- **Miscellaneous Math**
(*https://www.mersenneforum.org/forumdisplay.php?f=56*)

- - **visualisations of primes / cycle representations**
(*https://www.mersenneforum.org/showthread.php?t=27644*)

visualisations of primes / cycle representationsA 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. [URL]http://devalco.de/matrix_with_det_1/system_matrix_with_det_1.php[/URL] For mathematicians, who likes visualisations of prime pattern I suggest proudly my other implementations in php: [URL]http://devalco.de/System/system_natural.php[/URL] [URL]http://devalco.de/unit_circle/system_complex.php[/URL] [URL]http://devalco.de/unit_circle/system_unit_circle.php[/URL] [URL]http://devalco.de/unit_circle/system_tangens.php[/URL] 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. :s485122: :juggle: :camping: |

[QUOTE=bhelmes;601418]
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.[/QUOTE] After removing some bugs and some duplicates it looks nicer: [URL]http://devalco.de/matrix_with_det_1/system_matrix_with_det_1.php[/URL] 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. :redface: :hello: :sleep: |

[QUOTE=bhelmes;603067]<snip>
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 ? <snip>[/QUOTE]It's a bug. I note also that the determinant of your matrix isn't 1 (mod 37), but is rather Mod(24,37). [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)] ?[/code] |

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