Looking to create an "AI detector" is like asking which organelle in a cell contains the "soul". It's a fool's errand and uncomfortable truth that there is rarely a magic watermark of any sort. Honesty and integrity in authorship is a social problem.

That's not what it simplifies to using a real or complex number domains for x, it's abs(x). CAS need type inference assumptions and/or type qualifiers to be more powerful.

Edit: Fixed stuff.

For x = -i, square(x) = -1, sqrt(square(x)) = i. Meanwhile, abs(x) = 1. You're right that it simplifies to abs(x) for real x, but that no longer holds for arbitrary complex values.

for arbitrary complex values sqrt() gives 2 answers with +- signs

so sqrt(square(-i)) = +-i, one of which is x

I've never seen a CAS that gives two answers for sqrt. Mathematica doesn't, sympy doesn't, and IIRC Maxima also doesn't.

The sqrt function returns the principle square root, not both. That’s true for all numbers, positive, negative, and complex alike.

It's abs(x) only over the reals, for complex numbers it's more complicated.

That abs(x) (or |x| as we wrote it) used to catch out so many of us in HS trig and algebra.

Right, that's why you need further assumptions on x in order for that simplification to hold.

Not in general. As people have pointed out elsewhere, it's true if x is real. That isn't always a helpful assumption. (When x is real you can plug that assumption into Mathematica. Then Mathematica should agree with you.)

But consider sqrt(i) = sqrt(exp(i\pi/2)). That's exp(i\pi/4). Your rule would give 1 as the answer. It's not helpful for a serious math system to give that answer to this problem.

When I square 1 I don't get i.

It also equals x with appropriate assumptions (x > 0).

Well, then sin(x) = x if x is infinitely small

so there's an unconditionally correct answer (it's also equal to abs(x) for x>0), and then there is an answer that is only correct for half the domain, which requires an additional assumption.

sqrt(square(i)) != abs(i)

So no, it’s not unconditionally correct either.

Because it's manufactured consent and propaganda driven by deep pockets and ideologues. It was rammed through by the elites.

That's the plan in both Lebanon and Iran. Send out an initial impulse and steady stream of drones and ballistic missiles to expend expensive interceptors that take a long time to make. Make it seem like the traditional launch capability and stockpiles are low. After that time, Iran and/or Lebanon maintain an option to ready and launch underground-stockpiled Shaheeds and similar from improvised launchers on the back of pickup trucks and trailers by the hundreds/thousands to obliterate US bases and major Israeli cities like Haifa and Tel Aviv. That's the most likely scenario should Iran/Lebanon decide escalation would be essential for existential defense.

The only reasons I bought a case with a tempered glass side panel were its overall rating and it was extremely cheap. A similar situation happened for the Core V71 case I used for a Supermicro H11DSi dual EPYC virtual server and NAS for my home lab. It's one of a few features I don't care about but are difficult to avoid without incurring limitations like additional cost.

Back in my day™, I remember full super tower cases made from steel when they had 8-10 5.25" HH front bays. They were boat anchors and they were generally terrible at managing heat and airflow.

Beige was the only color case available until around 1992. And, sometimes, the floppy drive/s or HDDs didn't match the case at all. Off white cases were one of the first "innovations" before black, gray, and multi color cases arrived in the late 90's where I was. Then tempered glass and ARGB came in like an involuntary disco, a Ford Fiesta with ground effects, or a Trump apartment. All I wished was that Noctua and similar fan mfgrs offered standard monochrome black or white fans rather than brown turds or RGB fluorescent orange.

That's how fascist bootlickers roll.

Definitely use quality surge protectors on expensive equipment connected to generators.

PSA: UPSes and GFCI/GFI extension cords won't work properly when connected to a stand-alone generator with a bonded neutral. I've tried using enterprise UPSes on such generators, but they absolutely won't work. In such scenarios, debond the generator's ground from neutral, apply a very large warning label to it being debonded, and drive a massive ground rod electrode into the ground as close to the generator as possible and ground the neutral there. This does work and is much safer because there's a stable voltage reference source. It's more of a hassle but can be necessary for some off grid and temporary scenarios.

