It also has serious applications obviously. www.sympy.org/scipy-2017-codegen-tutorial/ mentions code generation capabilities, which sounds super cool!
Let's start with some basics. fractions:outputs:Note that this is an exact value, it does not get converted to floating-point numbers where precision could be lost!
from sympy import *
sympify(2)/3 + sympify(1)/27/6We can also do everything with symbols:outputs:We can now evaluate that expression object at any time:outputs:
from sympy import *
x, y = symbols('x y')
expr = x/3 + y/2
print(expr)x/3 + y/2expr.subs({x: 1, y: 2})4/3How about a square root?outputs:so we understand that the value was kept without simplification. And of course:outputs outputs:gives:
x = sqrt(2)
print(x)sqrt(2)sqrt(2)**22. Also:sqrt(-1)II is the imaginary unit. We can use that symbol directly as well, e.g.:I*I-1Let's do some trigonometry:gives:and:gives:The exponential also works:gives;
cos(pi)-1cos(pi/4)sqrt(2)/2exp(I*pi)-1Now for some calculus. To find the derivative of the natural logarithm:outputs:Just read that. One over x. Beauty. And now for some integration:outputs:OK.
from sympy import *
x = symbols('x')
print(diff(ln(x), x))1/xprint(integrate(1/x, x))log(x)Let's do some more. Let's solve a simple differential equation:Doing:outputs:which means:To be fair though, it can't do anything crazy, it likely just goes over known patterns that it has solvers for, e.g. if we change it to:it just blows up:Sad.
y''(t) - 2y'(t) + y(t) = sin(t)from sympy import *
x = symbols('x')
f, g = symbols('f g', cls=Function)
diffeq = Eq(f(x).diff(x, x) - 2*f(x).diff(x) + f(x), sin(x)**4)
print(dsolve(diffeq, f(x)))Eq(f(x), (C1 + C2*x)*exp(x) + cos(x)/2)diffeq = Eq(f(x).diff(x, x)**2 + f(x), 0)NotImplementedError: solve: Cannot solve f(x) + Derivative(f(x), (x, 2))**2Let's try some polynomial equations:which outputs:which is a not amazingly nice version of the quadratic formula. Let's evaluate with some specific constants after the fact:which outputsLet's see if it handles the quartic equation:Something comes out. It takes up the entire terminal. Naughty. And now let's try to mess with it:and this time it spits out something more magic:Oh well.
from sympy import *
x, a, b, c = symbols('x a b c d e f')
eq = Eq(a*x**2 + b*x + c, 0)
sol = solveset(eq, x)
print(sol)FiniteSet(-b/(2*a) - sqrt(-4*a*c + b**2)/(2*a), -b/(2*a) + sqrt(-4*a*c + b**2)/(2*a))sol.subs({a: 1, b: 2, c: 3})FiniteSet(-1 + sqrt(2)*I, -1 - sqrt(2)*I)x, a, b, c, d, e, f = symbols('x a b c d e f')
eq = Eq(e*x**4 + d*x**3 + c*x**2 + b*x + a, 0)
solveset(eq, x)x, a, b, c, d, e, f = symbols('x a b c d e f')
eq = Eq(f*x**5 + e*x**4 + d*x**3 + c*x**2 + b*x + a, 0)
solveset(eq, x)ConditionSet(x, Eq(a + b*x + c*x**2 + d*x**3 + e*x**4 + f*x**5, 0), Complexes)Let's try some linear algebra.Let's invert it:outputs:
m = Matrix([[1, 2], [3, 4]])m**-1Matrix([
[ -2, 1],
[3/2, -1/2]])Just like as for classic gates, we would like to be able to select quantum computer physical implementations that can represent one or a few gates that can be used to create any quantum circuit.
Unfortunately, in the case of quantum circuits this is obviously impossible, since the space of N x N unitary matrices is infinite and continuous.
Therefore, when we say that certain gates form a "set of universal quantum gates", we actually mean that "any unitary matrix can be approximated to arbitrary precision with enough of these gates".
Or if you like fancy Mathy words, you can say that the subgroup of the unitary group generated by our basic gate set is a dense subset of the unitary group.
This gate set alone is not a set of universal quantum gates.
Notably, circuits containing those gates alone can be fully simulated by classical computers according to the Gottesman-Knill theorem, so there's no way they could be universal.
This means that if we add any number of Clifford gates to a quantum circuit, we haven't really increased the complexity of the algorithm, which can be useful as a transformational device.
