mathgenerator/README.md

# mathgenerator
![PyPI download month](https://img.shields.io/pypi/dm/mathgenerator?label=PyPI%20downloads)

A math problem generator, created for the purpose of giving self-studying students and teaching organizations the means to easily get access to random math problems to suit their needs.

To try out generators, go to <https://todarith.ml/generate/>

If you have an idea for a generator, please add it as an issue and tag it with the "New Generator" label.

## Table of Contents
* [Installation](#installation)
* [Basic Usage](#basic-usage)
  * [More Complicated Usage](#more-complicated-usage)
* [Documentation](#documentation)
* [List of Generators](#list-of-generators)
  * [algebra](#algebra)
  * [basic_math](#basic_math)
  * [calculus](#calculus)
  * [computer_science](#computer_science)
  * [geometry](#geometry)
  * [misc](#misc)
  * [statistics](#statistics)

## Installation

The project can be install via pip

```bash
pip install mathgenerator
```

## Basic Usage
Here is an example of how you would generate an addition problem:

```python
from mathgenerator import mathgen

#generate an addition problem
problem, solution = mathgen.addition()

#another way to generate an addition problem using genById()
problem, solution = mathgen.genById(0)
```
### More Complicated Usage

```
import sys
from mathgenerator import mathgen

worksheet = mathgen.make_worksheet("2020-11-29")
mathgen.add_section_with_task_to_worksheet(worksheet, 105, 5)
mathgen.add_section_with_task_to_worksheet(worksheet, 2, 5)
mathgen.write_pdf(worksheet)
```

## Documentation
* `getGenList()` returns a list of all generators in the repository in the format `[id, title, self, funcname, subjectname]`

* `genById(id)` generates a problem, solution set with generator id `id` in the format `[problem, solution]`

* `make_pdf(id, count)` creates a printable pdf worksheet with `count` problems generated by the generator with id `id`.

