From 86c03db25be898b805d9b28dfcc01e97008409a7 Mon Sep 17 00:00:00 2001
From: Stanislav <vissi@vissi.su>
Date: Fri, 16 Oct 2026 02:25:36 +0400
Subject: [PATCH] Sphere: do not rewrite Sphere[] and Sphere[p]; fill in
 defaults when drawing

In WMA Sphere[c] is an inert symbolic primitive: it stays Sphere[c] and
the default radius 1 is only used when it is rendered. Mathics3 rewrote
Sphere[c] to Sphere[c, 1] (and Sphere[] to Sphere[{0, 0, 0}, 1]) with
rules that cannot be cleared, so packages that use Sphere[n] as an inert
head (e.g. Sphere[7] for S^7) break.

SphereBox now accepts 0, 1 or 2 arguments and fills in the default
center and radius itself.

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
---
 mathics/builtin/box/graphics3d.py     | 14 ++++++++++----
 mathics/builtin/drawing/graphics3d.py | 11 +++++++----
 test/builtin/drawing/test_plot.py     | 10 ++++++++++
 3 files changed, 27 insertions(+), 8 deletions(-)

diff --git a/mathics/builtin/box/graphics3d.py b/mathics/builtin/box/graphics3d.py
index b362a94a4d..999c2a7663 100644
--- a/mathics/builtin/box/graphics3d.py
+++ b/mathics/builtin/box/graphics3d.py
@@ -13,7 +13,7 @@
     PolygonBox,
 )
 from mathics.builtin.colors.color_directives import Opacity, RGBColor, _ColorObject
-from mathics.builtin.drawing.graphics3d import Graphics3D, Style3D
+from mathics.builtin.drawing.graphics3d import Coords3D, Graphics3D, Style3D
 from mathics.builtin.drawing.graphics_internals import GLOBALS3D
 from mathics.core.exceptions import BoxExpressionError
 from mathics.core.symbols import Symbol
@@ -284,11 +284,17 @@ def init(self, graphics, style, item):
         self.edge_opacity, self.face_opacity = style.get_style(
             Opacity, face_element=True
         )
-        if len(item.elements) != 2:
+        # Sphere[] and Sphere[positions] stay unevaluated, as in WMA;
+        # the default center and radius are filled in here.
+        elements = item.elements
+        if len(elements) > 2:
             raise BoxExpressionError
 
-        self.points = expr_to_list_of_3d_points(item.elements[0])
-        self.radius = item.elements[1].to_python()
+        if elements:
+            self.points = expr_to_list_of_3d_points(elements[0])
+        else:
+            self.points = (Coords3D(pos=(0, 0, 0)),)
+        self.radius = elements[1].to_python() if len(elements) == 2 else 1
 
     def extent(self):
         result = []
diff --git a/mathics/builtin/drawing/graphics3d.py b/mathics/builtin/drawing/graphics3d.py
index 73cf69f62f..5dc1acc415 100644
--- a/mathics/builtin/drawing/graphics3d.py
+++ b/mathics/builtin/drawing/graphics3d.py
@@ -355,13 +355,16 @@ class Sphere(Builtin):
 
     >> Graphics3D[{Yellow, Sphere[{{-1, 0, 0}, {1, 0, 0}, {0, 0, Sqrt[3.]}}, 1]}]
      = -Graphics3D-
+
+    'Sphere' is a symbolic representation: it does not evaluate, and the \
+    default center and radius are only used when it is drawn:
+    >> {Sphere[], Sphere[{1, 2, 3}]}
+     = {Sphere[], Sphere[{1, 2, 3}]}
+    >> Graphics3D[Sphere[{1, 2, 3}]]
+     = -Graphics3D-
     """
 
     summary_text = "represent a sphere"
-    rules = {
-        "Sphere[]": "Sphere[{0, 0, 0}, 1]",
-        "Sphere[positions_]": "Sphere[positions, 1]",
-    }
 
 
 class Tube(Builtin):
diff --git a/test/builtin/drawing/test_plot.py b/test/builtin/drawing/test_plot.py
index db7fced865..d6bc4a29f3 100644
--- a/test/builtin/drawing/test_plot.py
+++ b/test/builtin/drawing/test_plot.py
@@ -202,6 +202,16 @@ def test__listplot():
             ),
             "Background 3D",
         ),
+        ("Sphere[]", None, "Sphere[]", "Sphere is inert"),
+        ("Sphere[{1, 2, 3}]", None, "Sphere[{1, 2, 3}]", "Sphere is inert"),
+        ("f[Sphere[n_]] := n; f[Sphere[7]]", None, "7", "Sphere[n] as a head"),
+        (
+            "StringContainsQ[Graphics3D[Sphere[{1, 2, 3}]]//TeXForm//ToString, "
+            '"sphere((1, 2, 3), 1)"]',
+            None,
+            "True",
+            "default radius when drawn",
+        ),
         (
             "Graphics3D[Point[Table[{Sin[t], Cos[t], 0}, {t, 0, 2. Pi, Pi / 15.}]]] //Chop//TeXForm//ToString",
             None,