gh-35073: refactor(34773): combinatorial polyhedron: move list of pairs to dedicated class
    
### 📚 Description

`CombinatorialPolyhedron` currently contains a lot of code related to
(possibly long) lists of pairs. This code can and should be moved
elsewhere. This is a step towards better readability and allowing future
changes to the code.

This is a first step of #34773.

Along the way I update my outdated email address.

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### 📝 Checklist

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### ⌛ Dependencies
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URL: #35073
Reported by: Jonathan Kliem
Reviewer(s): Jonathan Kliem, Matthias Köppe, Travis Scrimshaw

Author: Release Manager

src/sage/data_structures/list_of_pairs.pxd

@@ -0,0 +1,14 @@
+cimport cython
+
+cdef struct pair_s:
+    size_t first
+    size_t second
+
+@cython.final
+cdef class ListOfPairs:
+    cdef pair_s** _lists
+    cdef size_t length
+
+    cdef inline int enlarge(self) except -1
+    cdef inline int add(self, size_t first, size_t second) except -1
+    cdef inline pair_s* get(self, size_t index) except NULL

src/sage/data_structures/list_of_pairs.pyx

@@ -0,0 +1,121 @@
+r"""
+A data structure to store lists of integer pairs of large size.
+"""
+
+# ****************************************************************************
+#       Copyright (C) 2022 Jonathan Kliem <[email protected]>
+#
+# This program is free software: you can redistribute it and/or modify
+# it under the terms of the GNU General Public License as published by
+# the Free Software Foundation, either version 2 of the License, or
+# (at your option) any later version.
+#                  https://www.gnu.org/licenses/
+# ****************************************************************************
+
+from cysignals.memory cimport check_reallocarray, check_allocarray, sig_free
+from sage.rings.integer cimport smallInteger
+
+# Should be a power of two.
+# Should be neither exposed nor modified.
+cdef size_t length_per_list = 16348
+
+cdef class ListOfPairs:
+    def __dealloc__(self):
+        cdef size_t n_lists = self.length // length_per_list
+        cdef size_t i
+        for i in range(n_lists):
+            sig_free(self._lists[i])
+        sig_free(self._lists)
+
+    cdef inline int enlarge(self) except -1:
+        """
+        Increase size of list by one.
+        """
+        if self.length % length_per_list:
+            self.length += 1
+            return 0
+
+        cdef size_t n_lists = self.length // length_per_list
+        self._lists = <pair_s**> check_reallocarray(self._lists, n_lists + 1, sizeof(pair_s*))
+        self._lists[n_lists] = <pair_s*> check_allocarray(length_per_list, sizeof(pair_s))
+        self.length += 1
+
+    cdef inline pair_s* get(self, size_t index) except NULL:
+        """
+        Return a pointer to a pair of the list corresponding to the ``index``.
+        """
+        if not (0 <= index < self.length):
+            raise IndexError
+
+        cdef size_t list_index = index // length_per_list
+        cdef size_t index_in_list = index - list_index * length_per_list
+
+        return &self._lists[list_index][index_in_list]
+
+    def __getitem__(self, size_t index):
+        r"""
+        Get item of specified index.
+
+        EXAMPLES::
+
+            sage: from sage.data_structures.list_of_pairs import ListOfPairs
+            sage: l = ListOfPairs()
+            sage: l[0] = [1, 5]
+            sage: l[0]
+            (1, 5)
+            sage: l[1]
+            Traceback (most recent call last):
+            ...
+            IndexError
+            sage: l[-1]
+            Traceback (most recent call last):
+            ...
+            OverflowError: can't convert negative value to size_t
+        """
+        cdef pair_s* pair = self.get(index)
+        return (smallInteger(pair.first), smallInteger(pair.second))
+
+    def __setitem__(self, size_t index, value):
+        r"""
+        Set item of specified index.
+
+        Allows increasing the size of the list by at most 1.
+
+        EXAMPLES::
+
+            sage: from sage.data_structures.list_of_pairs import ListOfPairs
+            sage: l = ListOfPairs()
+            sage: l[0] = (2, 1)
+            sage: l[1] = (1, 2)
+            sage: l[0]
+            (2, 1)
+            sage: l[1]
+            (1, 2)
+            sage: l[10] = (5, 3)
+            Traceback (most recent call last):
+            ...
+            IndexError
+            sage: l[2] = 2
+            Traceback (most recent call last):
+            ...
+            TypeError: 'sage.rings.integer.Integer' object is not iterable
+        """
+        cdef size_t first, second
+        (first, second) = value
+
+        if index == self.length:
+            self.add(first, second)
+            return
+
+        cdef pair_s* pair_pt = self.get(index)
+        pair_pt.first = first
+        pair_pt.second = second
+
+    cdef inline int add(self, size_t first, size_t second) except -1:
+        """
+        Add a pair to the list.
+        """
+        self.enlarge()
+        cdef pair_s* last = self.get(self.length - 1)
+        last.first = first
+        last.second = second

