diff --git a/Project.toml b/Project.toml
index cec494303ee9..a80b63710926 100644
--- a/Project.toml
+++ b/Project.toml
@@ -25,22 +25,22 @@ UUIDs = "cf7118a7-6976-5b1a-9a39-7adc72f591a4"
 cohomCalg_jll = "5558cf25-a90e-53b0-b813-cadaa3ae7ade"
 
 [compat]
-AbstractAlgebra = "0.41.3"
-AlgebraicSolving = "0.5.0"
+AbstractAlgebra = "0.42.0"
+AlgebraicSolving = "0.5.1"
 Distributed = "1.6"
 GAP = "0.10.2"
-Hecke = "0.32.0"
+Hecke = "0.33.0"
 JSON = "^0.20, ^0.21"
 JSON3 = "1.13.2"
 LazyArtifacts = "1.6"
 Markdown = "1.6"
-Nemo = "0.45.5"
+Nemo = "0.46.0"
 Pkg = "1.6"
 Polymake = "0.11.19"
 Random = "1.6"
 RandomExtensions = "0.4.3"
 Serialization = "1.6"
-Singular = "0.23.1"
+Singular = "0.23.4"
 TOPCOM_jll = "0.17.8"
 UUIDs = "1.6"
 cohomCalg_jll = "0.32.0"
diff --git a/docs/src/Rings/rational.md b/docs/src/Rings/rational.md
index 1fa833cd8f40..a110f13011dd 100644
--- a/docs/src/Rings/rational.md
+++ b/docs/src/Rings/rational.md
@@ -273,7 +273,7 @@ ERROR: DivideError: integer division error
 Test if ``a`` is an ``n``-th power. If so, return ```true``` and the root,
 ```false``` and any rational otherwise.
 
-* `is_power(a::QQFieldElem) -> Int, QQFieldElem`
+* `is_perfect_power_with_data(a::QQFieldElem) -> Int, QQFieldElem`
 
 Find the largest ``n`` such that ``a`` is an ``n``-th power. Return ``n`` and the root.
 
@@ -288,7 +288,7 @@ julia> is_power(QQ(8), 3)
 julia> is_power(QQ(8), 2)
 (false, 8)
 
-julia> is_power(QQ(9//16))
+julia> is_perfect_power_with_data(QQ(9//16))
 (2, 3//4)
 
 julia> root(QQ(25//9), 2)
diff --git a/experimental/IntersectionTheory/src/blowup.jl b/experimental/IntersectionTheory/src/blowup.jl
index 800a48ef2458..859c62f00969 100644
--- a/experimental/IntersectionTheory/src/blowup.jl
+++ b/experimental/IntersectionTheory/src/blowup.jl
@@ -169,7 +169,7 @@ function  present_finite_extension_ring(F::Oscar.AffAlgHom)
 	       y -= q * gensB_lift[i]
 	     end; ans)
 
-  FM = FreeModule(R, g)
+  FM = free_module(R, g)
   gB = elem_type(FM)[FM(push!([j == i ? R(1) : R() for j in 1:g-1], -gensB_lift[i])) for i in 1:g-1]
   gJ = elem_type(FM)[FM([j==i ? x : R() for j in 1:g]) for x in gens(J) for i in 1:g]
   U  = vcat(gB, gJ)
diff --git a/experimental/SymmetricIntersections/src/representations.jl b/experimental/SymmetricIntersections/src/representations.jl
index db61a903ce0f..920583e4c19c 100644
--- a/experimental/SymmetricIntersections/src/representations.jl
+++ b/experimental/SymmetricIntersections/src/representations.jl
@@ -1062,7 +1062,7 @@ function _has_pfr(G::Oscar.GAPGroup, dim::Int)
   G_gap = G.X
   f_gap = GG.EpimorphismSchurCover(G_gap)::GapObj
   H_gap = GG.Source(f_gap)::GapObj
-  n, p = is_power(GG.Size(H_gap))::Tuple{Int, Int}
+  n, p = is_perfect_power_with_data(GG.Size(H_gap))::Tuple{Int, Int}
   if is_prime(p)
     fff_gap = GG.EpimorphismPGroup(H_gap, p)::GapObj
     E_gap = fff_gap(H_gap)::GapObj
diff --git a/src/Groups/matrices/linear_isconjugate.jl b/src/Groups/matrices/linear_isconjugate.jl
index ec339862db09..f6157fd61261 100644
--- a/src/Groups/matrices/linear_isconjugate.jl
+++ b/src/Groups/matrices/linear_isconjugate.jl
@@ -43,7 +43,7 @@ is_semisimple(x::MatrixGroupElem{T}) where T <: FinFieldElem = is_coprime(order(
 
 Return whether `x` is unipotent, i.e. its order is a power of the characteristic of its base ring.
