Algebra solvers: linear systems, polynomials & complex
Five algebra tools: simultaneous linear systems (2–4 unknowns), cubic and quartic root finders, complex-number arithmetic with polar form, and prime factorization with GCD/LCM. (The quadratic solver has its own page.)
Linear systems matrix solver
$$A\mathbf{x}=\mathbf{b}\ \Longrightarrow\ \mathbf{x}=A^{-1}\mathbf{b}$$
Solved by Gaussian elimination with partial pivoting. Enter one equation per line as the augmented row a₁ a₂ … aₙ | b (spaces or commas). Source: 1728 Software Systems.
Cubic polynomial root finder
$$ax^3+bx^2+cx+d=0$$
All three roots (real or complex) via Durand–Kerner iteration. Source: 1728 Software Systems.
Quartic polynomial root finder
$$ax^4+bx^3+cx^2+dx+e=0$$
All four roots (real or complex) via Durand–Kerner iteration. Source: 1728 Software Systems.
Complex arithmetic & polar form
$$r=\sqrt{a^2+b^2},\quad \theta=\operatorname{atan2}(b,a),\quad (a+bi)(c+di)=(ac-bd)+(ad+bc)i$$
Add, subtract, multiply or divide two complex numbers; result shown in both rectangular and polar form. Source: 1728 Software Systems.
| Result (rectangular) | — | |
| Modulus r | — | |
| Argument θ | — | |
| Polar form | — |
Prime factorization & GCD/LCM
$$\text{lcm}(a,b)=\frac{|a\cdot b|}{\gcd(a,b)}$$
Trial-division factorization and the Euclidean algorithm for GCD. Source: 1728 Software Systems.
| Factorization of a | — | |
| Factorization of b | — | |
| GCD(a, b) | — | |
| LCM(a, b) | — |