20220310, 02:54  #1 
Mar 2016
2^{2}×101 Posts 
visualisations of primes / cycle representations
A peaceful night for you,
this is a visualisation for the exponentation of 2*2 matrixs with determant 1 mod f. I think it is mathematical correct, but perhaps there might be a more beautiful visualisation possible. http://devalco.de/matrix_with_det_1/...with_det_1.php For mathematicians, who likes visualisations of prime pattern I suggest proudly my other implementations in php: http://devalco.de/System/system_natural.php http://devalco.de/unit_circle/system_complex.php http://devalco.de/unit_circle/system_unit_circle.php http://devalco.de/unit_circle/system_tangens.php All my friends ask me daily, if there is a new Mp arrived. Some friends asked me also, if the amound of Mp is not limited. The problem is, if I try to explain them some Number theory, they shut down immediatly. I am glad, that spring is arriving and removes some depressiv moods. Last fiddled with by Dr Sardonicus on 20220402 at 14:58 Reason: fix typo in title 
20220402, 00:42  #2  
Mar 2016
2^{2}×101 Posts 
Quote:
http://devalco.de/matrix_with_det_1/...with_det_1.php The matrixs mod p, with p=3 mod 4 look o.k. but the other matrixs mod p, with p=1 mod 4 contain elements which do not "lead" to the identity matrix: For example: p:=37 (16, 23, 23, 33)^(36*38)=/=(1,0,0,1). Why ? or is it a bug ? There might be a more mathematically accurate title for this thread: something like : visualisation of different fields mod p Perhaps a mod could improve the title. 

20220403, 14:07  #3  
Feb 2017
Nowhere
13401_{8} Posts 
Quote:
Code:
? M=Mod(1,37)*[16,23;23,23] %1 = [Mod(16, 37) Mod(23, 37)] [Mod(23, 37) Mod(23, 37)] ? M^(36*38) %2 = [Mod(1, 37) Mod(0, 37)] [Mod(0, 37) Mod(1, 37)] ? 

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