Update all uses of roots

src/EllCrv/RationalPointSearch.jl

@@ -830,7 +830,7 @@ mutable struct NegativityCertificate
     end
 
 
-    rr = roots(f, AcbField(64, cached = false))
+    rr = roots(AcbField(64, cached = false), f)
     r = sort!(map(real, filter!(isreal, rr)))
 
     # Let's first consider what happens between two roots

src/LocalField/Conjugates.jl

@@ -75,7 +75,7 @@ The roots of $f$ in $Q$, $f$ has to be square-free (at least the roots have to b
 """
 function roots(Q::FlintQadicField, f::ZZPolyRingElem; max_roots::Int = degree(f))
   k, mk = residue_field(Q)
-  rt = roots(f, k)
+  rt = roots(k, f)
   RT = qadic[]
   for r = rt
     push!(RT, newton_lift(f, preimage(mk, r)))
@@ -98,7 +98,7 @@ function roots(C::qAdicRootCtx, n::Int = 10)
     Q.prec_max = n
     for x = lf
       if is_splitting(C) || degree(x[1]) == degree(Q)
-        append!(rt, roots(x[1], Q, max_roots = 1))
+        append!(rt, roots(Q, x[1], max_roots = 1))
       end
     end
   end

src/LocalField/automorphisms.jl

@@ -122,7 +122,7 @@ function absolute_automorphism_list(K::LocalField{qadic, S}) where S
   auts = morphism_type(K)[]
   for f in autsk
     fnew = map_coefficients(f, defining_polynomial(K))
-    rt = roots(fnew, K)
+    rt = roots(K, fnew)
     for x in rt
       push!(auts, hom(K, K, f, x))
     end

src/Map/FiniteField.jl

@@ -90,7 +90,7 @@ end
 #Function that finds an embedding of k into K
 function Nemo.embed_any(k::FinField, K::FinField)
   f = defining_polynomial(k)
-  rt = roots(f, K)[1]
+  rt = roots(K, f)[1]
   return hom(k, K, rt)
 end
 

src/Map/automorphisms.jl

@@ -13,7 +13,7 @@ function _automorphisms(K::NfAbsNS; is_abelian::Bool = false)
   pols = QQPolyRingElem[is_univariate(x)[2] for x in K.pol]
   rt = Vector{Vector{NfAbsNSElem}}(undef, length(pols))
   for i = 1:length(pols)
-    rt[i] = roots(pols[i], K)
+    rt[i] = roots(K, pols[i])
   end
   auts = Vector{NfAbsNSToNfAbsNS}(undef, prod(length(x) for x in rt))
   ind = 1
@@ -677,7 +677,7 @@ function absolute_automorphism_list(K::NumField)
 end
 
 function _automorphisms(K::NumField{QQFieldElem}, F::NumField, L::QQField)
-  rt = roots(defining_polynomial(K), F)
+  rt = roots(F, defining_polynomial(K))
   auts = morphism_type(K, F)[hom(K, F, x) for x in rt]
   return auts
 end

src/Misc/FiniteField.jl

@@ -293,7 +293,7 @@ function splitting_field(f::PolyElem{<:FinFieldElem}; do_roots::Bool = false)
     embed(k, K)
   end
   if do_roots
-    return K, roots(f, K)
+    return K, roots(K, f)
   end
   return K
-end  
+end

src/Misc/Poly.jl

@@ -711,14 +711,14 @@ function roots(f::ZZPolyRingElem, ::QQField; max_roots::Int=degree(f))
 end
 
 function roots(f::ZZPolyRingElem; max_roots::Int=degree(f))
-  r = roots(f, FlintQQ, max_roots=max_roots)
+  r = roots(FlintQQ, f, max_roots=max_roots)
   return ZZRingElem[FlintZZ(x) for x = r if denominator(x) == 1]
 end
 