GFCI works correctly either way. Their operating mode doesn't care at all about ground: Whether bonded, not bonded, or not even present (look, ma! only two wires!), they still perform the same way.

They respond to an imbalance in current flow betwixt line and neutral. What goes out must return; if it doesn't, then switch off.

Ground is not part of the equation at all.

That extra unbonded ground rod is the worst thing you can possibly do to make your generator vulnerable to lightning strikes.

That's an extreme edge-case and a strawman. Anyone operating temporary equipment on a generator during a severe storm will obviously unplug sensitive stuff to not take unnecessary chances regardless of safety precautions already in place.

Ground rods are required in certain situations according to the NEC.

Ground rods are for lightning protection, transient surges (over voltage), and induced surges; not for short protection, ground faults, or making ordinary extension cord use of bonded generators "safer".

Typically, they're required whenever it's a system that powers a building on its own, i.e., off-grid setup or with a floating neutral generator connected via a switched neutral transfer switch.

> In such scenarios, debond the generator's ground from neutral

eeeeep. Please for the love of all that is holy, CONTACT AN ELECTRICIAN before messing around with that - or before creating a ground bond where none should be (i.e. TT grid [1]). You may end up endangering yourself if you do not exactly know what you are doing - in the case of TT, you get ground potential difference current from other parts of the grid flowing to ground via your generator's bond. Best case you're getting problems with electrochemical corrosion (including in your foundation), worst case enough current flows to turn your bond wire into a thermal fuse.

Also, take great care if your grounding is provided via municipal water service, or if your original grounding rod has dried out to the point it's ineffective.

Let me repeat: LET ELECTRICIANS DEAL WITH GROUNDING AND SURGE PROTECTION. Floating grounds and improper ground connections CAN BE LETHAL OR POSE A SERIOUS FIRE RISK.

AND YES THAT INCLUDES "ISLAND" SCENARIOS OR EMERGENCY POWER INPUTS (e.g. via CEE plugs and transfer switches).

[1] https://de.wikipedia.org/wiki/TT-System

I'm not sure I'd leave something like this to an electrician. Or if so at least make that electrician be experienced in this field. I think you'd want an electrical engineer to be involved with the plan to some degree.

Electrical engineers don’t know code requirements and wiring guidelines for household electrical wiring. They’re absolutely not the correct default. Electricians with specialization in generator setups, sure, but an electrician engineer on average is likely going to be more uninformed on code requirements than an electrician.

Electrical engineers know the theory but lack the practical knowledge which grid form is used at your specific address (yes, here in Germany we have a few towns where one half side of a street runs TT and the other one is already migrated to TN-C or TN-C-S).

An electrician specializing in lightning protection, uninterruptible power installation or in radio installations can sort out all of that far better than an engineer can.

Not completely correct, nuanced, or comprehensive.

Direct lighting strikes cannot be defended against without extreme costs. This type of risk is generally extremely unlikely except for certain niche use-cases like equipment or facilities on tall peaks.

Transients from lightning (E2) nearby and distant nuclear detonations can be defended against, and often require additional protection of telco and internet entry points. Whole house type 1 SPD devices exist for residential applications. This is much more likely than direct lightning strikes, especially in certain areas and can be defended against for reasonable cost. The main issue of lacking it is the unseen, cumulative degradation of semiconductor components that lead to instantaneous or eventual failure, especially in high value devices like electrically-communicated motors in HVAC systems. There is no reasonable expectation of defense against a direct lightning strike even with type 1 SPD, and there are different types of lightning with vastly different amounts of energy. A positive strike direct hit will totally fry anything and everything.

What generally isn't defended against at all in any infrastructure or system except some military equipment is H/NEMP E1 (short duration impulses) or E3 (E3a or E3b; long duration surges larger than lightning) such as from unusual space weather events or nuclear blasts.

I grew up in San Jose CA in the 80's and 90'd on a street with a perpetually bad transformer. We had UPSes on every computer and proper surge protectors on everything of value.