pretty printing for quotients, graded and localized multivariate poly…

…nomial rings (#2184)

Project.toml

@@ -23,7 +23,7 @@ UUIDs = "cf7118a7-6976-5b1a-9a39-7adc72f591a4"
 cohomCalg_jll = "5558cf25-a90e-53b0-b813-cadaa3ae7ade"
 
 [compat]
-AbstractAlgebra = "0.30.2"
+AbstractAlgebra = "0.30.7"
 AlgebraicSolving = "0.3.0"
 DocStringExtensions = "0.8, 0.9"
 GAP = "0.9.4"

docs/src/CommutativeAlgebra/GroebnerBases/groebner_bases.md

@@ -71,10 +71,7 @@ julia> default_ordering(F)
 degrevlex([x, y, z])*lex([gen(1), gen(2)])
 
 julia> S, _ = grade(R, [1, 2, 3])
-(Multivariate polynomial ring in 3 variables over QQ graded by
- x -> [1]
- y -> [2]
- z -> [3], MPolyDecRingElem{QQFieldElem, QQMPolyRingElem}[x, y, z])
+(Graded multivariate polynomial ring in 3 variables over QQ, MPolyDecRingElem{QQFieldElem, QQMPolyRingElem}[x, y, z])
 
 julia> default_ordering(S)
 wdegrevlex([x, y, z], [1, 2, 3])

docs/src/CommutativeAlgebra/affine_algebras.md

@@ -219,7 +219,9 @@ julia> a = ideal(A, [x-y, z^4])
 ideal(x - y, z^4)
 
 julia> base_ring(a)
-Quotient of Multivariate polynomial ring in 3 variables over QQ by ideal(-x^2 + y, -x^3 + z)
+Quotient
+ of multivariate polynomial ring in 3 variables over QQ
+ by ideal(-x^2 + y, -x^3 + z)
 
 julia> gens(a)
 2-element Vector{MPolyQuoRingElem{QQMPolyRingElem}}:
@@ -350,16 +352,10 @@ julia> para = hom(D1, C1, V1)
 Map with following data
 Domain:
 =======
-Multivariate polynomial ring in 4 variables over QQ graded by
- w -> [1]
- x -> [1]
- y -> [1]
- z -> [1]
+Graded multivariate polynomial ring in 4 variables over QQ
 Codomain:
 =========
-Multivariate polynomial ring in 2 variables over QQ graded by
- s -> [1]
- t -> [1]
+Graded multivariate polynomial ring in 2 variables over QQ
 
 julia> twistedCubic = kernel(para)
 ideal(-x*z + y^2, -w*z + x*y, -w*y + x^2)
@@ -374,17 +370,10 @@ julia> proj = hom(D2, C2, V2)
 Map with following data
 Domain:
 =======
-Multivariate polynomial ring in 3 variables over QQ graded by
- a -> [1]
- b -> [1]
- c -> [1]
+Graded multivariate polynomial ring in 3 variables over QQ
 Codomain:
 =========
-Quotient of Multivariate polynomial ring in 4 variables over QQ graded by
- w -> [1]
- x -> [1]
- y -> [1]
- z -> [1] by ideal(-x*z + y^2, -w*z + x*y, -w*y + x^2)
+Quotient of multivariate polynomial ring by ideal with 3 generators
 
 julia> nodalCubic = kernel(proj)
 ideal(-a^2*c + b^3 - 2*b^2*c + b*c^2)
@@ -443,7 +432,7 @@ Domain:
 Multivariate polynomial ring in 3 variables over QQ
 Codomain:
 =========
-Quotient of Multivariate polynomial ring in 3 variables over QQ by ideal(-b^3 + c)
+Quotient of multivariate polynomial ring by ideal with 1 generator
 
 julia> is_surjective(F)
 true
@@ -523,19 +512,19 @@ julia> L[2]
 Map with following data
 Domain:
 =======
-Quotient of Multivariate polynomial ring in 3 variables over QQ by ideal(x*y, x*z)
+Quotient of multivariate polynomial ring by ideal with 2 generators
 Codomain:
 =========
-Quotient of Multivariate polynomial ring in 3 variables over QQ by ideal(2*x^2 + x*y, 10*x^2 + 5*x*y + x*z)
+Quotient of multivariate polynomial ring by ideal with 2 generators
 
