diff --git a/examples/Chapter1.ipynb b/examples/Chapter1.ipynb
index f3ce06a..a7c9dd7 100644
--- a/examples/Chapter1.ipynb
+++ b/examples/Chapter1.ipynb
@@ -2,7 +2,7 @@
  "metadata": {
   "language": "common-lisp",
   "name": "",
-  "signature": "sha256:a754fbeaa1dab0ce169c2df3836c81485925a3dac487688816cd112a3bc45b33"
+  "signature": "sha256:ce53837f0f933b602cdca49e885032e60c5523054bbed0154b1b627bcc3a6755"
  },
  "nbformat": 3,
  "nbformat_minor": 0,
@@ -29,13 +29,13 @@
       {
        "metadata": {},
        "output_type": "pyout",
-       "prompt_number": 1,
+       "prompt_number": 51,
        "text": [
         "(\"kenzo\")"
        ]
       }
      ],
-     "prompt_number": 1
+     "prompt_number": 51
     },
     {
      "cell_type": "code",
@@ -57,13 +57,13 @@
       {
        "metadata": {},
        "output_type": "pyout",
-       "prompt_number": 2,
+       "prompt_number": 52,
        "text": [
         "NIL"
        ]
       }
      ],
-     "prompt_number": 2
+     "prompt_number": 52
     },
     {
      "cell_type": "heading",
@@ -85,7 +85,7 @@
       {
        "metadata": {},
        "output_type": "pyout",
-       "prompt_number": 3,
+       "prompt_number": 53,
        "text": [
         "\"--------------------------------------------------------------[function-doc]\n",
         "F-CMPR\n",
@@ -96,7 +96,7 @@
        ]
       }
      ],
-     "prompt_number": 3
+     "prompt_number": 53
     },
     {
      "cell_type": "code",
@@ -110,13 +110,13 @@
       {
        "metadata": {},
        "output_type": "pyout",
-       "prompt_number": 3,
+       "prompt_number": 54,
        "text": [
         ":LESS"
        ]
       }
      ],
-     "prompt_number": 3
+     "prompt_number": 54
     },
     {
      "cell_type": "code",
@@ -130,7 +130,7 @@
       {
        "metadata": {},
        "output_type": "pyout",
-       "prompt_number": 7,
+       "prompt_number": 55,
        "text": [
         "\"--------------------------------------------------------------[function-doc]\n",
         "S-CMPR\n",
@@ -142,7 +142,7 @@
        ]
       }
      ],
-     "prompt_number": 7
+     "prompt_number": 55
     },
     {
      "cell_type": "code",
@@ -156,13 +156,13 @@
       {
        "metadata": {},
        "output_type": "pyout",
-       "prompt_number": 4,
+       "prompt_number": 56,
        "text": [
         ":GREATER"
        ]
       }
      ],
-     "prompt_number": 4
+     "prompt_number": 56
     },
     {
      "cell_type": "code",
@@ -176,7 +176,7 @@
       {
        "metadata": {},
        "output_type": "pyout",
-       "prompt_number": 8,
+       "prompt_number": 57,
        "text": [
         "\"--------------------------------------------------------------[function-doc]\n",
         "L-CMPR\n",
@@ -187,7 +187,7 @@
        ]
       }
      ],
-     "prompt_number": 8
+     "prompt_number": 57
     },
     {
      "cell_type": "code",
@@ -201,13 +201,13 @@
       {
        "metadata": {},
        "output_type": "pyout",
-       "prompt_number": 5,
+       "prompt_number": 58,
        "text": [
         ":GREATER"
        ]
       }
      ],
-     "prompt_number": 5
+     "prompt_number": 58
     },
     {
      "cell_type": "heading",
@@ -229,7 +229,7 @@
       {
        "metadata": {},
        "output_type": "pyout",
-       "prompt_number": 9,
+       "prompt_number": 59,
        "text": [
         "\"--------------------------------------------------------------[function-doc]\n",
         "CMBN\n",
@@ -242,7 +242,7 @@
        ]
       }
      ],
-     "prompt_number": 9
+     "prompt_number": 59
     },
     {
      "cell_type": "code",
@@ -256,7 +256,7 @@
       {
        "metadata": {},
        "output_type": "pyout",
-       "prompt_number": 6,
+       "prompt_number": 60,
        "text": [
         "\n",
         "----------------------------------------------------------------------{CMBN 1}\n",
@@ -268,7 +268,7 @@
        ]