 function roots(f::QQPolyRingElem; max_roots::Int=degree(f))
-  Zx, x = polynomial_ring(FlintZZ, cached=false)
-  g = Zx(denominator(f) * f)
-  return roots(g, FlintQQ)
+  Zx, x = polynomial_ring(FlintZZ, cached = false)
+  g = Zx(denominator(f)*f)
+  return roots(FlintQQ, g)
 end
 
 function roots(R::AcbField, f::Union{ZZPolyRingElem, QQPolyRingElem}, abs_tol::Int=R.prec, initial_prec::Int...)
@@ -740,7 +740,7 @@ function factor(R::AcbField, f::Union{ZZPolyRingElem, QQPolyRingElem}, abs_tol::
   d = Dict{acb_poly, Int}()
   Rt, t = polynomial_ring(R, String(var(parent(f))), cached = false)
   for (k,v) = g.fac
-    for r = roots(k, R)
+    for r = roots(R, k)
       d[t-r] = v
     end
   end
@@ -753,7 +753,7 @@ function roots(R::ArbField, f::Union{ZZPolyRingElem, QQPolyRingElem}, abs_tol::I
   C = AcbField(precision(R))
   for k = keys(g.fac)
     s, _ = signature(k)
-    rt = roots(k, C)
+    rt = roots(C, k)
     append!(r, map(real, rt[1:s]))
   end
   return r
@@ -766,7 +766,7 @@ function factor(R::ArbField, f::Union{ZZPolyRingElem, QQPolyRingElem}, abs_tol::
   C = AcbField(precision(R))
   for (k,v) = g.fac
     s, t = signature(k)
-    r = roots(k, C)
+    r = roots(C, k)
     for i=1:s
       d[x-real(r[i])] = v
     end

src/Misc/RelFiniteField.jl

@@ -669,7 +669,7 @@ function absolute_field(F::RelFinField{T}; cached::Bool = true) where T <: FinFi
   K, gK = Native.FiniteField(p, d, "a", cached = cached)
   k, mk = absolute_field(base_field(F))
   def_pol_new = map_coefficients(pseudo_inv(mk), defining_polynomial(F))
-  img_gen_k = roots(defining_polynomial(k), K)[1]
+  img_gen_k = roots(K, defining_polynomial(k))[1]
   mp = hom(k, K, img_gen_k)
   g = map_coefficients(mp, def_pol_new)
   img_gen_F = roots(g)[1]

src/Misc/nmod_poly.jl

@@ -1276,7 +1276,7 @@ function FlintFiniteField(f::fqPolyRepPolyRingElem, s::AbstractString = "o"; cac
   k = base_ring(f)
   p = characteristic(k)
   K, o = FlintFiniteField(p, degree(k)*degree(f), s, cached = cached)
-  r = roots(f, K)[1]  # not working, embeddings are missing
+  r = roots(K, f)[1]  # not working, embeddings are missing
   fl || error("s.th. went wrong")
   return K, r
 end

src/NumField/NfAbs/MPolyAbsFact.jl

@@ -444,7 +444,7 @@ function analytic_roots(f::ZZMPolyRingElem, r::ZZRingElem, pr::Int = 10; prec::I
   g = evaluate(f, [Hecke.Globals.Zx(r), gen(Hecke.Globals.Zx)])
   @assert is_squarefree(g)
   C = AcbField(prec)
-  rt = Hecke.roots(g, C)[1:max_roots]
+  rt = Hecke.roots(C, g)[1:max_roots]
   @assert all(x->parent(x) == C, rt)
   Cs, s = power_series_ring(C, pr+2, "s", cached = false)
   Cst, t = polynomial_ring(Cs, cached = false)
@@ -476,7 +476,7 @@ function symbolic_roots(f::ZZMPolyRingElem, r::ZZRingElem, pr::Int = 10; max_roo
   g = evaluate(f, [Hecke.Globals.Zx(r), gen(Hecke.Globals.Zx)])
   @assert is_squarefree(g)
   lg = factor(g)
-  rt = vcat([Hecke.roots(x, number_field(x)[1]) for x = keys(lg.fac)]...)
+  rt = vcat([Hecke.roots(number_field(x)[1], x) for x = keys(lg.fac)]...)
   rt = rt[1:min(length(rt), max_roots)]
   RT = []
   for i = 1:length(rt)

