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How about this. I'll leave it as an exercise to handle the divide by zero:
sage: F.<a>=GF(16)
sage: def T(x,y,c):
... return ((y/x + y^3/x^3)*(c^2 + c + 1)*c^2 + (y/x + y^4/x^4)*c^2)*x/(c*y^2/x^2 + y^4/x^4 + 1) + sqrt(x*y)
sage: for x,y in CartesianProduct(list(F),list(F)):
... try:
... print x, '\t', y, '\t', T(x, y, c=1)
... except Exception, e:
... print e
0 0 division by zero in finite field.
0 a division by zero in finite field.
0 a^2 division by zero in finite field.
0 a^3 division by zero in finite field.
0 a + 1 division by zero in finite field.
0 a^2 + a division by zero in finite field.
0 a^3 + a^2 division by zero in finite field.
0 a^3 + a + 1 division by zero in finite field.
0 a^2 + 1 division by zero in finite field.
0 a^3 + a division by zero in finite field.
0 a^2 + a + 1 division by zero in finite field.
0 a^3 + a^2 + a division by zero in finite field.
0 a^3 + a^2 + a + 1 division by zero in finite field.
0 a^3 + a^2 + 1 division by zero in finite field.
0 a^3 + 1 division by zero in finite field.
0 1 division by zero in finite field.
a 0 0
a a a
a a^2 a
a a^3 a
a a + 1 a
a a^2 + a a
a a^3 + a^2 division by zero in finite field.
a a^3 + a + 1 a
a a^2 + 1 a^3 + a
a a^3 + a a
a a^2 + a + 1 a
a a^3 + a^2 + a division by zero in finite field.
a a^3 + a^2 + a + 1 a^2 + a
a a^3 + a^2 + 1 a
a a^3 + 1 a^3
a 1 a^2
a^2 0 0
a^2 a a^3
a^2 a^2 a^2
a^2 a^3 a^2
a^2 a + 1 a^2
a^2 a^2 + a a^2
a^2 a^3 + a^2 a^2
a^2 a^3 + a + 1 division by zero in finite field.
a^2 a^2 + 1 a^2
a^2 a^3 + a a^2 + a + 1
a^2 a^2 + a + 1 a^2
a^2 a^3 + a^2 + a a^2
a^2 a^3 + a^2 + a + 1 division by zero in finite field.
a^2 a^3 + a^2 + 1 a^3 + a^2
a^2 a^3 + 1 a^2
a^2 1 a + 1
a^3 0 0
a^3 a a^2 + a
a^3 a^2 a + 1
a^3 a^3 a^3
a^3 a + 1 a^3
a^3 a^2 + a a^3
a^3 a^3 + a^2 a^3
a^3 a^3 + a + 1 a^3
a^3 a^2 + 1 division by zero in finite field.
a^3 a^3 + a a^3
a^3 a^2 + a + 1 a^3 + a^2 + a
a^3 a^3 + a^2 + a a^3
a^3 a^3 + a^2 + a + 1 a^3
a^3 a^3 + a^2 + 1 division by zero in finite field.
a^3 a^3 + 1 a^3 + a + 1
a^3 1 a^3
a + 1 0 0
a + 1 a a + 1
a + 1 a^2 a^3 + a^2
a + 1 a^3 a^2 + a
a + 1 a + 1 a + 1
a + 1 a^2 + a a + 1
a + 1 a^3 + a^2 a + 1
a + 1 a^3 + a + 1 a + 1
a + 1 a^2 + 1 a + 1
a + 1 a^3 + a division by zero in finite field.
a + 1 a^2 + a + 1 a + 1
a + 1 a^3 + a^2 + a a^3 + a^2 + a + 1
a + 1 a^3 + a^2 + a + 1 a + 1
a + 1 a^3 + a^2 + 1 a + 1
a + 1 a^3 + 1 division by zero in finite field.
a + 1 1 a^2 + 1
a^2 + a 0 0
a^2 + a a a^3 + a
a^2 + a a^2 a^2 + a
a^2 + a a^3 a^3 + a + 1
a^2 + a a + 1 a^3 + a^2
a^2 + a a^2 + a a^2 + a
a^2 + a a^3 + a^2 a^2 + a
a^2 + a a^3 + a + 1 a^2 + a
a^2 + a a^2 + 1 a^2 + a
a^2 + a a^3 + a a^2 + a
a^2 + a a^2 + a + 1 division by zero in finite field.
a^2 + a a^3 + a^2 + a a^2 + a
a^2 + a a^3 + a^2 + a + 1 a^3 + a^2 + 1
a^2 + a a^3 + a^2 + 1 a^2 + a
a^2 + a a^3 + 1 a^2 + a
a^2 + a 1 division by zero in finite field.
a^3 + a^2 0 0
a^3 + a^2 a division by zero in finite field.
