Algebra — ChatMath Wiki

Factoring & Simplification — Implemented

Faktorisiere( <Ausdruck> )

Aliases: factor, Factor

✓ Done

Factors an expression over the rationals. Also factors integers into primes (CAS mode).

Faktorisiere(x^2 + x - 6)    → (x + 3)(x - 2)
Faktorisiere(x^2 - 4)         → (x - 2)(x + 2)
Faktorisiere(360)              → 2³ · 3² · 5

Multipliziere( <Ausdruck> )

Aliases: expand, Expand

✓ Done

Expands (multiplies out) a factored expression.

Multipliziere((x+2)(x-3))     → x² - x - 6
Multipliziere((2x-1)^2 + 2x)  → 4x² - 2x + 1

Vereinfache( <Ausdruck> )

Aliases: simplify, Simplify

✓ Done

Simplifies an expression by combining like terms and reducing fractions.

Vereinfache(3x + 4x + 2x)     → 9x
Vereinfache((x^2-1)/(x-1))    → x + 1

VollständigesQuadrat( <QuadratFunktion> )

Aliases: completesquare, CompleteSquare

✓ Done

Rewrites a quadratic in vertex form a(x − h)² + k.

VollständigesQuadrat(x^2 - 4x + 7)   → (x - 2)² + 3

Divisibility & Number Theory — Implemented

GGT( <a>, )

Aliases: gcd, GCD

✓ Done

Greatest Common Divisor. Also accepts a list: GGT({12, 30, 18}).

GGT(12, 15)           → 3
GGT({12, 30, 18})     → 6

KGV( <a>, )

Aliases: lcm, LCM

✓ Done

Least Common Multiple. Also accepts a list.

KGV(12, 15)           → 60
KGV({4, 6, 10})       → 60

Mod( <dividend>, <divisor> )

Aliases: mod

✓ Done

Remainder after division. Also works for polynomial modulo.

Mod(9, 4)     → 1
Mod(17, 5)    → 2

Division( <dividend>, <divisor> )

Aliases: divide

✓ Done

Returns {quotient, remainder} as a list. Also works for polynomial division.

Division(16, 3)                     → {5, 1}
Division(x^2 + 3x + 1, x - 1)      → {x+4, 5}

Teiler( <n> ) / Teilerliste( <n> ) / Teilersumme( <n> )

✓ Done

Divisor count, list of all divisors, and sum of all divisors of n.

Teiler(15)       → 4  (divisors: 1, 3, 5, 15)
Teilerliste(15)  → {1, 3, 5, 15}
Teilersumme(15)  → 24

Primfaktoren( <n> )

Aliases: primefactors

✓ Done

Prime factorization — returns list of all prime factors (with repetition).

Primfaktoren(42)     → {2, 3, 7}
Primfaktoren(1024)   → {2,2,2,2,2,2,2,2,2,2}

IstPrimzahl( <n> )

Aliases: isprime, IsPrime

✓ Done

Returns true if n is prime, false otherwise.

IstPrimzahl(11)    → true
IstPrimzahl(10)    → false

NächstePrimzahl( <n> ) / VorherigePrimzahl( <n> )

Aliases: nextprime / prevprime

✓ Done

Smallest prime greater than n, or largest prime less than n.

NächstePrimzahl(10000)     → 10007
VorherigePrimzahl(10000)   → 9973

Min / Max — Implemented

Max( <Liste> ) / Min( <Liste> )

Aliases: max, min

✓ Done

Maximum or minimum of a list. Also accepts two numbers directly.

Max({-2, 12, -23, 17, 15})   → 17
Min({-2, 12, -23, 17, 15})   → -23
Max(12, 15)                   → 15

Base Conversion — Implemented

VonBasis( <"Zahl">, <Basis> ) / ZuBasis( <n>, <Basis> )

Aliases: frombase / tobase

✓ Done

Convert numbers to/from any base (2–36). Input for VonBasis must be a string.

VonBasis("FF", 16)         → 255
VonBasis("100000000", 2)   → 256
ZuBasis(255, 16)           → "FF"
ZuBasis(256, 2)            → "100000000"

Coming Soon

GemeinsamerNenner( <a>, )

⏳ Soon

Least common denominator of two rational expressions.

GemeinsamerNenner(3/(2x+1), 3/(4x²+4x+1))
→ 4x² + 4x + 1

IFaktorisiere( <Polynom> )

⏳ Soon

Irrational factoring — factors over irrationals (includes roots). More complete than Faktorisiere.

IFaktorisiere(x^2 - 2)   → (x - √2)(x + √2)

LinkeSeite( <Gleichung> ) / RechteSeite( <Gleichung> )

⏳ Soon

Extract the left or right side of an equation. Useful for rewriting systems.

LinkeSeite(4x = 1 - 3y)    → 4x
RechteSeite(x + 2 = 3x+1)  → 3x + 1

Max( <Funktion>, <a>, ) / Min( <Funktion>, <a>, )

⏳ Soon

Maximum or minimum of a function over interval [a, b] — returns the point (x, y).

Max(x^3 + 2x^2 - 1, -2, 0)   → (-1.33, 0.19)

🔢 Algebra & Number Theory