 julia> L[3]
 Map with following data
 Domain:
 =======
-Quotient of Multivariate polynomial ring in 3 variables over QQ by ideal(2*x^2 + x*y, 10*x^2 + 5*x*y + x*z)
+Quotient of multivariate polynomial ring by ideal with 2 generators
 Codomain:
 =========
-Quotient of Multivariate polynomial ring in 3 variables over QQ by ideal(x*y, x*z)
+Quotient of multivariate polynomial ring by ideal with 2 generators
 
 ```
 ## Normalization

docs/src/CommutativeAlgebra/localizations.md

@@ -114,7 +114,9 @@ julia> P = ideal(R, [x])
 ideal(x)
 
 julia> U = complement_of_prime_ideal(P)
-complement of ideal(x)
+Complement
+ of prime ideal(x)
+ in multivariate polynomial ring in 3 variables over QQ
 
 julia> Rloc, _ = localization(U);
 
@@ -139,7 +141,9 @@ julia> P = ideal(R, [y-1, x-a])
 ideal(y - 1, x - a)
 
 julia> U = complement_of_prime_ideal(P)
-complement of ideal(y - 1, x - a)
+Complement
+ of prime ideal(y - 1, x - a)
+ in multivariate polynomial ring in 2 variables over number field
 
 julia> RQ, _ = quo(R, I);
 
@@ -180,7 +184,9 @@ julia> P = ideal(R, [x])
 ideal(x)
 
 julia> U = complement_of_prime_ideal(P)
-complement of ideal(x)
+Complement
+ of prime ideal(x)
+ in multivariate polynomial ring in 3 variables over QQ
 
 julia> Rloc, iota = localization(U);
 
@@ -225,7 +231,9 @@ julia> P = ideal(R, [y-1, x-a])
 ideal(y - 1, x - a)
 
 julia> U = complement_of_prime_ideal(P)
-complement of ideal(y - 1, x - a)
+Complement
+ of prime ideal(y - 1, x - a)
+ in multivariate polynomial ring in 2 variables over number field
 
 julia> RQ, p = quo(R, I);
 
@@ -284,15 +292,19 @@ julia> P = ideal(R, [x])
 ideal(x)
 
 julia> U = complement_of_prime_ideal(P)
-complement of ideal(x)
+Complement
+ of prime ideal(x)
+ in multivariate polynomial ring in 3 variables over QQ
 
 julia> Rloc, iota = localization(U);
 
 julia> f = iota(x)/iota(y)
 x/y
 
 julia> parent(f)
-localization of Multivariate polynomial ring in 3 variables over QQ at the complement of ideal(x)
+Localization
+ of multivariate polynomial ring in 3 variables over QQ
+ at complement of prime ideal(x)
 
 julia> g = iota(y)/iota(z)
 y/z
@@ -321,7 +333,9 @@ julia> P = ideal(R, [y-1, x-a])
 ideal(y - 1, x - a)
 
 julia> U = complement_of_prime_ideal(P)
-complement of ideal(y - 1, x - a)
+Complement
+ of prime ideal(y - 1, x - a)
+ in multivariate polynomial ring in 2 variables over number field
 
 julia> RQ, p = quo(R, I);
 
@@ -333,7 +347,9 @@ julia> f = phi(x)
 x
 
 julia> parent(f)
-Localization of Quotient of Multivariate polynomial ring in 2 variables over number field by ideal(2*x^2 - y^3, 2*x^2 - y^5) at the multiplicative set complement of ideal(y - 1, x - a)
+Localization
+ of quotient of multivariate polynomial ring by ideal with 2 generators
+ at complement of prime ideal(y - 1, x - a)
 
 julia> g = f/phi(y)
 x/y
@@ -421,7 +437,11 @@ julia> U = complement_of_point_ideal(R, [0, 0]);
 julia> Rloc, _ = localization(R, U);
 
 julia> MI = ideal(Rloc, V)
-ideal in localization of Multivariate polynomial ring in 2 variables over QQ at the complement of maximal ideal corresponding to point with coordinates QQFieldElem[0, 0] generated by [3*x^2, 4*y^3]
+Ideal
+ of localized ring
+with 2 generators
+ 3*x^2
+ 4*y^3
 ```
 