a^3 + a^2 a^2 a^2 + a + 1
a^3 + a^2 a^3 a^3 + a^2
a^3 + a^2 a + 1 a^2 + 1
a^3 + a^2 a^2 + a a^3 + a + 1
a^3 + a^2 a^3 + a^2 a^3 + a^2
a^3 + a^2 a^3 + a + 1 a^3 + a^2
a^3 + a^2 a^2 + 1 a^3 + a^2
a^3 + a^2 a^3 + a a^3 + a^2
a^3 + a^2 a^2 + a + 1 a^3 + a^2
a^3 + a^2 a^3 + a^2 + a division by zero in finite field.
a^3 + a^2 a^3 + a^2 + a + 1 a^3 + a^2
a^3 + a^2 a^3 + a^2 + 1 a^3 + 1
a^3 + a^2 a^3 + 1 a^3 + a^2
a^3 + a^2 1 a^3 + a^2
a^3 + a + 1 0 0
a^3 + a + 1 a a^3 + a + 1
a^3 + a + 1 a^2 division by zero in finite field.
a^3 + a + 1 a^3 a^3 + a^2 + a
a^3 + a + 1 a + 1 a^3 + a + 1
a^3 + a + 1 a^2 + a a^3 + a
a^3 + a + 1 a^3 + a^2 a^2 + 1
a^3 + a + 1 a^3 + a + 1 a^3 + a + 1
a^3 + a + 1 a^2 + 1 a^3 + a + 1
a^3 + a + 1 a^3 + a a^3 + a + 1
a^3 + a + 1 a^2 + a + 1 a^3 + a + 1
a^3 + a + 1 a^3 + a^2 + a a^3 + a + 1
a^3 + a + 1 a^3 + a^2 + a + 1 division by zero in finite field.
a^3 + a + 1 a^3 + a^2 + 1 a^3 + a + 1
a^3 + a + 1 a^3 + 1 1
a^3 + a + 1 1 a^3 + a + 1
a^2 + 1 0 0
a^2 + 1 a a^2 + 1
a^2 + 1 a^2 a^2 + 1
a^2 + 1 a^3 division by zero in finite field.
a^2 + 1 a + 1 a^3 + a^2 + a + 1
a^2 + 1 a^2 + a a^2 + 1
a^2 + 1 a^3 + a^2 a^2 + a + 1
a^2 + 1 a^3 + a + 1 a^3 + a
a^2 + 1 a^2 + 1 a^2 + 1
a^2 + 1 a^3 + a a^2 + 1
a^2 + 1 a^2 + a + 1 a^2 + 1
a^2 + 1 a^3 + a^2 + a a^2 + 1
a^2 + 1 a^3 + a^2 + a + 1 a^2 + 1
a^2 + 1 a^3 + a^2 + 1 division by zero in finite field.
a^2 + 1 a^3 + 1 a^2 + 1
a^2 + 1 1 a
a^3 + a 0 0
a^3 + a a a^2
a^3 + a a^2 a^3 + a
a^3 + a a^3 a^3 + a
a^3 + a a + 1 division by zero in finite field.
a^3 + a a^2 + a a^3 + a^2 + 1
a^3 + a a^3 + a^2 a^3 + a
a^3 + a a^3 + a + 1 a^3 + a^2 + a
a^3 + a a^2 + 1 a^2 + a + 1
a^3 + a a^3 + a a^3 + a
a^3 + a a^2 + a + 1 a^3 + a
a^3 + a a^3 + a^2 + a a^3 + a
a^3 + a a^3 + a^2 + a + 1 a^3 + a
a^3 + a a^3 + a^2 + 1 a^3 + a
a^3 + a a^3 + 1 division by zero in finite field.
a^3 + a 1 a^3 + a
a^2 + a + 1 0 0
a^2 + a + 1 a a^2 + a + 1
a^2 + a + 1 a^2 a^3
a^2 + a + 1 a^3 a^2 + a + 1
a^2 + a + 1 a + 1 a^2 + a + 1
a^2 + a + 1 a^2 + a division by zero in finite field.
a^2 + a + 1 a^3 + a^2 a^3 + 1
a^2 + a + 1 a^3 + a + 1 a^2 + a + 1
a^2 + a + 1 a^2 + 1 a^3 + a^2 + a + 1
a^2 + a + 1 a^3 + a a^3 + a^2 + a
a^2 + a + 1 a^2 + a + 1 a^2 + a + 1
a^2 + a + 1 a^3 + a^2 + a a^2 + a + 1
a^2 + a + 1 a^3 + a^2 + a + 1 a^2 + a + 1
a^2 + a + 1 a^3 + a^2 + 1 a^2 + a + 1
a^2 + a + 1 a^3 + 1 a^2 + a + 1
a^2 + a + 1 1 division by zero in finite field.
a^3 + a^2 + a 0 0
a^3 + a^2 + a a division by zero in finite field.
