TODO.md

MathFlow | TODO

A list of features to add to mathflow - based on numpy, mathjs and more.

1. Numbers and Big Numbers

• add(a, b, ...): Adds all numbers.
• sub(a, b): Subtracts the second number from the first.
• mul(a, b, ...): Multiplies all numbers.
• div(a, b): Divides the first number by the second.
• mod(a, b): Returns the remainder of division of two numbers.
• abs(x): Returns the absolute value of a number.
• ceil(x): Rounds a number up to the nearest integer.
• floor(x): Rounds a number down to the nearest integer.
• sign(x): Returns the sign of a number: -1, 0, or 1.
• sqrt(x): Returns the square root of a number.
• pow(x, y): Raises x to the power of y.
• cbrt(x): Computes the cube root of a number.
• root(x, n): Computes the n-th root of a number.
• trunc(x): Removes the fractional part of a number, leaving the integer part.
• round(x, n?): Rounds a number to the nearest integer or to n decimal places.
• gcd(a, b, ...): Calculates the greatest common divisor of all numbers.
• lcm(a, b, ...): Computes the least common multiple of all numbers.
• rand(min?, max?): Generates a random number within a specified range.
• randi(min, max): Generates a random integer between the specified min and max values.
• complex(re, im): Creates a complex number with real and imaginary parts.
• bignumber(x): Creates a big number with arbitrary precision.
• fraction(x): Creates a fraction from a number or a string.
• clamp(x, min, max): Clamps a value between a minimum and maximum value.
• modExp(base, exponent, modulus): Computes the modular exponentiation of a number.
• fix(x): Rounds towards zero, removing the fractional part.
• precision(x, n): Adjusts a number to n significant digits.
• sigFigs(x, n): Rounds a number to n significant figures.
• roundToNearest(x, step): Rounds x to the nearest multiple of step.

2. Matrices and Arrays

• matrix(data): Creates a matrix from an array or other data format.
• identity(n): Creates an identity matrix of size n.
• transpose(matrix): Returns the transpose of a matrix.
• det(matrix): Calculates the determinant of a matrix.
• inv(matrix): Computes the inverse of a matrix.
• concat(a, b, dim?): Concatenates two arrays or matrices along the specified dimension.
• size(matrix): Returns the size (dimensions) of a matrix.
• reshape(matrix, sizes): Reshapes a matrix to the specified sizes.
• flatten(matrix): Flattens a multi-dimensional matrix into a single dimension.
• dot(a, b): Computes the dot product of two vectors or matrices.
• cross(a, b): Calculates the cross product of two 3D vectors.
• subset(matrix, index, replacement?): Retrieves or sets a subset of a matrix.
• diag(matrix, k?): Extracts or creates a diagonal matrix.
• norm(matrix, p?): Computes the norm of a matrix or vector.
• trace(matrix): Computes the trace (sum of diagonal elements) of a matrix.
• zeros(m, n): Creates a matrix filled with zeros of specified dimensions.
• ones(m, n): Creates a matrix filled with ones of specified dimensions.
• range(start, end, step?): Generates an array of numbers from start to end with a specified step.
• sort(matrix, compare?): Sorts the elements of a matrix according to a compare function.
• magnitude(vector): Computes the magnitude (length) of a vector.
• normalize(vector): Normalizes a vector to a unit length.

3. Algebra

• simplify(expr, rules?): Simplifies an algebraic expression using optional rules.
• solve(equation, variable?): Solves an equation for a specified variable.
• expand(expr): Expands an algebraic expression.
• evaluate(expr, scope?): Evaluates an expression given optional variable values.
• derivative(expr, variable): Computes the derivative of an expression with respect to a variable.
• parse(expr): Parses a string into an expression tree.
• rationalize(expr, scope?): Converts an expression into a rational fraction form.
• binomialCoefficient(n, k): Computes the binomial coefficient, representing combinations of n items taken k at a time.

