| 21. | For example, a hyperelliptic Weierstrass point, as above, has weight g ( g-1 ) / 2.
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| 22. | For real hyperelliptic curves, there are two points at infinity, \ infty _ 1 and \ infty _ 2.
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| 23. | Thus for " g " = 3 the canonical curves ( non-hyperelliptic case ) are quartic plane curves.
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| 24. | Another extension of the theory appears in where the underlying space of the Riemann Hilbert problem is a compact hyperelliptic Riemann surface.
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| 25. | However to represent an element of the trace zero variety more bits are needed compared with elements of elliptic or hyperelliptic curves.
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| 26. | Actually, B�zout's theorem states that a straight line and a hyperelliptic curve of genus 2 intersect in 5 points.
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| 27. | This was done first by A . Stein and H . G . Zimmer in the case of real hyperelliptic function fields.
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| 28. | He obtained results for the case of hyperelliptic curve, and conjectured the further main points of the theory as applied to curves.
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| 29. | When the degree is equal to 2 " g " + 1, the curve is called an imaginary hyperelliptic curve.
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| 30. | Such functions were first introduced to study hyperelliptic integrals, i . e . for the case where S is a hyperelliptic curve.
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