## List of Generators
## algebra
| Id   | Skill | Example problem | Example Solution | Function Name | Kwargs |
|------|-------|-----------------|------------------|---------------|--------|
| 11 | Basic Algebra | 7x + 9 = 9 | 0 | basic_algebra | `maxVariable=10`  |
| 12 | Logarithm | log2(32) | 5 | log | `maxBase=3` `maxVal=8`  |
| 17 | Integer Multiplication with 2x2 Matrix | 1 * [[9, 0], [1, 4]] =  | [[9,0],[1,4]] | multiply_int_to_22_matrix | `maxMatrixVal=10` `maxRes=100`  |
| 20 | Midpoint of the two point | (0,9),(10,-1)= | (5.0,4.0) | midpoint_of_two_points | `maxValue=20`  |
| 21 | Factoring Quadratic | x^2+x-20 | (x-4)(x+5) | factoring | `range_x1=10` `range_x2=10`  |
| 23 | Solve a System of Equations in R^2 | -x + 9y = -80, -10x - 7y = -24 | x = 8, y = -8 | system_of_equations | `range_x=10` `range_y=10` `coeff_mult_range=10`  |
| 24 | Distance between 2 points | Find the distance between (-2, 1) and (-1, 1) | sqrt(1) | distance_two_points | `maxValXY=20` `minValXY=-20`  |
| 26 | Linear Equations | 6x + 15y = 300, 1x + 15y = 275 | x = 5, y = 18 | linear_equations | `n=2` `varRange=20` `coeffRange=20`  |
| 41 | Intersection of Two Lines | Find the point of intersection of the two lines: y = -6/6x + 1 and y = 7/4x - 4 | (20/11, -9/11) | intersection_of_two_lines | `minM=-10` `maxM=10` `minB=-10` `maxB=10` `minDenominator=1` `maxDenominator=6`  |
| 43 | Cross Product of 2 Vectors | [-7, 3, -16] X [9, -4, 5] =  | [-49, -109, 1] | vector_cross | `minVal=-20` `maxVal=20`  |
| 45 | Simple Interest | Simple interest for a principle amount of 4672 dollars, 4% rate of interest and for a time period of 1 years is =  | 186.88 | simple_interest | `maxPrinciple=10000` `maxRate=10` `maxTime=10`  |
| 46 | Multiplication of two matrices | Multiply<table><tr><td>6</td><td>1</td><td>4</td><td>0</td></tr><tr><td>-4</td><td>-5</td><td>-5</td><td>-9</td></tr></table>and<table><tr><td>-5</td><td>1</td><td>-10</td><td>-7</td></tr><tr><td>-1</td><td>0</td><td>8</td><td>-4</td></tr><tr><td>0</td><td>-8</td><td>-7</td><td>-5</td></tr><tr><td>3</td><td>-6</td><td>10</td><td>1</td></tr></table> | <table><tr><td>-31</td><td>-26</td><td>-80</td><td>-66</td></tr><tr><td>-2</td><td>90</td><td>-55</td><td>64</td></tr></table> | matrix_multiplication | `maxVal=100` `max_dim=10`  |
| 50 | Quadratic Equation | Zeros of the Quadratic Equation 16x^2+181x+77=0 | [-0.44, -10.87] | quadratic_equation | `maxVal=100`  |
| 65 | Multiplication of 2 complex numbers | (-5-14j) * (-13-7j) =  | (-33+217j) | multiply_complex_numbers | `minRealImaginaryNum=-20` `maxRealImaginaryNum=20`  |
| 72 | Dot Product of 2 Vectors | [10, 14, 7] . [-3, -10, 14] =  | -72 | vector_dot | `minVal=-20` `maxVal=20`  |
| 74 | Inverse of a Matrix | Inverse of Matrix Matrix([[49, 4, 29], [43, 15, 10], [11, 77, 74]]) is: | Matrix([[170/47803, 1937/95606, -395/95606], [-1536/47803, 3307/95606, 757/95606], [1573/47803, -3729/95606, 563/95606]]) | invert_matrix | `SquareMatrixDimension=3` `MaxMatrixElement=99` `OnlyIntegerElementsInInvertedMatrix=False`  |
| 77 | Determinant to 2x2 Matrix | Det([[67, 21], [69, 23]]) =  |  92 | int_matrix_22_determinant | `maxMatrixVal=100`  |
| 78 | Compound Interest | Compound interest for a principle amount of 8340 dollars, 8% rate of interest and for a time period of 9 year is =  | 16671.7 | compound_interest | `maxPrinciple=10000` `maxRate=10` `maxTime=10`  |
| 100 | complex Quadratic Equation | Find the roots of given Quadratic Equation 3x^2 + 9x + 3 = 0 | simplified solution : ((-0.382, -2.618)), generalized solution : ((-9 + sqrt(45))/2*3, (-9 - sqrt(45))/2*3) | complex_quadratic | `prob_type=0` `max_range=10`  |