 ### Data Associated to Ideals

docs/src/CommutativeAlgebra/rings.md

@@ -356,10 +356,7 @@ julia> typeof(f)
 QQMPolyRingElem
 
 julia> S, (x, y, z) = grade(R)
-(Multivariate polynomial ring in 3 variables over QQ graded by
- x -> [1]
- y -> [1]
- z -> [1], MPolyDecRingElem{QQFieldElem, QQMPolyRingElem}[x, y, z])
+(Graded multivariate polynomial ring in 3 variables over QQ, MPolyDecRingElem{QQFieldElem, QQMPolyRingElem}[x, y, z])
 
 julia> g = 3*x^2+y*z
 3*x^2 + y*z

experimental/PlaneCurve/docs/src/elliptic_curves.md

@@ -48,10 +48,7 @@ julia> S, (x, y, z) = polynomial_ring(QQ, ["x", "y", "z"])
 (Multivariate polynomial ring in 3 variables over QQ, QQMPolyRingElem[x, y, z])
 
 julia> T, _ = grade(S)
-(Multivariate polynomial ring in 3 variables over QQ graded by
- x -> [1]
- y -> [1]
- z -> [1], MPolyDecRingElem{QQFieldElem, QQMPolyRingElem}[x, y, z])
+(Graded multivariate polynomial ring in 3 variables over QQ, MPolyDecRingElem{QQFieldElem, QQMPolyRingElem}[x, y, z])
 
 julia> E = Oscar.ProjEllipticCurve(T(y^2*z - x^3 + 2*x*z^2))
 Projective elliptic curve defined by -x^3 + 2*x*z^2 + y^2*z
@@ -124,10 +121,7 @@ julia> S, (x,y,z) = polynomial_ring(A, ["x", "y", "z"])
 (Multivariate polynomial ring in 3 variables over ZZ/(4453), AbstractAlgebra.Generic.MPoly{ZZModRingElem}[x, y, z])
 
 julia> T, _ = grade(S)
-(Multivariate polynomial ring in 3 variables over ZZ/(4453) graded by
- x -> [1]
- y -> [1]
- z -> [1], MPolyDecRingElem{ZZModRingElem, AbstractAlgebra.Generic.MPoly{ZZModRingElem}}[x, y, z])
+(Graded multivariate polynomial ring in 3 variables over ZZ/(4453), MPolyDecRingElem{ZZModRingElem, AbstractAlgebra.Generic.MPoly{ZZModRingElem}}[x, y, z])
 
 julia> E = Oscar.ProjEllipticCurve(T(y^2*z - x^3 - 10*x*z^2 + 2*z^3))
 Projective elliptic curve defined by 4452*x^3 + 4443*x*z^2 + y^2*z + 2*z^3

experimental/PlaneCurve/src/DivisorCurve.jl

@@ -84,10 +84,7 @@ julia> S, (x,y,z) = polynomial_ring(QQ, ["x", "y", "z"])
 (Multivariate polynomial ring in 3 variables over QQ, QQMPolyRingElem[x, y, z])
 
 julia> T, _ = grade(S)
-(Multivariate polynomial ring in 3 variables over QQ graded by
- x -> [1]
- y -> [1]
- z -> [1], MPolyDecRingElem{QQFieldElem, QQMPolyRingElem}[x, y, z])
+(Graded multivariate polynomial ring in 3 variables over QQ, MPolyDecRingElem{QQFieldElem, QQMPolyRingElem}[x, y, z])
 
 julia> C = Oscar.ProjPlaneCurve(T(y^2 + y*z + x^2))
 Projective plane curve defined by x^2 + y^2 + y*z
@@ -305,10 +302,7 @@ julia> S, (x,y,z) = polynomial_ring(QQ, ["x", "y", "z"])
 (Multivariate polynomial ring in 3 variables over QQ, QQMPolyRingElem[x, y, z])
 