src/NumField/NfAbs/NfAbs.jl

@@ -396,7 +396,7 @@ end
 
 function _issubfield(K::AnticNumberField, L::AnticNumberField)
   f = K.pol
-  R = roots(f, L, max_roots = 1)
+  R = roots(L, f, max_roots = 1)
   if isempty(R)
     return false, L()
   else
@@ -875,7 +875,7 @@ The normal closure of $K$ together with the embedding map.
 """
 function normal_closure(K::AnticNumberField)
   s = splitting_field(K.pol)
-  r = roots(K.pol, s)[1]
+  r = roots(s, K.pol)[1]
   return s, hom(K, s, r, check = false)
 end
 

src/NumField/NfAbs/Simplify.jl

@@ -145,7 +145,7 @@ function _sieve_primitive_elements(B::Vector{NfAbsNSElem})
   Ft = polynomial_ring(F, "t", cached = false)[1]
   rt = Vector{Vector{fqPolyRepFieldElem}}(undef, ngens(K))
   for i = 1:length(pols)
-    rt[i] = roots(pols[i], F)
+    rt[i] = roots(F, pols[i])
   end
   rt_all = Vector{Vector{fqPolyRepFieldElem}}(undef, degree(K))
   ind = 1
@@ -219,7 +219,7 @@ function _sieve_primitive_elements(B::Vector{nf_elem})
   Ft = polynomial_ring(F, "t", cached = false)[1]
   ap = zero(Ft)
   fit!(ap, degree(K)+1)
-  rt = roots(f, F)
+  rt = roots(F, f)
 
   n = degree(K)
   indices = Int[]
@@ -358,7 +358,7 @@ function polredabs(K::AnticNumberField)
   Ft = polynomial_ring(F, "t", cached = false)[1]
   ap = zero(Ft)
   fit!(ap, degree(K)+1)
-  rt = roots(f, F)
+  rt = roots(F, f)
 
   n = degree(K)
 

src/NumField/NfRel/NfRelNSMor.jl

@@ -282,7 +282,7 @@ end
 
 function _automorphisms(L::NfRelNS{T}) where T
   Kx, _ = polynomial_ring(base_field(L), "x", cached = false)
-  rts = Vector{elem_type(L)}[roots(to_univariate(Kx, x), L) for x in L.pol]
+  rts = Vector{elem_type(L)}[roots(L, to_univariate(Kx, x)) for x in L.pol]
   auts = Vector{morphism_type(L)}(undef, prod(length(x) for x in rts))
   ind = 1
   it = cartesian_product_iterator([1:length(rts[i]) for i in 1:length(rts)], inplace = true)

src/NumField/NfRel/Simplify.jl

@@ -152,7 +152,7 @@ function _setup_block_system(Lrel::NfRel{nf_elem})
   Fpx = polynomial_ring(Fp, cached = false)[1]
   F = FlintFiniteField(p, abs_deg, "w", cached = false)[1]
   Fx = polynomial_ring(F, cached = false)[1]
-  rt_base_field = roots(Zx(K.pol), F)
+  rt_base_field = roots(F, Zx(K.pol))
   tmp = Fpx()
   g = Lrel.pol
   rt = Dict{FqPolyRepFieldElem, Vector{FqPolyRepFieldElem}}()
@@ -276,7 +276,7 @@ function _setup_block_system(Lrel::NfRelNS{nf_elem})
   Fpx = polynomial_ring(Fp, cached = false)[1]
   F = FlintFiniteField(p, abs_deg, "w", cached = false)[1]
   Fx = polynomial_ring(F, cached = false)[1]
-  rt_base_field = roots(Zx(K.pol), F)
+  rt_base_field = roots(F, Zx(K.pol))
   rt = Dict{FqPolyRepFieldElem, Vector{Vector{FqPolyRepFieldElem}}}()
   Rxy = polynomial_ring(F, ngens(Lrel), cached = false)[1]
   tmp = Fpx()

