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jjgarzellajjgarzella
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Add series precision for large p
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+179
-3
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4 files changed

+179
-3
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‎src/PrecisionEstimate.jl‎

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Original file line numberDiff line numberDiff line change
@@ -21,6 +21,37 @@ function frobenius_precision(k, q)
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return r
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end
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"""
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impreciselog(p,a)
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log with any base, via the log rules,
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though I think there should be floating point error.
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"""
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impreciselog(p,a) = log(a) / log(p)
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"""
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integral_basis_multiplier_bound(p,m,n)
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Calculates the smallest integer t such that
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p^t* ω is in the integral latticee of the cohomology,
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for all ω in the griffiths-dwork basis of cohomology.
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Here, `m` is the pole order,
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and the bound we have depends only on p, m, and n.
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This is called ϕ in Costa's thesis, and it is
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called f in Abbott-Kedlaya-Roe.
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This method implements theorem 3.4.6 only of
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Abbott-Kedlaya-Roe.
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"""
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function integral_basis_multiplier_bound(p,m,n)
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sum = 0
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for i in 1:n
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sum += floor(Int,impreciselog(p,max(1,m-i)))
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end
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sum
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end
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"""
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calculate_relative_precision(HP, slope, hodge_numbers, weight, p)
@@ -67,6 +98,20 @@ function calculate_relative_precision(polygon, weight, p)
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return reverse(r_vector)
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end
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function calculate_series_precision(p,n,r_m)
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if p < 2*(n+1) + maximum(r_m)
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println("Unsupported p: $p. Returning nonsense.")
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return zeros(Int,n)
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end
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# TODO update for small p
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N = [(r_m[i] == 0 ? 0 : n+1 + r_m[i] - (i+1)) for i in 1:n]
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N
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end
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"""
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relative_precision()
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‎test/CurvesAndSurfaces.jl‎

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@@ -149,8 +149,6 @@ Data computed using Edgar Costa's `controlledreduction` library.
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function test_highergenus_1(p)
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n = 2
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d = 3
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series_precision = (4,4)
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abs_precision = 7
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F = GF(p)
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R, (x,y,z) = polynomial_ring(F, ["x$i" for i in 0:n])

‎test/Precision.jl‎

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@@ -20,10 +20,125 @@ end
2020

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# TODO: copy of gpl license
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function test_series_precision()
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function test_series_precision_example(p,n,d)
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r_m = DeRham.calculate_relative_precision(hodge_polygon(p,n,d),n-1,p)
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N = DeRham.calculate_series_precision(p,n,r_m)
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if ( n == 2 && d == 3 )
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if ( p < 5)
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@test N == [2 3]
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elseif ( 5 <= p && p < 17 )
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@test N == [2,2]
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elseif ( 17 <= p )
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@test N == [0,1]
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end
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elseif ( n == 2 && d == 4 )
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if ( p < 5)
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@test N == [4,4]
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elseif ( 5 <= p && p < 17 )
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@test N == [3,3]
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elseif ( 17 <= p )
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@test N == [2,2]
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end
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elseif ( n == 2 && d == 5 )
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if ( p < 5)
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@test N == [6,6]
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elseif ( 5 <= p && p < 7 )
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@test N == [4,5]
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elseif ( 7 <= p )
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@test N == [4,4]
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end
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elseif ( n == 2 && d == 6 )
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if ( p < 5)
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@test N == [8,9]
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elseif ( 5 <= p && p < 7 )
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@test N == [7,7]
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elseif ( 7 <= p && p < 11 )
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@test N == [6,7]
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elseif ( 11 <= p )
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@test N == [6,6]
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end
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elseif ( n == 2 && d == 7 )
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if ( p < 5)
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@test N == [11,11]
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elseif ( 5 <= p && p < 7 )
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@test N == [10,10]
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elseif ( 7 <= p && p < 11 )
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@test N == [10,10]
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elseif ( 11 <= p && p < 17 )
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@test N == [9,9]
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elseif ( 17 <= p )
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@test N == [8,8]
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end
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elseif ( n == 2 && d == 8 )
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if ( p < 5)
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@test N == [14,14]
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elseif ( 5 <= p && p < 7 )
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@test N == [13,13]
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elseif ( 7 <= p && p < 13 )
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@test N == [13,13]
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elseif ( 13 <= p && p < 17 )
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@test N == [12,13]
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elseif ( 17 <= p )
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@test N == [11,11]
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end
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elseif ( n == 2 && d == 9 )
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if ( p < 5)
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@test N == [18,18]
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elseif ( 5 <= p && p < 7 )
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@test N == [16,16]
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elseif ( 7 <= p && p < 11 )
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@test N == [16,16]
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elseif ( 11 <= p && p < 17 )
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@test N == [16,16]
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elseif ( 17 <= p )
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@test N == [15,15]
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end
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elseif ( n == 3 && d == 4 )
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if ( p < 5)
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@test N == [7,7,8]
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elseif ( 5 <= p && p < 7 )
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@test N == [4,5,5]
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elseif ( 7 <= p && p < 23 )
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@test N == [4,4,3]
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elseif ( 23 <= p && p < 43 )
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@test N == [3,3,3]
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elseif ( 43 <= p )
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@test N == [3,3,2]
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end
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elseif ( n == 3 && d == 5 )
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if ( p < 5)
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@test N == [11,11,10]
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elseif ( 5 <= p && p < 7 )
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@test N == [8,8,9]
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elseif ( 7 <= p && p < 11 )
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@test N == [8,8,7]
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elseif ( 11 <= p && p < 23 )
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@test N == [7,7,6]
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elseif ( 23 <= p && p < 29 )
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@test N == [6,6,6]
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elseif ( 29 <= p )
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@test N == [6,6,5]
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end
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elseif ( n == 3 && d == 6 )
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if ( p < 5)
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@test N == [17,18,17]
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elseif ( 5 <= p && p < 7 )
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@test N == [15,15,14]
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elseif ( 7 <= p && p < 11 )
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@test N == [15,15,14]
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elseif ( 11 <= p && p < 17 )
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@test N == [14,14,13]
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elseif ( 17 <= p && p < 23 )
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@test N == [13,13,12]
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elseif ( 23 <= p )
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@test N == [12,12,11]
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end
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end
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25139
end
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27142
function test_algorithm_precision_example(p,n,d)
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29144
r_m = DeRham.calculate_relative_precision(hodge_polygon(p,n,d),n-1,p)
@@ -183,9 +298,26 @@ function test_algorithm_precision()
183298
test_algorithm_precision_example(p,3,4)
184299
test_algorithm_precision_example(p,3,5)
185300
end
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end
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303+
function test_series_precision()
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#TODO: add the bound and fix for small p
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# p = 11
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test_series_precision_example(11,2,3)
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test_series_precision_example(11,2,4)
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# p = 13
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test_series_precision_example(13,2,3)
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test_series_precision_example(13,2,4)
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test_series_precision_example(13,2,5)
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# k3 surfaces
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test_series_precision_example(11,3,4)
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test_series_precision_example(13,3,4)
187318
end
188319

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189321
function test_hodge_polygon_values()
190322
k3 = DeRham.SlopesPolygon([1,20,1])
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‎test/runtests.jl‎

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@@ -69,6 +69,7 @@ end
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test_hodge_polygon_values()
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test_hodge_polygon_examples()
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test_algorithm_precision()
72+
test_series_precision()
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end
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#@testset "Elliptic curves" begin

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