Add left division operator for matrix and vector

src/ops.jl

@@ -422,6 +422,19 @@ end
     frommandel(SymmetricFourthOrderTensor{dim}, inv(tomandel(x)))
 end
 
+@generated function Base.:\(A::AbstractSquareTensor{dim}, b::AbstractVec{dim}) where {dim}
+    exps_A = [:(Tuple(A)[$i]) for i in independent_indices(A)]
+    exps_b = [:(Tuple(b)[$i]) for i in independent_indices(b)]
+    quote
+        @_inline_meta
+        @inbounds begin
+            SA = SMatrix{dim, dim}($(exps_A...))
+            Sb = SVector{dim}($(exps_b...))
+        end
+        Vec{dim}(Tuple(SA \ Sb))
+    end
+end
+
 """
     cross(x::Vec{3}, y::Vec{3}) -> Vec{3}
     cross(x::Vec{2}, y::Vec{2}) -> Vec{3}

test/ops.jl

@@ -161,6 +161,15 @@ end
             @test (@inferred inv(y))::typeof(y) ⊡ y ≈ one(y)
         end
     end
+    @testset "solve" begin
+        for T in (Float32, Float64), dim in 1:4
+            A = rand(SecondOrderTensor{dim, T})
+            S = rand(SymmetricSecondOrderTensor{dim, T})
+            b = rand(Vec{dim, T})
+            @test (@inferred A \ b)::Vec{dim, T} |> Array ≈ Array(A) \ Array(b)
+            @test (@inferred S \ b)::Vec{dim, T} |> Array ≈ Array(S) \ Array(b)
+        end
+    end
     @testset "cross" begin
         for T in (Float32, Float64), dim in 1:3
             x = rand(Vec{dim, T})