a^3 + a^2 + a a^2 a^3 + a^2 + a
a^3 + a^2 + a a^3 a + 1
a^3 + a^2 + a a + 1 a^3 + a^2 + a
a^3 + a^2 + a a^2 + a a^3 + a^2 + a
a^3 + a^2 + a a^3 + a^2 division by zero in finite field.
a^3 + a^2 + a a^3 + a + 1 1
a^3 + a^2 + a a^2 + 1 a^3 + a^2 + a
a^3 + a^2 + a a^3 + a a^3 + a^2 + 1
a^3 + a^2 + a a^2 + a + 1 a^3 + a^2 + a + 1
a^3 + a^2 + a a^3 + a^2 + a a^3 + a^2 + a
a^3 + a^2 + a a^3 + a^2 + a + 1 a^3 + a^2 + a
a^3 + a^2 + a a^3 + a^2 + 1 a^3 + a^2 + a
a^3 + a^2 + a a^3 + 1 a^3 + a^2 + a
a^3 + a^2 + a 1 a^3 + a^2 + a
a^3 + a^2 + a + 1 0 0
a^3 + a^2 + a + 1 a a^3 + a^2 + a + 1
a^3 + a^2 + a + 1 a^2 division by zero in finite field.
a^3 + a^2 + a + 1 a^3 a^3 + a^2 + a + 1
a^3 + a^2 + a + 1 a + 1 a^2 + a
a^3 + a^2 + a + 1 a^2 + a a^3 + a^2 + a + 1
a^3 + a^2 + a + 1 a^3 + a^2 a^3 + a^2 + a + 1
a^3 + a^2 + a + 1 a^3 + a + 1 division by zero in finite field.
a^3 + a^2 + a + 1 a^2 + 1 a
a^3 + a^2 + a + 1 a^3 + a a^3 + a^2 + a + 1
a^3 + a^2 + a + 1 a^2 + a + 1 a^3 + 1
a^3 + a^2 + a + 1 a^3 + a^2 + a a^3 + a^2 + 1
a^3 + a^2 + a + 1 a^3 + a^2 + a + 1 a^3 + a^2 + a + 1
a^3 + a^2 + a + 1 a^3 + a^2 + 1 a^3 + a^2 + a + 1
a^3 + a^2 + a + 1 a^3 + 1 a^3 + a^2 + a + 1
a^3 + a^2 + a + 1 1 a^3 + a^2 + a + 1
a^3 + a^2 + 1 0 0
a^3 + a^2 + 1 a a^3 + a^2 + 1
a^3 + a^2 + 1 a^2 a^3 + a^2 + 1
a^3 + a^2 + 1 a^3 division by zero in finite field.
a^3 + a^2 + 1 a + 1 a^3 + a^2 + 1
a^3 + a^2 + 1 a^2 + a a^3 + a^2
a^3 + a^2 + 1 a^3 + a^2 a^3 + a^2 + 1
a^3 + a^2 + 1 a^3 + a + 1 a^3 + a^2 + 1
a^3 + a^2 + 1 a^2 + 1 division by zero in finite field.
a^3 + a^2 + 1 a^3 + a a^2
a^3 + a^2 + 1 a^2 + a + 1 a^3 + a^2 + 1
a^3 + a^2 + 1 a^3 + a^2 + a 1
a^3 + a^2 + 1 a^3 + a^2 + a + 1 a^3 + 1
a^3 + a^2 + 1 a^3 + a^2 + 1 a^3 + a^2 + 1
a^3 + a^2 + 1 a^3 + 1 a^3 + a^2 + 1
a^3 + a^2 + 1 1 a^3 + a^2 + 1
a^3 + 1 0 0
a^3 + 1 a a^3 + 1
a^3 + 1 a^2 a^3 + 1
a^3 + 1 a^3 a^3 + 1
a^3 + 1 a + 1 division by zero in finite field.
a^3 + 1 a^2 + a a^3 + 1
a^3 + 1 a^3 + a^2 a^3 + a + 1
a^3 + 1 a^3 + a + 1 a^3 + 1
a^3 + 1 a^2 + 1 a^3 + 1
a^3 + 1 a^3 + a division by zero in finite field.
a^3 + 1 a^2 + a + 1 a^3
a^3 + 1 a^3 + a^2 + a a^3 + 1
a^3 + 1 a^3 + a^2 + a + 1 a
a^3 + 1 a^3 + a^2 + 1 1
a^3 + 1 a^3 + 1 a^3 + 1
a^3 + 1 1 a^3 + 1
1 0 0
1 a 1
1 a^2 1
1 a^3 1
1 a + 1 1
1 a^2 + a division by zero in finite field.
1 a^3 + a^2 1
1 a^3 + a + 1 a^2 + 1
1 a^2 + 1 1
1 a^3 + a 1
1 a^2 + a + 1 division by zero in finite field.
1 a^3 + a^2 + a a + 1
1 a^3 + a^2 + a + 1 1
1 a^3 + a^2 + 1 a^2
1 a^3 + 1 a
1 1 1
