# Tag Info

## Hot answers tagged abstract-algebra

18 Steps ...
• 3,351

### (-a) × (-a) = a × a

18 steps Different from the already posted 18-step solution. ...
• 370

### (-a) × (-a) = a × a

29 26 Steps No lemmas! Comment if you see anything wrong. (It's very easy to make a mistake) ...
• 11.4k

### How does the square end?

Google Sheets, 52 51 47 bytes =ArrayFormula(Join(",",Unique(Mod(Row(A:A)^2,A1 Saved 4 bytes thanks to Taylor Scott Sheets will automatically add 4 ...
• 8,669
Accepted

### Demonstrate some advanced abstract algebra

Proof of impossibility The only anti-distributive operator when $S=\mathbb Z$ is such that $\forall a, \forall b, a*b=0$. Indeed, suppose that $*$ is anti-distributive. Then $*$ has the ...
• 15.2k

### (-a) × (-a) = a × a

18 steps Not the first 18-step proof, but it’s simpler than the others. ...
• 37.9k
Accepted

### Factor a polynomial over a finite field or the integers

GolfScript (222 bytes) ...
• 42.8k
Accepted

### Counting groups of a given size

CJam, 189 187 bytes This one's gonna be tough to explain... Time complexity is guaranteed to be O(scary). ...
• 1,434
Accepted

### Cycling with Rubik's

Pyth, 66 63 bytes l.uum.rW}Hdd@_sm_B.iFP.>c3Zk3xZHG_r_Xz\'\39Nf!s}RTcZ2y=Z"UDLRFB Try it online: Demonstration or Test Suite. Notice that the program is kinda ...
• 21.8k
Accepted

### Compute the inverse of an integer modulo 100000000003

Pyth, 24 bytes L-b*/bJ+3^T11Jy*uy^GT11Q Test suite This uses the fact that a^(p-2) mod p = a^-1 mod p. First, I manually reimplement modulus, for the specific ...
• 41.4k

### Fundamental Solution of the Pell Equation

Piet, 612 codels Takes n from standard input. Outputs y then x, space-separated. Codel size 1: Codel size 4, for easier viewing: Explanation Check out this NPiet trace, which shows the program ...
• 1,651

### Multiply elements of the dihedral group

J, 23 bytes ~:/I.@,~4|[:-/1#;._1@,] Try it online! Takes a boolean vector where 0 represents ...
• 66.1k

### Cycling with Rubik's

GAP, 792 783 782 749 650 Bytes This seems to be working. If it messes up with something let me know. Thanks to @Lynn for suggesting that I decompose some of the primitive moves. Thanks to @Neil for ...
• 3,175

### ∀ a b. a + b = b + a

Lean, 451 449 445 439 414 407 bytes ...

### Define a field with 256 elements

Python 2, 11 + 45 = 56 bytes Addition (11 bytes): int.__xor__ Multiplication (45 bytes): ...
• 61.1k

23 steps ...
• 363

### ∀ a b. a + b = b + a

Lean, 268 bytes ...
• 37.9k