Change argument order in factor and roots (#2433)

* Update all uses of `factor`

* Update all uses of `roots`

experimental/GModule/AlgClosureFp.jl

@@ -113,7 +113,7 @@ function Oscar.roots(a::AlgClosureElem, b::Int)
   d = mapreduce(degree, lcm, keys(lf.fac), init = 1)
   d = lcm(d, degree(parent(ad)))
   K = ext_of_degree(parent(a), d)
-  r = roots(f, K)
+  r = roots(K, f)
   return [AlgClosureElem(x, parent(a)) for x = r]
 end
 
@@ -126,7 +126,7 @@ function Oscar.roots(a::Generic.Poly{AlgClosureElem{T}}) where T
   d = mapreduce(degree, lcm, keys(lf.fac), init = 1)
   d = lcm(d, degree(parent(b[1])))
   K = ext_of_degree(A, d)
-  r = roots(f, K)
+  r = roots(K, f)
   return [AlgClosureElem(x, A) for x = r]
 end
 

experimental/GModule/Misc.jl

@@ -19,7 +19,7 @@ function Hecke.number_field(::QQField, a::qqbar; cached::Bool = false)
       return b
     end
     f = minpoly(x)
-    r = roots(f, k)
+    r = roots(k, f)
     pr = 10
     while true
       C = AcbField(pr)

src/AlgebraicGeometry/Surfaces/K3Auto.jl

@@ -1928,7 +1928,7 @@ function ample_class(S::ZZLat)
     else
       rv = (r*gram_matrix(S)*transpose(v))[1,1]
       p = x^2*vsq + 2*x*rv + rsq
-      rp = roots(p, CalciumQQBar)
+      rp = roots(CalciumQQBar, p)
       a = rp[1]
       b = rp[2]
       if a > b

src/NumberTheory/GaloisGrp/GaloisGrp.jl

@@ -476,7 +476,7 @@ mutable struct ComplexRootCtx
   rt::Vector{acb}
   function ComplexRootCtx(f::ZZPolyRingElem)
     @assert ismonic(f)
-    rt = roots(f, AcbField(20))
+    rt = roots(AcbField(20), f)
     return new(f, 20, rt)
   end
   function ComplexRootCtx(f::QQPolyRingElem)
@@ -492,7 +492,7 @@ function Hecke.roots(C::GaloisCtx{ComplexRootCtx}, pr::Int = 10; raw::Bool = fal
   if C.C.pr >= pr
     return C.C.rt
   end
-  rt = roots(C.C.f, AcbField(pr))
+  rt = roots(AcbField(pr), C.C.f)
   C.C.pr = pr
   n = length(rt)
   for i=1:n
@@ -580,7 +580,7 @@ function Nemo.roots_upper_bound(f::ZZMPolyRingElem, t::Int = 0)
   F = evaluate(f, [x, Qsx(s)])
   dis = numerator(discriminant(F))
   @assert !iszero(dis(t))
-  rt = roots(dis, AcbField(20))
+  rt = roots(AcbField(20), dis)
   r = Hecke.lower_bound(minimum([abs(x-t) for x = rt]), ZZRingElem)
   @assert r > 0
   ff = map_coefficients(abs, f)
@@ -1664,13 +1664,13 @@ If `prime` is given, no search is performed.
 function find_prime(f::QQPolyRingElem, extra::Int = 5; prime::Int = 0, pStart::Int = 2*degree(f), filter_prime = x->true, filter_pattern = x->true)
   if prime != 0
     p = prime
-    lf = factor(f, GF(p))
+    lf = factor(GF(p), f)
     return p, Set([CycleType(map(degree, collect(keys(lf.fac))))])
   end
   if pStart < 0
     error("should no longer happen")
     p = -pStart
-    lf = factor(f, GF(p))
+    lf = factor(GF(p), f)
     return p, Set([CycleType(map(degree, collect(keys(lf.fac))))])
   end
 
@@ -1693,7 +1693,7 @@ function find_prime(f::QQPolyRingElem, extra::Int = 5; prime::Int = 0, pStart::I
     if k(leading_coefficient(f)) == 0
       continue
     end
-    lf = factor(f, GF(p))
+    lf = factor(GF(p), f)
     if any(x->x>1, values(lf.fac))
       continue
     end
@@ -2466,7 +2466,7 @@ ideal(x4^4 - 2, x3^3 + x3^2*x4 + x3*x4^2 + x4^3, x2^2 + x2*x3 + x2*x4 + x3^2 + x
 julia> k, _ = number_field(i);
 
 
-julia> length(roots(x^4-2, k))
+julia> length(roots(k, x^4-2))
 4
 
 ```
@@ -2532,7 +2532,7 @@ function galois_ideal(C::GaloisCtx, extra::Int = 5)
         push!(id, sum(evaluate(I^length(h), x) for I = PE) - v)
       end
       h = Hecke.power_sums_to_polynomial(h)
-      q = roots(h, number_field(C.f)[1])
+      q = roots(number_field(C.f)[1], h)
       @assert length(q) > 0
       q = parent(defining_polynomial(parent(q[1])))(q[1])
       #TODO: think h(q(y)) is probably boring, while q(y) == pe might be 

src/NumberTheory/GaloisGrp/Qt.jl

@@ -118,7 +118,7 @@ function _subfields(FF::Generic.FunctionField, f::ZZMPolyRingElem; tStart::Int =
   @vprint :Subfields 2 "for $f\n"
 
   d = numerator(discriminant(FF))
-  rt = roots(d, AcbField(20))
+  rt = roots(AcbField(20), d)
   t = tStart
   local g::ZZPolyRingElem
   while true
@@ -140,7 +140,7 @@ function _subfields(FF::Generic.FunctionField, f::ZZMPolyRingElem; tStart::Int =
   @vprint :Subfields 2 "now looking for a nice prime...\n"
   p, _ = find_prime(defining_polynomial(K), pStart = 200)
 
-  d = lcm(map(degree, collect(keys(factor(g, GF(p)).fac))))
+  d = lcm(map(degree, collect(keys(factor(GF(p), g).fac))))
 
   @assert evaluate(evaluate(f, [X, T+t]), [gen(Zx), zero(Zx)]) == g
 

test/NumberTheory/galthy.jl

@@ -8,7 +8,7 @@
   U = trivial_subgroup(G)[1]
   L = fixed_field(C, U)
   @test degree(L) == order(G)
-  @test length(roots(k.pol, L)) == 5
+  @test length(roots(L, k.pol)) == 5
 
   R, x = polynomial_ring(QQ, "x")
   pol = x^6 - 366*x^4 - 878*x^3 + 4329*x^2 + 14874*x + 10471