simple-math library

A library that includes functions for solving equations and tasks using formulas from a school mathematics course.

Installition

• Using DUB in console:

dub add simple_math

• Using dub.json:

"dependecies": {
	"simple-math": "~>1.1.0"
}

• Using dub.sdl:

dependency "simple-math" version="~>1.1.0"

Tools

Module progressions

Arithmetical

• public T findArithmeticalD(T)(T[] progression)
  Finds the difference of the arithmetic progression in an array consisting of numbers.

• public bool isArithmeticProgression(T)(T[] array)
  Checks whether the passed array is an arithmetic progression.

• public T findAN(T)(T[] progression, T n)

• public T findAN(T)(T a1, T d, T n)
  Finds a member of the arithmetic progression at position N.

• public T findArithmeticSN(T)(T[] progression, T n)

• public T findArithmeticSN(T)(T a1, T d, T n)
  Finds the sum of N members of the arithmetic progression.

Example

// findArithmeticalD:
assert(findArithmeticalD!ubyte([2, 3, 4, 5]) == 1);
assert(findArithmeticalD!byte([5, 2]) == -3);

// isArithmeticProgression:
assert(isArithmeticProgression!ubyte([3, 2, 1]));
assert(!isArithmeticProgression!ubyte([1, 5, 25]));

// findAN(T)(T[] progression, T n):
assert(findAN!ubyte([2, 3], 3) == 4);
assert(findAN!float([5, 1, -3], 6) == -15.0);

// findAN(T)(T a1, T d, T n):
assert(findAN!ubyte(2, 1, 3) == 4);
assert(findAN!float(5, -4, 6) == -15.0);

// findArithmeticSN(T)(T[] progression, T n):
assert(findArithmeticSN!ubyte([1, 2, 3], 5) == 15);
assert(findArithmeticSN!byte([1, -2], 4) == -12);

// findArithmeticSN(T)(T a1, T d, T n):
assert(findArithmeticSN!ubyte(1, 1, 5) == 15);
assert(findArithmeticSN!byte(1, -3, 4) == -12);

Geometrical

• public T findGeometricQ(T)(T[] progression)
  Finds the difference of the geometric progression in an array consisting of numbers.

• public bool isGeometricProgression(T)(T[] array)
  Checks whether the passed array is an geometric progression.

• public bool isSequence(T)(T[] progression)
  Checks whether the array is a sequence (q = 1, [1, 1, 1, ...]).

• public T findBN(T)(T[] progression, T n)

• public T findBN(T)(T b1, T q, T n)
  Finds a member of the geometric progression at position N.

• public T findGeometricSN(T)(T[] progression, T n)

• public T findGeometricSN(T)(T b1, T q, T n)
  Finds the sum of N members of the geometric progression.

Example

// findGeometricQ:
assert(findGeometricQ!ubyte([25, 50, 100]) == 2);
assert(findGeometricQ!byte([-2, -6, -18]) == 3);

// isGeometricProgression:
assert(isGeometricProgression!ubyte([1, 4, 16]));
assert(!isGeometricProgression!ubyte([8, 10, 16]));

// isSequence:
assert(isSequence([2, 2]));
assert(!isSequence([1, 2]));

// findBN(T)(T[] progression, T n):
assert(findBN!byte([-2, -6], 3) == -18);
assert(findBN!float([100, 50, 25], 4) == 12.5);

// findBN(T)(T b1, T q, T n):
assert(findBN!byte(-2, 3, 3) == -18);
assert(findBN!float(100, 0.5, 4) == 12.5);

// findGeometricSN(T)(T[] progression, T n):
assert(findGeometricSN!ubyte([1, 2], 3) == 7);
assert(findGeometricSN!float([100, 25], 3) == 131.25);

// findGeometricSN(T)(T b1, T q, T n):
assert(findGeometricSN!ubyte(1, 2, 3) == 7);
assert(findGeometricSN!float(100, 0.25, 3) == 131.25);

Module chances

• public T chance(T)(T value, T from)
  Finds the chance of value shares falling out of from.

Example

assert(chance!byte(5, 25) == 20);
assert(chance!byte(19, 20) == 95);

Module percents

• public T percents(T)(real value, real from)
  Finds the percentage of value from from parameter.

• public T[] percentsCaptures(T)(T[] captures, T from)
  Finds the percentage for each element in the array relative to the from parameter.

Example

// percents:
assert(percents!ubyte(5, 10) == 50);
assert(percents!float(2.5, 10) == 25.0);

// percentsCaptures:
float[] percentsOfTen = percentsCaptures!float([2.5, 7.5], 10);
float[] expectedResults = [25.0, 75.0];

foreach (ubyte i; 0 .. 2)
	assert(percentsOfTen[i] == expectedResults[i]);

Module square_equations

• public T findDesc(T)(T a, T b, T c)
  Finds the discriminant of the square equation based on the coefficients a, b and `c'.

• public T[] resolveFull(T)(T a, T b, T c)
  Finds the roots of the full square equation and, if there are none, throws an error.

• public T[] resolveAB(T)(T a, T b)
  Finds the roots of an incomplete square equation (a, b).

Example

// findDesc:
assert(findDesc!byte(-1, 4, -3) == 4);
assert(findDesc!byte(1, -1, 0) == 1);

// resolveFull:
int[] result = resolveFull!int(-1, 4, -3);
int[] expectedResults = [1, 3];

foreach (ubyte i; 0 .. 2)
	assert(result[i] == expectedResults[i]);

// resolveAB:
int[] result = resolveAB!int(1, -1);
int[] expectedResults = [1, 0];

foreach (ubyte i; 0 .. 2)
	assert(result[i] == expectedResults[i]);

Module trigonometry

• public double sine(T)(T angleMeasure)
  Finds the sine of the angle by its degree measure.

• public double cosine(T)(T angleMeasure)
  Finds the cosine of the angle by its degree measure.

• public double tangents(T)(T angleMeasure)
  Finds the tangents of the angle by its degree measure.

• public double cotangents(T)(T angleMeasure)
  Finds the cotangents of the angle by its degree measure.

Example

assert(sine(30) == 0.5);
assert(cosine(60) == 0.5);
assert(tangents(45) == 1);
assert(cotangents(45) == 1);

Feedback

Open issues and pull requests if it's mandatory. Thanks for reading and downloading.