The first two that you should study are:
They are the finite projective special linear groups.
This was the first infinite family of simple groups discovered after the simple cyclic groups and alternating groups. The first case discovered was by Galois. You should understand that one first.
Mathematics and Statistics course of the University of Oxford Updated 2025-05-23 +Created 1970-01-01
How Microwaves Work by National MagLab (2017)
Source. A bit meh. Does not mention the word cavity magnetron!How a Microwave Oven Works by EngineerGuy
. Source. Cool demonstration of the standing waves in the cavity with cheese! How to use an Oxford Nanopore MinION to extract DNA from river water and determine which bacteria live in it Bioinformatics Updated 2025-05-23 +Created 1970-01-01
Because Ciro's a software engineer, and he's done enough staring in computers for a lifetime already, and he believes in the power of Git, he didn't pay much attention to this part ;-)
According to the eLife paper, the code appears to have been uploaded to: github.com/d-j-k/puntseq. TODO at least mention the key algorithms used more precisely.
Ciro can however see that it does present interesting problems!
Because it was necessary to wait for 2 days to get our data, the workshop first reused sample data from previous collections done earlier in the year to illustrate the software.
First there is some signal processing/machine learning required to do the base calling, which is not trivial in the Oxford Nanopore, since neighbouring bases can affect the signal of each other. This is mostly handled by Oxford Nanopore itself, or by hardcore programmers in the field however.
After the base calling was done, the data was analyzed using computer programs that match the sequenced 16S sequences to a database of known sequenced species.
This is of course not just a simple direct string matching problem, since like any in experiment, the DNA reads have some errors, so the program has to find the best match even though it is not exact.
The PuntSeq team would later upload the data to well known open databases so that it will be preserved forever! When ready, a link to the data would be uploaded to: www.puntseq.co.uk/data
How to use an Oxford Nanopore MinION to extract DNA from river water and determine which bacteria live in it Sample collection Updated 2025-05-23 +Created 1970-01-01
As you would expect, not much secret here, we just dumped a 1 liter glass bottle with a rope attached around the neck in a few different locations of the river, and pulled it out with the rope.
Just like a classic programmer does not need to understand the intricacies of how transistors are implemented and CMOS semiconductors, the quantum programmer does not understand physical intricacies of the underlying physical implementation.
The main difference to keep in mind is that quantum computers cannot save and observe intermediate quantum state, so programming a quantum computer is basically like programming a combinatorial-like circuit with gates that operate on (qu)bits:
For this reason programming a quantum computer is much like programming a classical combinatorial circuit as you would do with SPICE, verilog-or-vhdl, in which you are basically describing a graph of gates that goes from the input to the output
For this reason, we can use the words "program" and "circuit" interchangeably to refer to a quantum program
Also remember that and there is no no clocks in combinatorial circuits because there are no registers to drive; and so there is no analogue of clock in the quantum system either,
x86 Paging Tutorial Multiple addresses translate to a single physical address Updated 2025-05-23 +Created 1970-01-01
The same linear address can translate to different physical addresses for different processes, depending only on the value inside
cr3.Both linear addresses
00002 000 from process 1 and 00004 000 from process 2 point to the same physical address 00003 000. This is completely allowed by the hardware, and it is up to the operating system to handle such cases.This often in normal operation because of Copy-on-write (COW), which be explained elsewhere.
Such mappings are sometime called "aliases".
gfx_v11_0_priv_reg_irq: register access in command stream Updated 2025-05-23 +Created 1970-01-01
Had this happen on P14s on Ubuntu 23.10 while causally using Chromium. The screen went blank for a few seconds, but it apparently managed to reboot itself, and things started working again, except that and most windows were killed:It appears to be a bug in the AMDGPU open source driver.
[drm:gfx_v11_0_priv_reg_irq [amdgpu]] *ERROR* Illegal register access in command stream
[drm:amdgpu_job_timedout [amdgpu]] *ERROR* ring gfx_0.0.0 timeout, signaled seq=5774109, emitted seq=5774111
[drm:amdgpu_job_timedout [amdgpu]] *ERROR* Process information: process chrome pid 14023 thread chrome:cs0 pid 14087
amdgpu 0000:64:00.0: amdgpu: GPU reset begin!
