sqrt2

print "sqrt 2"

sqrt: :square-root

x: (1 + sqrt 2)

{

1 3  7  17 41 99

1 =
2 = 3 - 1
3 =
4 = 3 + 1       >1 , <=4    , f 4 = [ 3 1]
--------------
5 = 7 - 3 + 1 ,  >4 , >=11 , f 5  = [7 -3 1]
6 = 7 - 1                  , f 6 =  [7 -1]
7 =
8 = 7 + 1
9 = 7 + 3 - 1
10 = 7 + 3
11 = 7 + 3 + 1              . f 11 = [7 3 1]
------------------
12 = 17 - 7 + 3 - 1   >11 , <=28  , f 12 = [18 -7 1]
13
14
15
16 = 17 - 1
17 =
18 = 17 + 1
19 = 17 + 3 - 1

28 = 17 + 7 + 3  + 1
--------------------------
47 =
}

{
>> f 50 == [41 7 3 -1]

41 / sqrt 2 = 29
7 / sqrt 2 = 5
3 / sqrt 2  = 2
-1 / sqrt 2 = -1

29 + 5 + 2 - 1 = 35 , 50 / sqrt 2 = 35.35533905932737 , (50 * 50) - (2 * ( 35 * 35)) = 50

100 / sqrt 2 = 70.71067811865474
50 *  sqrt 2 = 70.71067811865476

200 / sqrt 2 = 141.42135623730948
100 * sqrt 2 = 141.42135623730948
}


index: [0 1  3  7  17 41 99 ]

m: 0

limit: clear copy [] ;
foreach n index [ m: m + n  insert tail limit m ]



;---------------------------------

f: func [ n /local m tmp i][

  i: 1

  tmp: clear copy []

   for m -1 + length? limit 1  -1 [

if all [ n > limit/:m n <= limit/(m + 1) ][n: n - index/(m + 1 )  insert tail tmp   index/(m + 1) * i  if n < 0 [ i: i * -1 ] n: abs n ]

]
return tmp
]
;----------------------


fn: func [ n /local m tmp i][

  i: 1

  tmp: clear copy []

   for m -1 + length? limit 1  -1 [

if all [ n > limit/:m n <= limit/(m + 1) ][n: n - index/(m + 1 )  insert tail tmp   (m ) * i  if n < 0 [ i: i * -1 ] n: abs n ]

]
return tmp
]

;-----------------------

gn: func [ n /local v u m ][

v:  fn  n

u: clear copy []

foreach m v [ insert tail u reduce [reduce [sign? m (abs m) - 1 ]]]

return u

]

;------------------


g: func [ v /local a b y n ][ a: 0 b: 0 n: 0 y: x  foreach  m v [ n: n + 1 if all [ n = length? v 1 = abs m ][y: 1]    a: a +  ((sign? m) * power y abs m) b: b +  ((sign? m) / power y  abs m ) ] return a * b ]

;---------------------------------------------------------

h: func [ v /local a b y n ][ a: 0 b: 0 n: 0 y: x  foreach  m v [   a: a +  ((sign? m/1) * power y abs m/2)

 b: b + either 1 = mod m/2 2 [((-1 * sign? m/1) / power y  abs m/2 )][ ((sign? m/1) / power y  abs m/2 ) ]

] return a * b ]


 ;---------------------------------------------------------------------

;==============================
{
(1+x^6+x^7)*(1+1/x^6-1/x^7)  =x^7+x^6+x+1 = 679                                              ;(x^2 - 2 x - 1) (x^12 + 3 x^11 + 7 x^10 + 17 x^9 + 41 x^8 + 99 x^7 + 240 x^6 - 99 x^5 + 41 x^4 - 17 x^3 + 7 x^2 - 3 x + 1)  (3 * 2 + 1)
}

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