyle{= a\int_0^1 dx = a^2}$

(luckily we don’t need change of variables!)

Hence, $\boxed{S = 8a^2}$. I found this problem to be visually challenging, though the surface area and volume follow directly from the general formulas.