From 3a613836e74ecf970fccd1ed74d1e6634bf2b893 Mon Sep 17 00:00:00 2001
From: varuntrehan7 <varuntrehan7@gmail.com>
Date: Mon, 1 Dec 2025 08:37:16 +0530
Subject: [PATCH 1/4] Clean up sqrt docs in manual

---
 docs/src/fraction.md       | 4 +---
 docs/src/function_field.md | 4 +---
 docs/src/polynomial.md     | 4 +---
 docs/src/puiseux.md        | 6 +-----
 docs/src/residue.md        | 4 +---
 docs/src/series.md         | 5 +----
 6 files changed, 6 insertions(+), 21 deletions(-)

diff --git a/docs/src/fraction.md b/docs/src/fraction.md
index 67a08d15bd..ffce261580 100644
--- a/docs/src/fraction.md
+++ b/docs/src/fraction.md
@@ -301,9 +301,7 @@ julia> h = gcd(f, g)
 
 ### Square root
 
-```@docs
-Base.sqrt(::FracElem{T}) where {T <: RingElem}
-```
+Methods for `is_square` and `sqrt` are provided for inputs of type `FracElem`.
 
 **Examples**
 
diff --git a/docs/src/function_field.md b/docs/src/function_field.md
index 9d4a015a2e..0d1c100687 100644
--- a/docs/src/function_field.md
+++ b/docs/src/function_field.md
@@ -162,9 +162,7 @@ julia> h = gcd(f, g)
 
 ### Square root
 
-```@docs
-Base.sqrt(::Generic.RationalFunctionFieldElem{T, U}) where {T <: FieldElem, U <: Union{PolyRingElem, MPolyRingElem}}
-```
+Methods for `is_square` and `sqrt` are provided for inputs of type `RationalFunctionFieldElem`.
 
 **Examples**
 
diff --git a/docs/src/polynomial.md b/docs/src/polynomial.md
index 5609d909ee..a49922fb75 100644
--- a/docs/src/polynomial.md
+++ b/docs/src/polynomial.md
@@ -674,9 +674,7 @@ deflate(::PolyRingElem)
 
 ### Square root
 
-```@docs
-Base.sqrt(::PolyRingElem{T}; check::Bool) where T <: RingElement
-```
+Methods for `is_square` and `sqrt` are provided for inputs of type `PolyRingElem`.
 
