gh-39797: Small changes in matroids
    
fixes #20175 about a better picture for one specific matroid

plus a bunch of other minor changes, adding typing annotations

### 📝 Checklist

- [x] The title is concise and informative.
- [x] The description explains in detail what this PR is about.
- [x] I have linked a relevant issue or discussion.
- [x] I have updated the documentation and checked the documentation
preview.
    
URL: #39797
Reported by: Frédéric Chapoton
Reviewer(s): Travis Scrimshaw

Author: Release Manager

src/sage/matroids/database_matroids.py

@@ -2133,7 +2133,7 @@ def Z(r, t=True, groundset=None):
     Id = Matrix(GF(2), identity_matrix(r))
     J = Matrix(GF(2), ones_matrix(r))
     tip = Matrix(GF(2), ones_matrix(r, 1))
-    A = Id.augment(J-Id).augment(tip)
+    A = Id.augment(J - Id).augment(tip)
 
     M = Matroid(A)
     X = [f'x{i}' for i in range(1, r + 1)]
@@ -2250,7 +2250,7 @@ def Spike(r, t=True, C3=[], groundset=None):
     else:
         for S in C3:
             for xy in S:
-                if xy not in X+Y:
+                if xy not in X + Y:
                     raise ValueError(
                         "The sets in C3 must contain elements xi and yi only."
                     )
@@ -2422,13 +2422,13 @@ def genbin(n, bs=""):
     for i in range(0, r):
         for k in range(1, r - 2):
             I0 = [f'a{i}', f'b{i}']
-            IK = [f'a{(i+k) % r}', f'b{(i+k) % r}']
+            IK = [f'a{(i + k) % r}', f'b{(i + k) % r}']
             for AB in generate_binary_strings(k - 1):
                 C = []
                 C += I0 + IK
                 j = 1
                 for z in AB:
-                    C += [f'{z}{(i+j) % r}']
+                    C += [f'{z}{(i + j) % r}']
                     j += 1
                 NSC += [C]
 
@@ -5029,6 +5029,17 @@ def BetsyRoss(groundset=None):
            'cjk', 'dfk', 'dgh', 'dij', 'efj', 'egk', 'ehi']
     M = Matroid(rank=3, nonspanning_circuits=NSC)
     M = _rename_and_relabel(M, "BetsyRoss", groundset)
+    pos = {'a': (0, 1.61000000000000),
+           'c': (0.946334256190882, -1.30251736094367),
+           'b': (1.53120099123520, 0.497517360943665),
+           'e': (-1.53120099123520, 0.497517360943665),
+           'd': (-0.946334256190882, -1.30251736094367),
+           'g': (0.590718333102580, -0.191936021350899),
+           'f': (0.365084007635076, 0.502495027562079),
+           'i': (-0.590718333102580, -0.191936021350899),
+           'h': (0, -0.621118012422360),
+           'k': (0, 0), 'j': (-0.365084007635076, 0.502495027562079)}
+    M._fix_positions(pos_dict=pos)
     return M
 
 
@@ -5246,6 +5257,6 @@ def _rename_and_relabel(M, name=None, groundset=None):
         M = M.relabel(dict(zip(M.groundset(), groundset)))
 
     if name is not None:
-        M.rename(name+": " + repr(M))
+        M.rename(name + ": " + repr(M))
 
     return M

src/sage/matroids/matroids_plot_helpers.py

@@ -74,14 +74,17 @@
 import scipy
 import scipy.interpolate
 import numpy as np
+
+from sage.matroids.advanced import newlabel
 from sage.misc.lazy_import import lazy_import
-lazy_import("sage.plot.all", ["Graphics", "line", "text", "polygon2d", "point", "points"])
-lazy_import("sage.plot.colors", "Color")
 from sage.sets.set import Set
-from sage.matroids.advanced import newlabel
+
+lazy_import("sage.plot.all", ["Graphics", "line", "text",
+                              "polygon2d", "point", "points"])
+lazy_import("sage.plot.colors", "Color")
 
 
-def it(M, B1, nB1, lps):
+def it(M, B1, nB1, lps) -> tuple[dict, list, list, list]:
     r"""
     Return points on and off the triangle and lines to be drawn for a rank 3
     matroid.
@@ -178,7 +181,7 @@ def it(M, B1, nB1, lps):
     return pts, trilines, nontripts, curvedlines
 
 
-def trigrid(tripts):
+def trigrid(tripts) -> list[list]:
     """
     Return a grid of 4 points inside given 3 points as a list.
 
@@ -205,7 +208,7 @@ def trigrid(tripts):
 
     .. NOTE::
 
-            This method does NOT do any checks.
+        This method does NOT do any checks.
     """
     pairs = [[0, 1], [1, 2], [0, 2]]
     cpt = [float(tripts[0][0] + tripts[1][0] + tripts[2][0]) / 3,
@@ -218,7 +221,7 @@ def trigrid(tripts):
     return grid
 
 
-def addnontripts(tripts_labels, nontripts_labels, ptsdict):
+def addnontripts(tripts_labels, nontripts_labels, ptsdict) -> dict:
     """
     Return modified ``ptsdict`` with additional keys and values corresponding
     to ``nontripts``.
@@ -260,16 +263,16 @@ def addnontripts(tripts_labels, nontripts_labels, ptsdict):
 
     .. NOTE::
 
