algcurves[homology] - Tretkoff's algorithm for finding a canonical homology basis
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Calling Sequence
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homology(f, x, y)
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Parameters
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f
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-
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irreducible polynomial in x and y
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x
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-
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variable
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y
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-
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variable
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Description
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The result of H:=homology(f, x, y) is a table H containing the following:
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3.
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H[genus] gives the genus g of the Riemann surface.
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6.
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H[canonicalcycles] is a table containing the explicit representation of the cycles and . These cycles are also given by cyclic lists. Again, the elements at odd positions of the list are sheetnumbers. The elements at even positions of the list are branchpoints, together with a number indicating how many times one has to circle around the branchpoint in the counter-clockwise direction. If this number is negative, one has to circle around to the branchpoint as many times in the clockwise direction.
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