32 lines
829 B
Lua
32 lines
829 B
Lua
--Solve the functional equation f' o f = id by ansatz:
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--assume f(x) = ax ^ b. Then
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--f' o f (x) = ba^b * x ^ ( b ( b-1 ) )
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local phi = 0.5 + math.sqrt( 5 ) / 2
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local ihp = 0.5 - math.sqrt( 5 ) / 2
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local a, b = math.pow( phi, ihp ), phi
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local function SeriesCoefficients( )
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local a, b = math.pow( phi, ihp ), phi
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local coefs = {[0] = phi}
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local c, d = a, b
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for i = 1, 150 do
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c = c * d
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d = d - 1
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coefs[i] = c * math.pow( phi, d )
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end
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return coefs
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end
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--SeriesCoefficients()
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local c, d = math.pow( ihp, phi ), ihp
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return {
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pos = function( x ) return a * math.pow( x, b ) end,
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dpo = function( x ) return a * b * math.pow( x, b - 1 ) end,
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neg = function( x ) return c * math.pow( x, d ) end,
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dne = function( x ) return c * d * math.pow( x, d - 1 ) end,
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coefs = SeriesCoefficients()
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} |