diff --git a/docs/src/quad_forms/basics.md b/docs/src/quad_forms/basics.md
index a612ba614c..e8e3a6967a 100644
--- a/docs/src/quad_forms/basics.md
+++ b/docs/src/quad_forms/basics.md
@@ -84,7 +84,7 @@ In all the other cases, we say that $V$ is *indefinite*.
 ```@docs
 is_regular(::AbstractSpace)
 is_quadratic(::AbstractSpace)
-ishermitian(::AbstractSpace)
+is_hermitian(::AbstractSpace)
 is_positive_definite(::AbstractSpace)
 is_negative_definite(::AbstractSpace)
 is_definite(::AbstractSpace)
@@ -102,7 +102,7 @@ E, b = number_field(t^2-a*t+1, "b");
 Q = quadratic_space(K, K[0 1; 1 0]);
 H = hermitian_space(E, 3);
 is_regular(Q), is_regular(H)
-is_quadratic(Q), ishermitian(H)
+is_quadratic(Q), is_hermitian(H)
 is_definite(Q), is_positive_definite(H)
 ```
 ---
diff --git a/src/QuadForm/Herm/Spaces.jl b/src/QuadForm/Herm/Spaces.jl
index efe9a902e3..ed22debd17 100644
--- a/src/QuadForm/Herm/Spaces.jl
+++ b/src/QuadForm/Herm/Spaces.jl
@@ -111,7 +111,7 @@ end
 
 is_quadratic(V::HermSpace) = false
 
-ishermitian(V::HermSpace) = true
+is_hermitian(V::HermSpace) = true
 
 _base_algebra(V::HermSpace) = V.E
 
diff --git a/src/QuadForm/Quad/Spaces.jl b/src/QuadForm/Quad/Spaces.jl
index 8e61d36b8c..625b5156ee 100644
--- a/src/QuadForm/Quad/Spaces.jl
+++ b/src/QuadForm/Quad/Spaces.jl
@@ -73,7 +73,7 @@ end
 
 is_quadratic(V::QuadSpace) = true
 
-ishermitian(V::QuadSpace) = false
+is_hermitian(V::QuadSpace) = false
 
 _base_algebra(V::QuadSpace) = V.K
 
diff --git a/src/QuadForm/Spaces.jl b/src/QuadForm/Spaces.jl
index a0f6def2de..af272d7aba 100644
--- a/src/QuadForm/Spaces.jl
+++ b/src/QuadForm/Spaces.jl
@@ -1,4 +1,4 @@
-export ambient_space, rank, gram_matrix, inner_product, involution, ishermitian, is_quadratic, is_regular,
+export ambient_space, rank, gram_matrix, inner_product, involution, is_hermitian, is_quadratic, is_regular,
        is_local_square, is_isometric, is_rationally_isometric, is_isotropic, is_isotropic_with_vector, quadratic_space,
        hermitian_space, diagonal, invariants, hasse_invariant, witt_invariant, orthogonal_basis, fixed_field,
        restrict_scalars, orthogonal_complement, orthogonal_projection
@@ -173,7 +173,7 @@ is_quadratic(::AbstractSpace)
 
 Return whether the space `V` is hermitian.
 """
-ishermitian(::AbstractSpace)
+is_hermitian(::AbstractSpace)
 
