Haskell – jblog

Sudoku Generation

Over two years ago, I wrote a basic 3×3-sudoku solver which uses both fundamental rule-based elimination and guessing to arrive at the solution. Revisiting the topic of computer-aided sudoku manipulation, I wrote a generalized sudoku generator (sudoku.hs).

    | 4  
  3 |    
---------
  2 | 1  
  4 |    

./sudoku 5 2

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23rd of Mar, 201924th of Mar, 2019 by jfrech Categories: Games, Haskell, ProgrammingTags: generator, puzzle, sudoku Leave a comment

Symbolic Closed-Form Fibonacci

Let $V := \{(a_j)_{j\in\mathbb{N}}\subset\mathbb{C}|a_n=a_{n-1}+a_{n-2}\forall n>1\}$ be the two-dimensional complex vector space of sequences adhering to the Fibonacci recurrence relation with basis $B := ((0,1,\dots), (1,0,\dots))$ .
Let furthermore $f: V\to V, (a_j)_{j\in\mathbb{N}}\mapsto(a_{j+1})_{j\in\mathbb{N}}$ be the sequence shift endomorphism represented by the transformation matrix

$A := M^B_B(f) = \begin{pmatrix}1&1\\1&0\end{pmatrix}$ .

By iteratively applying the sequence shift a closed-form solution for the standard Fibonacci sequence follows.

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01st of Dec, 201801st of Dec, 2018 by jfrech Categories: Haskell, Mathematics, ProgrammingTags: 2018, diagonalization, fibonacci Leave a comment