From 01a3d57420b327239babad41a2528897d91f4489 Mon Sep 17 00:00:00 2001 From: Gerd Heber Date: Sun, 10 Jan 2016 13:53:28 -0500 Subject: [PATCH] Updated notebooks. --- examples/Chapter1.ipynb | 1125 ++++++++++--------- examples/Overview.ipynb | 2267 +++------------------------------------ 2 files changed, 747 insertions(+), 2645 deletions(-) diff --git a/examples/Chapter1.ipynb b/examples/Chapter1.ipynb index bb5b5af..b3c99fe 100644 --- a/examples/Chapter1.ipynb +++ b/examples/Chapter1.ipynb @@ -40,6 +40,28 @@ "metadata": { "collapsed": false }, + "outputs": [ + { + "data": { + "text/plain": [ + "#" + ] + }, + "execution_count": 2, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "(in-package \"CAT\")" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "collapsed": false + }, "outputs": [ { "name": "stdout", @@ -55,13 +77,13 @@ "NIL" ] }, - "execution_count": 2, + "execution_count": 3, "metadata": {}, "output_type": "execute_result" } ], "source": [ - "(cat:cat-init)" + "(cat-init)" ] }, { @@ -72,6 +94,33 @@ "\n", "## Introduction\n", "\n", + "A *chain complex* $(C_p, d_p)$ is a collection of free $\\mathbb{Z}$-modules $(C_p)$, one for each\n", + "$p \\in \\mathbb{Z}$, together with a homomorphism $d_p : C_p \\rightarrow C_{p-1}$, such\n", + "that, for all $p$, $d_{p-1} \\circ d_p = 0$. (See, for example, __P.J. Giblin__ in *Graph, Surface and Homology*, Chapman and Hall Math. series, 1981.)\n", + "\n", + "__In the Kenzo program__, a *morphism* $f=(f_p)$, of degree $k$, from a chain complex $(C_p, d_p)$ to another $(C'_p, d'_p)$ is a collection of homomorphisms\n", + "\n", + "$$f_p : C_p \\rightarrow C'_{p+k}.$$\n", + "\n", + "This is expressed by the following diagram, generally __not assumend commutative__.\n", + "\n", + "$$\n", + "\\begin{aligned}\n", + "\\cdots & \\leftarrow & C_{p-1} & \\quad\\xleftarrow{d_p} & C_p & \\quad\\xleftarrow{d_{p+1}} & C_{p+1} & \\quad\\leftarrow & \\cdots \\\\\n", + " & & f_{p-1} \\Bigg\\downarrow & & f_p \\Bigg\\downarrow & & f_{p+1} \\Bigg\\downarrow \\\\\n", + "\\cdots & \\leftarrow & C'_{p+k-1} & \\quad\\xleftarrow{d'_{p+k}} & C'_{p+k} & \\quad\\xleftarrow{d'_{p+k+1}} & C'_{p+k+1} & \\quad\\leftarrow & \\cdots \\end{aligned}\n", + "$$\n", + "\n", + "Three types of morphisms are most generally considered.\n", + "\n", + "1. $k=0$. If the commutativity relation $d'_p\\circ f_p=f_{p-1}\\circ d_p$ holds for every $p$, then the morphism $f$ is an ordinary chain complex morphism or *chain map*.\n", + "2. $k=-1$. If $(C_p,d_p)=(C'_p,d'_p)$ and $f_p=d_p$, then $f$ is the *differential* of the chain complex $(C_p,d_p)$ and, in fact, this differential is implemented in the ${\\tt Kenzo}$ program as a morphism of degree $-1$.\n", + "3. $k=+1$. In this case, $f$ is usually a *homotopy operator*, that is, some relation $$d'_{p+1}\\circ f_p+f_{p-1}\\circ d_p=g_p-g'_p$$ is satisfied for two (ordinary) chain complex morphisms $g$ and $g'$.\n", + "\n", + "For technical reasons, these three types of morphisms have been implemented in the $\\texttt{Kenzo}$ program\n", + "in a unique type.\n", + "\n", + "\n", "## Generators, terms, and combinations\n", "\n", "To become familiar with the Lisp functions implementing the chain complexes, the best is to begin with an example. *Simplicial complexes* are good candidates for this purpose, and we shall take as a typical example the following simplicial complex." @@ -79,7 +128,7 @@ }, { "cell_type": "code", - "execution_count": 3, + "execution_count": 4, "metadata": { "collapsed": false }, @@ -88,16 +137,16 @@ "data": { "image/png": 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", "text/plain": [ - "#" + "#" ] }, - "execution_count": 3, + "execution_count": 4, "metadata": {}, "output_type": "execute_result" } ], "source": [ - "(png-from-file \"diabolo.png\")" + "(cl-jupyter-user:png-from-file \"diabolo.png\")" ] }, { @@ -116,7 +165,7 @@ "\n", "### Representation of a combination\n", "\n", - "A combination is represented internally in the system by a list habing the following general form:\n", + "A combination is represented internally in the system by a list having the following general form:\n", "$$\\texttt{(:cmbn degree}\\quad(\\lambda_1\\cdot\\sigma_1)\\dots(\\lambda_k\\cdot\\sigma_k)\\texttt{)}$$\n", "and containing\n", "\n", @@ -130,7 +179,7 @@ }, { "cell_type": "code", - "execution_count": 4, + "execution_count": 5, "metadata": { "collapsed": false }, @@ -146,18 +195,18 @@ "------------------------------------------------------------------------------\"" ] }, - "execution_count": 4, + "execution_count": 5, "metadata": {}, "output_type": "execute_result" } ], "source": [ - "(documentation 'cat:f-cmpr 'function)" + "(documentation 'f-cmpr 'function)" ] }, { "cell_type": "code", - "execution_count": 5, + "execution_count": 6, "metadata": { "collapsed": false }, @@ -168,18 +217,18 @@ ":LESS" ] }, - "execution_count": 5, + "execution_count": 6, "metadata": {}, "output_type": "execute_result" } ], "source": [ - "(cat:f-cmpr 123 789)" + "(f-cmpr 123 789)" ] }, { "cell_type": "code", - "execution_count": 6, + "execution_count": 7, "metadata": { "collapsed": false }, @@ -196,18 +245,18 @@ "------------------------------------------------------------------------------\"" ] }, - "execution_count": 6, + "execution_count": 7, "metadata": {}, "output_type": "execute_result" } ], "source": [ - "(documentation 'cat:s-cmpr 'function)" + "(documentation 's-cmpr 'function)" ] }, { "cell_type": "code", - "execution_count": 7, + "execution_count": 8, "metadata": { "collapsed": false }, @@ -218,18 +267,18 @@ ":GREATER" ] }, - "execution_count": 7, + "execution_count": 8, "metadata": {}, "output_type": "execute_result" } ], "source": [ - "(cat:s-cmpr 'circulation 'circular)" + "(s-cmpr 'circulation 'circular)" ] }, { "cell_type": "code", - "execution_count": 8, + "execution_count": 9, "metadata": { "collapsed": false }, @@ -245,18 +294,18 @@ "------------------------------------------------------------------------------\"" ] }, - "execution_count": 8, + "execution_count": 9, "metadata": {}, "output_type": "execute_result" } ], "source": [ - "(documentation 'cat:l-cmpr 'function)" + "(documentation 'l-cmpr 'function)" ] }, { "cell_type": "code", - "execution_count": 9, + "execution_count": 10, "metadata": { "collapsed": false }, @@ -267,13 +316,13 @@ ":GREATER" ] }, - "execution_count": 9, + "execution_count": 10, "metadata": {}, "output_type": "execute_result" } ], "source": [ - "(cat:l-cmpr '(1 a b) '(1 a))" + "(l-cmpr '(1 a b) '(1 a))" ] }, { @@ -285,7 +334,7 @@ }, { "cell_type": "code", - "execution_count": 10, + "execution_count": 11, "metadata": { "collapsed": false }, @@ -303,18 +352,18 @@ "------------------------------------------------------------------------------\"" ] }, - "execution_count": 10, + "execution_count": 11, "metadata": {}, "output_type": "execute_result" } ], "source": [ - "(documentation 'cat:cmbn 'function)" + "(documentation 'cmbn 'function)" ] }, { "cell_type": "code", - "execution_count": 11, + "execution_count": 12, "metadata": { "collapsed": false }, @@ -331,18 +380,18 @@ "------------------------------------------------------------------------------\n" ] }, - "execution_count": 11, + "execution_count": 12, "metadata": {}, "output_type": "execute_result" } ], "source": [ - "(cat:def comb1 (cat:cmbn 1 1 'u 2 'v 3 'w 4 'z))" + "(def comb1 (cmbn 1 1 'u 2 'v 3 'w 4 'z))" ] }, { "cell_type": "code", - "execution_count": 12, + "execution_count": 13, "metadata": { "collapsed": false }, @@ -357,42 +406,13 @@ "------------------------------------------------------------------------------\"" ] }, - "execution_count": 12, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "(documentation 'cat:cmbn-non-zero-p 'function)" - ] - }, - { - "cell_type": "code", - "execution_count": 13, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "data": { - "text/plain": [ - "T" - ] - }, "execution_count": 13, "metadata": {}, "output_type": "execute_result" } ], "source": [ - "(cat:cmbn-non-zero-p comb1)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "The reader function $\\texttt{cat:cmbn-list}$ gets the list of terms of the combination $\\texttt{cmbn}$. Beware: a term is not a Kenzo object." + "(documentation 'cmbn-non-zero-p 'function)" ] }, { @@ -405,7 +425,7 @@ { "data": { "text/plain": [ - "((1 . U) (2 . V) (3 . W) (4 . Z))" + "T" ] }, "execution_count": 14, @@ -414,7 +434,14 @@ } ], "source": [ - "(cat:cmbn-list comb1)" + "(cmbn-non-zero-p comb1)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The reader function $\\texttt{cat:cmbn-list}$ gets the list of terms of the combination $\\texttt{cmbn}$. Beware: a term is not a Kenzo object." ] }, { @@ -427,7 +454,7 @@ { "data": { "text/plain": [ - "(3 . W)" + "((1 . U) (2 . V) (3 . W) (4 . Z))" ] }, "execution_count": 15, @@ -436,7 +463,7 @@ } ], "source": [ - "(cat:def term3 (third (cat:cmbn-list comb1)))" + "(cmbn-list comb1)" ] }, { @@ -445,6 +472,28 @@ "metadata": { "collapsed": false }, + "outputs": [ + { + "data": { + "text/plain": [ + "(3 . W)" + ] + }, + "execution_count": 16, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "(def term3 (third (cmbn-list comb1)))" + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "metadata": { + "collapsed": false + }, "outputs": [ { "data": { @@ -456,18 +505,18 @@ "------------------------------------------------------------------------------\"" ] }, - "execution_count": 16, + "execution_count": 17, "metadata": {}, "output_type": "execute_result" } ], "source": [ - "(documentation 'cat:cffc 'function)" + "(documentation 'cffc 'function)" ] }, { "cell_type": "code", - "execution_count": 17, + "execution_count": 18, "metadata": { "collapsed": false }, @@ -478,18 +527,18 @@ "3" ] }, - "execution_count": 17, + "execution_count": 18, "metadata": {}, "output_type": "execute_result" } ], "source": [ - "(cat:cffc term3)" + "(cffc term3)" ] }, { "cell_type": "code", - "execution_count": 18, + "execution_count": 19, "metadata": { "collapsed": false }, @@ -504,18 +553,18 @@ "------------------------------------------------------------------------------\"" ] }, - "execution_count": 18, + "execution_count": 19, "metadata": {}, "output_type": "execute_result" } ], "source": [ - "(documentation 'cat:gnrt 'function)" + "(documentation 'gnrt 'function)" ] }, { "cell_type": "code", - "execution_count": 19, + "execution_count": 20, "metadata": { "collapsed": false }, @@ -526,18 +575,18 @@ "W" ] }, - "execution_count": 19, + "execution_count": 20, "metadata": {}, "output_type": "execute_result" } ], "source": [ - "(cat:gnrt term3)" + "(gnrt term3)" ] }, { "cell_type": "code", - "execution_count": 20, + "execution_count": 21, "metadata": { "collapsed": false }, @@ -552,18 +601,18 @@ "------------------------------------------------------------------------------\"" ] }, - "execution_count": 20, + "execution_count": 21, "metadata": {}, "output_type": "execute_result" } ], "source": [ - "(documentation 'cat:cmbn-opps 'function)" + "(documentation 'cmbn-opps 'function)" ] }, { "cell_type": "code", - "execution_count": 21, + "execution_count": 22, "metadata": { "collapsed": false }, @@ -580,18 +629,18 @@ "------------------------------------------------------------------------------\n" ] }, - "execution_count": 21, + "execution_count": 22, "metadata": {}, "output_type": "execute_result" } ], "source": [ - "(cat:def mcomb1 (cat:cmbn-opps comb1))" + "(def mcomb1 (cmbn-opps comb1))" ] }, { "cell_type": "code", - "execution_count": 22, + "execution_count": 23, "metadata": { "collapsed": false }, @@ -606,18 +655,18 @@ "------------------------------------------------------------------------------\"" ] }, - "execution_count": 22, + "execution_count": 23, "metadata": {}, "output_type": "execute_result" } ], "source": [ - "(documentation 'cat:n-cmbn 'function)" + "(documentation 'n-cmbn 'function)" ] }, { "cell_type": "code", - "execution_count": 23, + "execution_count": 24, "metadata": { "collapsed": false }, @@ -634,18 +683,18 @@ "------------------------------------------------------------------------------\n" ] }, - "execution_count": 23, + "execution_count": 24, "metadata": {}, "output_type": "execute_result" } ], "source": [ - "(cat:def comb2 (cat:n-cmbn 10 comb1))" + "(def comb2 (n-cmbn 10 comb1))" ] }, { "cell_type": "code", - "execution_count": 24, + "execution_count": 25, "metadata": { "collapsed": false }, @@ -663,18 +712,18 @@ "------------------------------------------------------------------------------\"" ] }, - "execution_count": 24, + "execution_count": 25, "metadata": {}, "output_type": "execute_result" } ], "source": [ - "(documentation 'cat:2cmbn-add 'function)" + "(documentation '2cmbn-add 'function)" ] }, { "cell_type": "code", - "execution_count": 25, + "execution_count": 26, "metadata": { "collapsed": false }, @@ -691,18 +740,18 @@ "------------------------------------------------------------------------------\n" ] }, - "execution_count": 25, + "execution_count": 26, "metadata": {}, "output_type": "execute_result" } ], "source": [ - "(cat:def cmb12 (cat:2cmbn-add #'cat:s-cmpr comb1 comb2))" + "(def cmb12 (2cmbn-add #'s-cmpr comb1 comb2))" ] }, { "cell_type": "code", - "execution_count": 26, + "execution_count": 27, "metadata": { "collapsed": false }, @@ -720,18 +769,18 @@ "------------------------------------------------------------------------------\"" ] }, - "execution_count": 26, + "execution_count": 27, "metadata": {}, "output_type": "execute_result" } ], "source": [ - "(documentation 'cat:2cmbn-sbtr 'function)" + "(documentation '2cmbn-sbtr 'function)" ] }, { "cell_type": "code", - "execution_count": 27, + "execution_count": 28, "metadata": { "collapsed": false }, @@ -748,18 +797,18 @@ "------------------------------------------------------------------------------\"" ] }, - "execution_count": 27, + "execution_count": 28, "metadata": {}, "output_type": "execute_result" } ], "source": [ - "(documentation 'cat:ncmbn-add 'function)" + "(documentation 'ncmbn-add 'function)" ] }, { "cell_type": "code", - "execution_count": 28, + "execution_count": 29, "metadata": { "collapsed": false }, @@ -776,14 +825,14 @@ "------------------------------------------------------------------------------\n" ] }, - "execution_count": 28, + "execution_count": 29, "metadata": {}, "output_type": "execute_result" } ], "source": [ - "(cat:ncmbn-add #'cat:s-cmpr\n", - " comb1 comb2 comb1 comb2 comb1 comb2 comb1 comb2 comb1 comb2)" + "(ncmbn-add #'s-cmpr\n", + " comb1 comb2 comb1 comb2 comb1 comb2 comb1 comb2 comb1 comb2)" ] }, { @@ -797,28 +846,6 @@ "#### A first example of a chain complex" ] }, - { - "cell_type": "code", - "execution_count": 29, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "data": { - "text/plain": [ - "#" - ] - }, - "execution_count": 29, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "(cat:def diabolo-cmpr #'cat:s-cmpr)" - ] - }, { "cell_type": "code", "execution_count": 30, @@ -829,7 +856,7 @@ { "data": { "text/plain": [ - "#" + "#" ] }, "execution_count": 30, @@ -838,12 +865,7 @@ } ], "source": [ - "(cat:def diabolo-basis #'(lambda (dmn)\n", - " (case dmn\n", - " (0 '(s0 s1 s2 s3 s4 s5))\n", - " (1 '(s01 s02 s12 s23 s34 s35 s45))\n", - " (2 '(s345))\n", - " (otherwise nil))))" + "(def diabolo-cmpr #'s-cmpr)" ] }, { @@ -856,7 +878,7 @@ { "data": { "text/plain": [ - "S0" + "#" ] }, "execution_count": 31, @@ -865,7 +887,12 @@ } ], "source": [ - "(cat:def diabolo-bspn 's0)" + "(def diabolo-basis #'(lambda (dmn)\n", + " (case dmn\n", + " (0 '(s0 s1 s2 s3 s4 s5))\n", + " (1 '(s01 s02 s12 s23 s34 s35 s45))\n", + " (2 '(s345))\n", + " (otherwise nil))))" ] }, { @@ -878,7 +905,7 @@ { "data": { "text/plain": [ - "#" + "S0" ] }, "execution_count": 32, @@ -887,23 +914,7 @@ } ], "source": [ - "(cat:def diabolo-pure-dffr\n", - " #'(lambda (dmn gnr)\n", - " (unless (<= 0 dmn 2)\n", - " (error \"Incorrect dimension for diabolo-dp.\"))\n", - " (case dmn\n", - " (0 (cat:cmbn -1)) ; Note the null combination of degree -1\n", - " (1 (case gnr\n", - " (s01 (cat:cmbn 0 -1 's0 1 's1))\n", - " (s02 (cat:cmbn 0 -1 's0 1 's2))\n", - " (s12 (cat:cmbn 0 -1 's1 1 's2))\n", - " (s23 (cat:cmbn 0 -1 's2 1 's3))\n", - " (s34 (cat:cmbn 0 -1 's3 1 's4))\n", - " (s35 (cat:cmbn 0 -1 's3 1 's5))\n", - " (s45 (cat:cmbn 0 -1 's4 1 's5))))\n", - " (2 (case gnr\n", - " (s345 (cat:cmbn 1 1 's34 -1 's35 1 's45))))\n", - " (otherwise (error \"Bad generator for complex diabolo\")))))" + "(def diabolo-bspn 's0)" ] }, { @@ -916,7 +927,7 @@ { "data": { "text/plain": [ - ":GNRT" + "#" ] }, "execution_count": 33, @@ -925,7 +936,23 @@ } ], "source": [ - "(cat:def diabolo-strt :GNRT)" + "(def diabolo-pure-dffr\n", + " #'(lambda (dmn gnr)\n", + " (unless (<= 0 dmn 2)\n", + " (error \"Incorrect dimension for diabolo-dp.\"))\n", + " (case dmn\n", + " (0 (cmbn -1)) ; Note the null combination of degree -1\n", + " (1 (case gnr\n", + " (s01 (cmbn 0 -1 's0 1 's1))\n", + " (s02 (cmbn 0 -1 's0 1 's2))\n", + " (s12 (cmbn 0 -1 's1 1 's2))\n", + " (s23 (cmbn 0 -1 's2 1 's3))\n", + " (s34 (cmbn 0 -1 's3 1 's4))\n", + " (s35 (cmbn 0 -1 's3 1 's5))\n", + " (s45 (cmbn 0 -1 's4 1 's5))))\n", + " (2 (case gnr\n", + " (s345 (cmbn 1 1 's34 -1 's35 1 's45))))\n", + " (otherwise (error \"Bad generator for complex diabolo\")))))" ] }, { @@ -938,7 +965,7 @@ { "data": { "text/plain": [ - "(DIABOLO-FOR-EXAMPLE)" + ":GNRT" ] }, "execution_count": 34, @@ -947,7 +974,7 @@ } ], "source": [ - "(cat:def diabolo-orgn '(diabolo-for-example))" + "(def diabolo-strt :GNRT)" ] }, { @@ -956,6 +983,28 @@ "metadata": { "collapsed": false }, + "outputs": [ + { + "data": { + "text/plain": [ + "(DIABOLO-FOR-EXAMPLE)" + ] + }, + "execution_count": 35, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "(def diabolo-orgn '(diabolo-for-example))" + ] + }, + { + "cell_type": "code", + "execution_count": 36, + "metadata": { + "collapsed": false + }, "outputs": [ { "data": { @@ -992,18 +1041,18 @@ "------------------------------------------------------------------------------\"" ] }, - "execution_count": 35, + "execution_count": 36, "metadata": {}, "output_type": "execute_result" } ], "source": [ - "(documentation 'cat:build-chcm 'function)" + "(documentation 'build-chcm 'function)" ] }, { "cell_type": "code", - "execution_count": 36, + "execution_count": 37, "metadata": { "collapsed": false }, @@ -1014,20 +1063,20 @@ "[K1 Chain-Complex]" ] }, - "execution_count": 36, + "execution_count": 37, "metadata": {}, "output_type": "execute_result" } ], "source": [ - "(cat:def diabolo (cat:build-chcm :cmpr diabolo-cmpr :basis diabolo-basis\n", - " :bsgn diabolo-bspn :intr-dffr diabolo-pure-dffr\n", - " :strt diabolo-strt :orgn diabolo-orgn))" + "(def diabolo (build-chcm :cmpr diabolo-cmpr :basis diabolo-basis\n", + " :bsgn diabolo-bspn :intr-dffr diabolo-pure-dffr\n", + " :strt diabolo-strt :orgn diabolo-orgn))" ] }, { "cell_type": "code", - "execution_count": 37, + "execution_count": 38, "metadata": { "collapsed": false }, @@ -1043,35 +1092,13 @@ "------------------------------------------------------------------------------\"" ] }, - "execution_count": 37, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "(documentation 'cat:chcm 'function)" - ] - }, - { - "cell_type": "code", - "execution_count": 38, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "data": { - "text/plain": [ - "[K1 Chain-Complex]" - ] - }, "execution_count": 38, "metadata": {}, "output_type": "execute_result" } ], "source": [ - "(cat:chcm 1)" + "(documentation 'chcm 'function)" ] }, { @@ -1084,7 +1111,7 @@ { "data": { "text/plain": [ - "(DIABOLO-FOR-EXAMPLE)" + "[K1 Chain-Complex]" ] }, "execution_count": 39, @@ -1093,7 +1120,7 @@ } ], "source": [ - "(cat:orgn diabolo)" + "(chcm 1)" ] }, { @@ -1106,7 +1133,7 @@ { "data": { "text/plain": [ - "1" + "(DIABOLO-FOR-EXAMPLE)" ] }, "execution_count": 40, @@ -1115,7 +1142,7 @@ } ], "source": [ - "(cat:idnm diabolo)" + "(orgn diabolo)" ] }, { @@ -1128,7 +1155,7 @@ { "data": { "text/plain": [ - "(S0 S1 S2 S3 S4 S5)" + "1" ] }, "execution_count": 41, @@ -1137,7 +1164,7 @@ } ], "source": [ - "(cat:basis diabolo 0)" + "(idnm diabolo)" ] }, { @@ -1150,7 +1177,7 @@ { "data": { "text/plain": [ - "(S01 S02 S12 S23 S34 S35 S45)" + "(S0 S1 S2 S3 S4 S5)" ] }, "execution_count": 42, @@ -1159,7 +1186,7 @@ } ], "source": [ - "(cat:basis diabolo 1)" + "(basis diabolo 0)" ] }, { @@ -1172,7 +1199,7 @@ { "data": { "text/plain": [ - "(S345)" + "(S01 S02 S12 S23 S34 S35 S45)" ] }, "execution_count": 43, @@ -1181,7 +1208,7 @@ } ], "source": [ - "(cat:basis diabolo 2)" + "(basis diabolo 1)" ] }, { @@ -1194,7 +1221,7 @@ { "data": { "text/plain": [ - "NIL" + "(S345)" ] }, "execution_count": 44, @@ -1203,7 +1230,7 @@ } ], "source": [ - "(cat:basis diabolo 10)" + "(basis diabolo 2)" ] }, { @@ -1212,6 +1239,28 @@ "metadata": { "collapsed": false }, + "outputs": [ + { + "data": { + "text/plain": [ + "NIL" + ] + }, + "execution_count": 45, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "(basis diabolo 10)" + ] + }, + { + "cell_type": "code", + "execution_count": 46, + "metadata": { + "collapsed": false + }, "outputs": [ { "data": { @@ -1224,44 +1273,13 @@ "------------------------------------------------------------------------------\n" ] }, - "execution_count": 45, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "(cat:dffr diabolo 2 's345)" - ] - }, - { - "cell_type": "code", - "execution_count": 46, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "data": { - "text/plain": [ - "\n", - "----------------------------------------------------------------------{CMBN 0}\n", - "------------------------------------------------------------------------------\n" - ] - }, "execution_count": 46, "metadata": {}, "output_type": "execute_result" } ], "source": [ - "(cat:dffr diabolo (cat:dffr diabolo 2 's345))" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "#### An important trivial case: the unit chain complex, $\\mathbb{Z}$" + "(dffr diabolo 2 's345)" ] }, { @@ -1274,7 +1292,9 @@ { "data": { "text/plain": [ - "[K3 Chain-Complex]" + "\n", + "----------------------------------------------------------------------{CMBN 0}\n", + "------------------------------------------------------------------------------\n" ] }, "execution_count": 47, @@ -1283,20 +1303,14 @@ } ], "source": [ - "(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))))" + "(dffr diabolo *)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "#### An important trivial case: the unit chain complex, $\\mathbb{Z}$" ] }, { @@ -1305,6 +1319,41 @@ "metadata": { "collapsed": false }, + "outputs": [ + { + "data": { + "text/plain": [ + "[K3 Chain-Complex]" + ] + }, + "execution_count": 48, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "(def ZCC\n", + " (the chain-complex\n", + " (build-chcm\n", + " :cmpr #'(lambda (gnrt1 gnrt2)\n", + " (declare (ignore gnrt1 gnrt2))\n", + " (the cmpr :equal))\n", + " :basis #'(lambda (n)\n", + " (the list\n", + " (if (zerop n) '(:Z-gnrt) +empty-list+)))\n", + " :bsgn :Z-gnrt\n", + " :intr-dffr #'(lambda (cmbn)\n", + " (the cmbn (zero-cmbn (1- (cmbn-degr cmbn)))))\n", + " :strt :cmbn\n", + " :orgn '(zcc-constant))))" + ] + }, + { + "cell_type": "code", + "execution_count": 49, + "metadata": { + "collapsed": false + }, "outputs": [ { "data": { @@ -1316,13 +1365,13 @@ "------------------------------------------------------------------------------\"" ] }, - "execution_count": 48, + "execution_count": 49, "metadata": {}, "output_type": "execute_result" } ], "source": [ - "(documentation 'cat:z-chcm 'function)" + "(documentation 'z-chcm 'function)" ] }, { @@ -1334,35 +1383,43 @@ }, { "cell_type": "code", - "execution_count": 49, + "execution_count": 50, "metadata": { "collapsed": false }, "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "REDEFINITION-WITH-DEFUN: \n", + " #\n" + ] + }, { "data": { "text/plain": [ "CIRCLE" ] }, - "execution_count": 49, + "execution_count": 50, "metadata": {}, "output_type": "execute_result" } ], "source": [ "(defun CIRCLE ()\n", - " (the cat:chain-complex\n", - " (cat:build-chcm\n", + " (the chain-complex\n", + " (build-chcm\n", " :cmpr #'(lambda (gnrt1 gnrt2)\n", " (declare (ignore gnrt1 gnrt2))\n", - " (the cat:cmpr :equal))\n", + " (the cmpr :equal))\n", " :basis #'(lambda (dmns)\n", " (the list\n", " (case dmns (0 '(*)) (1 '(s1))\n", - " (otherwise cat:+empty-list+))))\n", + " (otherwise +empty-list+))))\n", " :bsgn '*\n", - " :intr-dffr #'cat:zero-intr-dffr\n", + " :intr-dffr #'zero-intr-dffr\n", " :strt :cmbn\n", " :orgn '(circle))))" ] @@ -1376,7 +1433,7 @@ }, { "cell_type": "code", - "execution_count": 50, + "execution_count": 51, "metadata": { "collapsed": false }, @@ -1435,13 +1492,13 @@ "-----------------------------------------------------------------------------\"" ] }, - "execution_count": 50, + "execution_count": 51, "metadata": {}, "output_type": "execute_result" } ], "source": [ - "(documentation 'cat:morphism 'type)" + "(documentation 'morphism 'type)" ] }, { @@ -1453,7 +1510,7 @@ }, { "cell_type": "code", - "execution_count": 51, + "execution_count": 52, "metadata": { "collapsed": false }, @@ -1491,13 +1548,13 @@ "------------------------------------------------------------------------------\"" ] }, - "execution_count": 51, + "execution_count": 52, "metadata": {}, "output_type": "execute_result" } ], "source": [ - "(documentation 'cat:build-mrph 'function)" + "(documentation 'build-mrph 'function)" ] }, { @@ -1509,7 +1566,7 @@ }, { "cell_type": "code", - "execution_count": 52, + "execution_count": 53, "metadata": { "collapsed": false }, @@ -1528,35 +1585,13 @@ "NIL" ] }, - "execution_count": 52, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "(cat:cat-init)" - ] - }, - { - "cell_type": "code", - "execution_count": 53, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "data": { - "text/plain": [ - "[K1 Chain-Complex]" - ] - }, "execution_count": 53, "metadata": {}, "output_type": "execute_result" } ], "source": [ - "(cat:def ZCC (cat:z-chcm))" + "(cat-init)" ] }, { @@ -1569,7 +1604,7 @@ { "data": { "text/plain": [ - "[K3 Cohomology-Class on K1 of degree 1]" + "[K1 Chain-Complex]" ] }, "execution_count": 54, @@ -1578,13 +1613,7 @@ } ], "source": [ - "(cat:def zero-morphism (cat:build-mrph :sorc ZCC\n", - " :trgt ZCC\n", - " :degr -1\n", - " :intr #'(lambda (comb)\n", - " (cat:cmbn (1- (cat:degr comb))))\n", - " :strt :cmbn\n", - " :orgn '(zero morphism on ZCC)))" + "(def ZCC (z-chcm))" ] }, { @@ -1597,7 +1626,7 @@ { "data": { "text/plain": [ - "[K4 Cohomology-Class on K1 of degree 0]" + "[K3 Cohomology-Class on K1 of degree 1]" ] }, "execution_count": 55, @@ -1606,12 +1635,40 @@ } ], "source": [ - "(cat:def id-morphism (cat:build-mrph :sorc ZCC\n", - " :trgt ZCC\n", - " :degr 0\n", - " :intr #'identity\n", - " :strt :cmbn\n", - " :orgn '(identity morphism on ZCC)))" + "(def zero-morphism (build-mrph :sorc ZCC\n", + " :trgt ZCC\n", + " :degr -1\n", + " :intr #'(lambda (comb)\n", + " (cmbn (1- (degr comb))))\n", + " :strt :cmbn\n", + " :orgn '(zero morphism on ZCC)))" + ] + }, + { + "cell_type": "code", + "execution_count": 56, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "[K4 Cohomology-Class on K1 of degree 0]" + ] + }, + "execution_count": 56, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "(def id-morphism (build-mrph :sorc ZCC\n", + " :trgt ZCC\n", + " :degr 0\n", + " :intr #'identity\n", + " :strt :cmbn\n", + " :orgn '(identity morphism on ZCC)))" ] }, { @@ -1623,31 +1680,6 @@ "### Functions defining morphisms" ] }, - { - "cell_type": "code", - "execution_count": 56, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "data": { - "text/plain": [ - "#" - ] - }, - "execution_count": 56, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "(cat:def ccn-boundary #'(lambda (dgr gnr)\n", - " (if (evenp (+ dgr gnr))\n", - " (cat:cmbn (1- dgr) 1 (- gnr 10))\n", - " (cat:cmbn (1- dgr)))))" - ] - }, { "cell_type": "code", "execution_count": 57, @@ -1658,7 +1690,7 @@ { "data": { "text/plain": [ - "[K5 Chain-Complex]" + "#" ] }, "execution_count": 57, @@ -1667,12 +1699,10 @@ } ], "source": [ - "(cat:def ccn (cat:build-chcm :cmpr #'cat:f-cmpr\n", - " :basis #'(lambda (n) (cat: K5]" + "[K5 Chain-Complex]" ] }, "execution_count": 58, @@ -1694,10 +1724,12 @@ } ], "source": [ - "(cat:def upper-shift (cat:build-mrph\n", - " :sorc ccn :trgt ccn :strt :gnrt :degr +1\n", - " :intr #'(lambda (d gn) (cat:cmbn (1+ d) 1 (+ gn 10)))\n", - " :orgn '(ccn shift +10)))" + "(def ccn (build-chcm :cmpr #'f-cmpr\n", + " :basis #'(lambda (n) ( K5]" + "[K7 Morphism (degree 1): K5 -> K5]" ] }, "execution_count": 59, @@ -1719,10 +1751,10 @@ } ], "source": [ - "(cat:def lower-shift (cat:build-mrph\n", - " :sorc ccn :trgt ccn :strt :gnrt :degr -1\n", - " :intr #'(lambda (d gn) (cat:cmbn (1- d) 1 (- gn 10)))\n", - " :orgn '(ccn shift -10)))" + "(def upper-shift (build-mrph\n", + " :sorc ccn :trgt ccn :strt :gnrt :degr +1\n", + " :intr #'(lambda (d gn) (cmbn (1+ d) 1 (+ gn 10)))\n", + " :orgn '(ccn shift +10)))" ] }, { @@ -1735,10 +1767,7 @@ { "data": { "text/plain": [ - "\n", - "----------------------------------------------------------------------{CMBN 1}\n", - "<1 * 12>\n", - "------------------------------------------------------------------------------\n" + "[K8 Morphism (degree -1): K5 -> K5]" ] }, "execution_count": 60, @@ -1747,7 +1776,10 @@ } ], "source": [ - "(cat:? ccn 2 22)" + "(def lower-shift (build-mrph\n", + " :sorc ccn :trgt ccn :strt :gnrt :degr -1\n", + " :intr #'(lambda (d gn) (cmbn (1- d) 1 (- gn 10)))\n", + " :orgn '(ccn shift -10)))" ] }, { @@ -1761,7 +1793,8 @@ "data": { "text/plain": [ "\n", - "----------------------------------------------------------------------{CMBN 0}\n", + "----------------------------------------------------------------------{CMBN 1}\n", + "<1 * 12>\n", "------------------------------------------------------------------------------\n" ] }, @@ -1771,7 +1804,7 @@ } ], "source": [ - "(cat:? ccn (cat:? ccn 2 22))" + "(? ccn 2 22)" ] }, { @@ -1780,6 +1813,30 @@ "metadata": { "collapsed": false }, + "outputs": [ + { + "data": { + "text/plain": [ + "\n", + "----------------------------------------------------------------------{CMBN 0}\n", + "------------------------------------------------------------------------------\n" + ] + }, + "execution_count": 62, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "(? ccn *)" + ] + }, + { + "cell_type": "code", + "execution_count": 63, + "metadata": { + "collapsed": false + }, "outputs": [ { "data": { @@ -1792,18 +1849,18 @@ "------------------------------------------------------------------------------\n" ] }, - "execution_count": 62, + "execution_count": 63, "metadata": {}, "output_type": "execute_result" } ], "source": [ - "(cat:def combn (cat:cmbn 5 1 50 5 55 9 59))" + "(def combn (cmbn 5 1 50 5 55 9 59))" ] }, { "cell_type": "code", - "execution_count": 63, + "execution_count": 64, "metadata": { "collapsed": false }, @@ -1818,37 +1875,13 @@ "------------------------------------------------------------------------------\n" ] }, - "execution_count": 63, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "(cat:? ccn combn)" - ] - }, - { - "cell_type": "code", - "execution_count": 64, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "data": { - "text/plain": [ - "\n", - "----------------------------------------------------------------------{CMBN 3}\n", - "------------------------------------------------------------------------------\n" - ] - }, "execution_count": 64, "metadata": {}, "output_type": "execute_result" } ], "source": [ - "(cat:? ccn (cat:? ccn combn))" + "(? ccn combn)" ] }, { @@ -1862,8 +1895,7 @@ "data": { "text/plain": [ "\n", - "----------------------------------------------------------------------{CMBN 1}\n", - "<1 * 16>\n", + "----------------------------------------------------------------------{CMBN 3}\n", "------------------------------------------------------------------------------\n" ] }, @@ -1873,7 +1905,7 @@ } ], "source": [ - "(cat:? upper-shift 0 6)" + "(? ccn *)" ] }, { @@ -1887,8 +1919,8 @@ "data": { "text/plain": [ "\n", - "----------------------------------------------------------------------{CMBN 4}\n", - "<1 * 41>\n", + "----------------------------------------------------------------------{CMBN 1}\n", + "<1 * 16>\n", "------------------------------------------------------------------------------\n" ] }, @@ -1898,7 +1930,7 @@ } ], "source": [ - "(cat:? lower-shift 5 51)" + "(? upper-shift 0 6)" ] }, { @@ -1912,8 +1944,8 @@ "data": { "text/plain": [ "\n", - "----------------------------------------------------------------------{CMBN 3}\n", - "<1 * 31>\n", + "----------------------------------------------------------------------{CMBN 4}\n", + "<1 * 41>\n", "------------------------------------------------------------------------------\n" ] }, @@ -1923,7 +1955,7 @@ } ], "source": [ - "(cat:? lower-shift (cat:? lower-shift 5 51))" + "(? lower-shift 5 51)" ] }, { @@ -1937,11 +1969,8 @@ "data": { "text/plain": [ "\n", - "----------------------------------------------------------------------{CMBN 1}\n", - "<1 * 10>\n", - "<2 * 11>\n", - "<3 * 12>\n", - "<4 * 13>\n", + "----------------------------------------------------------------------{CMBN 3}\n", + "<1 * 31>\n", "------------------------------------------------------------------------------\n" ] }, @@ -1951,7 +1980,7 @@ } ], "source": [ - "(cat:def comb1 (cat:cmbn 1 1 10 2 11 3 12 4 13))" + "(? lower-shift (? lower-shift 5 51))" ] }, { @@ -1960,50 +1989,6 @@ "metadata": { "collapsed": false }, - "outputs": [ - { - "data": { - "text/plain": [ - "[K9 Morphism (degree 0): K5 -> K5]" - ] - }, - "execution_count": 69, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "(cat:def identity? (cat:cmps upper-shift lower-shift))" - ] - }, - { - "cell_type": "code", - "execution_count": 70, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "data": { - "text/plain": [ - "0" - ] - }, - "execution_count": 70, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "(cat:degr identity?)" - ] - }, - { - "cell_type": "code", - "execution_count": 71, - "metadata": { - "collapsed": false - }, "outputs": [ { "data": { @@ -2017,13 +2002,57 @@ "------------------------------------------------------------------------------\n" ] }, + "execution_count": 69, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "(def comb1 (cmbn 1 1 10 2 11 3 12 4 13))" + ] + }, + { + "cell_type": "code", + "execution_count": 70, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "[K9 Morphism (degree 0): K5 -> K5]" + ] + }, + "execution_count": 70, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "(def identity? (cmps upper-shift lower-shift))" + ] + }, + { + "cell_type": "code", + "execution_count": 71, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "0" + ] + }, "execution_count": 71, "metadata": {}, "output_type": "execute_result" } ], "source": [ - "(cat:? identity? comb1)" + "(degr identity?)" ] }, { @@ -2038,6 +2067,10 @@ "text/plain": [ "\n", "----------------------------------------------------------------------{CMBN 1}\n", + "<1 * 10>\n", + "<2 * 11>\n", + "<3 * 12>\n", + "<4 * 13>\n", "------------------------------------------------------------------------------\n" ] }, @@ -2047,7 +2080,7 @@ } ], "source": [ - "(cat:2cmbn-sbtr (cat:cmpr ccn) comb1 (cat:? identity? comb1))" + "(? identity? comb1)" ] }, { @@ -2060,7 +2093,9 @@ { "data": { "text/plain": [ - "[K10 Morphism (degree 2): K5 -> K5]" + "\n", + "----------------------------------------------------------------------{CMBN 1}\n", + "------------------------------------------------------------------------------\n" ] }, "execution_count": 73, @@ -2069,7 +2104,7 @@ } ], "source": [ - "(cat:def upper-shift2 (cat:cmps upper-shift upper-shift))" + "(2cmbn-sbtr (cmpr ccn) comb1 *)" ] }, { @@ -2082,7 +2117,7 @@ { "data": { "text/plain": [ - "2" + "[K10 Morphism (degree 2): K5 -> K5]" ] }, "execution_count": 74, @@ -2091,7 +2126,7 @@ } ], "source": [ - "(cat:degr upper-shift2)" + "(def upper-shift2 (cmps upper-shift upper-shift))" ] }, { @@ -2100,6 +2135,28 @@ "metadata": { "collapsed": false }, + "outputs": [ + { + "data": { + "text/plain": [ + "2" + ] + }, + "execution_count": 75, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "(degr upper-shift2)" + ] + }, + { + "cell_type": "code", + "execution_count": 76, + "metadata": { + "collapsed": false + }, "outputs": [ { "data": { @@ -2113,35 +2170,13 @@ "------------------------------------------------------------------------------\n" ] }, - "execution_count": 75, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "(cat:? upper-shift2 comb1)" - ] - }, - { - "cell_type": "code", - "execution_count": 76, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "data": { - "text/plain": [ - "[K11 Morphism (degree 1): K5 -> K5]" - ] - }, "execution_count": 76, "metadata": {}, "output_type": "execute_result" } ], "source": [ - "(cat:def twice-up-shift (cat:add upper-shift upper-shift))" + "(? upper-shift2 comb1)" ] }, { @@ -2154,7 +2189,7 @@ { "data": { "text/plain": [ - "1" + "[K11 Morphism (degree 1): K5 -> K5]" ] }, "execution_count": 77, @@ -2163,7 +2198,7 @@ } ], "source": [ - "(cat:degr twice-up-shift)" + "(def twice-up-shift (add upper-shift upper-shift))" ] }, { @@ -2172,6 +2207,28 @@ "metadata": { "collapsed": false }, + "outputs": [ + { + "data": { + "text/plain": [ + "1" + ] + }, + "execution_count": 78, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "(degr twice-up-shift)" + ] + }, + { + "cell_type": "code", + "execution_count": 79, + "metadata": { + "collapsed": false + }, "outputs": [ { "data": { @@ -2185,35 +2242,13 @@ "------------------------------------------------------------------------------\n" ] }, - "execution_count": 78, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "(cat:? twice-up-shift comb1)" - ] - }, - { - "cell_type": "code", - "execution_count": 79, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "data": { - "text/plain": [ - "[K12 Morphism (degree 0): K5 -> K5]" - ] - }, "execution_count": 79, "metadata": {}, "output_type": "execute_result" } ], "source": [ - "(cat:def up-d (cat:cmps upper-shift (cat:dffr1 ccn)))" + "(? twice-up-shift comb1)" ] }, { @@ -2226,7 +2261,7 @@ { "data": { "text/plain": [ - "[K13 Morphism (degree 0): K5 -> K5]" + "[K12 Morphism (degree 0): K5 -> K5]" ] }, "execution_count": 80, @@ -2235,7 +2270,7 @@ } ], "source": [ - "(cat:def d-up (cat:cmps (cat:dffr1 ccn) upper-shift))" + "(def up-d (cmps upper-shift (dffr1 ccn)))" ] }, { @@ -2248,10 +2283,7 @@ { "data": { "text/plain": [ - "\n", - "----------------------------------------------------------------------{CMBN 1}\n", - "<1 * 11>\n", - "------------------------------------------------------------------------------\n" + "[K13 Morphism (degree 0): K5 -> K5]" ] }, "execution_count": 81, @@ -2260,7 +2292,7 @@ } ], "source": [ - "(cat:? up-d 1 11)" + "(def d-up (cmps (dffr1 ccn) upper-shift))" ] }, { @@ -2275,6 +2307,7 @@ "text/plain": [ "\n", "----------------------------------------------------------------------{CMBN 1}\n", + "<1 * 11>\n", "------------------------------------------------------------------------------\n" ] }, @@ -2284,7 +2317,7 @@ } ], "source": [ - "(cat:? d-up 1 11)" + "(? up-d 1 11)" ] }, { @@ -2299,12 +2332,6 @@ "text/plain": [ "\n", "----------------------------------------------------------------------{CMBN 1}\n", - "<1 * 10>\n", - "<2 * 11>\n", - "<3 * 12>\n", - "<4 * 13>\n", - "<5 * 14>\n", - "<6 * 15>\n", "------------------------------------------------------------------------------\n" ] }, @@ -2314,7 +2341,7 @@ } ], "source": [ - "(cat:def comb3 (cat:cmbn 1 1 10 2 11 3 12 4 13 5 14 6 15))" + "(? d-up 1 11)" ] }, { @@ -2329,8 +2356,11 @@ "text/plain": [ "\n", "----------------------------------------------------------------------{CMBN 1}\n", + "<1 * 10>\n", "<2 * 11>\n", + "<3 * 12>\n", "<4 * 13>\n", + "<5 * 14>\n", "<6 * 15>\n", "------------------------------------------------------------------------------\n" ] @@ -2341,7 +2371,7 @@ } ], "source": [ - "(cat:? up-d comb3)" + "(def comb3 (cmbn 1 1 10 2 11 3 12 4 13 5 14 6 15))" ] }, { @@ -2350,6 +2380,33 @@ "metadata": { "collapsed": false }, + "outputs": [ + { + "data": { + "text/plain": [ + "\n", + "----------------------------------------------------------------------{CMBN 1}\n", + "<2 * 11>\n", + "<4 * 13>\n", + "<6 * 15>\n", + "------------------------------------------------------------------------------\n" + ] + }, + "execution_count": 85, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "(? up-d comb3)" + ] + }, + { + "cell_type": "code", + "execution_count": 86, + "metadata": { + "collapsed": false + }, "outputs": [ { "data": { @@ -2362,13 +2419,13 @@ "------------------------------------------------------------------------------\n" ] }, - "execution_count": 85, + "execution_count": 86, "metadata": {}, "output_type": "execute_result" } ], "source": [ - "(cat:? d-up comb3)" + "(? d-up comb3)" ] }, { @@ -2380,7 +2437,7 @@ }, { "cell_type": "code", - "execution_count": 86, + "execution_count": 87, "metadata": { "collapsed": false }, @@ -2391,18 +2448,18 @@ "[K1 Chain-Complex]" ] }, - "execution_count": 86, + "execution_count": 87, "metadata": {}, "output_type": "execute_result" } ], "source": [ - "(cat:k 1)" + "(k 1)" ] }, { "cell_type": "code", - "execution_count": 87, + "execution_count": 88, "metadata": { "collapsed": false }, @@ -2423,18 +2480,18 @@ "NIL" ] }, - "execution_count": 87, + "execution_count": 88, "metadata": {}, "output_type": "execute_result" } ], "source": [ - "(cat:kd 1)" + "(kd 1)" ] }, { "cell_type": "code", - "execution_count": 88, + "execution_count": 89, "metadata": { "collapsed": false }, @@ -2445,18 +2502,18 @@ "[K3 Cohomology-Class on K1 of degree 1]" ] }, - "execution_count": 88, + "execution_count": 89, "metadata": {}, "output_type": "execute_result" } ], "source": [ - "(cat:k 3)" + "(k 3)" ] }, { "cell_type": "code", - "execution_count": 89, + "execution_count": 90, "metadata": { "collapsed": false }, @@ -2477,18 +2534,18 @@ "NIL" ] }, - "execution_count": 89, + "execution_count": 90, "metadata": {}, "output_type": "execute_result" } ], "source": [ - "(cat:kd 3)" + "(kd 3)" ] }, { "cell_type": "code", - "execution_count": 90, + "execution_count": 91, "metadata": { "collapsed": false }, @@ -2509,18 +2566,18 @@ "NIL" ] }, - "execution_count": 90, + "execution_count": 91, "metadata": {}, "output_type": "execute_result" } ], "source": [ - "(cat:kd 8)" + "(kd 8)" ] }, { "cell_type": "code", - "execution_count": 