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Smath solve & plot Diophantine

Diophantine function x y f 3 x 2^* 4 y * - 7 - :

n sol x y f n isolve maple :

n Sol n sol mat2sys :

Dioph n Sol sys2mat :

integer n fractional n 21 mat # # 3 - 2 - 1 - 0123 # # 111 mat typical: n 2.5 21 mat ≡

n 2.5 - :

Diophantine Segments XY 14 n * - 34 n * - 21 mat 1 - 6 n * - 12 n 2^* + 518 n * - 12 n 2^* + 21 mat augment :

U XY 21 el : V XY 11 el : 12 mat

u XY 22 el : v XY 12 el : 12 mat

Diophantine solutions wrt 'n' 14 n * - 34 n * - 21 mat 1 - 6 n * - 12 n 2^* + 518 n * - 12 n 2^* + 21 mat f 50736321 mat

U V 21 mat 3 U 2^(* 3 V 2^(* 21 mat augment 135071136322 mat

34 n * - 14 n * - 21 mat 131121 mat

Diophantine Generatrix x y q 3 x 2^* 4 y * - 7 - :

The Diophantine segment supports fractional 'n'. Interesting to animate ... q & f plot same

x Interp XY 1 col XY 2 col x linterp :

x XY 11 el 1 + : 12

x Interp 107

xy x x Interp augment : 1210712 mat

plot f XY xy 31 sys :

XY 11891312522 mat

xy 1210712 mat

plot

U V f u v f 21 mat 4564651221 mat