a10c4891-2aa6-4196-9820-98e3231b3488 59 4 5 false false 0 0 decimal

&[DATE] &[TIME] - &[FILENAME]

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

solve/plot Diophantine

x y f n isolve maple

y 1 - 6 n * 1 - 2 n * + (* + = x 14 n * - = y 56 n * 3 - 2 n * + (* + = x 34 n * - = mat

yxyx n Sol 1 - 6 n * 1 - 2 n * + (* + 14 n * - 56 n * 3 - 2 n * + (* + 34 n * - 41 mat :

n 2.5 - :

Diophantine Segments XY n Sol 2 el n Sol 4 el 21 mat n Sol 1 el n Sol 3 el 21 mat augment :

XY 11891312522 mat

n Sol transpose 89111251314 mat

x Interp XY 1 col XY 2 col x cinterp :

Experiment XY 11 el 0 + XY 11 el 1 + XY 11 el 2 + 31 mat ≡

x XY 11 el 1 + : 12

x Interp 107

xy x x Interp augment : 1210712 mat

p vx 15 - 15 14.5 - range : i 1 vx rows range vy i el 0.75 vx i el 2^* eval : for vx vy augment 31 line :

Trace0 blue ≡

Trace1 solid red 5 ≡

Trace2 transparent dot 6 black ≡

Trace3 + black ≡

XY 1 row xy XY 2 row 31 mat 118912 mat 1210712 mat 1312512 mat 31 mat

x 1 : y 1 : 12 mat

plot p XY xy 31 sys :

ζ 3 x 2^* 4 y * / : 0.75

plot 0 0 + 1000 black 1 5 mat 2 1 sys

solve Diophantine chemical balance
... implicit of integer solutions

f 2 a * 2 c * ≡ 4 a * c e + ≡ 6 a * 2 b * + 4 c * d + 4 e * + ≡ 2 b * 2 d * 2 e * + ≡ 41 mat :

seed a 1 ≡ b 1 ≡ c 1 ≡ d 1 ≡ 41 mat :

expeiment/observe ε 1015 -^:

exclusive of seed e 3 :

a b c d 41 mat f seed ε FindRoot : 1.000000000000000 7.000000000000000 1.000000000000000 4.000000000000000 41 mat

sanity Matcad 5 a b c d e 51 mat 1714351 mat

2 a * 2 c * - 4 a * c e + (- 6 a * 2 b * + 4 c * d + 4 e * + (- 2 b * 2 d * 2 e * + (- 41 mat 0.000000000000000 0.000000000000000 0.000000000000000 0.000000000000000 41 mat

e Clear 1

e 2.7183