| 105 | Combine Like terms | 2x^1 + 3x^2 + 1x^1 | 3x^1 + 3x^2  | combine_like_terms | `maxCoef=10` `maxExp=20` `maxTerms=10`  |
| 111 | Expanding Factored Binomial | (-5x-6)(-5x-3) | 25*x^2+45*x+18 | expanding | `range_x1=10` `range_x2=10` `range_a=10` `range_b=10`  |
## basic_math
| Id   | Skill | Example problem | Example Solution | Function Name | Kwargs |
|------|-------|-----------------|------------------|---------------|--------|
| 0 | Addition | 47+14= | 61 | addition | `maxSum=99` `maxAddend=50`  |
| 1 | Subtraction | 57-36= | 21 | subtraction | `maxMinuend=99` `maxDiff=99`  |
| 2 | Multiplication | 1*7= | 7 | multiplication | `maxMulti=12`  |
| 3 | Division | 45/15= | 3 | division | `maxA=25` `maxB=25`  |
| 6 | Square Root | sqrt(25)= | 5 | square_root | `minNo=1` `maxNo=12`  |
| 8 | Square | 7^2= | 49 | square | `maxSquareNum=20`  |
| 13 | Complex Division | 67/23= | 2.91 | complex_division | `maxRes=99` `maxDivid=99`  |
| 16 | Fraction Division | (7/4)/(7/6) | 3/2 | divide_fractions | `maxVal=10`  |
| 28 | Fraction Multiplication | (6/10)*(7/5) | 21/25 | fraction_multiplication | `maxVal=10`  |
| 31 | Factorial | 3! =  | 6 | factorial | `maxInput=6`  |
| 44 | Compare Fractions | Which symbol represents the comparison between 3/7 and 6/5? | < | compare_fractions | `maxVal=10`  |
| 47 | Cube Root | What is the cube root of 466 up to 2 decimal places? | 7.75 | cube_root | `minNo=1` `maxNo=1000`  |
| 53 | Exponentiation | 8^4 = | 4096 | exponentiation | `maxBase=20` `maxExpo=10`  |
| 71 | Absolute difference between two numbers | |33--24|= | 57 | absolute_difference | `maxA=100` `maxB=100`  |
| 80 | Percentage of a number | What is 95% of 67? | 63.65 | percentage | `maxValue=99` `maxpercentage=99`  |
| 90 | isprime | Is 78 prime? | No | is_prime | `max_num=100`  |
| 97 | Power of Powers | Simplify 49^1^1= | 49^1 | power_of_powers | `maxBase=50` `maxPower=10`  |
## calculus
| Id   | Skill | Example problem | Example Solution | Function Name | Kwargs |
|------|-------|-----------------|------------------|---------------|--------|
| 7 | Power Rule Differentiation | 4x^9 + 8x^10 + 1x^7 | 36x^8 + 80x^9 + 7x^6 | power_rule_differentiation | `maxCoef=10` `maxExp=10` `maxTerms=5`  |
| 48 | Power Rule Integration | 7x^3 + 3x^1 + 7x^3 + 3x^3 | (7/3)x^4 + (3/1)x^2 + (7/3)x^4 + (3/3)x^4 + c | power_rule_integration | `maxCoef=10` `maxExp=10` `maxTerms=5`  |
| 88 | Differentiation | differentiate w.r.t x : d(sin(x)+6*x^4)/dx | 24*x^3 + cos(x) | differentiation | `diff_lvl=2`  |
| 89 | Definite Integral of Quadratic Equation | The definite integral within limits 0 to 1 of the equation 5x^2 + 6x + 46 is =  | 50.6667 | definite_integral | `max_coeff=100`  |
| 110 | Stationary Points | f(x)=3*x^3 + 8*x^2 + 7*x + 4 | (-1,2),(-7/9,482/243) | stationary_points | `maxExp=3` `maxCoef=10`  |
## computer_science
| Id   | Skill | Example problem | Example Solution | Function Name | Kwargs |
|------|-------|-----------------|------------------|---------------|--------|
| 4 | Binary Complement 1s | 1100= | 0011 | binary_complement_1s | `maxDigits=10`  |
| 5 | Modulo Division | 84%82= | 2 | modulo_division | `maxRes=99` `maxModulo=99`  |
| 14 | Decimal to Binary | Binary of 20= | 10100 | decimal_to_binary | `max_dec=99`  |
| 15 | Binary to Decimal | 1100111 | 103 | binary_to_decimal | `max_dig=10`  |
| 56 | Fibonacci Series | The Fibonacci Series of the first 12 numbers is ? | [0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89] | fibonacci_series | `minNo=1`  |
