Merge pull request #61 from ederc/handling-zero-ideal

Handling zero ideal as input

src/algorithms/groebner-bases.jl

@@ -150,7 +150,7 @@ function _core_groebner_basis(
 
     # convert ideal to flattened arrays of ints
     if !(is_probable_prime(field_char))
-        error("At the moment we only supports finite fields.")
+        error("At the moment we only support finite fields.")
     end
 
     # nr_gens might change if F contains zero polynomials

src/algorithms/solvers.jl

@@ -65,6 +65,9 @@ function _core_msolve(
         )
 
     F = I.gens
+    if (is_zero(F))
+        error("Dimension of ideal is greater than zero, no solutions provided.")
+    end
     R = first(F).parent
     nr_vars     = nvars(R)
     nr_gens     = length(F)
@@ -86,7 +89,7 @@ function _core_msolve(
         error("At the moment we only support the rationals as ground field.")
     end
     # convert Singular ideal to flattened arrays of ints
-    lens, cfs, exps = _convert_to_msolve(F)
+    lens, cfs, exps, nr_gens = _convert_to_msolve(F)
 
     res_ld      = Ref(Cint(0))
     res_nr_vars = Ref(Cint(0))
@@ -214,7 +217,7 @@ Given an ideal `I` with a finite solution set over the complex numbers, return
 the rational parametrization of the ideal with a given precision (default 32 bits).
 
 **Note**: At the moment only QQ is supported as ground field. If the dimension of the ideal
-is greater then zero an empty array is returned.
+is greater than zero an ErrorException is thrown.
 
 # Arguments
 - `I::Ideal{T} where T <: MPolyRingElem`: input generators.
@@ -364,7 +367,7 @@ Given an ideal `I` with a finite solution set over the complex numbers, return
 the real roots of the ideal with a given precision (default 32 bits).
 
 **Note**: At the moment only QQ is supported as ground field. If the dimension of the ideal
-is greater than zero an empty array is returned.
+is greater than zero an ErrorException is thrown.
 
 # Arguments
 - `I::Ideal{T} where T <: MPolyRingElem`: input generators.

src/imports.jl

@@ -31,6 +31,7 @@ import Nemo:
     is_probable_prime,
     is_square,
     is_unit,
+    is_zero,
     isqrtrem,
     jacobi_symbol,
     leading_coefficient,

test/algorithms/solvers.jl

@@ -61,8 +61,14 @@
     @test_throws ErrorException real_solutions(I, interval=true)
 	@test_throws ErrorException rational_solutions(I)
 
-    # check variable permutation
     R, (x, y) = polynomial_ring(QQ,["x","y"])
+    # issue 54
+    I = Ideal([R(0)])
+	@test_throws ErrorException real_solutions(I)
+    I = Ideal([x-1,y+2,R(0)])
+    @test sort(real_solutions(I)) == sort(Vector{QQFieldElem}[[1, -2]])
+
+    # check variable permutation
     I = Ideal([x^2-1, y])
     sols = Vector{QQFieldElem}[
         [-1, 0],