vedicmaths 0.1.0

Python helpers for learning and applying Vedic mathematics techniques.

Vedic Mathematics

Python helpers for learning and applying Vedic mathematics techniques. The library focuses on two things:

• returning correct arithmetic results as simple Python values
• exposing step-by-step workings that teachers, students, notebooks, and apps can display

This project is early-stage and intended to grow into an open-source package of well-tested Vedic mathematics methods.

The first implementation pass is guided by the parsed source chunks in the larger Mr Rishi project, especially data/processed/Vedic_mathematics_chunks.jsonl.

Install for Development

git clone https://github.com/ksriniv2/vedicmaths.git
cd vedicmaths
python -m pip install -e ".[dev]"

If you are working from this local starter folder:

cd C:\Users\KARTH\OneDrive\Documents\vedicmathematics
python -m pip install -e ".[dev]"

Quick Start

from vedicmathematics import (
    nikhilam_multiply,
    nikhilam_steps,
    square_ending_in_5,
    urdhva_tiryagbhyam_multiply,
)

print(nikhilam_multiply(98, 97))
# 9506

print(urdhva_tiryagbhyam_multiply(123, 456))
# 56088

print(square_ending_in_5(35))
# 1225

trace = nikhilam_steps(98, 97)
for step in trace.steps:
    print(step.title, step.expression, "=>", step.value)

You can also use the shorter package alias:

from vedicmaths import nikhilam_multiply

Available Functions

Function	Purpose
digit_sum(number)	Sums the decimal digits of a number.
sum_digits_until_single(number)	Repeated digit sum, equivalent to digital root.
nikhilam_multiply(a, b, base=None)	Multiplies numbers using a nearby base, commonly a power of ten.
nikhilam_steps(a, b, base=None)	Returns the worked steps for Nikhilam multiplication.
anurupyena_multiply(a, b, working_base, theoretical_base=None)	Proportionate-base multiplication when a multiple or sub-multiple is more convenient.
anurupyena_steps(a, b, working_base, theoretical_base=None)	Worked steps for proportionate-base multiplication.
urdhva_tiryagbhyam_multiply(a, b)	General multiplication using the vertically-and-crosswise digit method.
urdhva_tiryagbhyam_steps(a, b)	Returns the worked steps for vertically-and-crosswise multiplication.
left_to_right_add(a, b)	Addition with a trace-friendly column process.
left_to_right_add_steps(a, b)	Worked steps for addition.
subtract_using_complement(a, b)	Subtraction by complementing the subtrahend from a power of ten.
subtract_using_complement_steps(a, b)	Worked steps for complement subtraction.
complement(number, base=None)	Complement from a supplied base or next power of ten.
all_from_9_last_from_10(number)	Nikhilam-style complement helper.
vinculum_digits(number)	Signed digit representation for digits above 5.
multiply_by_5(number)	Shortcut for multiplication by 5.
multiply_by_9(number)	Shortcut for multiplication by 9.
multiply_by_11(number)	Adjacent-sum shortcut for multiplication by 11.
multiply_by_11_steps(number)	Worked steps for multiplication by 11.
multiply_by_12(number)	Shortcut for multiplication by 12.
multiply_by_15(number)	Shortcut for multiplication by 15.
multiply_by_25(number)	Shortcut for multiplication by 25.
multiply_by_50(number)	Shortcut for multiplication by 50.
multiply_by_75(number)	Shortcut for multiplication by 75.
multiply_by_99(number)	Shortcut for multiplication by 99.
multiply_by_125(number)	Shortcut for multiplication by 125.
multiply_by_999(number)	Shortcut for multiplication by 999.
multiply_by_repeated_9(number, count)	Multiply by 9, 99, 999, etc.
square_ending_in_5(number)	Squares numbers ending in 5 using the "one more than the previous" pattern.
square_ending_in_5_steps(number)	Returns the worked steps for squaring a number ending in 5.
square_near_base(number, base=None)	Squares numbers close to a power-of-ten base.
square_near_base_steps(number, base=None)	Worked steps for near-base squaring.
square_near_50(number)	Shortcut for squaring values near 50.
cube_ending_in_5(number)	Cubes numbers ending in 5.
divide_by_5(number)	Division by 5 as doubling then dividing by 10.
divide_by_25(number)	Division by 25 as multiplying by 4 then dividing by 100.
recurring_decimal_unit_fraction(denominator, limit=None)	Decimal expansion of 1 / denominator, with repeating cycles in parentheses.
osculator_for_ending_9(divisor)	Ekadhika-style osculator for divisors ending in 9.
fraction_to_percent(numerator, denominator)	Converts fractions to percentages.
percent_of(percent, number)	Calculates percent of a number.
transpose_percent(percent, number)	Uses a% of b = b% of a.
is_divisible_by_3(number)	Divisibility by 3 using digit sum.
is_divisible_by_9(number)	Divisibility by 9 using digit sum.
is_divisible_by_11(number)	Divisibility by 11 using alternating digit sums.
square_root_if_perfect(number)	Returns the integer square root for perfect squares, otherwise None.
cube_root_if_perfect(number)	Returns the integer cube root for perfect cubes, otherwise None.
digital_root(number)	Computes a number's digital root.
casting_out_nines_check(a, b, result, operator="*")	Verifies +, -, or * results using digital roots.

Example Step Trace

from vedicmathematics import nikhilam_steps

trace = nikhilam_steps(98, 97)
print(trace.result)
# 9506

for step in trace.steps:
    print(f"{step.title}: {step.expression} = {step.value}")

Output:

Choose base: base = 100 = 100
Find deviations: 98 - 100, 97 - 100 = -2, -3
Cross subtract: 98 + (-3) = 95
Multiply deviations: (-2) * (-3) = 6
Combine: (95 * 100) + (6) = 9506

Roadmap

Good next functions to add:

• division using Paravartya Yojayet
• multiplication by 9, 99, 999, and related bases
• straight division and auxiliary fractions
• simple and complex oscillators for divisibility
• cube-root techniques
• fraction simplification and recurring decimal patterns
• richer renderers for traces, such as Markdown and HTML

Development

Run tests:

python -m pytest

Project structure:

vedicmathematics/
  vedicmathematics/
    __init__.py
    arithmetic.py
  tests/
    test_arithmetic.py
  pyproject.toml
  README.md

Contributing

Contributions are welcome. Please include:

• a clear function name and docstring
• tests for regular cases and edge cases
• a *_steps variant when the method is teachable step by step
• examples in the README when adding a major new method

License

MIT