| 62 | nth Fibonacci number | What is the 12th Fibonacci number? | 144 | nth_fibonacci_number | `maxN=100`  |
| 64 | Binary to Hexidecimal | 00111 | 0x7 | binary_to_hex | `max_dig=10`  |
| 73 | Binary 2's Complement | 2's complement of 1010 = | 110 | binary_2s_complement | `maxDigits=10`  |
| 79 | Decimal to Hexadecimal | Binary of 864= | 0x360 | decimal_to_hexadeci | `max_dec=1000`  |
| 84 | Converts decimal to octal | The decimal number 1800 in Octal is:  | 0o3410 | decimal_to_octal | `maxDecimal=4096`  |
| 91 | Binary Coded Decimal to Integer | Integer of Binary Coded Decimal 1 is =  | 5432 | bcd_to_decimal | `maxNumber=10000`  |
| 103 | Decimal to Binary Coded Decimal | BCD of Decimal Number 4344 is =  | 10158 | decimal_to_bcd | `maxNumber=10000`  |
## geometry
| Id   | Skill | Example problem | Example Solution | Function Name | Kwargs |
|------|-------|-----------------|------------------|---------------|--------|
| 18 | Area of Triangle | Area of triangle with side lengths: 6 19 7 =  | (4.024600061217022e-15+65.72670690061993j) | area_of_triangle | `maxA=20` `maxB=20` `maxC=20`  |
| 19 | Triangle exists check | Does triangle with sides 31, 29 and 48 exist? | Yes | valid_triangle | `maxSideLength=50`  |
| 22 | Third Angle of Triangle | Third angle of triangle with angles 41 and 10 =  | 129 | third_angle_of_triangle | `maxAngle=89`  |
| 25 | Pythagorean Theorem | The hypotenuse of a right triangle given the other two lengths 18 and 16 =  | 24.08 | pythagorean_theorem | `maxLength=20`  |
| 29 | Angle of a Regular Polygon | Find the angle of a regular polygon with 8 sides | 135.0 | angle_regular_polygon | `minVal=3` `maxVal=20`  |
| 32 | Surface Area of Cube | Surface area of cube with side = 18m is | 1944 m^2 | surface_area_cube | `maxSide=20` `unit='m'`  |
| 33 | Surface Area of Cuboid | Surface area of cuboid with sides = 2m, 1m, 6m is | 40 m^2 | surface_area_cuboid | `maxSide=20` `unit='m'`  |
| 34 | Surface Area of Cylinder | Surface area of cylinder with height = 28m and radius = 4m is | 804 m^2 | surface_area_cylinder | `maxRadius=20` `maxHeight=50` `unit='m'`  |
| 35 | Volum of Cube | Volume of cube with side = 16m is | 4096 m^3 | volume_cube | `maxSide=20` `unit='m'`  |
| 36 | Volume of Cuboid | Volume of cuboid with sides = 16m, 5m, 3m is | 240 m^3 | volume_cuboid | `maxSide=20` `unit='m'`  |
| 37 | Volume of cylinder | Volume of cylinder with height = 18m and radius = 19m is | 20414 m^3 | volume_cylinder | `maxRadius=20` `maxHeight=50` `unit='m'`  |
| 38 | Surface Area of cone | Surface area of cone with height = 5m and radius = 17m is | 1854 m^2 | surface_area_cone | `maxRadius=20` `maxHeight=50` `unit='m'`  |
| 39 | Volume of cone | Volume of cone with height = 36m and radius = 19m is | 13609 m^3 | volume_cone | `maxRadius=20` `maxHeight=50` `unit='m'`  |
| 49 | Fourth Angle of Quadrilateral | Fourth angle of quadrilateral with angles 165 , 14, 158 = | 23 | fourth_angle_of_quadrilateral | `maxAngle=180`  |
| 57 | Trigonometric Values | What is tan(0)? | 0 | basic_trigonometry | `angles=[0, 30, 45, 60, 90]` `functions=['sin', 'cos', 'tan']`  |
| 58 | Sum of Angles of Polygon | Sum of angles of polygon with 11 sides =  | 1620 | sum_of_polygon_angles | `maxSides=12`  |
| 60 | Surface Area of Sphere | Surface area of Sphere with radius = 11m is | 1520.5308443374597 m^2 | surface_area_sphere | `maxSide=20` `unit='m'`  |
| 61 | Volume of Sphere | Volume of sphere with radius 77 m =  | 1912320.9585617452 m^3 | volume_sphere | `maxRadius=100`  |