 julia> T, _ = grade(S)
-(Multivariate polynomial ring in 3 variables over QQ graded by
- x -> [1]
- y -> [1]
- z -> [1], MPolyDecRingElem{QQFieldElem, QQMPolyRingElem}[x, y, z])
+(Graded multivariate polynomial ring in 3 variables over QQ, MPolyDecRingElem{QQFieldElem, QQMPolyRingElem}[x, y, z])
 
 julia> C = Oscar.ProjPlaneCurve(T(y^2 + y*z + x^2))
 Projective plane curve defined by x^2 + y^2 + y*z
@@ -452,10 +446,7 @@ julia> S, (x,y,z) = polynomial_ring(QQ, ["x", "y", "z"])
 (Multivariate polynomial ring in 3 variables over QQ, QQMPolyRingElem[x, y, z])
 
 julia> T, _ = grade(S)
-(Multivariate polynomial ring in 3 variables over QQ graded by
- x -> [1]
- y -> [1]
- z -> [1], MPolyDecRingElem{QQFieldElem, QQMPolyRingElem}[x, y, z])
+(Graded multivariate polynomial ring in 3 variables over QQ, MPolyDecRingElem{QQFieldElem, QQMPolyRingElem}[x, y, z])
 
 julia> C = Oscar.ProjPlaneCurve(T(y^2 + y*z + x^2))
 Projective plane curve defined by x^2 + y^2 + y*z
@@ -600,10 +591,7 @@ julia> S, (x, y, z) = polynomial_ring(QQ, ["x", "y", "z"])
 (Multivariate polynomial ring in 3 variables over QQ, QQMPolyRingElem[x, y, z])
 
 julia> T, _ = grade(S)
-(Multivariate polynomial ring in 3 variables over QQ graded by
- x -> [1]
- y -> [1]
- z -> [1], MPolyDecRingElem{QQFieldElem, QQMPolyRingElem}[x, y, z])
+(Graded multivariate polynomial ring in 3 variables over QQ, MPolyDecRingElem{QQFieldElem, QQMPolyRingElem}[x, y, z])
 
 julia> C = Oscar.ProjPlaneCurve(T(y^2*z - x*(x-z)*(x+3*z)))
 Projective plane curve defined by -x^3 - 2*x^2*z + 3*x*z^2 + y^2*z
@@ -699,10 +687,7 @@ julia> S, (x, y, z) = polynomial_ring(QQ, ["x", "y", "z"])
 (Multivariate polynomial ring in 3 variables over QQ, QQMPolyRingElem[x, y, z])
 
 julia> T, _ = grade(S)
-(Multivariate polynomial ring in 3 variables over QQ graded by
- x -> [1]
- y -> [1]
- z -> [1], MPolyDecRingElem{QQFieldElem, QQMPolyRingElem}[x, y, z])
+(Graded multivariate polynomial ring in 3 variables over QQ, MPolyDecRingElem{QQFieldElem, QQMPolyRingElem}[x, y, z])
 
 julia> C = Oscar.ProjPlaneCurve(T(y^2*z - x*(x-z)*(x+3*z)))
 Projective plane curve defined by -x^3 - 2*x^2*z + 3*x*z^2 + y^2*z
@@ -743,10 +728,7 @@ julia> S, (x, y, z) = polynomial_ring(QQ, ["x", "y", "z"])
 (Multivariate polynomial ring in 3 variables over QQ, QQMPolyRingElem[x, y, z])
 
 julia> T, _ = grade(S)
-(Multivariate polynomial ring in 3 variables over QQ graded by
- x -> [1]
- y -> [1]
- z -> [1], MPolyDecRingElem{QQFieldElem, QQMPolyRingElem}[x, y, z])
+(Graded multivariate polynomial ring in 3 variables over QQ, MPolyDecRingElem{QQFieldElem, QQMPolyRingElem}[x, y, z])
 
 julia> C = Oscar.ProjPlaneCurve(T(y^2*z - x*(x-z)*(x+3*z)))
 Projective plane curve defined by -x^3 - 2*x^2*z + 3*x*z^2 + y^2*z
@@ -785,10 +767,7 @@ julia> S, (x, y, z) = polynomial_ring(QQ, ["x", "y", "z"])
 (Multivariate polynomial ring in 3 variables over QQ, QQMPolyRingElem[x, y, z])
 