[drm:mes_v11_0_submit_pkt_and_poll_completion.constprop.0 [amdgpu]] *ERROR* MES failed to response msg=3
[drm:amdgpu_mes_unmap_legacy_queue [amdgpu]] *ERROR* failed to unmap legacy queue
[drm:mes_v11_0_submit_pkt_and_poll_completion.constprop.0 [amdgpu]] *ERROR* MES failed to response msg=3
[drm:amdgpu_mes_unmap_legacy_queue [amdgpu]] *ERROR* failed to unmap legacy queue
[drm:mes_v11_0_submit_pkt_and_poll_completion.constprop.0 [amdgpu]] *ERROR* MES failed to response msg=3
[drm:amdgpu_mes_unmap_legacy_queue [amdgpu]] *ERROR* failed to unmap legacy queue
[drm:mes_v11_0_submit_pkt_and_poll_completion.constprop.0 [amdgpu]] *ERROR* MES failed to response msg=3
[drm:amdgpu_mes_unmap_legacy_queue [amdgpu]] *ERROR* failed to unmap legacy queue
[drm:mes_v11_0_submit_pkt_and_poll_completion.constprop.0 [amdgpu]] *ERROR* MES failed to response msg=3
[drm:amdgpu_mes_unmap_legacy_queue [amdgpu]] *ERROR* failed to unmap legacy queue
[drm:mes_v11_0_submit_pkt_and_poll_completion.constprop.0 [amdgpu]] *ERROR* MES failed to response msg=3
[drm:amdgpu_mes_unmap_legacy_queue [amdgpu]] *ERROR* failed to unmap legacy queue
[drm:mes_v11_0_submit_pkt_and_poll_completion.constprop.0 [amdgpu]] *ERROR* MES failed to response msg=3
[drm:amdgpu_mes_unmap_legacy_queue [amdgpu]] *ERROR* failed to unmap legacy queue
[drm:mes_v11_0_submit_pkt_and_poll_completion.constprop.0 [amdgpu]] *ERROR* MES failed to response msg=3
[drm:amdgpu_mes_unmap_legacy_queue [amdgpu]] *ERROR* failed to unmap legacy queue
[drm:mes_v11_0_submit_pkt_and_poll_completion.constprop.0 [amdgpu]] *ERROR* MES failed to response msg=3
[drm:amdgpu_mes_unmap_legacy_queue [amdgpu]] *ERROR* failed to unmap legacy queue
[drm:gfx_v11_0_cp_gfx_enable.isra.0 [amdgpu]] *ERROR* failed to halt cp gfx
Dec 27 15:03:38 ciro-p14s kernel: amdgpu 0000:64:00.0: amdgpu: MODE2 reset
Dec 27 15:03:38 ciro-p14s kernel: amdgpu 0000:64:00.0: amdgpu: GPU reset succeeded, trying to resume
Dec 27 15:03:38 ciro-p14s kernel: [drm] PCIE GART of 512M enabled (table at 0x0000008000900Related reports:
I think this was on Wayland. Possibly relatd but on X Window System, crashed the UI, showed message "oh no! Something has gone wrong."
2024-01-13_21-55-07@ciro@ciro-p14s$ cat /var/log/apport.log
ERROR: apport (pid 975172) 2024-01-13 21:41:02,087: host pid 3528 crashed in a separate mount namespace, ignoring
INFO: apport (pid 975227) 2024-01-13 21:41:02,398: called for pid 2728, signal 5, core limit 0, dump mode 1
INFO: apport (pid 975227) 2024-01-13 21:41:02,401: executable: /usr/bin/gnome-shell (command line "/usr/bin/gnome-shell")
INFO: apport (pid 975227) 2024-01-13 21:41:12,667: wrote report /var/crash/_usr_bin_gnome-shell.1000.crashFFFFF 000 points to its own physical address FFFFF 000. This kind of translation is called an "identity mapping", and can be very convenient for OS-level debugging.Happening multiple times a day on Ubuntu 22.04 for Chromium, even though I turn computer on and off daily, unbearable:
- askubuntu.com/questions/1412575/pending-update-of-snap-store
- askubuntu.com/questions/1412140/pending-update-of-firefox-snap-close-the-app-to-avoid-disruptions
- forum.snapcraft.io/t/how-to-disable-snapd-update-notifications-permanently/31117 Settings > Notifications > Snapd User Session Agent
- www.reddit.com/r/Ubuntu/comments/v1s919/disable_pending_update_of_snap_message_kiosk/
- forum.snapcraft.io/t/refresh-app-awareness-call-for-testing/29123
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