4. Statistics

• mean(arr): Computes the mean (average) of an array of numbers.
• median(arr): Finds the median value in an array of numbers.
• mode(arr): Identifies the mode (most frequent value) in an array.
• variance(arr, normalization?): Calculates the variance of a data set.
• std(arr, normalization?): Computes the standard deviation of a data set.
• sum(arr): Computes the sum of all elements in an array.
• prod(arr): Calculates the product of all elements in an array.
• min(arr): Finds the minimum value in an array.
• max(arr): Finds the maximum value in an array.
• quantileSeq(arr, prob, sorted?): Computes the specified quantile of a sorted array.
• mad(arr): Computes the mean absolute deviation of an array.
• entropy(arr): Calculates the entropy of a data set.
• covariance(arr1, arr2): Computes the covariance between two data sets.
• corr(arr1, arr2): Calculates the correlation coefficient between two data sets.
• weightedMean(values, weights): Computes the weighted mean of values given their weights.
• geometricMean(values): Calculates the geometric mean of a set of values.
• harmonicMean(values): Computes the harmonic mean of a set of values.
• skewness(arr): Measures the skewness of a data set, indicating asymmetry.
• kurtosis(arr): Measures the kurtosis of a data set, indicating the tails' heaviness.

5. Probability and Combinatorics

• combinations(n, k): Calculates the number of ways to choose k items from n.
• permutations(n, k): Computes the number of ways to arrange k items out of n.
• random(min?, max?): Generates a random number within a range.
• randomInt(min, max): Generates a random integer between specified bounds.
• pickRandom(arr): Randomly selects an element from an array.
• shuffle(arr): Randomly shuffles the elements of an array.
• factorial(n): Computes the factorial of a number.
• stirlingApproximation(n): Approximates the factorial of n using Stirling's formula.
• isPrime(n): Checks if a number is a prime number.
• primeFactors(n): Returns the prime factors of a number.
• fibonacci(n): Calculates the n-th Fibonacci number.
• birthdayProblem(p, n): Computes the probability of a shared birthday in a group of n.

6. Trigonometry

• deg(x): Converts the angle from radians to degrees.
• rad(x): Converts the angle from degrees to radians.
• sin(x): Computes the sine of an angle (in radians).
• cos(x): Computes the cosine of an angle (in radians).
• tan(x): Computes the tangent of an angle (in radians).
• sind(x): Computes the sine of an angle (in degrees).
• cosd(x): Computes the cosine of an angle (in degrees).
• tand(x): Computes the tangent of an angle (in degrees).
• sec(x): Computes the secant of an angle.
• csc(x): Computes the cosecant of an angle.
• cot(x): Computes the cotangent of an angle.
• asin(x): Computes the inverse sine of a value.
• acos(x): Computes the inverse cosine of a value.
• atan(x): Computes the inverse tangent of a value.
• atan2(y, x): Computes the angle from the x-axis to a point (x, y).
• sinh(x): Computes the hyperbolic sine of a value.
• cosh(x): Computes the hyperbolic cosine of a value.
• tanh(x): Computes the hyperbolic tangent of a value.
• asinh(x): Computes the inverse hyperbolic sine of a value.
• acosh(x): Computes the inverse hyperbolic cosine of a value.
• atanh(x): Computes the inverse hyperbolic tangent of a value.
• hypot(a, b, ...): Computes the square root of the sum of squares (Euclidean norm).
• versin(x): Computes the versine of an angle (in radians).
• versind(x): Computes the versine of an angle (in degrees).
• coversin(x): Computes the coversine of an angle (in radians).
• coversin(x): Computes the coversine of an angle (in degrees).

7. Calculus

• derivative(expr, variable): Calculates the derivative of an expression.
• integrate(expr, variable): Computes the integral of an expression.
• numericDerivative(func, x): Numerically computes the derivative at a point.

