diff --git a/Project.toml b/Project.toml
index 95873c18..fc0c157c 100644
--- a/Project.toml
+++ b/Project.toml
@@ -14,23 +14,20 @@ TupleTools = "9d95972d-f1c8-5527-a6e0-b4b365fa01f6"
 VectorInterface = "409d34a3-91d5-4945-b6ec-7529ddf182d8"
 WignerSymbols = "9f57e263-0b3d-5e2e-b1be-24f2bb48858b"
 
-[weakdeps]
-ChainRulesCore = "d360d2e6-b24c-11e9-a2a3-2a2ae2dbcce4"
-
-[extensions]
-TensorKitChainRulesCoreExt = "ChainRulesCore"
-
 [compat]
 HalfIntegers = "1"
 LRUCache = "1.0.2"
 PackageExtensionCompat = "1"
 Strided = "2"
-TensorOperations = "4.0.6"
+TensorOperations = "4.0.6 - 4.0.7"
 TupleTools = "1.1"
 VectorInterface = "0.4"
 WignerSymbols = "1,2"
 julia = "1.6"
 
+[extensions]
+TensorKitChainRulesCoreExt = "ChainRulesCore"
+
 [extras]
 ChainRulesCore = "d360d2e6-b24c-11e9-a2a3-2a2ae2dbcce4"
 ChainRulesTestUtils = "cdddcdb0-9152-4a09-a978-84456f9df70a"
@@ -46,3 +43,6 @@ WignerSymbols = "9f57e263-0b3d-5e2e-b1be-24f2bb48858b"
 
 [targets]
 test = ["Combinatorics", "HalfIntegers", "LinearAlgebra", "Random", "TensorOperations", "Test", "TestExtras", "WignerSymbols", "ChainRulesCore", "ChainRulesTestUtils", "FiniteDifferences"]
+
+[weakdeps]
+ChainRulesCore = "d360d2e6-b24c-11e9-a2a3-2a2ae2dbcce4"
diff --git a/src/auxiliary/linalg.jl b/src/auxiliary/linalg.jl
index bc57d4c6..815f9900 100644
--- a/src/auxiliary/linalg.jl
+++ b/src/auxiliary/linalg.jl
@@ -56,6 +56,14 @@ using LinearAlgebra: BlasFloat, BlasReal, BlasComplex, checksquare
 using ..TensorKit: OrthogonalFactorizationAlgorithm,
                    QL, QLpos, QR, QRpos, LQ, LQpos, RQ, RQpos, SVD, SDD, Polar
 
+# only defined in >v1.7
+@static if VERSION < v"1.7-"
+    _rf_findmax((fm, im), (fx, ix)) = isless(fm, fx) ? (fx, ix) : (fm, im)
+    _argmax(f, domain) = mapfoldl(x -> (f(x), x), _rf_findmax, domain)[2]
+else
+    _argmax(f, domain) = argmax(f, domain)
+end
+
 # TODO: define for CuMatrix if we support this
 function one!(A::DenseMatrix)
     Threads.@threads for j in 1:size(A, 2)
@@ -273,12 +281,12 @@ function eig!(A::StridedMatrix{T}; permute::Bool=true, scale::Bool=true) where {
     while j <= n
         if DI[j] == 0
             vr = view(VR, :, j)
-            s = conj(sign(argmax(abs, vr)))
+            s = conj(sign(_argmax(abs, vr)))
             V[:, j] .= s .* vr
         else
             vr = view(VR, :, j)
             vi = view(VR, :, j + 1)
-            s = conj(sign(argmax(abs, vr))) # vectors coming from lapack have already real absmax component
+            s = conj(sign(_argmax(abs, vr))) # vectors coming from lapack have already real absmax component
             V[:, j] .= s .* (vr .+ im .* vi)
             V[:, j + 1] .= s .* (vr .- im .* vi)
             j += 1
@@ -296,7 +304,7 @@ function eig!(A::StridedMatrix{T}; permute::Bool=true,
                          A)[[2, 4]]
     for j in 1:n
         v = view(V, :, j)
-        s = conj(sign(argmax(abs, v)))
+        s = conj(sign(_argmax(abs, v)))
         v .*= s
     end
     return D, V
@@ -308,7 +316,7 @@ function eigh!(A::StridedMatrix{T}) where {T<:BlasFloat}
     D, V = LAPACK.syevr!('V', 'A', 'U', A, 0.0, 0.0, 0, 0, -1.0)
     for j in 1:n
         v = view(V, :, j)
-        s = conj(sign(argmax(abs, v)))
+        s = conj(sign(_argmax(abs, v)))
         v .*= s
     end
     return D, V
diff --git a/src/planar/macros.jl b/src/planar/macros.jl
index 1d76cc48..e10308d2 100644
--- a/src/planar/macros.jl
+++ b/src/planar/macros.jl
@@ -23,7 +23,7 @@ function planarparser(planarexpr, kwargs...)
 