 **Examples**
 
diff --git a/docs/src/puiseux.md b/docs/src/puiseux.md
index 75b2c529de..7676d81401 100644
--- a/docs/src/puiseux.md
+++ b/docs/src/puiseux.md
@@ -328,11 +328,7 @@ true
 Base.log(a::Generic.PuiseuxSeriesElem)
 Base.exp(a::Generic.PuiseuxSeriesElem)
 ```
-
-```@docs
-Base.sqrt(a::Generic.PuiseuxSeriesElem)
-```
-
+Methods for `is_square` and `sqrt` are provided for inputs of type `PuiseuxSeriesElem`.
 
 **Examples**
 
diff --git a/docs/src/residue.md b/docs/src/residue.md
index 842faefd64..849d578835 100644
--- a/docs/src/residue.md
+++ b/docs/src/residue.md
@@ -264,9 +264,7 @@ julia> h = gcd(f, g)
 
 ### Square Root
 
-```@docs
-Base.sqrt{T <: Integer}(::ResFieldElem{T})
-```
+Methods for `is_square` and `sqrt` are provided for inputs of type `ResFieldElem`.
 
 **Examples**
 
diff --git a/docs/src/series.md b/docs/src/series.md
index 2d051bb760..f368d08693 100644
--- a/docs/src/series.md
+++ b/docs/src/series.md
@@ -686,10 +686,7 @@ Base.log(a::SeriesElem{T}) where T <: FieldElem
 ```@docs
 Base.exp(a::RelPowerSeriesRingElem)
 ```
-
-```@docs
-Base.sqrt(a::RelPowerSeriesRingElem)
-```
+Methods for `is_square` and `sqrt` are provided for inputs of type `RelPowerSeriesRingElem`.
 
 
 **Examples**

From 1466006083eb8db629928ecfe21f1e559f7e83bf Mon Sep 17 00:00:00 2001
From: varuntrehan7 <varuntrehan7@gmail.com>
Date: Mon, 1 Dec 2025 21:05:32 +0530
Subject: [PATCH 2/4] Remove sqrt docs; add generic sqrt interface docstring

---
 src/AbsSeries.jl                     |  7 -------
 src/Fraction.jl                      |  6 ------
 src/NCRings.jl                       | 11 +++++++++++
 src/Poly.jl                          |  6 ------
 src/RelSeries.jl                     |  7 -------
 src/ResidueField.jl                  |  6 ------
 src/Rings.jl                         |  7 -------
 src/generic/LaurentSeries.jl         |  7 -------
 src/generic/PuiseuxSeries.jl         |  7 -------
 src/generic/RationalFunctionField.jl |  6 ------
 temp/Project.toml                    |  3 +++
 11 files changed, 14 insertions(+), 59 deletions(-)
 create mode 100644 temp/Project.toml

diff --git a/src/AbsSeries.jl b/src/AbsSeries.jl
index d875c5e409..791c463c36 100644
--- a/src/AbsSeries.jl
+++ b/src/AbsSeries.jl
@@ -905,13 +905,6 @@ function sqrt_classical(a::AbsPowerSeriesRingElem; check::Bool=true)
    return true, asqrt
 end
 
-@doc raw"""
-    sqrt(a::AbsPowerSeriesRingElem; check::Bool=true)
-
-Return the square root of the power series $a$. By default the function will
-throw an exception if the input is not square. If `check=false` this test is
-omitted.
-"""
 function Base.sqrt(a::AbsPowerSeriesRingElem; check::Bool=true)
    flag, q = sqrt_classical(a; check=check)
    if check && !flag
diff --git a/src/Fraction.jl b/src/Fraction.jl
index 85cc369424..6c70158a94 100644
--- a/src/Fraction.jl
+++ b/src/Fraction.jl
@@ -697,12 +697,6 @@ function is_square(a::FracElem{T}) where T <: RingElem
    return is_square(numerator(a)) && is_square(denominator(a))
 end
 
-@doc raw"""
-    Base.sqrt(a::FracElem{T}; check::Bool=true) where T <: RingElem
-
-Return the square root of $a$. By default the function will throw an
-exception if the input is not square. If `check=false` this test is omitted.
-"""
 function Base.sqrt(a::FracElem{T}; check::Bool=true) where T <: RingElem
    return parent(a)(sqrt(numerator(a); check=check), sqrt(denominator(a); check=check))
 end
diff --git a/src/NCRings.jl b/src/NCRings.jl
index f9feafac7b..a2a65140b0 100644
--- a/src/NCRings.jl
+++ b/src/NCRings.jl
@@ -184,6 +184,17 @@ See also `is_square(M::MatElem)` which tests whether a matrix has square shape.
 """
 function is_square end
 
+@doc raw"""
+    sqrt(a::T; check::Bool=true) where {T <: NCRingElement}
+
+Return a square root of `a`, if it exists. By default (`check=true`),
+implementations should raise an exception if `a` is not a square in its ring.
+If `check=false`, implementations may skip this verification.
+
+See also `is_square` and `is_square_with_sqrt`.
+"""
+sqrt
+
 ###############################################################################
 #
 #   Characteristic
diff --git a/src/Poly.jl b/src/Poly.jl
index ad1ae5115d..76630c99ad 100644
--- a/src/Poly.jl
+++ b/src/Poly.jl
@@ -1825,12 +1825,6 @@ function sqrt_classical(f::PolyRingElem{T}; check::Bool=true) where T <: RingEle
    return true, q
 end
 
-@doc raw"""
-    Base.sqrt(f::PolyRingElem{T}; check::Bool=true) where T <: RingElement
-
-Return the square root of $f$. By default the function checks the input is
-square and raises an exception if not. If `check=false` this check is omitted.
-"""
 function Base.sqrt(f::PolyRingElem{T}; check::Bool=true) where T <: RingElement
    flag, q = sqrt_classical(f; check=check)
    check && !flag && error("Not a square in sqrt")
diff --git a/src/RelSeries.jl b/src/RelSeries.jl
index fd9370a060..9b3119242a 100644
--- a/src/RelSeries.jl
+++ b/src/RelSeries.jl
@@ -1172,13 +1172,6 @@ function sqrt_classical(a::RelPowerSeriesRingElem; check::Bool=true)
    return true, asqrt
 end
 
-@doc raw"""
-    sqrt(a::RelPowerSeriesRingElem)
-
