0.600000000000000
<type 'sage.rings.rational.Rational'>
3/5 = 0
0
1.37065555196861
1.39852837567751
sqrt((1/2*(e^2 - 2*e^(1/2) - 3)*e^(-3/2) + 8.54270702105600)^2)
9.913362573024607
9.941235396733509
1/2*abs(e^2 - 2*e^(1/2) - 3)*e^(-3/2)
x
-1/6*(x - 1)*(x - 2)*x*e - 1/2*(x + 1)*(x - 2)*x*e^(-1) + 1/6*(x + 1)*(x - 2)*x*e^(-2)
[x == -sqrt(2/35*sqrt(30) + 3/7), x == sqrt(2/35*sqrt(30) + 3/7), x == -sqrt(-2/35*sqrt(30) + 3/7), x == sqrt(-2/35*sqrt(30) + 3/7)]
1.37065555196861
1.39852837567751
sqrt((1/2*(e^2 - 2*e^(1/2) - 3)*e^(-3/2) + 8.54270702105600)^2)
9.913362573024607
9.941235396733509
1/2*abs(e^2 - 2*e^(1/2) - 3)*e^(-3/2)
0.0900243711092997*(x + 0.885819298766930)*(x + 0.0740251485476346)*(x - 1.07402514854763) - 0.373399955130276*(x + 0.885819298766930)*(x + 0.0740251485476346)*(x - 1.88581929876693) + 0.802728841958563*(x + 0.885819298766930)*(x - 1.07402514854763)*(x - 1.88581929876693) - 0.571257167284918*(x + 0.0740251485476346)*(x - 1.07402514854763)*(x - 1.88581929876693)
-1/6*(x - 1)*(x - 2)*x*e - 1/2*(x + 1)*(x - 2)*x*e^(-1) + 1/6*(x + 1)*(x - 2)*x*e^(-2)
0.116167595984182*(x + 0.791704467391079)*(x + 0.00997156537728427)*(x - 1.00997156537728) - 0.495492470126893*(x + 0.791704467391079)*(x + 0.00997156537728427)*(x - 1.79170446739108) + 0.978004473650812*(x + 0.791704467391079)*(x - 1.00997156537728)*(x - 1.79170446739108) - 0.650217267384311*(x + 0.00997156537728427)*(x - 1.00997156537728)*(x - 1.79170446739108)
1.39852837567751
9.941235396733509
The first root is -0.861136311594053
The second root is 0.861136311594053
The third root is -0.339981043584856
The forth root is 0.339981043584856
0.0900243711092997*(x + 0.885819298766930)*(x + 0.0740251485476346)*(x - 1.07402514854763) - 0.373399955130276*(x + 0.885819298766930)*(x + 0.0740251485476346)*(x - 1.88581929876693) + 0.802728841958563*(x + 0.885819298766930)*(x - 1.07402514854763)*(x - 1.88581929876693) - 0.571257167284918*(x + 0.0740251485476346)*(x - 1.07402514854763)*(x - 1.88581929876693)
1.37065555196861
9.913362573024607
The first Chevyshev point is 1.88581929876693
The second Chevyshev point is 1.07402514854763
The third Chevyshev point is -0.0740251485476346
The forth Chevyshev point is -0.885819298766930
-1/6*(x - 1)*(x - 2)*x*e - 1/2*(x + 1)*(x - 2)*x*e^(-1) + 1/6*(x + 1)*(x - 2)*x*e^(-2)
sqrt((1/2*(e^2 - 2*e^(1/2) - 3)*e^(-3/2) + 8.54270702105600)^2)
1/2*abs(e^2 - 2*e^(1/2) - 3)*e^(-3/2)
[-1.00, -0.985, -0.970, -0.955, -0.940, -0.925, -0.910, -0.895, -0.880, -0.865, -0.850, -0.835, -0.820, -0.805, -0.790, -0.775, -0.760, -0.745, -0.730, -0.715, -0.700, -0.685, -0.670, -0.655, -0.640, -0.625, -0.610, -0.595, -0.580, -0.565, -0.550, -0.535, -0.520, -0.505, -0.490, -0.475, -0.460, -0.445, -0.430, -0.415, -0.400, -0.385, -0.370, -0.355, -0.340, -0.325, -0.310, -0.295, -0.280, -0.265, -0.250, -0.235, -0.220, -0.205, -0.190, -0.175, -0.160, -0.145, -0.130, -0.115, -0.100, -0.0850, -0.0700, -0.0550, -0.0400, -0.0250, -0.00995, 0.00500, 0.0200, 0.0350, 0.0500, 0.0651, 0.0801, 0.0950, 0.110, 0.125, 0.140, 0.155, 0.170, 0.185, 0.200, 0.215, 0.230, 0.245, 0.260, 0.275, 0.290, 0.305, 0.320, 0.335, 0.350, 0.365, 0.380, 0.395, 0.410, 0.425, 0.440, 0.455, 0.470, 0.485, 0.500, 0.515, 0.530, 0.545, 0.560, 0.575, 0.590, 0.605, 0.620, 0.635, 0.650, 0.665, 0.680, 0.695, 0.710, 0.725, 0.740, 0.755, 0.770, 0.785, 0.800, 0.815, 0.830, 0.845, 0.860, 0.875, 0.890, 0.905, 0.920, 0.935, 0.950, 0.965, 0.980, 0.995, 1.01, 1.03, 1.04, 1.05, 1.07, 1.08, 1.10, 1.11, 1.13, 1.15, 1.16, 1.18, 1.19, 1.21, 1.22, 1.24, 1.25, 1.27, 1.28, 1.30, 1.31, 1.32, 1.34, 1.35, 1.37, 1.39, 1.40, 1.42, 1.43, 1.45, 1.46, 1.48, 1.49, 1.51, 1.52, 1.54, 1.55, 1.56, 1.58, 1.59, 1.61, 1.62, 1.64, 1.66, 1.67, 1.69, 1.70, 1.72, 1.73, 1.75, 1.76, 1.78, 1.79, 1.81, 1.82, 1.83, 1.85, 1.86, 1.88, 1.90, 1.91, 1.93, 1.94, 1.96, 1.97, 1.99]
<type 'sage.rings.real_mpfr.RealNumber'>
-0.99
0.0150000000000000
<built-in function abs>
5
5*sqrt(2)
<class 'sage.structure.sequence.Sequence_generic'>
[x == -1, x == 1]
[x == -1, x == 1]
x == -1
<type 'sage.symbolic.expression.Expression'>
-1
[-1, 1]