>>> import sympy
>>> x0,x1,x2,x3,x4,x5=sympy.var('x0 x1 x2 x3 x4 x5')
>>> eqns=[x0**2 - x0, x0*x1 - x1, x0*x2 - x2, x0*x3 - x3, x0*x4 - x4, x0*x5 - x5, x0*x1 - x1, -x0/3 + x1**2 - 2*x2/3, x1*x2 - x1/3 - x2/3 - x3/3, x1*x3 - x2/3 - x3/3 - x4/3, x1*x4 - 2*x3/3 - x5/3, x1*x5 - x4, x0*x2 - x2, x1*x2 - x1/3 - x2/3 - x3/3, -x0/6 - x1/6 + x2**2 - x2/6 - x3/3 - x4/6, -x1/6 + x2*x3 - x2/3 - x3/6 - x4/6 - x5/6, x2*x4 - x2/3 - x3/3 - x4/3, x2*x5 - x3, x0*x3 - x3, x1*x3 - x2/3 - x3/3 - x4/3, -x1/6 + x2*x3 - x2/3 - x3/6 - x4/6 - x5/6, -x0/6 - x1/6 - x2/6 + x3**2 - x3/3 - x4/6, -x1/3 - x2/3 + x3*x4 - x3/3, -x2 + x3*x5, x0*x4 - x4, x1*x4 - 2*x3/3 - x5/3, x2*x4 - x2/3 - x3/3 - x4/3, -x1/3 - x2/3 + x3*x4 - x3/3, -x0/3 - 2*x2/3 + x4**2, -x1 + x4*x5, x0*x5 - x5, x1*x5 - x4, x2*x5 - x3, -x2 + x3*x5, -x1 + x4*x5, -x0 + x5**2, x0 - 1]
>>> sympy.solve(eqns)
[{_Dummy_25: 1/36, _Dummy_20: -2/3, _Dummy_24: 1/6, _Dummy_27: 4/9, _Dummy_19: 1, _Dummy_21: 4/9, _Dummy_29: 1, _Dummy_28: 1, _Dummy_22: 1/6, _Dummy_26: -2/3, _Dummy_23: 1/36, _Dummy_18: 1}, {_Dummy_25: 1/4, _Dummy_20: 0, _Dummy_24: 1/2, _Dummy_27: 0, _Dummy_19: 1, _Dummy_21: 0, _Dummy_29: 1, _Dummy_28: -1, _Dummy_22: -1/2, _Dummy_26: 0, _Dummy_23: 1/4, _Dummy_18: 1}, {_Dummy_25: 1/6, _Dummy_20: 0, _Dummy_24: 0, _Dummy_27: 1/3, _Dummy_19: 1, _Dummy_21: 1/3, _Dummy_29: 1, _Dummy_28: 0, _Dummy_22: 0, _Dummy_26: 0, _Dummy_23: 1/6, _Dummy_18: 1}, {_Dummy_25: 1/9, _Dummy_20: 1/3, _Dummy_24: -1/3, _Dummy_27: 1/9, _Dummy_19: 1, _Dummy_21: 1/9, _Dummy_29: 1, _Dummy_28: 1, _Dummy_22: -1/3, _Dummy_26: 1/3, _Dummy_23: 1/9, _Dummy_18: 1}, {_Dummy_25: 1, _Dummy_20: 1, _Dummy_24: 1, _Dummy_27: 1, _Dummy_19: 1, _Dummy_21: 1, _Dummy_29: 1, _Dummy_28: 1, _Dummy_22: 1, _Dummy_26: 1, _Dummy_23: 1, _Dummy_18: 1}, {_Dummy_25: 1/9, _Dummy_20: -sqrt(5)/3, _Dummy_24: -1/3, _Dummy_27: 5/9, _Dummy_19: 1, _Dummy_21: 5/9, _Dummy_29: 1, _Dummy_28: -1, _Dummy_22: 1/3, _Dummy_26: sqrt(5)/3, _Dummy_23: 1/9, _Dummy_18: 1}, {_Dummy_25: 1/9, _Dummy_20: sqrt(5)/3, _Dummy_24: -1/3, _Dummy_27: 5/9, _Dummy_19: 1, _Dummy_21: 5/9, _Dummy_29: 1, _Dummy_28: -1, _Dummy_22: 1/3, _Dummy_26: -sqrt(5)/3, _Dummy_23: 1/9, _Dummy_18: 1}]
>>> sympy.solve(eqns[:-1])
[{x5**2: x0, x0**2: x0, x1**2: x0/3, x5: 0, x2**2: x0/6, x1: 0, x2: 0, x3**2: x0/6, x4: 0, x4**2: x0/3, x3: 0}, {x5**2: 1, x3**2: 1/6, x1: 0, x3: 0, x0**2: 1, x1**2: 1/3, x5: 0, x2**2: 1/6, x4**2: 1/3, x2: 0, x0: 1, x4: 0}, {x5**2: 1, x3**2: 1/6, x1: 0, x3: 0, x0**2: 1, x1**2: 1/3, x5: 0, x2**2: 1/6, x4**2: 1/3, x4: 0, x0: 1, x2: 0}, {x5**2: 1, x3**2: 1/6, x1: 0, x3: 0, x0**2: 1, x1**2: 1/3, x5: 0, x2**2: 1/6, x4**2: 1/3, x2: 0, x0: 1, x4: 0}, {x5**2: 1, x3**2: 1/6, x1: 0, x3: 0, x0**2: 1, x1**2: 1/3, x5: 0, x2**2: 1/6, x4**2: 1/3, x2: 0, x0: 1, x4: 0}, {x5**2: 1, x3**2: 1/6, x1: 0, x3: 0, x0**2: 1, x1**2: 1/3, x5: 0, x2**2: 1/6, x4**2: 1/3, x4: 0, x0: 1, x2: 0}, {x5**2: 1, x3**2: 1/6, x1: 0, x3: 0, x0**2: 1, x1**2: 1/3, x5: 0, x2**2: 1/6, x4**2: 1/3, x2: 0, x0: 1, x4: 0}, {x5**2: 1, x3**2: 1/6, x1: 0, x3: 0, x0**2: 1, x1**2: 1/3, x5: 0, x2**2: 1/6, x4**2: 1/3, x2: 0, x0: 1, x4: 0}, {x5**2: 1, x3**2: 1/6, x1: 0, x3: 0, x0**2: 1, x1**2: 1/3, x5: 0, x2**2: 1/6, x4**2: 1/3, x4: 0, x0: 1, x2: 0}]
>>> x0-1
x0 - 1
>>>