-Return the square root of the power series $a$. By default the function raises
-an exception if the input is not a square. If `check=false` this check is
-omitted.
-"""
 function Base.sqrt(a::RelPowerSeriesRingElem; check::Bool=true)
    flag, q = sqrt_classical(a; check=check)
    if check && !flag
diff --git a/src/ResidueField.jl b/src/ResidueField.jl
index a454024b42..76ab69176a 100644
--- a/src/ResidueField.jl
+++ b/src/ResidueField.jl
@@ -349,12 +349,6 @@ function is_square(a::ResFieldElem{T}) where T <: Integer
    return isone(a^pm1div2)
 end
 
-@doc raw"""
-    sqrt(a::ResFieldElem{T}; check::Bool=true) where T <: Integer
-
-Return the square root of $a$. By default the function will throw an exception
-if the input is not square. If `check=false` this test is omitted.
-"""
 function Base.sqrt(a::ResFieldElem{T}; check::Bool=true) where T <: Integer
    U = parent(a)
    p = modulus(a)
diff --git a/src/Rings.jl b/src/Rings.jl
index b6b2041243..c8594a5fa3 100644
--- a/src/Rings.jl
+++ b/src/Rings.jl
@@ -160,13 +160,6 @@ end
 #
 ################################################################################
 
-@doc raw"""
-    sqrt(a::FieldElem)
-
-Return the square root of the element `a`. By default the function will
-throw an exception if the input is not square. If `check=false` this test is
-omitted.
-"""
 function Base.sqrt(a::FieldElem; check::Bool=true)
   R = parent(a)
   R, t = polynomial_ring(R, :t; cached = false)
diff --git a/src/generic/LaurentSeries.jl b/src/generic/LaurentSeries.jl
index ff51d6031e..a06dcd0d85 100644
--- a/src/generic/LaurentSeries.jl
+++ b/src/generic/LaurentSeries.jl
@@ -1395,13 +1395,6 @@ function sqrt_classical(a::LaurentSeriesElem; check::Bool=true)
     return true, asqrt
 end
 
-@doc raw"""
-    sqrt(a::Generic.LaurentSeriesElem; check::Bool=true)
-
-Return the square root of the power series $a$. By default the function will
-throw an exception if the input is not square. If `check=false` this test is
-omitted.
-"""
 function Base.sqrt(a::LaurentSeriesElem; check::Bool=true)
    flag, s = sqrt_classical(a, check=check)
    check && !flag && error("Not a square in sqrt")
diff --git a/src/generic/PuiseuxSeries.jl b/src/generic/PuiseuxSeries.jl
index 6e71d2fe78..5bc6e0ec73 100644
--- a/src/generic/PuiseuxSeries.jl
+++ b/src/generic/PuiseuxSeries.jl
@@ -613,13 +613,6 @@ function sqrt_classical(a::PuiseuxSeriesElem{T}; check::Bool=true) where T <: Ri
    return true, S(s, sscale)
 end
 
-@doc raw"""
-    sqrt(a::Generic.PuiseuxSeriesElem{T}; check::Bool=true) where T <: RingElement
-
-Return the square root of the given Puiseux series $a$. By default the function
-will throw an exception if the input is not square. If `check=false` this test
-is omitted.
-"""
 function Base.sqrt(a::PuiseuxSeriesElem{T}; check::Bool=true) where T <: RingElement
    flag, s = sqrt_classical(a; check=check)
    check && !flag && error("Not a square in sqrt")
diff --git a/src/generic/RationalFunctionField.jl b/src/generic/RationalFunctionField.jl
index 49d9b8b104..41defbe5df 100644
--- a/src/generic/RationalFunctionField.jl
+++ b/src/generic/RationalFunctionField.jl
@@ -455,12 +455,6 @@ function is_square(a::RationalFunctionFieldElem)
    return is_square(data(a))
 end
 
-@doc raw"""
-    Base.sqrt(a::RationalFunctionFieldElem; check::Bool=true)
-
-Return the square root of $a$. By default the function will throw an exception
-if the input is not square. If `check=false` this test is omitted.
-"""
 function Base.sqrt(a::RationalFunctionFieldElem; check::Bool=true)
    R = parent(a)
    return R(sqrt(data(a); check=check))
diff --git a/temp/Project.toml b/temp/Project.toml
new file mode 100644
index 0000000000..bef9dc5df0
--- /dev/null
+++ b/temp/Project.toml
@@ -0,0 +1,3 @@
+[deps]
+Hecke = "3e1990a7-5d81-5526-99ce-9ba3ff248f21"
+Oscar = "f1435218-dba5-11e9-1e4d-f1a5fab5fc13"

From d4eecc6c8cc7b98dac603dc595bb24a9859f5736 Mon Sep 17 00:00:00 2001
From: varuntrehan7 <varuntrehan7@gmail.com>
Date: Mon, 1 Dec 2025 22:05:30 +0530
Subject: [PATCH 3/4] Cleanup sqrt docs and add unified documentation.

---
 docs/src/ring.md  | 18 ++++++++++++++++++
 src/NCRings.jl    |  4 ++--
 temp/Project.toml |  3 ---
 3 files changed, 20 insertions(+), 5 deletions(-)
 delete mode 100644 temp/Project.toml

diff --git a/docs/src/ring.md b/docs/src/ring.md
index dfcd078a50..fbc904fa9d 100644
--- a/docs/src/ring.md
+++ b/docs/src/ring.md
@@ -252,6 +252,24 @@ evaluate(a::Fac)
 getindex(a::Fac, b)
 setindex!(a::Fac{Int}, c::Int, b::Int)
 ```
+## Square root
+
+Many rings in AbstractAlgebra provide functionality for detecting and computing
+square roots. Two functions form the basic interface:
+
+- `is_square(a)` – return `true` if the element `a` is a square in its ring.
+- `sqrt(a; check=true)` – return a square root of `a`, when available.
+
+The exact behaviour depends on the ring. Some rings provide both operations,
+while others only implement `is_square`. If `check=false`, the square root
+check may be omitted.
+
+The following entries link to the generic interface documentation:
+
+```@docs
+is_square
+sqrt(::NCRingElem)
+```
 
