From 278b93f390a1caf8e511409e2ee0e39697aed8c3 Mon Sep 17 00:00:00 2001 From: Matthias Koeppe Date: Sun, 17 Jul 2022 21:37:15 -0700 Subject: [PATCH] sage.geometry: More # optional - sage.rings.number_field --- src/sage/geometry/polyhedron/base3.py | 4 ++-- src/sage/geometry/polyhedron/base6.py | 12 ++++++------ 2 files changed, 8 insertions(+), 8 deletions(-) diff --git a/src/sage/geometry/polyhedron/base3.py b/src/sage/geometry/polyhedron/base3.py index 0b85c4f944c..ff144d04e39 100644 --- a/src/sage/geometry/polyhedron/base3.py +++ b/src/sage/geometry/polyhedron/base3.py @@ -136,8 +136,8 @@ def slack_matrix(self): [1 0 1 0 0 1] [1 0 0 0 1 1] - sage: P = polytopes.dodecahedron().faces(2)[0].as_polyhedron() - sage: P.slack_matrix() + sage: P = polytopes.dodecahedron().faces(2)[0].as_polyhedron() # optional - sage.rings.number_field + sage: P.slack_matrix() # optional - sage.rings.number_field [1/2*sqrt5 - 1/2 0 0 1 1/2*sqrt5 - 1/2 0] [ 0 0 1/2*sqrt5 - 1/2 1/2*sqrt5 - 1/2 1 0] [ 0 1/2*sqrt5 - 1/2 1 0 1/2*sqrt5 - 1/2 0] diff --git a/src/sage/geometry/polyhedron/base6.py b/src/sage/geometry/polyhedron/base6.py index 9044f3db4d9..c6ed839ba77 100644 --- a/src/sage/geometry/polyhedron/base6.py +++ b/src/sage/geometry/polyhedron/base6.py @@ -1176,9 +1176,9 @@ def affine_hull_projection(self, A vertex at (2, 0, 0), A vertex at (1, 3/2, 0), A vertex at (1, 1/2, 4/3)) - sage: A = S.affine_hull_projection(orthonormal=True, extend=True); A + sage: A = S.affine_hull_projection(orthonormal=True, extend=True); A # optional - sage.rings.number_field A 3-dimensional polyhedron in AA^3 defined as the convex hull of 4 vertices - sage: A.vertices() + sage: A.vertices() # optional - sage.rings.number_field (A vertex at (0.7071067811865475?, 0.4082482904638630?, 1.154700538379252?), A vertex at (0.7071067811865475?, 1.224744871391589?, 0.?e-18), A vertex at (1.414213562373095?, 0.?e-18, 0.?e-18), @@ -1187,11 +1187,11 @@ def affine_hull_projection(self, With the parameter ``minimal`` one can get a minimal base ring:: sage: s = polytopes.simplex(3) - sage: s_AA = s.affine_hull_projection(orthonormal=True, extend=True) - sage: s_AA.base_ring() + sage: s_AA = s.affine_hull_projection(orthonormal=True, extend=True) # optional - sage.rings.number_field + sage: s_AA.base_ring() # optional - sage.rings.number_field Algebraic Real Field - sage: s_full = s.affine_hull_projection(orthonormal=True, extend=True, minimal=True) - sage: s_full.base_ring() + sage: s_full = s.affine_hull_projection(orthonormal=True, extend=True, minimal=True) # optional - sage.rings.number_field + sage: s_full.base_ring() # optional - sage.rings.number_field Number Field in a with defining polynomial y^4 - 4*y^2 + 1 with a = 0.5176380902050415? More examples with the ``orthonormal`` parameter::