     # braiding tensors need to be instantiated before kwargs are processed
     push!(parser.preprocessors, _construct_braidingtensors)
-    
+
     for (name, val) in kwargs
         if name == :order
             isexpr(val, :tuple) ||
@@ -62,7 +62,7 @@ function planarparser(planarexpr, kwargs...)
             throw(ArgumentError("Unknown keyword argument `name`."))
         end
     end
-    
+
     treebuilder = parser.contractiontreebuilder
     treesorter = parser.contractiontreesorter
     costcheck = parser.contractioncostcheck
diff --git a/test/ad.jl b/test/ad.jl
index 3b82c0b4..d686a834 100644
--- a/test/ad.jl
+++ b/test/ad.jl
@@ -61,7 +61,7 @@ end
 
 # Float32 and finite differences don't mix well
 precision(::Type{<:Union{Float32,Complex{Float32}}}) = 1e-2
-precision(::Type{<:Union{Float64,Complex{Float64}}}) = 1e-8
+precision(::Type{<:Union{Float64,Complex{Float64}}}) = 1e-6
 
 # rrules for functions that destroy inputs
 # ----------------------------------------
@@ -111,7 +111,7 @@ Vlist = ((ℂ^2, (ℂ^3)', ℂ^3, ℂ^2, (ℂ^2)'),
           ℂ[Z2Irrep](0 => 3, 1 => 2)',
           ℂ[Z2Irrep](0 => 2, 1 => 3),
           ℂ[Z2Irrep](0 => 2, 1 => 2)),
-         (ℂ[U1Irrep](0 => 1, 1 => 2, -1 => 2),
+         (ℂ[U1Irrep](0 => 2, 1 => 2, -1 => 2),
           ℂ[U1Irrep](0 => 3, 1 => 1, -1 => 1),
           ℂ[U1Irrep](0 => 2, 1 => 2, -1 => 1)',
           ℂ[U1Irrep](0 => 1, 1 => 2, -1 => 2),
@@ -227,7 +227,7 @@ Vlist = ((ℂ^2, (ℂ^3)', ℂ^3, ℂ^2, (ℂ^2)'),
         C = TensorMap(randn, T, V[1] ⊗ V[2] ← V[1] ⊗ V[2])
         H = TensorMap(randn, T, V[3] ⊗ V[4] ← V[3] ⊗ V[4])
         H = (H + H') / 2
-        atol = 1e-6
+        atol = precision(T)
 
         for alg in (TensorKit.QR(), TensorKit.QRpos())
             test_rrule(leftorth, A; fkwargs=(; alg=alg), atol)
@@ -312,7 +312,8 @@ Vlist = ((ℂ^2, (ℂ^3)', ℂ^3, ℂ^2, (ℂ^2)'),
             T <: Complex && remove_svdgauge_depence!(ΔU, ΔV, U, S, V)
             test_rrule(tsvd, C; atol, output_tangent=(ΔU, ΔS, ΔV, 0.0))
 
-            c, = argmax(x -> sqrt(dim(x[1])) * maximum(diag(x[2])), blocks(S))
+            c, = TensorKit.MatrixAlgebra._argmax(x -> sqrt(dim(x[1])) * maximum(diag(x[2])),
+                                                 blocks(S))
             U, S, V, ϵ = tsvd(C; trunc=truncdim(2 * dim(c)))
             ΔU = TensorMap(randn, scalartype(U), space(U))
             ΔS = TensorMap(randn, scalartype(S), space(S))
diff --git a/test/planar.jl b/test/planar.jl
index 062e41b6..bf3efc19 100644
--- a/test/planar.jl
+++ b/test/planar.jl
@@ -71,29 +71,29 @@ end
 
 @testset "@planar" verbose = true begin
     T = ComplexF64
-    
+
     @testset "contractcheck" begin
         V = ℂ^2
         A = TensorMap(rand, T, V ⊗ V ← V)
         B = TensorMap(rand, T, V ⊗ V ← V')
         @tensor C1[i j; k l] := A[i j; m] * B[k l; m]
-        @tensor contractcheck=true C2[i j; k l] := A[i j; m] * B[k l; m]
+        @tensor contractcheck = true C2[i j; k l] := A[i j; m] * B[k l; m]
         @test C1 ≈ C2
         B2 = TensorMap(rand, T, V ⊗ V ← V) # wrong duality for third space
         @test_throws SpaceMismatch("incompatible spaces for m: $V ≠ $(V')") begin
             @tensor contractcheck = true C3[i j; k l] := A[i j; m] * B2[k l; m]
         end
-        
+
         A = TensorMap(rand, T, V ← V ⊗ V)
         B = TensorMap(rand, T, V ⊗ V ← V)
         @planar C1[i; j] := A[i; k l] * τ[k l; m n] * B[m n; j]
-        @planar contractcheck=true C2[i; j] := A[i; k l] * τ[k l; m n] * B[m n; j]
+        @planar contractcheck = true C2[i; j] := A[i; k l] * τ[k l; m n] * B[m n; j]
         @test C1 ≈ C2
         @test_throws SpaceMismatch("incompatible spaces for l: $V ≠ $(V')") begin
-            @planar contractcheck=true C3[i; j] := A[i; k l] * τ[k l; m n] * B[n j; m]
+            @planar contractcheck = true C3[i; j] := A[i; k l] * τ[k l; m n] * B[n j; m]
         end
     end
-    
+
     @testset "MPS networks" begin
         P = ℂ^2
         Vmps = ℂ^12