       }
      ],
-     "prompt_number": 6
+     "prompt_number": 60
     },
     {
      "cell_type": "code",
@@ -282,7 +282,7 @@
       {
        "metadata": {},
        "output_type": "pyout",
-       "prompt_number": 8,
+       "prompt_number": 61,
        "text": [
         "\"-----------------------------------------------------------------[macro-doc]\n",
         "CMBN-NON-ZERO-P\n",
@@ -292,7 +292,7 @@
        ]
       }
      ],
-     "prompt_number": 8
+     "prompt_number": 61
     },
     {
      "cell_type": "code",
@@ -306,13 +306,13 @@
       {
        "metadata": {},
        "output_type": "pyout",
-       "prompt_number": 7,
+       "prompt_number": 62,
        "text": [
         "T"
        ]
       }
      ],
-     "prompt_number": 7
+     "prompt_number": 62
     },
     {
      "cell_type": "code",
@@ -326,13 +326,13 @@
       {
        "metadata": {},
        "output_type": "pyout",
-       "prompt_number": 10,
+       "prompt_number": 63,
        "text": [
         "((1 . U) (2 . V) (3 . W) (4 . Z))"
        ]
       }
      ],
-     "prompt_number": 10
+     "prompt_number": 63
     },
     {
      "cell_type": "code",
@@ -346,13 +346,13 @@
       {
        "metadata": {},
        "output_type": "pyout",
-       "prompt_number": 11,
+       "prompt_number": 64,
        "text": [
         "(3 . W)"
        ]
       }
      ],
-     "prompt_number": 11
+     "prompt_number": 64
     },
     {
      "cell_type": "code",
@@ -366,13 +366,13 @@
       {
        "metadata": {},
        "output_type": "pyout",
-       "prompt_number": 12,
+       "prompt_number": 64,
        "text": [
         "3"
        ]
       }
      ],
-     "prompt_number": 12
+     "prompt_number": 64
     },
     {
      "cell_type": "code",
@@ -386,13 +386,13 @@
       {
        "metadata": {},
        "output_type": "pyout",
-       "prompt_number": 13,
+       "prompt_number": 64,
        "text": [
         "W"
        ]
       }
      ],
-     "prompt_number": 13
+     "prompt_number": 64
     },
     {
      "cell_type": "code",
@@ -406,7 +406,7 @@
       {
        "metadata": {},
        "output_type": "pyout",
-       "prompt_number": 14,
+       "prompt_number": 64,
        "text": [
         "\"--------------------------------------------------------------[function-doc]\n",
         "CMBN-OPPS\n",
@@ -416,7 +416,7 @@
        ]
       }
      ],
-     "prompt_number": 14
+     "prompt_number": 64
     },
     {
      "cell_type": "code",
@@ -430,7 +430,7 @@
       {
        "metadata": {},
        "output_type": "pyout",
-       "prompt_number": 15,
+       "prompt_number": 64,
        "text": [
         "\n",
         "----------------------------------------------------------------------{CMBN 1}\n",
@@ -442,7 +442,7 @@
        ]
       }
      ],
-     "prompt_number": 15
+     "prompt_number": 64
     },
     {
      "cell_type": "code",
@@ -456,7 +456,7 @@
       {
        "metadata": {},
        "output_type": "pyout",
-       "prompt_number": 16,
+       "prompt_number": 64,
        "text": [
         "\"--------------------------------------------------------------[function-doc]\n",
         "N-CMBN\n",
@@ -466,7 +466,7 @@
        ]
       }
      ],
-     "prompt_number": 16
+     "prompt_number": 64
     },
     {
      "cell_type": "code",
@@ -480,7 +480,7 @@
       {
        "metadata": {},
        "output_type": "pyout",
-       "prompt_number": 17,
+       "prompt_number": 64,
        "text": [
         "\n",
         "----------------------------------------------------------------------{CMBN 1}\n",
@@ -492,7 +492,7 @@
        ]
       }
      ],
-     "prompt_number": 17
+     "prompt_number": 64
     },
     {
      "cell_type": "code",
@@ -506,7 +506,7 @@
       {
        "metadata": {},
        "output_type": "pyout",
-       "prompt_number": 18,
+       "prompt_number": 64,
        "text": [