 ## Miscellaneous
 
diff --git a/src/NCRings.jl b/src/NCRings.jl
index a2a65140b0..866cac5f03 100644
--- a/src/NCRings.jl
+++ b/src/NCRings.jl
@@ -185,7 +185,7 @@ See also `is_square(M::MatElem)` which tests whether a matrix has square shape.
 function is_square end
 
 @doc raw"""
-    sqrt(a::T; check::Bool=true) where {T <: NCRingElement}
+    sqrt(a::NCRingElem; check::Bool=true)
 
 Return a square root of `a`, if it exists. By default (`check=true`),
 implementations should raise an exception if `a` is not a square in its ring.
@@ -193,7 +193,7 @@ If `check=false`, implementations may skip this verification.
 
 See also `is_square` and `is_square_with_sqrt`.
 """
-sqrt
+sqrt(::NCRingElem)
 
 ###############################################################################
 #
diff --git a/temp/Project.toml b/temp/Project.toml
deleted file mode 100644
index bef9dc5df0..0000000000
--- a/temp/Project.toml
+++ /dev/null
@@ -1,3 +0,0 @@
-[deps]
-Hecke = "3e1990a7-5d81-5526-99ce-9ba3ff248f21"
-Oscar = "f1435218-dba5-11e9-1e4d-f1a5fab5fc13"

From 314d84246f1ebbd65534c8e2a1a7f2bdc9fd7259 Mon Sep 17 00:00:00 2001
From: varuntrehan7 <varuntrehan7@gmail.com>
Date: Wed, 3 Dec 2025 17:46:19 +0530
Subject: [PATCH 4/4] fix the manual for is_square and sqrt

---
 docs/src/ring.md | 11 ++---------
 1 file changed, 2 insertions(+), 9 deletions(-)

diff --git a/docs/src/ring.md b/docs/src/ring.md
index fbc904fa9d..52d82c2884 100644
--- a/docs/src/ring.md
+++ b/docs/src/ring.md
@@ -254,17 +254,10 @@ setindex!(a::Fac{Int}, c::Int, b::Int)
 ```
 ## Square root
 
-Many rings in AbstractAlgebra provide functionality for detecting and computing
-square roots. Two functions form the basic interface:
-
-- `is_square(a)` – return `true` if the element `a` is a square in its ring.
-- `sqrt(a; check=true)` – return a square root of `a`, when available.
+Rings may implement functionality for detecting and computing square roots.
 
 The exact behaviour depends on the ring. Some rings provide both operations,
-while others only implement `is_square`. If `check=false`, the square root
-check may be omitted.
-
-The following entries link to the generic interface documentation:
+while others only implement `is_square`.
 
 ```@docs
 is_square