fixes some Nemo quirks in doctests

Author: ederc

src/algorithms/groebner-bases.jl

@@ -27,13 +27,13 @@ At the moment the underlying algorithm is based on variants of Faugère's F4 Alg
 julia> using AlgebraicSolving
 
 julia> R, (x,y,z) = PolynomialRing(GF(101),["x","y","z"], ordering=:degrevlex)
-(Multivariate Polynomial Ring in x, y, z over Galois field with characteristic 101, Nemo.gfp_mpoly[x, y, z])
+(Multivariate polynomial ring in x, y, z over GF(101), Nemo.fpMPolyRingElem[x, y, z])
 
 julia> I = Ideal([x+2*y+2*z-1, x^2+2*y^2+2*z^2-x, 2*x*y+2*y*z-y])
-Nemo.gfp_mpoly[x + 2*y + 2*z + 100, x^2 + 2*y^2 + 2*z^2 + 100*x, 2*x*y + 2*y*z + 100*y]
+Nemo.fpMPolyRingElem[x + 2*y + 2*z + 100, x^2 + 2*y^2 + 2*z^2 + 100*x, 2*x*y + 2*y*z + 100*y]
 
 julia> eliminate(I, 2)
-1-element Vector{Nemo.gfp_mpoly}:
+1-element Vector{Nemo.fpMPolyRingElem}:
  z^4 + 38*z^3 + 95*z^2 + 95*z
 ```
 """
@@ -81,20 +81,20 @@ At the moment the underlying algorithm is based on variants of Faugère's F4 Alg
 julia> using AlgebraicSolving
 
 julia> R, (x,y,z) = PolynomialRing(GF(101),["x","y","z"], ordering=:degrevlex)
-(Multivariate Polynomial Ring in x, y, z over Galois field with characteristic 101, Nemo.gfp_mpoly[x, y, z])
+(Multivariate polynomial ring in x, y, z over GF(101), Nemo.fpMPolyRingElem[x, y, z])
 
 julia> I = Ideal([x+2*y+2*z-1, x^2+2*y^2+2*z^2-x, 2*x*y+2*y*z-y])
-Nemo.gfp_mpoly[x + 2*y + 2*z + 100, x^2 + 2*y^2 + 2*z^2 + 100*x, 2*x*y + 2*y*z + 100*y]
+emo.fpMPolyRingElem[x + 2*y + 2*z + 100, x^2 + 2*y^2 + 2*z^2 + 100*x, 2*x*y + 2*y*z + 100*y]
 
 julia> groebner_basis(I)
-4-element Vector{Nemo.gfp_mpoly}:
+4-element Vector{emo.fpMPolyRingElem}:
  x + 2*y + 2*z + 100
  y*z + 82*z^2 + 10*y + 40*z
  y^2 + 60*z^2 + 20*y + 81*z
  z^3 + 28*z^2 + 64*y + 13*z
 
 julia> groebner_basis(I, eliminate=2)
-1-element Vector{Nemo.gfp_mpoly}:
+1-element Vector{emo.fpMPolyRingElem}:
  z^4 + 38*z^3 + 95*z^2 + 95*z
 ```
 """

src/algorithms/solvers.jl

@@ -216,13 +216,13 @@ is greater then zero an empty array is returned.
 julia> using AlgebraicSolving
 
 julia> R,(x1,x2,x3) = PolynomialRing(QQ, ["x1","x2","x3"])
-(Multivariate Polynomial Ring in x1, x2, x3 over Rational Field, Nemo.fmpq_mpoly[x1, x2, x3])
+(Multivariate polynomial ring in x1, x2, x3 over QQ, Nemo.QQMPolyRingElem[x1, x2, x3])
 
 julia> I = Ideal([x1+2*x2+2*x3-1, x1^2+2*x2^2+2*x3^2-x1, 2*x1*x2+2*x2*x3-x2])
-Nemo.fmpq_mpoly[x1 + 2*x2 + 2*x3 - 1, x1^2 - x1 + 2*x2^2 + 2*x3^2, 2*x1*x2 + 2*x2*x3 - x2]
+Nemo.QQMPolyRingElem[x1 + 2*x2 + 2*x3 - 1, x1^2 - x1 + 2*x2^2 + 2*x3^2, 2*x1*x2 + 2*x2*x3 - x2]
 