         "\"--------------------------------------------------------------[function-doc]\n",
         "2CMBN-ADD\n",
@@ -519,7 +519,7 @@
        ]
       }
      ],
-     "prompt_number": 18
+     "prompt_number": 64
     },
     {
      "cell_type": "code",
@@ -533,7 +533,7 @@
       {
        "metadata": {},
        "output_type": "pyout",
-       "prompt_number": 20,
+       "prompt_number": 64,
        "text": [
         "\n",
         "----------------------------------------------------------------------{CMBN 1}\n",
@@ -545,7 +545,7 @@
        ]
       }
      ],
-     "prompt_number": 20
+     "prompt_number": 64
     },
     {
      "cell_type": "code",
@@ -559,7 +559,7 @@
       {
        "metadata": {},
        "output_type": "pyout",
-       "prompt_number": 21,
+       "prompt_number": 64,
        "text": [
         "\"--------------------------------------------------------------[function-doc]\n",
         "2CMBN-SBTR\n",
@@ -572,7 +572,7 @@
        ]
       }
      ],
-     "prompt_number": 21
+     "prompt_number": 64
     },
     {
      "cell_type": "code",
@@ -586,7 +586,7 @@
       {
        "metadata": {},
        "output_type": "pyout",
-       "prompt_number": 22,
+       "prompt_number": 64,
        "text": [
         "\"--------------------------------------------------------------[function-doc]\n",
         "NCMBN-ADD\n",
@@ -598,7 +598,7 @@
        ]
       }
      ],
-     "prompt_number": 22
+     "prompt_number": 64
     },
     {
      "cell_type": "code",
@@ -613,7 +613,7 @@
       {
        "metadata": {},
        "output_type": "pyout",
-       "prompt_number": 23,
+       "prompt_number": 64,
        "text": [
         "\n",
         "----------------------------------------------------------------------{CMBN 1}\n",
@@ -625,7 +625,7 @@
        ]
       }
      ],
-     "prompt_number": 23
+     "prompt_number": 64
     },
     {
      "cell_type": "heading",
@@ -655,13 +655,13 @@
       {
        "metadata": {},
        "output_type": "pyout",
-       "prompt_number": 24,
+       "prompt_number": 64,
        "text": [
-        "#<Compiled-function CAT:S-CMPR #x302001B0009F>"
+        "#<Compiled-function CAT:S-CMPR #x302001AC5DCF>"
        ]
       }
      ],
-     "prompt_number": 24
+     "prompt_number": 64
     },
     {
      "cell_type": "code",
@@ -680,13 +680,13 @@
       {
        "metadata": {},
        "output_type": "pyout",
-       "prompt_number": 25,
+       "prompt_number": 64,
        "text": [
-        "#<Anonymous Function #x302001CD7EBF>"
+        "#<Anonymous Function #x302001D901FF>"
        ]
       }
      ],
-     "prompt_number": 25
+     "prompt_number": 64
     },
     {
      "cell_type": "code",
@@ -700,13 +700,13 @@
       {
        "metadata": {},
        "output_type": "pyout",
-       "prompt_number": 26,
+       "prompt_number": 64,
        "text": [
         "S0"
        ]
       }
      ],
-     "prompt_number": 26
+     "prompt_number": 64
     },
     {
      "cell_type": "code",
@@ -736,13 +736,13 @@
       {
        "metadata": {},
        "output_type": "pyout",
-       "prompt_number": 28,
+       "prompt_number": 64,
        "text": [
-        "#<Anonymous Function #x302001D729CF>"
+        "#<Anonymous Function #x302001DC6D4F>"
        ]
       }
      ],
-     "prompt_number": 28
+     "prompt_number": 64
     },
     {
      "cell_type": "code",
@@ -756,13 +756,13 @@
       {
        "metadata": {},
        "output_type": "pyout",
-       "prompt_number": 29,
+       "prompt_number": 64,
        "text": [
         ":GNRT"
        ]
       }
      ],
-     "prompt_number": 29
+     "prompt_number": 64
     },
     {
      "cell_type": "code",
@@ -776,13 +776,13 @@
       {
        "metadata": {},
        "output_type": "pyout",
-       "prompt_number": 30,
+       "prompt_number": 64,
        "text": [
         "(DIABOLO-FOR-EXAMPLE)"
        ]
       }
      ],
-     "prompt_number": 30
+     "prompt_number": 64
