Xah Talk Show 2025-12-11 Ep723 Wolfram Language, Advent of Code 2025, Day 1, Part 2, take 2

Why Wolfram language QuotientRemainder[-10,3] return {-4, 2}, not {-3, 1}

QuotientRemainder[10,3]
(* {3, 1} *)

(* why does this not return {-3, 1} *)
QuotientRemainder[-10,3]
{-4, 2}

Quotient[-10,3]
(* -4 *)

because, it is to be consistent with Quotient function, and the Quotient function doc says:

Quotient[m,n] gives the greatest integer no larger than m/n.

in other words, it rounds using Floor.

• Quotient

why quotient(10,-3) return -4, not -3

• when doing quotient(10,-3) why does it return -4, not -3.
• what is the math convention, for quotient(-10,3) to return -3 or -4
• https://x.com/i/grok/share/CQV0w07CHxzYTpSs37s2PfHZk

grok gave several incorrect answer.

• 1. there is is no math.quotient in python.
• 2. grok ai saying that JavaScript quotient function truncates towards 0, is incorrect. because in JavaScript, there is no integer quotient function.
• 3. the reason it says the convention is remainder to be non-negative, but quotient(-10,3) return -3 is also valid, because -3*-3 = 9+1.

print(10 // 3)
# 3

print(-10 // 3)
# -4

• Python: Arithmetic Operators
• JS: Arithmetic Operators
• JS: Math (namespace)