 julia> T, _ = grade(S)
-(Multivariate polynomial ring in 3 variables over QQ graded by
- x -> [1]
- y -> [1]
- z -> [1], MPolyDecRingElem{QQFieldElem, QQMPolyRingElem}[x, y, z])
+(Graded multivariate polynomial ring in 3 variables over QQ, MPolyDecRingElem{QQFieldElem, QQMPolyRingElem}[x, y, z])
 
 julia> C = Oscar.ProjPlaneCurve(T(y^2*z - x*(x-z)*(x+3*z)))
 Projective plane curve defined by -x^3 - 2*x^2*z + 3*x*z^2 + y^2*z

experimental/PlaneCurve/src/ParaPlaneCurves.jl

@@ -186,12 +186,7 @@ where R is the basering.
 # Examples
 ```jldoctest
 julia> R, (v, w, x, y, z) = graded_polynomial_ring(QQ, ["v", "w", "x", "y", "z"])
-(Multivariate polynomial ring in 5 variables over QQ graded by
- v -> [1]
- w -> [1]
- x -> [1]
- y -> [1]
- z -> [1], MPolyDecRingElem{QQFieldElem, QQMPolyRingElem}[v, w, x, y, z])
+(Graded multivariate polynomial ring in 5 variables over QQ, MPolyDecRingElem{QQFieldElem, QQMPolyRingElem}[v, w, x, y, z])
 
 julia> M = matrix(R, 2, 4, [v w x y; w x y z])
 [v w x y]

experimental/PlaneCurve/src/PlaneCurve.jl

@@ -148,10 +148,7 @@ julia> R, (x,y,z) = polynomial_ring(QQ, ["x", "y", "z"])
 (Multivariate polynomial ring in 3 variables over QQ, QQMPolyRingElem[x, y, z])
 
 julia> T, _ = grade(R)
-(Multivariate polynomial ring in 3 variables over QQ graded by
- x -> [1]
- y -> [1]
- z -> [1], MPolyDecRingElem{QQFieldElem, QQMPolyRingElem}[x, y, z])
+(Graded multivariate polynomial ring in 3 variables over QQ, MPolyDecRingElem{QQFieldElem, QQMPolyRingElem}[x, y, z])
 
 julia> F = T(y^3*x^6 - y^6*x^2*z)
 x^6*y^3 - x^2*y^6*z
@@ -185,10 +182,7 @@ create the projective plane curve defined by `f`.
 # Examples
 ```jldoctest
 julia> R, (x,y,z) = graded_polynomial_ring(QQ, ["x", "y", "z"])
-(Multivariate polynomial ring in 3 variables over QQ graded by
- x -> [1]
- y -> [1]
- z -> [1], MPolyDecRingElem{QQFieldElem, QQMPolyRingElem}[x, y, z])
+(Graded multivariate polynomial ring in 3 variables over QQ, MPolyDecRingElem{QQFieldElem, QQMPolyRingElem}[x, y, z])
 
 julia> C = ProjPlaneCurve(z*x^2-y^3)
 Projective plane curve defined by x^2*z - y^3
@@ -475,8 +469,8 @@ julia> C = Oscar.AffinePlaneCurve(y^2+x-x^3)
 Affine plane curve defined by -x^3 + x + y^2
 
 julia> Oscar.ring(C)
-(Quotient of Multivariate polynomial ring in 2 variables over QQ by ideal(-x^3 + x + y^2), Map from
-Multivariate polynomial ring in 2 variables over QQ to Quotient of Multivariate polynomial ring in 2 variables over QQ by ideal(-x^3 + x + y^2) defined by a julia-function with inverse)
+(Quotient of multivariate polynomial ring by ideal with 1 generator, Map from
+Multivariate polynomial ring in 2 variables over QQ to Quotient of multivariate polynomial ring by ideal with 1 generator defined by a julia-function with inverse)
 ```
 """
 function ring(C::PlaneCurve)