     },
     {
      "cell_type": "code",
@@ -796,7 +796,7 @@
       {
        "metadata": {},
        "output_type": "pyout",
-       "prompt_number": 31,
+       "prompt_number": 64,
        "text": [
         "\"--------------------------------------------------------------[function-doc]\n",
         "BUILD-CHCM\n",
@@ -829,7 +829,7 @@
        ]
       }
      ],
-     "prompt_number": 31
+     "prompt_number": 64
     },
     {
      "cell_type": "code",
@@ -845,16 +845,334 @@
       {
        "metadata": {},
        "output_type": "pyout",
-       "prompt_number": 32,
+       "prompt_number": 64,
        "text": [
         "[K1 Chain-Complex]"
        ]
       }
      ],
-     "prompt_number": 32
+     "prompt_number": 64
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "(documentation 'cat:chcm 'function)"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [
+      {
+       "metadata": {},
+       "output_type": "pyout",
+       "prompt_number": 64,
+       "text": [
+        "\"--------------------------------------------------------------[function-doc]\n",
+        "CHCM\n",
+        "Args: (idnm)\n",
+        "Return from the list *CHCM-LIST* the chain complex instance with Kenzo\n",
+        "identifier IDNUM or NIL, if it doesn't exist.\n",
+        "------------------------------------------------------------------------------\""
+       ]
+      }
+     ],
+     "prompt_number": 64
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "(cat:chcm 1)"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [
+      {
+       "metadata": {},
+       "output_type": "pyout",
+       "prompt_number": 64,
+       "text": [
+        "[K1 Chain-Complex]"
+       ]
+      }
+     ],
+     "prompt_number": 64
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "(cat:orgn diabolo)"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [
+      {
+       "metadata": {},
+       "output_type": "pyout",
+       "prompt_number": 64,
+       "text": [
+        "(DIABOLO-FOR-EXAMPLE)"
+       ]
+      }
+     ],
+     "prompt_number": 64
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "(cat:idnm diabolo)"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [
+      {
+       "metadata": {},
+       "output_type": "pyout",
+       "prompt_number": 64,
+       "text": [
+        "1"
+       ]
+      }
+     ],
+     "prompt_number": 64
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "(cat:basis diabolo 0)"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [
+      {
+       "metadata": {},
+       "output_type": "pyout",
+       "prompt_number": 64,
+       "text": [
+        "(S0 S1 S2 S3 S4 S5)"
+       ]
+      }
+     ],
+     "prompt_number": 64
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "(cat:basis diabolo 1)"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [
+      {
+       "metadata": {},
+       "output_type": "pyout",
+       "prompt_number": 64,
+       "text": [
+        "(S01 S02 S12 S23 S34 S35 S45)"
+       ]
+      }
+     ],
+     "prompt_number": 64
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "(cat:basis diabolo 2)"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [
+      {
+       "metadata": {},
+       "output_type": "pyout",
+       "prompt_number": 64,
+       "text": [
+        "(S345)"
+       ]
+      }
+     ],
+     "prompt_number": 64
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "(cat:basis diabolo 10)"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [
+      {
+       "metadata": {},
+       "output_type": "pyout",
+       "prompt_number": 64,
+       "text": [
+        "NIL"
+       ]
+      }
+     ],
+     "prompt_number": 64
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "(cat:dffr diabolo 2 's345)"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [
+      {
+       "metadata": {},
+       "output_type": "pyout",
+       "prompt_number": 64,
+       "text": [
