a curve has dimension 1 by definition

Author: yyyyx4

src/sage/schemes/curves/affine_curve.py

@@ -908,11 +908,7 @@ def projection(self, indices, AS=None):
                To:   Affine Space of dimension 3 over Rational Field
                Defn: Defined on coordinates by sending (x, y, z, w) to
                      (x, y, z),
-             Closed subscheme of Affine Space of dimension 3 over Rational Field
-            defined by:
-               c - 1,
-               b - 3,
-               a - 2)
+             Affine Curve over Rational Field defined by c - 1, b - 3, a - 2)
 
         ::
 

src/sage/schemes/curves/curve.py

@@ -38,6 +38,8 @@
 from sage.schemes.generic.divisor_group import DivisorGroup
 from sage.schemes.generic.divisor import Divisor_curve
 
+from sage.rings.integer import Integer
+
 class Curve_generic(AlgebraicScheme_subscheme):
     r"""
     Generic curve class.
@@ -113,6 +115,24 @@ def _latex_(self):
             polys = ', '.join(f'${latex(p)}$' for p in self.defining_polynomials())
             return fr"\text{{{ambient_type} curve over ${ring}$ defined by {polys}}}"
 
+    def dimension(self):
+        r"""
+        Return the dimension of the curve.
+
+        Curves have dimension one by definition.
+
+        EXAMPLES::
+
+            sage: x = polygen(QQ)
+            sage: C = HyperellipticCurve(x^7 + x^4 + x)
+            sage: C.dimension()
+            1
+            sage: from sage.schemes.projective.projective_subscheme import AlgebraicScheme_subscheme_projective
+            sage: AlgebraicScheme_subscheme_projective.dimension(C)
+            1
+        """
+        return Integer(1)
+
     def defining_polynomial(self):
         """
         Return the defining polynomial of the curve.