 ################################################################################
 #
@@ -439,7 +439,7 @@ is_isometric(L::AbstractSpace, M::AbstractSpace)
 function _isdefinite(V::AbstractSpace)
   E = base_ring(V)
   K = fixed_field(V)
-  if (!is_totally_real(K)) || (ishermitian(V) && !is_totally_complex(E))
+  if (!is_totally_real(K)) || (is_hermitian(V) && !is_totally_complex(E))
     return zero(K)
   end
   D = diagonal(V)
@@ -467,7 +467,7 @@ Return whether the space `V` is positive definite.
 function is_positive_definite(V::AbstractSpace)
   E = base_ring(V)
   K = fixed_field(V)
-  if (!is_totally_real(K)) || (ishermitian(V) && !is_totally_complex(E))
+  if (!is_totally_real(K)) || (is_hermitian(V) && !is_totally_complex(E))
     return false
   end
   D = diagonal(V)
@@ -487,7 +487,7 @@ Return whether the space `V` is negative definite.
 function is_negative_definite(V::AbstractSpace)
   E = base_ring(V)
   K = fixed_field(V)
-  if (!is_totally_real(K)) || (ishermitian(V) && !is_totally_complex(E))
+  if (!is_totally_real(K)) || (is_hermitian(V) && !is_totally_complex(E))
     return false
   end
   D = diagonal(V)
@@ -679,7 +679,7 @@ end
 function _biproduct(x::Vector{T}) where T <: AbstractSpace
   K = base_ring(x[1])
   @req all(i -> base_ring(x[i]) === K, 2:length(x)) "All spaces must be defined over the same field"
-  @req is_quadratic(x[1]) ? all(i -> is_quadratic(x[i]), 2:length(x)) : all(i -> ishermitian(x[i]), 1:length(x)) "Spaces must be all hermitian or all quadratic"
+  @req is_quadratic(x[1]) ? all(i -> is_quadratic(x[i]), 2:length(x)) : all(i -> is_hermitian(x[i]), 1:length(x)) "Spaces must be all hermitian or all quadratic"
   G = diagonal_matrix(gram_matrix.(x))
   V = is_quadratic(x[1]) ? quadratic_space(K, G) : hermitian_space(K, G)
   n = sum(dim.(x))
diff --git a/src/QuadForm/indefiniteLLL.jl b/src/QuadForm/indefiniteLLL.jl
index 09d47fb27e..2ee6464637 100644
--- a/src/QuadForm/indefiniteLLL.jl
+++ b/src/QuadForm/indefiniteLLL.jl
@@ -281,7 +281,7 @@ julia> lll_gram_indef_with_transform(G)
 """
 function lll_gram_indef_with_transform(G::MatElem{ZZRingElem}; check::Bool = false)
 
-  @req !check || (issymmetric(G) && det(G) != 0 && _is_indefinite(change_base_ring(QQ,G))) "Input should be a non-degenerate indefinite Gram matrix."
+  @req !check || (is_symmetric(G) && det(G) != 0 && _is_indefinite(change_base_ring(QQ,G))) "Input should be a non-degenerate indefinite Gram matrix."
 
   red = lll_gram_indef_isotropic(G; base = true)
 
diff --git a/test/QuadForm/Herm/Spaces.jl b/test/QuadForm/Herm/Spaces.jl
index dd50371f10..f5d3c1f5e9 100644
--- a/test/QuadForm/Herm/Spaces.jl
+++ b/test/QuadForm/Herm/Spaces.jl
@@ -37,7 +37,7 @@
   V = @inferred hermitian_space(E, FlintQQ[1 2; 2 1])
   @test V === hermitian_space(E, FlintQQ[1 2; 2 1])
   @test V !== hermitian_space(E, FlintQQ[1 2; 2 1], cached = false)
-  @test ishermitian(V)
+  @test is_hermitian(V)
   @test !is_definite(V)
   @test involution(V) == s
   @test det(V) == -discriminant(V)
diff --git a/test/QuadForm/Quad/Spaces.jl b/test/QuadForm/Quad/Spaces.jl
index 0fe3d82bdd..340ea549d2 100644
--- a/test/QuadForm/Quad/Spaces.jl
+++ b/test/QuadForm/Quad/Spaces.jl
@@ -65,7 +65,7 @@
     @test (@inferred dim(V)) == 2
     @test (@inferred rank(V)) == 0
     @test @inferred is_quadratic(V)
-    @test @inferred !ishermitian(V)
+    @test @inferred !is_hermitian(V)
     @test (@inferred fixed_field(V)) === K
 
     @test_throws ArgumentError quadratic_space(K, zero_matrix(K, 1, 2))