| 70 | Angle between 2 vectors | angle between the vectors [930.31, 981.85, 804.37, 752.12, 365.53, 999.04, 145.81, 535.45, 830.04, 892.98] and [343.3, 858.49, 633.38, 397.4, 225.25, 612.5, 410.13, 294.0, 129.72, 344.08] is: | 0.44 radians | angle_btw_vectors | `maxEltAmt=20`  |
| 75 | Area of a Sector | Given radius, 31 and angle, 181. Find the area of the sector. | Area of sector = 1517.92158 | sector_area | `maxRadius=49` `maxAngle=359`  |
| 86 | Degrees to Radians | Angle 106 in radians is =  | 1.85 | degree_to_rad | `max_deg=360`  |
| 87 | Radians to Degrees | Angle 1 in degrees is =  | 57.3 | radian_to_deg | `max_rad=3`  |
| 95 | Curved surface area of a cylinder | What is the curved surface area of a cylinder of radius, 34 and height, 95? | CSA of cylinder = 20294.69 | curved_surface_area_cylinder | `maxRadius=49` `maxHeight=99`  |
| 96 | Perimeter of Polygons | The perimeter of a 5 sided polygon with lengths of [86, 48, 39, 31, 82]cm is:  | 286 | perimeter_of_polygons | `maxSides=12` `maxLength=120`  |
| 104 | Circumference | Circumference of circle with radius 69 | 433.53978619539146 | circumference | `maxRadius=100`  |
| 108 | Arc length of Angle | Given radius, 10 and angle, 237. Find the arc length of the angle. | Arc length of the angle = 41.36430 | arc_length | `maxRadius=49` `maxAngle=359`  |
| 112 | Area of Circle | Area of circle with radius 100 | 31428.571428571428 | area_of_circle | `maxRadius=100`  |
## misc
| Id   | Skill | Example problem | Example Solution | Function Name | Kwargs |
|------|-------|-----------------|------------------|---------------|--------|
| 9 | LCM (Least Common Multiple) | LCM of 5 and 18 = | 90 | lcm | `maxVal=20`  |
| 10 | GCD (Greatest Common Denominator) | GCD of 6 and 16 =  | 2 | gcd | `maxVal=20`  |
| 27 | Prime Factorisation | Find prime factors of 108 | [2, 2, 3, 3, 3] | prime_factors | `minVal=1` `maxVal=200`  |
| 40 | Common Factors | Common Factors of 94 and 48 =  | [1, 2] | common_factors | `maxVal=100`  |
| 51 | HCF (Highest Common Factor) | HCF of 18 and 4 =  | 2 | hcf | `maxVal=20`  |
| 55 | Comparing surds | Fill in the blanks 37^(1/8) _ 14^(1/2) | < | surds_comparison | `maxValue=100` `maxRoot=10`  |
| 63 | Profit or Loss Percent | Loss percent when CP = 683 and SP = 14 is:  | 97.9502196193265 | profit_loss_percent | `maxCP=1000` `maxSP=1000`  |
| 66 | Geometric Progression | For the given GP [6, 18, 54, 162, 486, 1458] ,Find the value of a,common ratio,7th term value, sum upto 6th term | The value of a is 6, common ratio is 3 , 7th term is 4374 , sum upto 6th term is 2184.0 | geometric_progression | `number_values=6` `min_value=2` `max_value=12` `n_term=7` `sum_term=5`  |
| 67 | Geometric Mean of N Numbers | Geometric mean of 2 numbers 41 and 75 =  | (41*75)^(1/2) = 55.452682532047085 | geometric_mean | `maxValue=100` `maxNum=4`  |
| 68 | Harmonic Mean of N Numbers | Harmonic mean of 3 numbers 60 , 5 and 46 =  |  3/((1/60) + (1/5) + (1/46)) = 12.583586626139818 | harmonic_mean | `maxValue=100` `maxNum=4`  |
| 69 | Euclidian norm or L2 norm of a vector | Euclidian norm or L2 norm of the vector[787.3844948140925, 238.00418481556463, 957.8185591527733] is: | 1262.5516729705996 | euclidian_norm | `maxEltAmt=20`  |
| 81 | Celsius To Fahrenheit | Convert 70 degrees Celsius to degrees Fahrenheit = | 158.0 | celsius_to_fahrenheit | `maxTemp=100`  |
| 82 | AP Term Calculation | Find the term number 47 of the AP series: 31, 69, 107 ...  | 1779 | arithmetic_progression_term | `maxd=100` `maxa=100` `maxn=100`  |
| 83 | AP Sum Calculation | Find the sum of first 78 terms of the AP series: -75, -163, -251 ...  | -270114.0 | arithmetic_progression_sum | `maxd=100` `maxa=100` `maxn=100`  |