91, + "execution_count": 92, "metadata": { "collapsed": false }, @@ -2541,18 +2598,18 @@ "NIL" ] }, - "execution_count": 91, + "execution_count": 92, "metadata": {}, "output_type": "execute_result" } ], "source": [ - "(cat:kd 5)" + "(kd 5)" ] }, { "cell_type": "code", - "execution_count": 92, + "execution_count": 93, "metadata": { "collapsed": false }, @@ -2573,18 +2630,18 @@ "NIL" ] }, - "execution_count": 92, + "execution_count": 93, "metadata": {}, "output_type": "execute_result" } ], "source": [ - "(cat:kd 9)" + "(kd 9)" ] }, { "cell_type": "code", - "execution_count": 93, + "execution_count": 94, "metadata": { "collapsed": false }, @@ -2613,13 +2670,13 @@ "(9 8 7)" ] }, - "execution_count": 93, + "execution_count": 94, "metadata": {}, "output_type": "execute_result" } ], "source": [ - "(cat:kd2 9)" + "(kd2 9)" ] } ], diff --git a/examples/Overview.ipynb b/examples/Overview.ipynb index 1f7f575..90a3c25 100644 --- a/examples/Overview.ipynb +++ b/examples/Overview.ipynb @@ -22,34 +22,11 @@ }, { "cell_type": "code", - "execution_count": 1, + "execution_count": null, "metadata": { "collapsed": false }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "To load \"kenzo\":\n", - " Load 1 ASDF system:\n", - " kenzo\n", - "\n", - "; Loading \"kenzo\"\n", - "\n" - ] - }, - { - "data": { - "text/plain": [ - "(\"kenzo\")" - ] - }, - "execution_count": 1, - "metadata": {}, - "output_type": "execute_result" - } - ], + "outputs": [], "source": [ "(ql:quickload \"kenzo\")" ] @@ -63,32 +40,24 @@ }, { "cell_type": "code", - "execution_count": 2, + "execution_count": null, "metadata": { "collapsed": false }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "\n", - "---done---" - ] - }, - { - "data": { - "text/plain": [ - "NIL" - ] - }, - "execution_count": 2, - "metadata": {}, - "output_type": "execute_result" - } - ], + "outputs": [], "source": [ - "(cat:cat-init)" + "(in-package \"CAT\")" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "(cat-init)" ] }, { @@ -100,33 +69,13 @@ }, { "cell_type": "code", - "execution_count": 3, + "execution_count": null, "metadata": { "collapsed": false }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "\n", - "*** Kenzo-Version 1.1.7 ***\n", - "\n" - ] - }, - { - "data": { - "text/plain": [ - "NIL" - ] - }, - "execution_count": 3, - "metadata": {}, - "output_type": "execute_result" - } - ], + "outputs": [], "source": [ - "(cat:kenzo-version)" + "(kenzo-version)" ] }, { @@ -140,24 +89,13 @@ }, { "cell_type": "code", - "execution_count": 4, + "execution_count": null, "metadata": { "collapsed": false }, - "outputs": [ - { - "data": { - "text/plain": [ - "[K1 Simplicial-Set]" - ] - }, - "execution_count": 4, - "metadata": {}, - "output_type": "execute_result" - } - ], + "outputs": [], "source": [ - "(cat:def m23 (cat:moore 2 3))" + "(def m23 (moore 2 3))" ] }, { @@ -169,22 +107,11 @@ }, { "cell_type": "code", - "execution_count": 5, + "execution_count": null, "metadata": { "collapsed": false }, - "outputs": [ - { - "data": { - "text/plain": [ - "[K1 Simplicial-Set]" - ] - }, - "execution_count": 5, - "metadata": {}, - "output_type": "execute_result" - } - ], + "outputs": [], "source": [ "m23" ] @@ -198,159 +125,13 @@ }, { "cell_type": "code", - "execution_count": 6, + "execution_count": null, "metadata": { "collapsed": false }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "\n", - "Computing boundary-matrix in dimension 0.\n", - "Rank of the source-module : 1.\n", - "\n", - "\n", - ";; Clock -> 2015-12-29, 1h 11m 1s.\n", - "Computing the boundary of the generator 1/1 (dimension 0) :\n", - "* \n", - "End of computing.\n", - "\n", - "\n", - "Computing boundary-matrix in dimension 1.\n", - "Rank of the source-module : 0.\n", - "\n", - "\n", - "\n", - "\n", - "Homology in dimension 0 :\n", - "\n", - "\n", - "Component Z\n", - "\n", - "\n", - "---done---\n", - "\n", - ";; Clock -> 2015-12-29, 1h 11m 1s.\n", - "\n", - "\n", - "Computing boundary-matrix in dimension 1.\n", - "Rank of the source-module : 0.\n", - "\n", - "\n", - "Computing boundary-matrix in dimension 2.\n", - "Rank of the source-module : 0.\n", - "\n", - "\n", - "\n", - "\n", - "Homology in dimension 1 :\n", - "\n", - "\n", - "\n", - "---done---\n", - "\n", - ";; Clock -> 2015-12-29, 1h 11m 1s.\n", - "\n", - "\n", - "Computing boundary-matrix in dimension 2.\n", - "Rank of the source-module : 0.\n", - "\n", - "\n", - "Computing boundary-matrix in dimension 3.\n", - "Rank of the source-module : 1.\n", - "\n", - "\n", - ";; Clock -> 2015-12-29, 1h 11m 1s.\n", - "Computing the boundary of the generator 1/1 (dimension 3) :\n", - "M3 \n", - "End of computing.\n", - "\n", - "\n", - "\n", - "\n", - "Homology in dimension 2 :\n", - "\n", - "\n", - "\n", - "---done---\n", - "\n", - ";; Clock -> 2015-12-29, 1h 11m 1s.\n", - "\n", - "\n", - "Computing boundary-matrix in dimension 3.\n", - "Rank of the source-module : 1.\n", - "\n", - "\n", - ";; Clock -> 2015-12-29, 1h 11m 1s.\n", - "Computing the boundary of the generator 1/1 (dimension 3) :\n", - "M3 \n", - "End of computing.\n", - "\n", - "\n", - "Computing boundary-matrix in dimension 4.\n", - "Rank of the source-module : 1.\n", - "\n", - "\n", - ";; Clock -> 2015-12-29, 1h 11m 1s.\n", - "Computing the boundary of the generator 1/1 (dimension 4) :\n", - "N4 \n", - "End of computing.\n", - "\n", - "\n", - "\n", - "\n", - "Homology in dimension 3 :\n", - "\n", - "\n", - "Component Z/2Z\n", - "\n", - "\n", - "---done---\n", - "\n", - ";; Clock -> 2015-12-29, 1h 11m 1s.\n", - "\n", - "\n", - "Computing boundary-matrix in dimension 4.\n", - "Rank of the source-module : 1.\n", - "\n", - "\n", - ";; Clock -> 2015-12-29, 1h 11m 1s.\n", - "Computing the boundary of the generator 1/1 (dimension 4) :\n", - "N4 \n", - "End of computing.\n", - "\n", - "\n", - "Computing boundary-matrix in dimension 5.\n", - "Rank of the source-module : 0.\n", - "\n", - "\n", - "\n", - "\n", - "Homology in dimension 4 :\n", - "\n", - "\n", - "\n", - "---done---\n", - "\n", - ";; Clock -> 2015-12-29, 1h 11m 1s.