Update Zariski-van Kampen functions

src/doc/en/reference/curves/index.rst

@@ -10,6 +10,7 @@ Curves
    sage/schemes/curves/projective_curve
    sage/schemes/curves/point
    sage/schemes/curves/closed_point
+   sage/schemes/curves/zariski_vankampen
 
    sage/schemes/jacobians/abstract_jacobian
 

src/sage/groups/finitely_presented.py

@@ -135,6 +135,7 @@
 from sage.libs.gap.libgap import libgap
 from sage.libs.gap.element import GapElement
 from sage.misc.cachefunc import cached_method
+from sage.groups.free_group import FreeGroup
 from sage.groups.free_group import FreeGroupElement
 from sage.functions.generalized import sign
 from sage.matrix.constructor import matrix
@@ -1426,6 +1427,35 @@ def simplified(self):
         """
         return self.simplification_isomorphism().codomain()
 
+    def sorted_presentation(self):
+        """
+        Return the same presentation with the relations sorted to ensure equality.
+
+        OUTPUT:
+
+        A new finitely presented group with the relations sorted.
+
+        EXAMPLES::
+
+            sage: G = FreeGroup(2) / [(1, 2, -1, -2), ()]; G
+            Finitely presented group < x0, x1 | x0*x1*x0^-1*x1^-1, 1 >
+            sage: G.sorted_presentation()
+            Finitely presented group < x0, x1 | 1, x1^-1*x0^-1*x1*x0 >
+        """
+        F = FreeGroup(self.ngens())
+        L0 = [r.Tietze() for r in self.relations()]
+        L1 = []
+        for rel in L0:
+            C = [rel]
+            for j in range(len(rel) - 1):
+                C.append(rel[j + 1:] + rel[:j + 1])
+            C1 = [tuple(-j for j in reversed(l)) for l in C]
+            C += C1
+            C.sort()
+            L1.append(C[0])
+        L1.sort()
+        return F/L1
+
     def epimorphisms(self, H):
         r"""
         Return the epimorphisms from `self` to `H`, up to automorphism of `H`.