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Fix factor #1639

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Fix factor #1639

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b7ea869
add xxgcd, make_exact and fix canonical unit
fieker Mar 22, 2024
a331534
fix Oscar #4170 - too low precision in factoring
fieker Oct 9, 2024
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1 change: 1 addition & 0 deletions src/Hecke.jl
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Original file line number Diff line number Diff line change
Expand Up @@ -74,6 +74,7 @@ using Pkg

import AbstractAlgebra
import AbstractAlgebra: get_cached!, @alias
import AbstractAlgebra: xxgcd, make_exact
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Suggested change
import AbstractAlgebra: xxgcd, make_exact

These don't seem to exist

┌ Hecke
│  WARNING: could not import AbstractAlgebra.xxgcd into Hecke
│  WARNING: could not import AbstractAlgebra.make_exact into Hecke
└

and are not needed for this fix?


import AbstractAlgebra: pretty, Lowercase, LowercaseOff, Indent, Dedent, terse, is_terse

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2 changes: 1 addition & 1 deletion src/NumField/NfAbs/Poly.jl
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Expand Up @@ -522,7 +522,7 @@ function cld_bound(f::PolyRingElem{AbsSimpleNumFieldElem}, k::Vector{Int})
g = Zx()
n = degree(base_ring(f))
for i=0:degree(f)
setcoeff!(g, i, Hecke.upper_bound(ZZRingElem, sqrt(t2(coeff(f, i))//n)))
setcoeff!(g, i, Hecke.upper_bound(ZZRingElem, sqrt(t2(coeff(f, i)))))
end
if is_monic(f)
setcoeff!(g, degree(f), ZZRingElem(1))
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5 changes: 3 additions & 2 deletions src/NumField/NfAbs/PolyFact.jl
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Expand Up @@ -558,6 +558,7 @@ function van_hoeij(f::PolyRingElem{AbsSimpleNumFieldElem}, P::AbsNumFieldOrderId
_, mK = residue_field(order(P), P)
mK = extend(mK, K)
r = length(factor(map_coefficients(mK, f, cached = false)))
prec_scale = max(r, prec_scale)
N = degree(f)
@vprintln :PolyFactor 1 "Having $r local factors for degree $N"

Expand Down Expand Up @@ -589,7 +590,7 @@ function van_hoeij(f::PolyRingElem{AbsSimpleNumFieldElem}, P::AbsNumFieldOrderId
- the bounds are monotonous in the abs value of the coeffs (I think they are using abs value of coeff)
- the math works for real coeffs as well
- thus create an ZZPolyRingElem with pos. coeffs. containing upper bounds of the conjugates of the
coeffs. DOne via T_2: sqrt(n*T_2(alpha) is an upper bounds for all conjugates
coeffs. Done via T_2: sqrt(T_2(alpha) is an upper bounds for all conjugates
- Fieker/ Friedrichs compares T_2 vs 2-norm (squared) of coeffs
- leading coeff as well as den are algebraic
CHECK: den*lead*cld in Z[alpha] (or in the order used)
Expand All @@ -603,7 +604,7 @@ function van_hoeij(f::PolyRingElem{AbsSimpleNumFieldElem}, P::AbsNumFieldOrderId
# 2nd block is for additional bits for rounding?
bb = landau_mignotte_bound(f)*upper_bound(ZZRingElem, sqrt(t2(den*leading_coefficient(f))))
#CHECK: landau... is a bound on the (abs value) of the coeffs of the factors,
# need everywhere sqrt(n*T_2)? to get conjugate bounds
# need everywhere sqrt(T_2)? to get conjugate bounds
kk = ceil(Int, degree(K)/2/log(norm(P))*(log2(c1*c2) + 2*nbits(bb)))
@vprintln :PolyFactor 2 "using CLD precision bounds $b"

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