| 85 | Converts decimal to Roman Numerals | The number 2239 in Roman Numerals is:  | MMCCXXXIX | decimal_to_roman_numerals | `maxDecimal=4000`  |
| 92 | Complex To Polar Form | rexp(itheta) =  | 11.4exp(i1.84) | complex_to_polar | `minRealImaginaryNum=-20, maxRealImaginaryNum=20`  |
| 93 | Union,Intersection,Difference of Two Sets | Given the two sets a={1, 3, 5, 7, 8} ,b={2, 4, 5, 6, 10}.Find the Union,intersection,a-b,b-a and symmetric difference | Union is {1, 2, 3, 4, 5, 6, 7, 8, 10},Intersection is {5}, a-b is {8, 1, 3, 7},b-a is {2, 10, 4, 6}, Symmetric difference is {1, 2, 3, 4, 6, 7, 8, 10} | set_operation | `minval=3` `maxval=7` `n_a=4` `n_b=5`  |
| 94 | Base Conversion | Convert 1A504 from base 12 to base 16. | 9754 | base_conversion | `maxNum=60000` `maxBase=16`  |
| 98 | Quotient of Powers with Same Base | The Quotient of 16^3 and 16^5 = 16^(3-5) = 16^-2 | 0.00390625 | quotient_of_power_same_base | `maxBase=50` `maxPower=10`  |
| 99 | Quotient of Powers with Same Power | The Quotient of 25^9 and 10^9 = (25/10)^9 = 2.5^9 | 3814.697265625 | quotient_of_power_same_power | `maxBase=50` `maxPower=10`  |
| 101 | Leap Year or Not | Year 1959  | is not a leap year | is_leap_year | `minNumber=1900` `maxNumber=2099`  |
| 102 | Minute to Hour conversion | Convert 251 minutes to Hours & Minutes | 4 hours and 11 minutes | minutes_to_hours | `maxMinutes=999`  |
| 106 | signum function | signum of 362 is = | 1 | signum_function | `min=-999` `max=999`  |
| 109 | Binomial distribution | A manufacturer of metal pistons finds that, on average, 32.59% of the pistons they manufacture are rejected because they are incorrectly sized. What is the probability that a batch of 15 pistons will contain no more than 4 rejected pistons? | 42.82 | binomial_distribution | ``  |
## statistics
| Id   | Skill | Example problem | Example Solution | Function Name | Kwargs |
|------|-------|-----------------|------------------|---------------|--------|
| 30 | Combinations of Objects | Number of combinations from 12 objects picked 8 at a time  | 495 | combinations | `maxlength=20`  |
| 42 | Permutations | Number of Permutations from 14 objects picked 5 at a time =   | 240240 | permutation | `maxlength=20`  |
| 52 | Probability of a certain sum appearing on faces of dice | If 2 dice are rolled at the same time, the probability of getting a sum of 9 = | 4/36 | dice_sum_probability | `maxDice=3`  |
| 54 | Confidence interval For sample S | The confidence interval for sample [293, 222, 205, 214, 255, 298, 209, 296, 287, 219, 211, 277, 269, 284, 270, 206, 273, 248, 223, 227, 282, 260, 275, 291, 246, 242, 251, 249, 263, 250, 207] with 90% confidence is | (260.5165684278054, 242.83827028187204) | confidence_interval | ``  |
| 59 | Mean,Standard Deviation,Variance | Find the mean,standard deviation and variance for the data[40, 6, 7, 46, 50, 30, 18, 29, 27, 38, 12, 15, 22, 44, 21] | The Mean is 27.0 , Standard Deviation is 188.93333333333334, Variance is 13.745302227791623 | data_summary | `number_values=15` `minval=5` `maxval=50`  |
| 76 | Mean and Median | Given the series of numbers [5, 98, 52, 58, 6, 50, 38, 55, 48, 16]. find the arithmatic mean and mdian of the series | Arithmetic mean of the series is 42.6 and Arithmetic median of this series is 49.0 | mean_median | `maxlen=10`  |
| 107 | Conditional Probability | Someone tested positive for a nasty disease which only 1.66% of population have. Test sensitivity (true positive) is equal to SN= 91.53% whereas test specificity (true negative) SP= 98.48%. What is the probability that this guy really has that disease? | 50.41% | conditional_probability | ``  |