Merge pull request #1476 from AlexD97/FreeResolutionModule

Improve simplify; make ext/tor work again, add test

src/Modules/UngradedModules.jl

@@ -4187,8 +4187,8 @@ function Hecke.ring(I::MPolyIdeal)
   return parent(gen(I, 1))
 end
 
-function *(I::MPolyIdeal{T}, F::FreeMod{T}) where {T<:RingElem}
-  return sub(F, [g*e for g in gens(I) for e in gens(F)])
+function *(I::MPolyIdeal{T}, M::ModuleFP{T}) where {T<:RingElem}
+  return sub(M, [g*e for g in gens(I) for e in gens(M)])
 end
 
 @doc Markdown.doc"""
@@ -4880,9 +4880,9 @@ end
 Compute $\text{Tor}_i(M,N)$.
 """
 function tor(M::ModuleFP, N::ModuleFP, i::Int)
-  free_res = free_resolution_via_kernels(M)[1:end-2]
-  lifted_resolution = tensor_product(free_res, N) #TODO only three homs are necessary
-  return homology(lifted_resolution,length(lifted_resolution)-i)
+  free_res = free_resolution(M)
+  lifted_resolution = tensor_product(free_res.C, N) #TODO only three homs are necessary
+  return homology(lifted_resolution,i)
 end
 
 #TODO, mF
@@ -5053,8 +5053,8 @@ end
 Compute $\text{Ext}^i(M,N)$.
 """
 function ext(M::ModuleFP, N::ModuleFP, i::Int)
-  free_res = free_resolution_via_kernels(M)[1:end-2]
-  lifted_resolution = hom(free_res, N) #TODO only three homs are necessary
+  free_res = free_resolution(M)
+  lifted_resolution = hom(free_res.C, N) #TODO only three homs are necessary
   return homology(lifted_resolution,i)
 end
 
@@ -5378,7 +5378,13 @@ function simplify(M::SubQuo)
   function rows_to_delete(A::MatElem, max_index::Int)
     to_delete_indices::Vector{Int} = []
     corresponding_row_index::Vector{Int} = []
+    if max_index < nrows(A)
+      A = vcat(A[(max_index+1):nrows(A),:],A[1:max_index,:])
+    end
     K = matrix_kernel(A)
+    if max_index < nrows(A)
+      K = hcat(K[:,(ncols(K)-max_index+1):ncols(K)],K[:,1:(ncols(K)-max_index)])
+    end
     for i=1:size(K)[1], j=1:max_index
       if is_unit(K[i,j])
         deletion_possible = true
@@ -5445,7 +5451,7 @@ function simplify(M::SubQuo)
 
   if length(new_generators)==0
     zero_module = FreeMod(R,0)
-    injection = FreeModuleHom(zero_module, M, [])
+    injection = FreeModuleHom(zero_module, M, Vector{ModuleFPElem}())
     projection = SubQuoHom(M, zero_module, [zero(zero_module) for i=1:ngens(M)])
     # TODO early return or register morphisms?
     return zero_module,injection,projection

test/Modules/UngradedModules.jl

@@ -211,6 +211,26 @@ end
 	end
 end
 
+@testset "Ext, Tor" begin
+	# These tests are only meant to check that the ext and tor function don't throw any error
+	# These tests don't check the correctness of ext and tor
+
+	R, (x, y, z) = PolynomialRing(QQ, ["x", "y", "z"])
+	A = R[x; y]
+	B = R[x^2; x*y; y^2; z^4]
+	M = SubQuo(A, B)
+	F = free_module(R, 1)
+	Q, _ = quo(F, [x*F[1]])
+	T0 = tor(Q, M, 0)
+	T1 = tor(Q, M, 1)
+	T2 =  tor(Q, M, 2)
+	@test iszero(T2)
+
+	E0 = ext(Q, M, 0)
+	E1 = ext(Q, M, 1)
+	E2 = ext(Q, M, 2)
+end
+
 @testset "Gröbner bases" begin
 	R, (x,y) = PolynomialRing(QQ, ["x", "y"])
 	F = FreeMod(R, 1)