Math Tools

Compute e^A for a square matrix A using scaling-and-squaring with a Taylor series.

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Compute the Frobenius, 1-norm, and infinity-norm of a matrix up to 6x6.

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Raise a 2×2 up to 6×6 matrix to an integer power by repeated matrix multiplication.

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Calculate the rank of any matrix — square or rectangular, up to 6×6 — by reducing it to row echelon form.

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Calculate the trace of a 2×2 up to 6×6 matrix — the sum of its main diagonal elements.

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Convert between decimal numbers and Mayan-style base-20 (vigesimal) positional notation with dots, bars, and a shell for zero.

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Calculate the mean, median, mode, and range of a set of numbers with full step-by-step working.

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Calculate the midpoint between two points in 2D or 3D.

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Add, subtract, multiply, or divide two mixed numbers, showing conversion to improper fractions and back.

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Convert a mixed number into an improper fraction by multiplying the whole number and adding the numerator.

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Approximate a Möbius strip's surface area and edge length from its center circle radius and width.

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Calculate base^exponent mod modulus using fast exponentiation (repeated squaring) — the technique behind modern cryptography.

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Calculate a mod b with the mathematically correct, always-non-negative result, including for negative a.

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Calculate the molarity of a solution from the mass of solute, its molar mass, and the solution volume.

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Calculate the molecular weight of a chemical formula, including nested parentheses.

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Find the centroidal moment of inertia for a rectangle, circle, or triangle.

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Calculate the momentum of a moving object from its mass and velocity.

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Multiply two arbitrary-degree polynomials by distributing every term and combining like terms.

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Multiply two square roots (√a × √b = √(ab)) and simplify the result to its simplest radical form.

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Estimate remaining nicotine in the body over time, using its commonly-cited 2-hour half-life.

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Calculate any nth root of a number, including cube roots, fifth roots, and beyond.

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Find the null space (kernel) basis and nullity of any matrix — square or rectangular, up to 6×6.

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Find the nth term and sum of an arithmetic or geometric sequence from its first term and common difference or ratio.

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Calculate voltage, current, resistance, or power from any two of voltage, current, and resistance.

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