yuriy-chumak / libol-algebra

The package for scientific computing with Otus Lisp

(otus algebra)

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

Installing

Just do make; make install inside the project folder.

Or do kiss install libol-algebra with ol-packages repository.

If you don't need fast inexact math support (meaning optimized C code for floating point machine types) or you don't have a C compiler available, you can just copy the "otus" folder to your project.

Usage

To access libol-algebra functions import (otus algebra) in your code.
To access unicode symbols and functions import (otus algebra unicode).

$ ol
Welcome to Otus Lisp 2.4
type ',help' to help, ',quit' to end session.
> (import (otus algebra))
> (dot-product [1 2 3] [8 -3 5])
17
> (infix-notation
     [1,3,-5] • [4,-2,-1]
  )
3

> (import (otus algebra))
> (import (otus algebra unicode))
> (define-values (a b c) (values 5 3 -26))
> (define D (infix-notation
     b ² − 4 * a * c
  ))
> (define X₁ (infix-notation
     (- b + √(D)) / (2 * a)
  ))
> (print "X₁ = " X₁)
X₁ = 2
> (define X₂ (infix-notation
     (- b - √(D)) / (2 * a)
  ))
> (print "X₂ = " X₂)
X₂ = -13/5
> (print (infix-notation
     a * (X₂)² + b * X₂ + c
))
0

> ,quit
bye-bye.

You can shorten infix-notation macro with any valid symbol

> (import (otus algebra))
> (import (otus algebra unicode))

; let's shorten infix-notation
> (define-macro @ (lambda args
     `(infix-notation ,args)))

; now use @ instead
> (print (@
     5 * (2)² + 3 * 2 - 26
))
0

A lot of usage examples avaiable in the "tests" folder and in the functions Reference.

Very Important Notes

All algebra objects 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".

> (ref [10 20 30 40] 1)
10
> (ref [10 20 30 40] 0)
#false
> (ref [10 20 30 40] -1)
40

By default all algebra math are exact. That means no loss of precision during calculations.
But some functions (like sin) can't be exact. And some functions (like sqrt can be exact and inexact). Some functions (like floor) can be exact only.

> (import (otus algebra))

; exact math:
> (define X 1)
> (infix-notation
    ((X * 1e40 + 42) - (X * 1e40))
  )
42

; inexact math:
> (define I (inexact 1)) ; or just #i1
> (infix-notation
    ((I * 1e40 + 42) - (I * 1e40))
  )
0.0

; one more exact math example
> (infix-notation
    3 ^ (2 ^ (3 ^ 2))
  )
19323349832288915105454068722019581055401465761603328550184537628902466746415537000017939429786029354390082329294586119505153509101332940884098040478728639542560550133727399482778062322407372338121043399668242276591791504658985882995272436541441