From 0e5b06116678a323bdf1fc433b910eac2d0b5c55 Mon Sep 17 00:00:00 2001
From: Simon Brandhorst <brandhorst@math.uni-sb.de>
Date: Mon, 16 Dec 2024 10:02:58 +0100
Subject: [PATCH] feat: pretty printing for elliptic curves and their points
 (#1677)

---
 docs/src/manual/elliptic_curves/basics.md     |  6 +-
 .../manual/elliptic_curves/finite_fields.md   |  5 +-
 src/EllCrv/EllCrv.jl                          | 74 +++++++++++++------
 src/EllCrv/Finite.jl                          | 17 ++---
 src/EllCrv/Isomorphisms.jl                    | 13 ++--
 5 files changed, 69 insertions(+), 46 deletions(-)

diff --git a/docs/src/manual/elliptic_curves/basics.md b/docs/src/manual/elliptic_curves/basics.md
index d23cd52c2c..c512e323f5 100644
--- a/docs/src/manual/elliptic_curves/basics.md
+++ b/docs/src/manual/elliptic_curves/basics.md
@@ -50,12 +50,10 @@ by setting `check = false`.
 julia> E = elliptic_curve(QQ, [1, 2]);
 
 julia> E([1, -2])
-Point  (1 : -2 : 1)  of Elliptic curve with equation
-y^2 = x^3 + x + 2
+(1 : -2 : 1)
 
 julia> E([2, -4, 2])
-Point  (1 : -2 : 1)  of Elliptic curve with equation
-y^2 = x^3 + x + 2
+(1 : -2 : 1)
 ```
 
 ```@docs
diff --git a/docs/src/manual/elliptic_curves/finite_fields.md b/docs/src/manual/elliptic_curves/finite_fields.md
index 19bc50fcfc..c752a3fe3a 100644
--- a/docs/src/manual/elliptic_curves/finite_fields.md
+++ b/docs/src/manual/elliptic_curves/finite_fields.md
@@ -15,12 +15,11 @@ end
 
 Return a random point on the elliptic curve $E$ defined over a finite field.
 
-```jldoctest; filter = r"Point.*"
+```jldoctest; filter = r"\(.*"
 julia> E = elliptic_curve(GF(3), [1, 2]);
 
 julia> rand(E)
-Point  (2 : 0 : 1)  of Elliptic curve with equation
-y^2 = x^3 + x + 2
+(2 : 0 : 1)
 ```
 
 ## Cardinality and orders
diff --git a/src/EllCrv/EllCrv.jl b/src/EllCrv/EllCrv.jl
index 52be1c875c..2cca8d7f75 100644
--- a/src/EllCrv/EllCrv.jl
+++ b/src/EllCrv/EllCrv.jl
@@ -167,12 +167,16 @@ disabled by setting `check = false`.
 
 ```jldoctest
 julia> elliptic_curve(QQ, [1, 2, 3, 4, 5])
-Elliptic curve with equation
-y^2 + x*y + 3*y = x^3 + 2*x^2 + 4*x + 5
+Elliptic curve
+  over rational field
+with equation
+  y^2 + x*y + 3*y = x^3 + 2*x^2 + 4*x + 5
 
 julia> elliptic_curve(GF(3), [1, 1])
-Elliptic curve with equation
-y^2 = x^3 + x + 1
+Elliptic curve
+  over prime field of characteristic 3
+with equation
+  y^2 = x^3 + x + 1
 ```
 """
 elliptic_curve
@@ -253,12 +257,16 @@ disabled by setting `check = false`.
 julia> Qx, x = QQ["x"];
 
 julia> elliptic_curve(x^3 + x + 1)
-Elliptic curve with equation
-y^2 = x^3 + x + 1
+Elliptic curve
+  over rational field
+with equation
+  y^2 = x^3 + x + 1
 
 julia> elliptic_curve(x^3 + x + 1, x)
-Elliptic curve with equation
-y^2 + x*y = x^3 + x + 1
+Elliptic curve
+  over rational field
+with equation
+  y^2 + x*y = x^3 + x + 1
 ```
 """
 function elliptic_curve(f::PolyRingElem{T}, h::PolyRingElem{T} = zero(parent(f)); check::Bool = true) where T
@@ -292,8 +300,10 @@ julia> K = GF(3)
 Prime field of characteristic 3
 
 julia> elliptic_curve_from_j_invariant(K(2))
-Elliptic curve with equation
-y^2 + x*y = x^3 + 1
+Elliptic curve
+  over prime field of characteristic 3
+with equation
+  y^2 + x*y = x^3 + 1
 ```
 """
 function elliptic_curve_from_j_invariant(j::FieldElem)
@@ -584,12 +594,10 @@ by setting `check = false`.
 julia> E = elliptic_curve(QQ, [1, 2]);
 
 julia> E([1, -2])
-Point  (1 : -2 : 1)  of Elliptic curve with equation
-y^2 = x^3 + x + 2
+(1 : -2 : 1)
 
 julia> E([2, -4, 2])
-Point  (1 : -2 : 1)  of Elliptic curve with equation
-y^2 = x^3 + x + 2
+(1 : -2 : 1)
 ```
 """
 function (E::EllipticCurve{T})(coords::Vector{S}; check::Bool = true) where {S, T}
@@ -754,8 +762,31 @@ end
 #
 ################################################################################
 
