more fixes on doc tests

Author: ederc

src/algorithms/groebner-bases.jl

@@ -27,7 +27,7 @@ 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 GF(101), Nemo.fpMPolyRingElem[x, y, z])
+(Multivariate polynomial ring in 3 variables 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.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]
@@ -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 GF(101), Nemo.fpMPolyRingElem[x, y, z])
+(Multivariate polynomial ring in 3 variables 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])
-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]
+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> groebner_basis(I)
-4-element Vector{emo.fpMPolyRingElem}:
+4-element Vector{Nemo.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{emo.fpMPolyRingElem}:
+1-element Vector{Nemo.fpMPolyRingElem}:
  z^4 + 38*z^3 + 95*z^2 + 95*z
 ```
 """

src/algorithms/solvers.jl

@@ -216,7 +216,7 @@ 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 QQ, Nemo.QQMPolyRingElem[x1, x2, x3])
+(Multivariate polynomial ring in 3 variables 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.QQMPolyRingElem[x1 + 2*x2 + 2*x3 - 1, x1^2 - x1 + 2*x2^2 + 2*x3^2, 2*x1*x2 + 2*x2*x3 - x2]
@@ -269,10 +269,10 @@ 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 QQ, Nemo.QQMPolyRingElem[[x1, x2, x3])
+(Multivariate polynomial ring in 3 variables 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.QQMPolyRingElem[[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{Nemo.QQFieldElem}}:
@@ -365,13 +365,13 @@ is greater than 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 3 variables 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> real_solutions(I)
-4-element Vector{Vector{fmpq}}:
+4-element Vector{Vector{Nemo.QQFieldElem}}:
  [5416829397//8589934592, 2708414699//8589934592, -2844258330290649520990905062759917788583//21778071482940061661655974875633165533184]
  [1, 0, 0]
  [1945971683//8589934592, 972985841//8589934592, 744426424910260862653434112767010536665//2722258935367507707706996859454145691648]

src/examples/katsura.jl

@@ -50,7 +50,7 @@ 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.QQMPolyRingElem[x, y, z])
+(Multivariate polynomial ring in 3 variables over QQ, Nemo.QQMPolyRingElem[x, y, z])
 
 julia> katsura(R)
 Nemo.QQMPolyRingElem[x + 2*y + 2*z - 1, x^2 - x + 2*y^2 + 2*z^2, 2*x*y + 2*y*z - y]