JSFH Kernel Curves: Maple Calculations 1. Models whose discriminant has a double zero at (a,b), b nonzero. 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NysvJkkiZEc2IjYkISIiRihGJC8mRiU2JCIiIUYoRiovJkYlNiQiIiJGKEYuLyZGJTYkRihGLEYyLyZGJTYkRixGLEY1LyZGJTYkRjBGLEY4LyZGJTYkRihGMEYsLyZGJTYkRixGMEYsLyZGJTYkRjBGMEYs NysvJkkiZEc2IjYkISIiRihGJC8mRiU2JCIiIUYoRiovJkYlNiQiIiJGKEYuLyZGJTYkRihGLEYyLyZGJTYkRixGLEY1LyZGJTYkRjBGLEYsLyZGJTYkRihGMEY7LyZGJTYkRixGMEYsLyZGJTYkRjBGMEYs 2.Models whose discriminant has a double zero at (a,b), b nonzero (using the prime decompostion of the radical of the ideal). 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 3. Models whose discriminant has a double zero at (a,0). 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 LCYqKEkidEc2IiIiIyZJImRHRiU2JCEiIiIiIkYrJkYoNiRGK0YrRishIiUqJkYkRiYmRig2JCIiIUYrRiZGKw== LCoqKEkidEc2IiIiIyZJImRHRiU2JCEiIiIiISIiIiZGKDYkRixGLEYsISIlKihGJEYmJkYoNiRGKkYsRiwmRig2JEYsRitGLEYvKihGJEYmJkYoNiRGK0YrRiwmRig2JEYrRixGLEYmKiZGJEYsRjhGLCEiIw== JSFH