+function show(io::IO, ::MIME"text/plain", E::EllipticCurve)
+  io = pretty(io)
+  println(io, "Elliptic curve")
+  print(io, Indent(), "over ", Lowercase())
+  print(io, base_field(E))
+  println(io, Dedent())
+  println(io, "with equation")
+  print(io, Indent())
+  _print_equation(io, E)
+  print(io, Dedent())
+end
+
 function show(io::IO, E::EllipticCurve)
-  print(io, "Elliptic curve with equation\n")
+  if is_terse(io)
+    print(io, "Elliptic curve")
+    return
+  end
+  io = pretty(io)
+  print(io, "Elliptic curve over ", Lowercase())
+  print(terse(io), base_field(E))
+  print(io, " with equation ")
+  _print_equation(io, E)
+end
+
+function _print_equation(io::IO, E::EllipticCurve)
   a1, a2, a3, a4, a6 = a_invariants(E)
   sum = Expr(:call, :+)
   push!(sum.args, Expr(:call, :^, :y, 2))
@@ -807,8 +838,10 @@ function show(io::IO, E::EllipticCurve)
   print(io, AbstractAlgebra.expr_to_string(AbstractAlgebra.canonicalize(sum)))
 end
 
+
 function show(io::IO, P::EllipticCurvePoint)
-  print(io, "Point  ($(P[1]) : $(P[2]) : $(P[3]))  of $(P.parent)")
+  io = pretty(io)
+  print(io, "($(P[1]) : $(P[2]) : $(P[3]))")
 end
 
 
@@ -832,8 +865,7 @@ julia> E = elliptic_curve(QQ, [1, 2]);
 julia> P = E([1, -2]);
 
 julia> P + P
-Point  (-1 : 0 : 1)  of Elliptic curve with equation
-y^2 = x^3 + x + 2
+(-1 : 0 : 1)
 ```
 """
 function +(P::EllipticCurvePoint{T}, Q::EllipticCurvePoint{T}) where T
@@ -1126,10 +1158,8 @@ julia> E = elliptic_curve(QQ, [1, 2]);
 
 julia> division_points(infinity(E), 2)
 2-element Vector{EllipticCurvePoint{QQFieldElem}}:
- Point  (0 : 1 : 0)  of Elliptic curve with equation
-y^2 = x^3 + x + 2
- Point  (-1 : 0 : 1)  of Elliptic curve with equation
-y^2 = x^3 + x + 2
+ (0 : 1 : 0)
+ (-1 : 0 : 1)
 ```
 """
 function division_points(P::EllipticCurvePoint, m::S) where S<:Union{Integer, ZZRingElem}
diff --git a/src/EllCrv/Finite.jl b/src/EllCrv/Finite.jl
index 292352b9a1..ca662ca397 100644
--- a/src/EllCrv/Finite.jl
+++ b/src/EllCrv/Finite.jl
@@ -1110,22 +1110,19 @@ Return a list of generators of the group of rational points on $E$.
 
 # Examples
 
-```jldoctest; filter = r"Point.*"
+```jldoctest; filter = r"\(.*"
 julia> E = elliptic_curve(GF(101, 2), [1, 2]);
 
 julia> gens(E)
 2-element Vector{EllipticCurvePoint{FqFieldElem}}:
- Point  (16*o + 42 : 88*o + 97 : 1)  of Elliptic curve with equation
-y^2 = x^3 + x + 2
- Point  (88*o + 23 : 94*o + 22 : 1)  of Elliptic curve with equation
-y^2 = x^3 + x + 2
+ (13*o + 83 : 90*o + 25 : 1)
+ (61*o + 62 : 19*o + 24 : 1)
 
 julia> E = elliptic_curve(GF(101), [1, 2]);
 
 julia> gens(E)
 1-element Vector{EllipticCurvePoint{FqFieldElem}}:
- Point  (85 : 58 : 1)  of Elliptic curve with equation
-y^2 = x^3 + x + 2
+ (27 : 57 : 1)
 ```
 """
 function gens(E::EllipticCurve{T}) where {T <: FinFieldElem}
@@ -1205,12 +1202,10 @@ argument.
 julia> E = elliptic_curve(GF(101), [1, 2]);
 
 julia> P = E([6, 74])
-Point  (6 : 74 : 1)  of Elliptic curve with equation
-y^2 = x^3 + x + 2
+(6 : 74 : 1)
 
 julia> Q = E([85, 43])
-Point  (85 : 43 : 1)  of Elliptic curve with equation
-y^2 = x^3 + x + 2
+(85 : 43 : 1)
 
 julia> disc_log(P, Q)
 13
diff --git a/src/EllCrv/Isomorphisms.jl b/src/EllCrv/Isomorphisms.jl
index f663fb800b..c87e2ae3a5 100644
--- a/src/EllCrv/Isomorphisms.jl
+++ b/src/EllCrv/Isomorphisms.jl
@@ -623,15 +623,16 @@ end
 #
 ################################################################################
 
-
-function show(io::IO, f::EllCrvIso)
+function show(io::IO, ::MIME"text/plain", f::EllCrvIso)
+  io = pretty(io)
   E1 = domain(f)
   E2 = codomain(f)
   fx, fy, fz = rational_maps(f)
-  print(io, "Isomorphism from
-  $(E1) to \n
-  $(E2) given by \n
-  (x : y : 1) -> ($(fx) : $(fy) : $(fz) )")
+  println(io, "Isomorphism")
+  println(io, Indent(), "from ", E1)
+  println(io, "to ", E2)
+  print(io,"given by ")
+  print(io, "(x : y : 1) -> ($(fx) : $(fy) : $(fz) )")
 end
 
 ################################################################################