+        "\n",
+        "----------------------------------------------------------------------{CMBN 1}\n",
+        "<1 * S34>\n",
+        "<-1 * S35>\n",
+        "<1 * S45>\n",
+        "------------------------------------------------------------------------------\n"
+       ]
+      }
+     ],
+     "prompt_number": 64
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "(cat:dffr diabolo (cat:dffr diabolo 2 's345))"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [
+      {
+       "metadata": {},
+       "output_type": "pyout",
+       "prompt_number": 64,
+       "text": [
+        "\n",
+        "----------------------------------------------------------------------{CMBN 0}\n",
+        "------------------------------------------------------------------------------\n"
+       ]
+      }
+     ],
+     "prompt_number": 64
+    },
+    {
+     "cell_type": "heading",
+     "level": 4,
+     "metadata": {},
+     "source": [
+      "An important trivial case: the unit chain complex, $\\mathbb{Z}$"
+     ]
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "(cat:def ZCC\n",
+      "         (the cat:chain-complex\n",
+      "              (cat:build-chcm\n",
+      "               :cmpr #'(lambda (gnrt1 gnrt2)\n",
+      "                               (declare (ignore gnrt1 gnrt2))\n",
+      "                               (the cat:cmpr :equal))\n",
+      "               :basis #'(lambda (n)\n",
+      "                                (the list\n",
+      "                                     (if (zerop n) '(:Z-gnrt) cat:+empty-list+)))\n",
+      "               :bsgn :Z-gnrt\n",
+      "               :intr-dffr #'(lambda (cmbn)\n",
+      "                                    (the cat:cmbn (cat:zero-cmbn (1- (cat:cmbn-degr cmbn)))))\n",
+      "               :strt :cmbn\n",
+      "               :orgn '(zcc-constant))))"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [
+      {
+       "metadata": {},
+       "output_type": "pyout",
+       "prompt_number": 64,
+       "text": [
+        "[K3 Chain-Complex]"
+       ]
+      }
+     ],
+     "prompt_number": 64
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "(documentation 'cat:z-chcm 'function)"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [
+      {
+       "metadata": {},
+       "output_type": "pyout",
+       "prompt_number": 64,
+       "text": [
+        "\"--------------------------------------------------------------[function-doc]\n",
+        "Z-CHCM\n",
+        "Args: ()\n",
+        "Build the unit chain complex.\n",
+        "------------------------------------------------------------------------------\""
+       ]
+      }
+     ],
+     "prompt_number": 64
+    },
+    {
+     "cell_type": "heading",
+     "level": 4,
+     "metadata": {},
+     "source": [
+      "The chain complex $\\texttt{circle}$"
+     ]
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "(defun CIRCLE ()\n",
+      "    (the cat:chain-complex\n",
+      "         (cat:build-chcm\n",
+      "          :cmpr #'(lambda (gnrt1 gnrt2)\n",
+      "                          (declare (ignore gnrt1 gnrt2))\n",
+      "                          (the cat:cmpr :equal))\n",
+      "          :basis #'(lambda (dmns)\n",
+      "                           (the list\n",
+      "                                (case dmns (0 '(*)) (1 '(s1))\n",
+      "                                    (otherwise cat:+empty-list+))))\n",
+      "          :bsgn '*\n",
+      "          :intr-dffr #'cat:zero-intr-dffr\n",
+      "          :strt :cmbn\n",
+      "          :orgn '(circle))))"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [
+      {
+       "metadata": {},
+       "output_type": "pyout",
+       "prompt_number": 64,
+       "text": [
+        "CIRCLE"
+       ]
+      }
+     ],
+     "prompt_number": 64
     }
    ],
    "metadata": {}
   }
  ]
-}
+}
\ No newline at end of file