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#  Zolotarev Polynomials Degree 2-5,
#  Version 1.0 - 17/05/20
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# deg 2 (quadratic) is easy there are many 
# here are the simplest
{1/2(x^2-2x-1) 1/3(x^2-3x-1), 1/4(x^2-4x-1)}
# deg 2 quadratic (b0,b1,b2,gamma,alpha,beta)
{{-1/2,-1,1/2,1,1,3},{-1/3,-1,1/3,3/2,2,4},{-1/4,-1,1/4,2,3,5}}
 
# deg 3 cubic (b0,b1,b2,b3,gamma,alpha,beta)

#1st r=-1, s=1/3
{11/16,-27/16,-27/16,27/16,1,1,5/3}

# 2nd r=-11/5, s=11/15
{131/144,-125/144,-275/144,125/144,5/3,11/5,13/5}
 
#3rd r=-13/8, s=13/24
{191/225,-256/225,-416/225,256/225,4/3,13/8,17/8}

#4th  r=-23/7, s=23/21 

#5th r=-11/4, s=11/12

#6th r=-13/3, s=13/9

#7th r=-37/28 s=37/84

# deg 4 quartic (b0,b1,b2,b3,b4,gamma,alpha,beta)

#1st r=-10/9, s=5/18
{4293/6400,1547/640,-2997/800,-2187/640,19683/6400,65/54,37/27,43/27}

#2nd r=-286/125, s=143/250
{467875/1168128,126947/44928,-33625/16224,-171875/44928,1953125/1168128,481/250,307/125,317/125}


#3rd r=-221/128, s=221/512
{489088/975375, 155617/57375, -57472/21675, -212992/57375, 2097152/975375,799/512,247/128,263/128}

# deg 5 quintic (b0,b1,b2,b3,b4,b5,gamma,alpha,beta)

#1st  r=-41/(5*Sqrt[145]) 
{-418129/746496, (228085*Sqrt[145])/746496, 1990879/373248, (-376855*Sqrt[145])/373248, -4310125/746496, (525625*Sqrt[145])/746496, (11*Sqrt[29/5])/25, 67/(5*Sqrt[145]), 77/(5*Sqrt[145])}

#2nd  r=-135/(7*Sqrt[385])
{-14874289/21233664, (1106875*Sqrt[385])/7077888, 66856625/10616832, (-5291825*Sqrt[385])/10616832, 
 -5187875/786432, (7263025*Sqrt[385])/21233664, 165/(7*Sqrt[385]), 185/(7*Sqrt[385]), 199/(7*Sqrt[385])}