QuadFormWithIsom patch 1

experimental/QuadFormAndIsom/README.md

@@ -24,9 +24,8 @@ of finite order with at most two prime divisors. The methods we resort to
 for this purpose are developed in the paper [BH23](@cite).
 
 We also provide some algorithms computing isomorphism classes of primitive
-embeddings of even lattices following Nikulin's theory. More precisely, the two
-functions `primitive_embeddings_in_primary_lattice` and
-`primitive_embeddings_of_primary_lattice` offer, under certain conditions,
+embeddings of even lattices following Nikulin's theory. More precisely, the
+function `primitive_embeddings` offers, under certain conditions,
 the possibility to compute representatives of primitive embeddings and classify
 them in different ways. Note nonetheless that these functions are not efficient
 in the case were the discriminant groups have a large number of subgroups.
@@ -39,8 +38,6 @@ there are still computational bottlenecks due to non-optimized algorithms.
 
 Among the possible improvements and extensions:
 * Implement extra methods for lattices with isometries of infinite order;
-* Extend the methods for classification of primitive embeddings to the more
-  general case (knowing that we lose efficiency for large discriminant groups);
 * Extend existing methods for equivariant primitive embeddings/extensions.
 
 ## Currently application of this project

experimental/QuadFormAndIsom/docs/src/introduction.md

@@ -24,9 +24,8 @@ of finite order with at most two prime divisors. The methods we resort to
 for this purpose are developed in the paper [BH23].
 
 We also provide some algorithms computing isomorphism classes of primitive
-embeddings of even lattices following Nikulin's theory. More precisely, the two
-functions `primitive_embeddings_in_primary_lattice` and
-`primitive_embeddings_of_primary_lattice` offer, under certain conditions,
+embeddings of even lattices following Nikulin's theory. More precisely, the
+function `primitive_embeddings` offers, under certain conditions,
 the possibility to compute representatives of primitive embeddings and classify
 them in different ways. Note nonetheless that these functions are not efficient
 in the case were the discriminant groups have a large number of subgroups.
@@ -39,8 +38,6 @@ there are still computational bottlenecks due to non-optimized algorithms.
 
 Among the possible improvements and extensions:
 * Implement extra methods for lattices with isometries of infinite order;
-* Extend the methods for classification of primitive embeddings to the more
-  general case (knowing that we lose efficiency for large discriminant groups);
 * Extend existing methods for equivariant primitive embeddings/extensions.
 
 ## Currently application of this project

experimental/QuadFormAndIsom/docs/src/primembed.md

@@ -31,31 +31,23 @@ and inefficient in general for large rank or determinant. But, in the case
 where the discriminant groups are (elementary) $p$-groups, the method can be
 more efficient.
 
-The ultimate goal of the project is to make all kind of computations of
-primitive embeddings available. For now, we only cover the case where one of
-the two lattices involved is *$p$-primary*, i.e. its discriminant is an abelian
-$p$-group. Note that this covers the case of unimodular lattices, of course.
 We provide 4 kinds of output:
 * A boolean, which only returns whether there exists a primitive embedding;
 * A single primitive embedding as soon as the algorithm computes one;
 * A list of representatives of isomorphism classes of primitive embeddings;
 * A list of representatives of isomorphism classes of primitive sublattices.
 
 ```@docs
-primitive_embeddings_in_primary_lattice(::ZZLat, ::ZZLat)
-primitive_embeddings_of_primary_lattice(::ZZLat, ::ZZLat)
+primitive_embeddings(::ZZLat, ::ZZLat)
 ```
 
 Note that the previous two functions require the first lattice of the input to be
 unique in its genus. Otherwise, one can specify a genus, or its invariants, as a
 first input:
 
 ```@docs
-primitive_embeddings_in_primary_lattice(::ZZGenus, ::ZZLat)
-primitive_embeddings_in_primary_lattice(::TorQuadModule, ::Tuple{Int, Int},
-::ZZLat)
-primitive_embeddings_of_primary_lattice(::ZZGenus, ::ZZLat)
-primitive_embeddings_of_primary_lattice(::TorQuadModule, ::Tuple{Int, Int},
+primitive_embeddings(::ZZGenus, ::ZZLat)
+primitive_embeddings(::TorQuadModule, ::Tuple{Int, Int},
 ::ZZLat)
 ```