8. Complex Numbers

• complex(re, im): Creates a complex number from real and imaginary parts.
• re(complex): Extracts the real part of a complex number.
• im(complex): Extracts the imaginary part of a complex number.
• arg(complex): Computes the argument (phase angle) of a complex number.
• conj(complex): Returns the complex conjugate of a complex number.
• iabs(complex): Computes the magnitude (absolute value) of a complex number.
• iadd(complex1, complex2): Adds two complex numbers.
• isub(complex1, complex2): Subtracts the second complex number from the first.
• imul(complex1, complex2): Multiplies two complex numbers.
• idiv(complex1, complex2): Divides the first complex number by the second.
• isqrt(complex): Computes the square root of a complex number.
• iexp(complex): Calculates the exponential of a complex number.
• ilog(complex): Computes the natural logarithm of a complex number.
• ipow(complex, exponent): Raises a complex number to a specified power.
• phase(complex): Returns the phase angle (argument) of a complex number.

9. Special Functions

• gamma(x): Computes the gamma function of x, an extension of the factorial.
• sinc(x): Computes the sinc function, defined as sin(x)/x.
• heaviside(x): Computes the Heaviside step function.
• erf(x): Computes the error function of x.
• beta(a, b): Calculates the beta function.
• lambertW(x): Computes the Lambert W function.
• digamma(x): Calculates the digamma function, the logarithmic derivative of the gamma function.
• zeta(s): Computes the Riemann zeta function of s.
• gammaIncomplete(a, x): Computes the incomplete gamma function.

11. Exponential and Logarithmic Functions

• exp(x): Computes e raised to the power of x.
• ln(x): Computes the natural logarithm of x.
• log(x, base): Computes the logarithm of x with a specified base.
• log10(x): Computes the base-10 logarithm of x.
• log2(x): Computes the base-2 logarithm of x.
• pow10(exp): Computes 10 raised to the power of exp.
• pow2(exp): Computes 2 raised to the power of exp.
• expm1(x): Computes e^x - [ ] 1, useful for small values of x to reduce numerical error.
• log1p(x): Computes log(1 + x), improving accuracy for small x.

12. Linear Algebra and Geometry

• dotProduct(a, b): Computes the dot product of two vectors.
• crossProduct(a, b): Computes the cross product of two 3D vectors.
• projection(u, v): Projects vector u onto vector v.
• angleBetween(u, v): Calculates the angle between two vectors.
• distance(p1, p2): Computes the Euclidean distance between two points.
• reflect(point, line): Reflects a point over a line.
• intersect(line1, line2): Finds the intersection point of two lines.

13. Signal Processing

• fft(arr): Computes the Fast Fourier Transform of an array.
• ifft(arr): Computes the inverse Fast Fourier Transform.
• dft(arr): Calculates the Discrete Fourier Transform of an array.
• idft(arr): Calculates the inverse Discrete Fourier Transform.
• convolve(arr1, arr2): Computes the convolution of two sequences.
• correlate(arr1, arr2): Computes the cross-correlation of two sequences.

14. Financial Math

• futureValue(principal, rate, periods): Computes the future value of an investment.
• presentValue(futureValue, rate, periods): Computes the present value given the future value.
• compoundInterest(principal, rate, timesCompounded, periods): Calculates compound interest over time.
• annuityPayment(rate, periods, presentValue): Computes the payment amount of an annuity.

15. Interpolation and Approximation

• lerp(a, b, t): Performs linear interpolation between two values a and b based on t.
• hermite(p0, p1, t): Performs Hermite interpolation.
• lagrange(points, x): Uses Lagrange polynomials to interpolate the value at x.
• spline(points, x): Computes spline interpolation at x.

16. Number Theory

• totient(n): Computes Euler’s totient function of n.
• mobius(n): Computes the Möbius function of n.
• isPerfectSquare(n): Checks whether a number is a perfect square.
• divisors(n): Lists all divisors of a number n.