JacobLee23 / riemann

A pure-Python package for computing Riemann sums of functions of several real variables.

riemann

Riemann, a pure-Python package for computing Riemann sums of functions of several real variables.

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Basic Usage

Riemann provides an intuitive syntax for calculating the Riemann sum of a function of several real variables over a closed multi-dimensional interval.

The below code snippet computes the Riemann sum of $f(x) = x^{2} + x$ over the interal $[0, 2]$ using 10 partitions using the left rule along the $x$-axis.

>>> import riemann
>>> from riemann import Interval
>>> f = lambda x: x ** 2 + x
>>> intervals = [Interval(0, 2, 10)]
>>> rules = [riemann.Left]
>>> riemann.riemann_sum(f, intervals, rules)
Decimal('2.28')

However, riemann is not restricted to computing Riemann sums only over one dimension. A similar syntax can be used to calculate the Riemann sum of a function of several real variables over a closed multi-dimensionl interval. Additionally, different combinations of rules can be used to compute the Riemann sum.

See Quickstart for additional example usage of the riemann module.

Features

• Fast computation of Riemann sums.
• Supports the computation of multi-dimensional Riemann sums.
• Supports the computation of the left, middle, and right Riemann sums.
• Supports the computation of the trapezoidal Riemann sum.
• Supports the computation of the upper and lower Darboux sums. (Under Development)

Requirements

Riemann requires Python 3.8+. This project does not require any additional dependencies.

Installation

$ pip install riemann

Documentation

The documentation for this project is available on Read the Docs.