src/NumField/SimpleNumField/Subfields.jl

@@ -22,7 +22,7 @@ function _principal_subfields_basis(K::SimpleNumField)
   #f in Kx
   #fk = Kx([coeff(f,i) for i in 0:n])
   #determine roots
-  rts = roots(f, K)
+  rts = roots(K, f)
   ar_lin_fac = elem_type(Kx)[x - root for root in rts]
   fK = change_base_ring(K, f, parent = Kx)
   ##divide by roots

src/NumField/Subfields.jl

@@ -145,7 +145,7 @@ function _subfield_primitive_element_from_basis(K::AnticNumberField, as::Vector{
   Ft = polynomial_ring(F, "t", cached = false)[1]
   ap = zero(Ft)
   fit!(ap, degree(K)+1)
-  rt = roots(f, F)
+  rt = roots(F, f)
   indices = Int[]
   for i = 1:length(as)
     b = _block(as[i], rt, ap)

src/NumFieldOrd/NfOrd/Ideal/Prime.jl

@@ -1384,7 +1384,7 @@ function prime_dec_nonindex(O::NfAbsOrd{NfAbsNS,NfAbsNSElem}, p::IntegerUnion, d
         t = x[ti]
         g = gcd(d, degree(t[1]))
         d = lcm(d, degree(t[1]))
-        r = roots(t[1], Fq)
+        r = roots(Fq, t[1])
         if g == 1
           push!(rt, [r[1]])
         else

src/NumFieldOrd/NfOrd/TorsionUnits.jl

@@ -486,7 +486,7 @@ function _torsion_units_gen(K::NumField)
     end
     for i = v:-1:1
       f = cyclotomic(Int(p)^i, x)
-      r = roots(f, K)
+      r = roots(K, f)
       if length(r) > 0
         mul!(gen, gen, r[1])
         ord *= Int(p)^(i)

src/RCF/autos.jl

@@ -277,7 +277,7 @@ end
 
 function rel_auto_generic(A::ClassField_pp)
   K = A.A
-  imgs = roots(K.pol, K)
+  imgs = roots(K, K.pol)
   homs = morphism_type(K)[hom(K, K, x, check = false) for x in imgs]
   return small_generating_set(homs, *)[1]
 end
@@ -594,7 +594,7 @@ function extend_generic(A::ClassField, autos::Vector{NfToNfMor}, p::ZZRingElem)
     imgs = Vector{NfRelNSElem{nf_elem}}(undef, length(Cp))
     for j = 1:length(gA)
       pol = map_coefficients(autos[i], Cp[j].A.pol)
-      imgs[j] = roots(pol, A)[1]
+      imgs[j] = roots(A, pol)[1]
     end
     rts[i] = imgs
   end

test/Misc/Poly.jl

@@ -20,7 +20,7 @@
     local l
 
     while p < 4096
-      l = roots(f, ArbField(p, cached = false))
+      l = roots(ArbField(p, cached = false), f)
       sgtpos = count(ispositive, l)
       sgtneg = count(isnegative, l)
       sgtz = count(iszero, l)

test/NfAbs/Elem.jl

@@ -157,7 +157,7 @@ end
   Qx, x = QQ["x"]
   f = x^3-39*x-65
   K, a = number_field(f, "a")
-  r = @inferred roots(f, K)
+  r = @inferred roots(K, f)
   @test length(r) == 3
   @test all(iszero, (f(b) for b in r))
 end