Polynomial roots explorer
Real coefficient polynomials of degree 1–12, with a nonzero leading coefficient.
Advanced mathematics and numerical methods ↗Advanced mathematics and numerical methods calculators
25 calculators. Search or choose one below.
Calculators
Polynomial long division
Finite real coefficients with up to 30 coefficients in each polynomial.
Advanced mathematics and numerical methods ↗Partial fraction decomposition
Supports proper rational functions with distinct real linear denominator factors, up to 12 poles.
Advanced mathematics and numerical methods ↗Function root by bisection
Assumes a continuous real function on the bracket; opposite endpoint signs alone do not prove continuity.
Advanced mathematics and numerical methods ↗Newton root iteration
Scalar Newton iteration with at most 100 updates.
Advanced mathematics and numerical methods ↗Numerical definite integration
Finite smooth real functions over a finite interval.
Advanced mathematics and numerical methods ↗Numerical differentiation
A fourth-order central stencil for sufficiently smooth real functions.
Advanced mathematics and numerical methods ↗Lagrange interpolation
One global interpolating polynomial through 2–25 distinct real nodes.
Advanced mathematics and numerical methods ↗Cubic spline interpolation
Sorts 2–100 distinct nodes by x and supports natural or clamped endpoint conditions.
Advanced mathematics and numerical methods ↗Least-squares polynomial fit
Weighted real least squares for degree 0–8 below the sample count, with positive matched weights.
Advanced mathematics and numerical methods ↗Simpson integration from samples
Composite Simpson’s 1/3 rule for an odd count of at least three uniformly spaced samples.
Advanced mathematics and numerical methods ↗Euler differential equation solver
A scalar first-order initial-value problem integrated forward with at most 1,000 coarse steps.
Advanced mathematics and numerical methods ↗Runge-Kutta differential equation solver
Forward scalar first-order IVP with at most 1,000 coarse steps.
Advanced mathematics and numerical methods ↗Vector dot product
Equal-length finite real vectors in Euclidean coordinates.
Advanced mathematics and numerical methods ↗Vector cross product
Three-dimensional right-handed Euclidean coordinates only.
Advanced mathematics and numerical methods ↗Vector projection
Projects one real Euclidean vector onto a nonzero direction of the same dimension.
Advanced mathematics and numerical methods ↗Matrix eigenvalues
Finite real square matrices up to 20×20.
Advanced mathematics and numerical methods ↗Matrix condition number
Up to 20×20 finite real matrices.
Advanced mathematics and numerical methods ↗LU factorization
Partial-pivoted LU for real square matrices up to 20×20.
Advanced mathematics and numerical methods ↗QR factorization
Full Householder QR for finite real matrices with each dimension at most 20.
Advanced mathematics and numerical methods ↗Singular value decomposition
Real thin SVD for tall, square or wide matrices up to 20 per dimension.
Advanced mathematics and numerical methods ↗Linear programming simplex demo
A bounded-size continuous LP, not integer or nonlinear optimisation.
Advanced mathematics and numerical methods ↗Discrete Fourier transform
Direct O(N²) real/complex DFT for at most 128 matched samples.
Advanced mathematics and numerical methods ↗Discrete convolution
Linear discrete convolution of two finite real sequences, with combined input length at most 500.
Advanced mathematics and numerical methods ↗Quaternion rotation
Right-handed active rotation in three-dimensional Euclidean coordinates, with quaternion order w,x,y,z.
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