 julia> rational_parametrization(I)
-AlgebraicSolving.RationalParametrization([:x1, :x2, :x3], fmpz[], 84*x^4 - 40*x^3 + x^2 + x, 336*x^3 - 120*x^2 + 2*x + 1, AbstractAlgebra.PolyElem[184*x^3 - 80*x^2 + 4*x + 1, 36*x^3 - 18*x^2 + 2*x])
+AlgebraicSolving.RationalParametrization([:x1, :x2, :x3], Nemo.ZZRingElem[], 84*x^4 - 40*x^3 + x^2 + x, 336*x^3 - 120*x^2 + 2*x + 1, AbstractAlgebra.PolyRingElem[184*x^3 - 80*x^2 + 4*x + 1, 36*x^3 - 18*x^2 + 2*x])
 ```
 """
 function rational_parametrization(
@@ -269,18 +269,18 @@ the rational roots of the ideal.
 julia> using AlgebraicSolving
 
 julia> R,(x1,x2,x3) = PolynomialRing(QQ, ["x1","x2","x3"])
-(Multivariate Polynomial Ring in x1, x2, x3 over Rational Field, Nemo.fmpq_mpoly[x1, x2, x3])
+(Multivariate polynomial ring in x1, x2, x3 over QQ, Nemo.QQMPolyRingElem[[x1, x2, x3])
 
 julia> I = Ideal([x1+2*x2+2*x3-1, x1^2+2*x2^2+2*x3^2-x1, 2*x1*x2+2*x2*x3-x2])
-Nemo.fmpq_mpoly[x1 + 2*x2 + 2*x3 - 1, x1^2 - x1 + 2*x2^2 + 2*x3^2, 2*x1*x2 + 2*x2*x3 - x2]
+Nemo.QQMPolyRingElem[[x1 + 2*x2 + 2*x3 - 1, x1^2 - x1 + 2*x2^2 + 2*x3^2, 2*x1*x2 + 2*x2*x3 - x2]
 
 julia> rat_sols = rational_solutions(I)
-2-element Vector{Vector{fmpq}}:
+2-element Vector{Vector{Nemo.QQFieldElem}}:
  [1, 0, 0]
  [1//3, 0, 1//3]
 
 julia> map(r->map(p->evaluate(p, r), I.gens), rat_sols)
-2-element Vector{Vector{fmpq}}:
+2-element Vector{Vector{Nemo.QQFieldElem}}:
  [0, 0, 0]
  [0, 0, 0]
 ```

src/examples/katsura.jl

@@ -25,7 +25,7 @@ Also note that indices have been shifted to start from 1.
 julia> using AlgebraicSolving
 
 julia> katsura(2)
-Nemo.fmpq_mpoly[x1 + 2*x2 + 2*x3 - 1, x1^2 + 2*x2^2 + 2*x3^2 - x1, 2*x1*x2 + 2*x2*x3 - x2]
+Nemo.QQMPolyRingElem[x1 + 2*x2 + 2*x3 - 1, x1^2 + 2*x2^2 + 2*x3^2 - x1, 2*x1*x2 + 2*x2*x3 - x2]
 ```
 """
 function katsura(log_solutions::Int, characteristic::Int=0)
@@ -50,10 +50,10 @@ Returns the Katsura ideal in the given polynomial ring `R`.
 julia> using AlgebraicSolving
 
 julia> R, _ = QQ["x", "y", "z"]
-(Multivariate Polynomial Ring in x, y, z over Rational Field, Nemo.fmpq_mpoly[x, y, z])
+(Multivariate polynomial ring in x, y, z over Rational Field, Nemo.QQMPolyRingElem[x, y, z])
 
 julia> katsura(R)
-Nemo.fmpq_mpoly[x + 2*y + 2*z - 1, x^2 - x + 2*y^2 + 2*z^2, 2*x*y + 2*y*z - y]
+Nemo.QQMPolyRingElem[x + 2*y + 2*z - 1, x^2 - x + 2*y^2 + 2*z^2, 2*x*y + 2*y*z - y]
 ```
 """
 function katsura(R::MPolyRing)

src/imports.jl

@@ -46,8 +46,11 @@ import Nemo:
     prime_field,
     primorial,
     QQ,
+    QQFieldElem,
+    QQMPolyRingElem,
     rising_factorial,
     root,
     unit,
     vars,
-    ZZ
+    ZZ,
+    ZZRingElem