src/sage/data_structures/sparse_bitset.pxd

@@ -6,7 +6,7 @@ This is a regular bitset to which we will add additional structure.
 In particular some representation of which limbs even contain data.
 """
 # ****************************************************************************
-#       Copyright (C) 2020 Jonathan Kliem <jonathan.kliem@fu-berlin.de>
+#       Copyright (C) 2020 Jonathan Kliem <jonathan.kliem@gmail.com>
 #
 # This program is free software: you can redistribute it and/or modify
 # it under the terms of the GNU General Public License as published by

src/sage/geometry/polyhedron/base.py

@@ -21,7 +21,7 @@
 #       Copyright (C) 2019      Julian Ritter
 #       Copyright (C) 2019-2020 Laith Rastanawi
 #       Copyright (C) 2019-2020 Sophia Elia
-#       Copyright (C) 2019-2021 Jonathan Kliem <jonathan.kliem@fu-berlin.de>
+#       Copyright (C) 2019-2021 Jonathan Kliem <jonathan.kliem@gmail.com>
 #
 # This program is free software: you can redistribute it and/or modify
 # it under the terms of the GNU General Public License as published by

src/sage/geometry/polyhedron/base0.py

@@ -21,7 +21,7 @@
 #       Copyright (C) 2019      Julian Ritter
 #       Copyright (C) 2019-2020 Laith Rastanawi
 #       Copyright (C) 2019-2020 Sophia Elia
-#       Copyright (C) 2019-2021 Jonathan Kliem <jonathan.kliem@fu-berlin.de>
+#       Copyright (C) 2019-2021 Jonathan Kliem <jonathan.kliem@gmail.com>
 #
 # This program is free software: you can redistribute it and/or modify
 # it under the terms of the GNU General Public License as published by

src/sage/geometry/polyhedron/base1.py

@@ -24,7 +24,7 @@
 #       Copyright (C) 2019      Julian Ritter
 #       Copyright (C) 2019-2020 Laith Rastanawi
 #       Copyright (C) 2019-2020 Sophia Elia
-#       Copyright (C) 2019-2021 Jonathan Kliem <jonathan.kliem@fu-berlin.de>
+#       Copyright (C) 2019-2021 Jonathan Kliem <jonathan.kliem@gmail.com>
 #
 # This program is free software: you can redistribute it and/or modify
 # it under the terms of the GNU General Public License as published by

src/sage/geometry/polyhedron/base2.py

@@ -21,7 +21,7 @@
 #       Copyright (C) 2019      Julian Ritter
 #       Copyright (C) 2019-2020 Laith Rastanawi
 #       Copyright (C) 2019-2020 Sophia Elia
-#       Copyright (C) 2019-2021 Jonathan Kliem <jonathan.kliem@fu-berlin.de>
+#       Copyright (C) 2019-2021 Jonathan Kliem <jonathan.kliem@gmail.com>
 #
 # This program is free software: you can redistribute it and/or modify
 # it under the terms of the GNU General Public License as published by

src/sage/geometry/polyhedron/base3.py

@@ -23,7 +23,7 @@
 #       Copyright (C) 2019      Julian Ritter
 #       Copyright (C) 2019-2020 Laith Rastanawi
 #       Copyright (C) 2019-2020 Sophia Elia
-#       Copyright (C) 2019-2021 Jonathan Kliem <jonathan.kliem@fu-berlin.de>
+#       Copyright (C) 2019-2021 Jonathan Kliem <jonathan.kliem@gmail.com>
 #
 # This program is free software: you can redistribute it and/or modify
 # it under the terms of the GNU General Public License as published by

src/sage/geometry/polyhedron/base4.py

@@ -24,7 +24,7 @@
 #       Copyright (C) 2019      Julian Ritter
 #       Copyright (C) 2019-2020 Laith Rastanawi
 #       Copyright (C) 2019-2020 Sophia Elia
-#       Copyright (C) 2019-2021 Jonathan Kliem <jonathan.kliem@fu-berlin.de>
+#       Copyright (C) 2019-2021 Jonathan Kliem <jonathan.kliem@gmail.com>
 #
 # This program is free software: you can redistribute it and/or modify
 # it under the terms of the GNU General Public License as published by

src/sage/geometry/polyhedron/base5.py

@@ -23,7 +23,7 @@
 #       Copyright (C) 2019      Julian Ritter
 #       Copyright (C) 2019-2020 Laith Rastanawi
 #       Copyright (C) 2019-2020 Sophia Elia
-#       Copyright (C) 2019-2021 Jonathan Kliem <jonathan.kliem@fu-berlin.de>
+#       Copyright (C) 2019-2021 Jonathan Kliem <jonathan.kliem@gmail.com>
 #
 # This program is free software: you can redistribute it and/or modify
 # it under the terms of the GNU General Public License as published by