mathai 0.4.4

Mathematics solving Ai tailored to NCERT

Math AI Documentation

Philosophy

I think it is a big realization in computer science and programming to realize that computers can solve mathematics.
This understanding should be made mainstream. It can help transform education, mathematical research, and computation of mathematical equations for work.

Societal Implications Of Such A Computer Program And The Author's Comment On Universities Of India

I think mathematics is valued by society because of education. Schools and universities teach them.
So this kind of software, if made mainstream, could bring real change.

The Author's Comments On The Universities In His Country

Educated Indians are having a low IQ and are good for nothing.
The Indian Institute of Technology (IITs) graduates are the leader of the fools.
Every educated Indian is beneath me.
Now learn how this Python library can solve the math questions of your exams.

The Summary Of How Computer "Solves" Math

Math equations are a tree data structure (TreeNode class).
We can manipulate the math equations using various algorithms (functions provided by the mathai library).
We first parse the math equation strings to get the tree data structure (parse function in mathai).

The Library

Import the library by doing:

from mathai import *

str_form

It is the string representation of a TreeNode math equation.

Example

(cos(x)^2)+(sin(x)^2)

Is represented internally as:

f_add
 f_pow
  f_cos
   v_0
  d_2
 f_pow
  f_sin
   v_0
  d_2

Leaf Nodes

Variables (start with a v_ prefix):

• v_0 -> x
• v_1 -> y
• v_2 -> z
• v_3 -> a

Numbers (start with d_ prefix; only integers):

• d_-1 -> -1
• d_0 -> 0
• d_1 -> 1
• d_2 -> 2

Branch Nodes

• f_add -> addition
• f_mul -> multiplication
• f_pow -> power

parse

Takes a math equation string and outputs a TreeNode object.

from mathai import *

equation = parse("sin(x)^2+cos(x)^2")
print(equation)

Output

(cos(x)^2)+(sin(x)^2)

printeq, printeq_str, printeq_log

Prints math equations in a more readable form than usual print.

from mathai import *

equation = simplify(parse("(x+1)/x"))
print(equation)
printeq(equation)

Output

(1+x)*(x^-1)
(1+x)/x

solve, simplify

simplify performs what solve does and more.
It simplifies and cleans up a given math equation.

from mathai import *

equation = simplify(parse("(x+x+x+x-1-1-1-1)*(4*x-4)*sin(sin(x+x+x)*sin(3*x))"))
printeq(equation)

Output

((-4+(4*x))^2)*sin((sin((3*x))^2))

Incomplete Documentation, Will be updated and completed later on

Example Demonstration [limits questions can also be solved other than this these, try limit()]

import sys, os, time
from mathai import *

sys.setrecursionlimit(10000)

def integration_byparts(item): return simplify(fraction(simplify(byparts(simplify(parse(item)))[0])))
def integration_apart(item): return simplify(fraction(integrate(apart(factor2(simplify(parse(item)))))[0]))
def integration_direct(item): return simplify(fraction(simplify(integrate(simplify(parse(item)))[0])))
def integration_trig(item): return simplify(trig0(integrate(trig1(simplify(parse(item))))[0]))
def algebra(item): return logic0(simplify(expand(simplify(parse(item)))))
def trig_basic(item): return logic0(simplify(expand(trig3(simplify(parse(item))))))
def trig_advanced(item): return logic0(simplify(trig0(trig1(trig4(simplify(fraction(trig0(simplify(parse(item))))))))))

all_tasks = [
    *[(item, trig_advanced) for item in [
        "cos(x)/(1+sin(x)) + (1+sin(x))/cos(x) = 2*sec(x)",
        "(1+sec(x))/sec(x) = sin(x)^2/(1-cos(x))"]],
    *[(item, integration_byparts) for item in ["sin(x)*x","x*sin(3*x)","x*log(abs(x))","arctan(x)"]],
    *[(item, integration_apart) for item in ["x/((x+1)*(x+2))","1/(x^2-9)"]],
    *[(item, integration_direct) for item in [
        "x*sqrt(x+2)","sin(cos(x))*sin(x)","2*x/(1+x^2)","sqrt(a*x+b)","cos(sqrt(x))/sqrt(x)","e^(arctan(x))/(1+x^2)","sqrt(sin(2*x))*cos(2*x"]], 
    *[(item, integration_trig) for item in ["sin(2*x+5)^2","sin(x)^4","cos(2*x)^4"]],
    *[(item, algebra) for item in ["(x+1)^2 = x^2+2*x+1","(x+1)*(x-1) = x^2-1"]],
    *[(item, trig_basic) for item in ["2*sin(x)*cos(x)=sin(2*x)"]],
]

def run_task(task):
    item, func = task
    try: result = func(item)
    except Exception as e: result = str(e)
    return item, result

if __name__=="__main__":
    print(f"Solving {len(all_tasks)} math questions...\n")
    start_time = time.time()
    for task in all_tasks:
        item, result = run_task(task)
        print(f"{item}  =>  {result}\n")
    print(f"All tasks completed in {time.time()-start_time:.2f} seconds")

Output

Running 21 tasks asynchronously on 8 cores...

x*log(abs(x))  =>  ((-2*(x^2))+(4*log(abs(x))*(x^2)))*(8^-1)

arctan(x)  =>  (log((abs((1+(x^2)))^-1))+(2*arctan(x)*x))*(2^-1)

sin(cos(x))*sin(x)  =>  cos(cos(x))

1/(x^2-9)  =>  (log(abs((-3+x)))+log((abs((3+x))^-1)))*(6^-1)

x/((x+1)*(x+2))  =>  log((abs((1+x))^-1))+log(((2+x)^2))

x*sin(3*x)  =>  ((-9*cos((3*x))*x)+(3*sin((3*x))))*(27^-1)

(1+sec(x))/sec(x) = sin(x)^2/(1-cos(x))  =>  true

e^(arctan(x))/(1+x^2)  =>  e^arctan(x)

cos(sqrt(x))/sqrt(x)  =>  2*sin((x^(2^-1)))

sqrt(a*x+b)  =>  2*(3^-1)*(((x*a)+b)^(3*(2^-1)))*(a^-1)

sin(x)*x  =>  (-1*cos(x)*x)+sin(x)

(x+1)^2 = x^2+2*x+1  =>  true

(x+1)*(x-1) = x^2-1  =>  true

cos(x)/(1+sin(x)) + (1+sin(x))/cos(x) = 2*sec(x)  =>  true

2*sin(x)*cos(x)=sin(2*x)  =>  true

sqrt(sin(2*x))*cos(2*x)  =>  (3^-1)*(sin((2*x))^(3*(2^-1)))

2*x/(1+x^2)  =>  log(abs((1+(x^2))))

sin(2*x+5)^2  =>  ((-1*(4^-1)*sin((10+(4*x))))+x)*(2^-1)

cos(2*x)^4  =>  ((4^-1)*x)+((64^-1)*sin((8*x)))+((8^-1)*sin((4*x)))+((8^-1)*x)

x*sqrt(x+2)  =>  ((-1*(4^-1)*((2+x)^(2+(2^-1))))+(-2*((2+x)^(2+(2^-1))))+(5*((2+x)^(1+(2^-1)))*x)+((2^-1)*((2+x)^(1+(2^-1)))*x)+((8^-1)*((2+x)^(1+(2^-1)))*x))*((1+(2^-1))^-3)*((2+(2^-1))^-1)

sin(x)^4  =>  (-1*(4^-1)*sin((2*x)))+((32^-1)*sin((4*x)))+((4^-1)*x)+((8^-1)*x)

All tasks completed in 129.78 seconds