(otus algebra)

A package for a smart math computing in the Ol (Otus Lisp).

Installing

Possible options:

• Just make; make install inside the project folder,
• Or kiss install libol-algebra using ol-packages repository,
• If you don't need the fast inexact math support (the optimized C code for floating point machine types) or you don't have the C compiler available, you can just copy the "otus" folder to your project.

Usage

Simple example:

$ ol
Welcome to Otus Lisp 2.5
type ',help' to help, ',quit' to end session.
> (import (otus algebra))
;; Library (otus algebra) added
;; Imported (otus algebra)
> (dot-product [1 2 3] [8 -3 5])
17

How to use infix notation inside Lisp (\\ is a short for infix-notation):

> (import (math infix-notation))
;; Library (math infix-notation) added
;; Imported (math infix-notation)
> (\\
     [1,3,-5] • [4,-2,-1]
  )
3

Additional unicode math symbols usage:

> (import (otus algebra unicode))
;; Library (otus algebra unicode) added
;; Imported (otus algebra unicode)

> (define-values (a b c) (values 5 3 -26))
;; All defined

> (define D (\\
     b ² − 4 * a * c
  ))
;; Defined D

> (define X₁ (\\
     (- b + √(D)) / (2 * a)
  ))
;; Defined X₁
> (print "X₁ = " X₁)
X₁ = 2

> (define X₂ (\\
     (- b - √(D)) / (2 * a)
  ))
;; Defined X₂
> (print "X₂ = " X₂)
X₂ = -13/5

> (print (\\
     a * (X₂)² + b * X₂ + c
))
0

A lot of examples available under the Reference page and in the "tests" folder.

Very Important Notes

• All algebra arrays in Ol are indexed starting from 1. From 1, as mathematicians do. Not from 0, as programmers do.
  Negative indices mean "counting from the end of".

• By default all algebra math are exact (but it's can be changed using environment variables). That means no loss of precision during calculations.

  • Some functions (like sin) can't be exact,
  • Some functions (like floor) can be exact only,
  • Most functions (like sqrt) can be exact and inexact depends on argument(s) exactness.

These and other package features described in detail on the main Reference page.

Good luck and happy calculations!

> (\\
    3 ^ (2 ^ (3 ^ 2))
  )
19323349832288915105454068722019581055401465761603328550184537628902466746415537000017939429786029354390082329294586119505153509101332940884098040478728639542560550133727399482778062322407372338121043399668242276591791504658985882995272436541441