 """
-is_unipotent(x::MatrixGroupElem{T}) where T <: FinFieldElem = isone(x) || is_power(order(Int, x))[2]==Int(characteristic(x.parent.ring))
+is_unipotent(x::MatrixGroupElem{T}) where T <: FinFieldElem = isone(x) || is_perfect_power_with_data(order(Int, x))[2]==Int(characteristic(x.parent.ring))
 
 
 
diff --git a/src/Groups/matrices/stuff_field_gen.jl b/src/Groups/matrices/stuff_field_gen.jl
index 4b16c56fe12e..49c801c34eff 100644
--- a/src/Groups/matrices/stuff_field_gen.jl
+++ b/src/Groups/matrices/stuff_field_gen.jl
@@ -8,14 +8,14 @@
 
 # changes the base ring of a polynomial ring into fqPolyRepFieldElem
 function _change_type(f::PolyRingElem{T}) where T <: FinFieldElem
-   e,p = is_power(order(base_ring(f)))
+   e,p = is_perfect_power_with_data(order(base_ring(f)))
    F = GF(Int(p),Int(e))
    t = polynomial_ring(F,"t"; cached=false)[2]
    return sum([t^i*F(lift(coeff(f,i))) for i in 0:degree(f)])
 end
 
 function _change_type(f::PolyRingElem{<: FqFieldElem})
-   e,p = is_power(order(base_ring(f)))
+   e,p = is_perfect_power_with_data(order(base_ring(f)))
    F = GF(Int(p),Int(e))
    t = polynomial_ring(F,"t"; cached=false)[2]
    return sum([t^i*F(lift(ZZ, coeff(f,i))) for i in 0:degree(f)])
diff --git a/src/Modules/UngradedModules/FreeMod.jl b/src/Modules/UngradedModules/FreeMod.jl
index 56db787f548e..6531cf49367c 100644
--- a/src/Modules/UngradedModules/FreeMod.jl
+++ b/src/Modules/UngradedModules/FreeMod.jl
@@ -77,7 +77,7 @@ free_module(R::MPolyLocRing, p::Int, name::VarName = :e; cached::Bool = false) =
 free_module(R::MPolyQuoLocRing, p::Int, name::VarName = :e; cached::Bool = false) = FreeMod(R, p, name, cached = cached)
 
 #=XXX this cannot be as it is inherently ambiguous
-  - FreeModule(R, n)
+  - free_module(R, n)
   - direct sum of rings, ie. a ring
   - set of n-th powers of R
 thus the "category" needs to be set explicitly
diff --git a/src/NumberTheory/GaloisGrp/GaloisGrp.jl b/src/NumberTheory/GaloisGrp/GaloisGrp.jl
index e4dd9baec094..deede28529fd 100644
--- a/src/NumberTheory/GaloisGrp/GaloisGrp.jl
+++ b/src/NumberTheory/GaloisGrp/GaloisGrp.jl
@@ -2172,7 +2172,7 @@ function isinteger(GC::GaloisCtx{Hecke.qAdicRootCtx}, B::BoundRingElem{ZZRingEle
   p = GC.C.p
   if e.length<2
     l = coeff(e, 0)
-    lz = lift(l)
+    lz = lift(ZZ, l)
     lz = Hecke.mod_sym(lz, ZZRingElem(p)^precision(l))
     if abs(lz) < value(B)
       return true, lz
diff --git a/src/NumberTheory/GaloisGrp/Qt.jl b/src/NumberTheory/GaloisGrp/Qt.jl
index 2ee6a30bf6fd..6ebd02221c3a 100644
--- a/src/NumberTheory/GaloisGrp/Qt.jl
+++ b/src/NumberTheory/GaloisGrp/Qt.jl
@@ -652,7 +652,7 @@ function isinteger(G::GaloisCtx, B::BoundRingElem{Tuple{ZZRingElem, Int, QQField
     