-            This method does NOT do any checks.
+        This method does NOT do any checks.
     """
     tripts = [list(ptsdict[p]) for p in tripts_labels]
     pairs = [[0, 1], [1, 2], [0, 2]]
     q = [tripts]
     num = len(nontripts_labels)
-    gridpts = [[float((tripts[0][0]+tripts[1][0]+tripts[2][0])/3),
-               float(tripts[0][1]+tripts[1][1]+tripts[2][1])/3]]
+    gridpts = [[float((tripts[0][0] + tripts[1][0] + tripts[2][0]) / 3),
+               float(tripts[0][1] + tripts[1][1] + tripts[2][1]) / 3]]
     n = 0
-    while n < num+1:
+    while n < num + 1:
         g = trigrid(q[0])
         q.extend([[g[0], q[0][pairs[0][0]], q[0][pairs[0][1]]],
                   [g[0], q[0][pairs[1][0]], q[0][pairs[1][1]]],
@@ -285,7 +288,7 @@ def addnontripts(tripts_labels, nontripts_labels, ptsdict):
     return ptsdict
 
 
-def createline(ptsdict, ll, lineorders2=None):
+def createline(ptsdict, ll, lineorders2=None) -> tuple[list, list, list, list]:
     """
     Return ordered lists of coordinates of points to be traversed to draw a
     2D line.
@@ -334,7 +337,7 @@ def createline(ptsdict, ll, lineorders2=None):
 
     .. NOTE::
 
-            This method does NOT do any checks.
+        This method does NOT do any checks.
     """
     x, lo = line_hasorder(ll, lineorders2)
     flip = False
@@ -367,7 +370,7 @@ def createline(ptsdict, ll, lineorders2=None):
     return sortedx, sortedy, x_i, y_i
 
 
-def slp(M1, pos_dict=None, B=None):
+def slp(M1, pos_dict=None, B=None) -> tuple:
     """
     Return simple matroid, loops and parallel elements of given matroid.
 
@@ -413,7 +416,7 @@ def slp(M1, pos_dict=None, B=None):
 
     .. NOTE::
 
-            This method does NOT do any checks.
+        This method does NOT do any checks.
     """
     L = set(M1.loops())
     nP = L | set(M1.simplify().groundset())
@@ -445,7 +448,7 @@ def slp(M1, pos_dict=None, B=None):
         return [M1.delete(L | P), L, P]
 
 
-def addlp(M, M1, L, P, ptsdict, G=None, limits=None):
+def addlp(M, M1, L, P, ptsdict, G=None, limits=None) -> tuple:
     """
     Return a graphics object containing loops (in inset) and parallel elements
     of matroid.
@@ -482,7 +485,7 @@ def addlp(M, M1, L, P, ptsdict, G=None, limits=None):
 
     .. NOTE::
 
-            This method does NOT do any checks.
+        This method does NOT do any checks.
     """
     if G is None:
         G = Graphics()
@@ -551,7 +554,7 @@ def addlp(M, M1, L, P, ptsdict, G=None, limits=None):
     return G, limits
 
 
-def line_hasorder(l, lodrs=None):
+def line_hasorder(l, lodrs=None) -> tuple[bool, list]:
     """
     Determine if an order is specified for a line.
 
@@ -581,7 +584,7 @@ def line_hasorder(l, lodrs=None):
 
     .. NOTE::
 
-            This method does NOT do any checks.
+        This method does NOT do any checks.
     """
     if lodrs is not None:
         set_l = Set(l)
@@ -592,7 +595,7 @@ def line_hasorder(l, lodrs=None):
     return False, []
 
 
-def lineorders_union(lineorders1, lineorders2):
+def lineorders_union(lineorders1, lineorders2) -> list:
     """
     Return a list of ordered lists of ground set elements that corresponds to
     union of two sets of ordered lists of ground set elements in a sense.
@@ -633,7 +636,7 @@ def lineorders_union(lineorders1, lineorders2):
         return None
 
 
-def posdict_is_sane(M1, pos_dict):
+def posdict_is_sane(M1, pos_dict) -> bool:
     """
     Return a boolean establishing sanity of ``posdict`` wrt matroid ``M``.
 
@@ -665,8 +668,8 @@ def posdict_is_sane(M1, pos_dict):
 
     .. NOTE::
 
-            This method does NOT do any checks. ``M1`` is assumed to be a
-            matroid and ``posdict`` is assumed to be a dictionary.
+        This method does NOT do any checks. ``M1`` is assumed to be a
+        matroid and ``posdict`` is assumed to be a dictionary.
     """
     L = set(M1.loops())
     nP = L | set(M1.simplify().groundset())
@@ -683,7 +686,7 @@ def posdict_is_sane(M1, pos_dict):
                for x in list(set(M1.groundset()) - (L | set(allP))))
 
 
-def tracklims(lims, x_i=[], y_i=[]):
+def tracklims(lims, x_i=[], y_i=[]) -> list:
     """
     Return modified limits list.
 
@@ -704,7 +707,7 @@ def tracklims(lims, x_i=[], y_i=[]):
 
     .. NOTE::
 
-            This method does NOT do any checks.
+        This method does NOT do any checks.
     """
     if lims is not None and lims[0] is not None and lims[1] is not None and \
        lims[2] is not None and lims[3] is not None:
@@ -752,7 +755,7 @@ def geomrep(M1, B1=None, lineorders1=None, pd=None, sp=False):
 
     .. NOTE::
 
-            This method does NOT do any checks.
+        This method does NOT do any checks.
     """
     G = Graphics()
     # create lists of loops and parallel elements and simplify given matroid