Add auxilliary files.

* aux-files/aut.txt, aux-files/correction_matrices.sage,
aux-files/gram_matrix.txt, aux-files/smith_gram_matrix.txt: New files.

aux-files/correction_matrices.sage

+#!/usr/bin/env sage
+# SPDX-FileCopyrightText: © 2022 Maik Herbers
+# SPDX-License-Identifier: GPL-3.0-or-later
+
+def left_matrix(width, height, replacement_spec):
+    r"""
+    Output a projection that maps basis vectors onto combinations of others
+
+    INPUT:
+
+    - ``width`` - dimension of the input space
+    - ``height`` - dimension of the output space
+    - ``replacement_spec`` - dictionary that maps indices of input basis
+      vectors to lists of pairs of replacement basis indices and their
+      multiplicities; all basis vectors not specified are mapped onto
+      themselves.
+    """
+
+    m = zero_matrix(height, width)
+    offset = 0
+    for idx in range(width):
+        if idx in replacement_spec:
+            # map `idx' onto specified linear combination
+            for replacement_idx, multiplicity in replacement_spec[idx]:
+                row = replacement_idx - offset
+                if replacement_idx > idx:
+                    row -= 1
+                m[row, idx] = multiplicity
+            offset += 1
+        else:
+            m[idx - offset, idx] = 1
+    return m
+
+def right_matrix(width, height, skip):
+    r"""
+    Output an embedding where into a specified subspace
+
+    INPUT:
+
+    - ``width`` - dimension of the input space
+    - ``height`` - dimension of the output space
+    - ``skip`` - list of basis vectors in the output space that are not in the
+      image
+    """
+
+    m = zero_matrix(height, width)
+    offset = 0
+    for i in range(height):
+        if i in skip:
+            offset += 1
+        else:
+            m[i, i - offset] = 1
+    return m
+
+def get_matrices(n, replacement_spec):
+    r"""
+    Compute the "change of basis" matrices
+
+    INPUT:
+
+    - ``n`` - size of the input basis
+    - ``replacement_spec`` - dictionary suitable for ``left_matrix``
+    """
+
+    new_size = n - len(replacement_spec)
+    left = left_matrix(n, new_size, replacement_spec)
+    right = right_matrix(new_size, n, replacement_spec.keys())
+    return left, right
+
+# 6A - 6E and 10A - 10C have indices 20 - 24 and 33 - 35 resp. in our
+# list of component functions
+replacement_spec = {
+    22: [(20, 2), (21, 2), (23, 1), (24, -4)],
+    34: [(33, -2), (35, 3)]
+}
+
+l, r = get_matrices(38, replacement_spec)
+
+print(f"left matrix:\n{l}\n\nright matrix:\n{r}")

aux-files/gram_matrix.txt

+ 6  2  2  2  2  0
+ 2  6  4  4 -2  2
+ 2  4  6  4 -2  2
+ 2  4  4  6  0  2
+ 2 -2 -2  0  6  2
+ 0  2  2  2  2  6

aux-files/smith_gram_matrix.txt

+   4   -2    2   -6    0    6
+  -2   16  -20   54   24  -12
+   2  -20   58 -144  -60   18
+  -6   54 -144  360  150  -48
+   0   24  -60  150   66  -18
+   6  -12   18  -48  -18   18