     if c.length < 2 || all(x->iszero(coeff(c, x)), 1:c.length-1)
       cc = coeff(c, 0)
-      l = Hecke.mod_sym(lift(cc), pr^precision(cc))
+      l = Hecke.mod_sym(lift(ZZ, cc), pr^precision(cc))
       if abs(l) > pr^p[1]
         return false, x
       end
diff --git a/test/Groups/matrixgroups.jl b/test/Groups/matrixgroups.jl
index e20eeacd67fe..53873b2d814b 100644
--- a/test/Groups/matrixgroups.jl
+++ b/test/Groups/matrixgroups.jl
@@ -657,7 +657,7 @@ end
       @test parent(s)==G
       @test parent(u)==G
       @test is_coprime(order(s),3)
-      @test isone(u) || is_power(order(u))[2]==3
+      @test isone(u) || is_perfect_power_with_data(order(u))[2]==3
       @test is_semisimple(s)
       @test is_unipotent(u)
       @test s*u==G(x)
diff --git a/test/Groups/subgroups_and_cosets.jl b/test/Groups/subgroups_and_cosets.jl
index 807006b737be..35831c72e215 100644
--- a/test/Groups/subgroups_and_cosets.jl
+++ b/test/Groups/subgroups_and_cosets.jl
@@ -352,12 +352,12 @@ end
    Lo = [order(l) for l in L]
    @test length(Lo)==length(factor(order(G)))
    @test prod(Lo) == order(G)
-   @test [is_prime(is_power(l)[2]) for l in Lo] == [1 for i in 1:length(L)]
+   @test [is_prime(is_perfect_power_with_data(l)[2]) for l in Lo] == [1 for i in 1:length(L)]
    L = complement_system(G)
    Lo = [index(G,l) for l in L]
    @test length(Lo)==length(factor(order(G)))
    @test prod(Lo) == order(G)
-   @test [is_prime(is_power(l)[2]) for l in Lo] == [1 for i in 1:length(L)]
+   @test [is_prime(is_perfect_power_with_data(l)[2]) for l in Lo] == [1 for i in 1:length(L)]
 
    L = hall_system(symmetric_group(4))
    @test is_subset(L[1], symmetric_group(4))
diff --git a/test/book/cornerstones/groups/auxiliary_code/main.jl b/test/book/cornerstones/groups/auxiliary_code/main.jl
index b0f0320b1744..a45c4464a04a 100644
--- a/test/book/cornerstones/groups/auxiliary_code/main.jl
+++ b/test/book/cornerstones/groups/auxiliary_code/main.jl
@@ -1,5 +1,5 @@
 import Pkg
-Pkg.add(name="GenericCharacterTables", version=v"0.2"; io=devnull)
+Pkg.add(name="GenericCharacterTables", version="0.2"; io=devnull)
 using GenericCharacterTables
 # for nicer printing
 using GenericCharacterTables: ParameterException
diff --git a/test/book/cornerstones/number-theory/galoismod.jlcon b/test/book/cornerstones/number-theory/galoismod.jlcon
index 7643ca5d472b..64c37466576c 100644
--- a/test/book/cornerstones/number-theory/galoismod.jlcon
+++ b/test/book/cornerstones/number-theory/galoismod.jlcon
@@ -88,4 +88,4 @@ julia> fl = is_free(M)
 false
 
 julia> defining_polynomial(K)
-x^8 + 735*x^6 + 11340*x^4 + 33075*x^2 + 11025
+x^8 + 105*x^6 + 3465*x^4 + 44100*x^2 + 176400