\n", - "\n" - ] - }, - { - "data": { - "text/plain": [ - "NIL" - ] - }, - "execution_count": 6, - "metadata": {}, - "output_type": "execute_result" - } - ], + "outputs": [], "source": [ - "(cat:homology m23 0 5)" + "(homology m23 0 5)" ] }, { @@ -362,24 +143,13 @@ }, { "cell_type": "code", - "execution_count": 7, + "execution_count": null, "metadata": { "collapsed": false }, - "outputs": [ - { - "data": { - "text/plain": [ - "[K10 Simplicial-Set]" - ] - }, - "execution_count": 7, - "metadata": {}, - "output_type": "execute_result" - } - ], + "outputs": [], "source": [ - "(cat:def m23xm23 (cat:crts-prdc m23 m23))" + "(def m23xm23 (crts-prdc m23 m23))" ] }, { @@ -391,46 +161,24 @@ }, { "cell_type": "code", - "execution_count": 8, + "execution_count": null, "metadata": { "collapsed": false }, - "outputs": [ - { - "data": { - "text/plain": [ - "( ...)" - ] - }, - "execution_count": 8, - "metadata": {}, - "output_type": "execute_result" - } - ], + "outputs": [], "source": [ - "(cat:basis m23xm23 6)" + "(basis m23xm23 6)" ] }, { "cell_type": "code", - "execution_count": 9, + "execution_count": null, "metadata": { "collapsed": false }, - "outputs": [ - { - "data": { - "text/plain": [ - "230" - ] - }, - "execution_count": 9, - "metadata": {}, - "output_type": "execute_result" - } - ], + "outputs": [], "source": [ - "(length (cat:basis m23xm23 6))" + "(length *)" ] }, { @@ -444,46 +192,24 @@ }, { "cell_type": "code", - "execution_count": 10, + "execution_count": null, "metadata": { "collapsed": false }, - "outputs": [ - { - "data": { - "text/plain": [ - "[K3 Chain-Complex]" - ] - }, - "execution_count": 10, - "metadata": {}, - "output_type": "execute_result" - } - ], + "outputs": [], "source": [ - "(cat:def t2m23 (cat:tnsr-prdc m23 m23))" + "(def t2m23 (tnsr-prdc m23 m23))" ] }, { "cell_type": "code", - "execution_count": 11, + "execution_count": null, "metadata": { "collapsed": false }, - "outputs": [ - { - "data": { - "text/plain": [ - "()" - ] - }, - "execution_count": 11, - "metadata": {}, - "output_type": "execute_result" - } - ], + "outputs": [], "source": [ - "(cat:basis t2m23 6)" + "(basis t2m23 6)" ] }, { @@ -495,288 +221,13 @@ }, { "cell_type": "code", - "execution_count": 12, + "execution_count": null, "metadata": { "collapsed": false }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "\n", - "Computing boundary-matrix in dimension 0.\n", - "Rank of the source-module : 1.\n", - "\n", - "\n", - ";; Clock -> 2015-12-29, 1h 11m 1s.\n", - "Computing the boundary of the generator 1/1 (dimension 0) :\n", - " \n", - "End of computing.\n", - "\n", - "\n", - "Computing boundary-matrix in dimension 1.\n", - "Rank of the source-module : 0.\n", - "\n", - "\n", - "\n", - "\n", - "Homology in dimension 0 :\n", - "\n", - "\n", - "Component Z\n", - "\n", - "\n", - "---done---\n", - "\n", - ";; Clock -> 2015-12-29, 1h 11m 1s.\n", - "\n", - "\n", - "Computing boundary-matrix in dimension 1.\n", - "Rank of the source-module : 0.\n", - "\n", - "\n", - "Computing boundary-matrix in dimension 2.\n", - "Rank of the source-module : 0.\n", - "\n", - "\n", - "\n", - "\n", - "Homology in dimension 1 :\n", - "\n", - "\n", - "\n", - "---done---\n", - "\n", - ";; Clock -> 2015-12-29, 1h 11m 1s.\n", - "\n", - "\n", - "Computing boundary-matrix in dimension 2.\n", - "Rank of the source-module : 0.\n", - "\n", - "\n", - "Computing boundary-matrix in dimension 3.\n", - "Rank of the source-module : 2.\n", - "\n", - "\n", - ";; Clock -> 2015-12-29, 1h 11m 1s.\n", - "Computing the boundary of the generator 1/2 (dimension 3) :\n", - " \n", - "End of computing.\n", - "\n", - "\n", - ";; Clock -> 2015-12-29, 1h 11m 1s.\n", - "Computing the boundary of the generator 2/2 (dimension 3) :\n", - " \n", - "End of computing.\n", - "\n", - "\n", - "\n", - "\n", - "Homology in dimension 2 :\n", - "\n", - "\n", - "\n", - "---done---\n", - "\n", - ";; Clock -> 2015-12-29, 1h 11m 1s.\n", - "\n", - "\n", - "Computing boundary-matrix in dimension 3.\n", - "Rank of the source-module : 2.\n", - "\n", - "\n", - ";; Clock -> 2015-12-29, 1h 11m 1s.\n", - "Computing the boundary of the generator 1/2 (dimension 3) :\n", - " \n", - "End of computing.\n", - "\n", - "\n", - ";; Clock -> 2015-12-29, 1h 11m 1s.\n", - "Computing the boundary of the generator 2/2 (dimension 3) :\n", - " \n", - "End of computing.\n", - "\n", - "\n", - "Computing boundary-matrix in dimension 4.\n", - "Rank of the source-module : 2.\n", - "\n", - "\n", - ";; Clock -> 2015-12-29, 1h 11m 1s.\n", - "Computing the boundary of the generator 1/2 (dimension 4) :\n", - " \n", - "End of computing.\n", - "\n", - "\n", - ";; Clock -> 2015-12-29, 1h 11m 1s.\n", - "Computing the boundary of the generator 2/2 (dimension 4) :\n", - " \n", - "End of computing.\n", - "\n", - "\n", - "\n", - "\n", - "Homology in dimension 3 :\n", - "\n", - "\n", - "Component Z/2Z\n", - "\n", - "Component Z/2Z\n", - "\n", - "\n", - "---done---\n", - "\n", - ";; Clock -> 2015-12-29, 1h 11m 1s.\n", - "\n", - "\n", - "Computing boundary-matrix in dimension 4.\n", - "Rank of the source-module : 2.\n", - "\n", - "\n", - ";; Clock -> 2015-12-29, 1h 11m 1s.\n", - "Computing the boundary of the generator 1/2 (dimension 4) :\n", - " \n", - "End of computing.\n", - "\n", - "\n", - ";; Clock -> 2015-12-29, 1h 11m 1s.\n", - "Computing the boundary of the generator 2/2 (dimension 4) :\n", - " \n", - "End of computing.\n", - "\n", - "\n", - "Computing boundary-matrix in dimension 5.\n", - "Rank of the source-module : 0.\n", - "\n", - "\n", - "\n", - "\n", - "Homology in dimension 4 :\n", - "\n", - "\n", - "\n", - "---done---\n", - "\n", - ";; Clock -> 2015-12-29, 1h 11m 1s.\n", - "\n", - "\n", - "Computing boundary-matrix in dimension 5.\n", - "Rank of the source-module : 0.\n", - "\n", - "\n", - "Computing boundary-matrix in dimension 6.\n", - "Rank of the source-module : 1.\n", - "\n", - "\n", - ";; Clock -> 2015-12-29, 1h 11m 1s.\n", - "Computing the boundary of the generator 1/1 (dimension 6) :\n", - " \n", - "End of computing.\n", - "\n", - "\n", - "\n", - "\n", - "Homology in dimension 5 :\n", - "\n", - "\n", - "\n", - "---done---\n", - "\n", - ";; Clock -> 2015-12-29, 1h 11m 1s.\n", - "\n", - "\n", - "Computing boundary-matrix in dimension 6.\n", - "Rank of the source-module : 1.\n", - "\n", - "\n", - ";; Clock -> 2015-12-29, 1h 11m 1s.\n", - "Computing the boundary of the generator 1/1 (dimension 6) :\n", - " \n", - "End of computing.\n", - "\n", - "\n", - "Computing boundary-matrix in dimension 7.\n", - "Rank of the source-module : 2.\n", - "\n", - "\n", - ";; Clock -> 2015-12-29, 1h 11m 1s.\n", - "Computing the boundary of the generator 1/2 (dimension 7) :\n", - " \n", - "End of computing.\n", - "\n", - "\n", - ";; Clock -> 2015-12-29, 1h 11m 1s.\n", - "Computing the boundary of the generator 2/2 (dimension 7) :\n", - " \n", - "End of computing.\n", - "\n", - "\n", - "\n", - "\n", - "Homology in dimension 6 :\n", - "\n", - "\n", - "Component Z/2Z\n", - "\n", - "\n", - "---done---\n", - "\n", - ";; Clock -> 2015-12-29, 1h 11m 1s.\n", - "\n", - "\n", - "Computing boundary-matrix in dimension 7.\n", - "Rank of the source-module : 2.\n", - "\n", - "\n", - ";; Clock -> 2015-12-29, 1h 11m 1s.\n", - "Computing the boundary of the generator 1/2 (dimension 7) :\n", - " \n", - "End of computing.\n", - "\n", - "\n", - ";; Clock -> 2015-12-29, 1h 11m 1s.\n", - "Computing the boundary of the generator 2/2 (dimension 7) :\n", - " \n", - "End of computing.\n", - "\n", - "\n", - "Computing boundary-matrix in dimension 8.\n", - "Rank of the source-module : 1.\n", - "\n", - "\n", - ";; Clock -> 2015-12-29, 1h 11m 1s.\n", - "Computing the boundary of the generator 1/1 (dimension 8) :\n", - " \n", - "End of computing.\n", - "\n", - "\n", - "\n", - "\n", - "Homology in dimension 7 :\n", - "\n", - "\n", - "Component Z/2Z\n", - "\n", - "\n", - "---done---\n", - "\n", - ";; Clock -> 2015-12-29, 1h 11m 1s.\n", - "\n" - ] - }, - { - "data": { - "text/plain": [ - "NIL" - ] - }, - "execution_count": 12, - "metadata": {}, - "output_type": "execute_result" - } - ], + "outputs": [], "source": [ - "(cat:homology m23xm23 0 8)" + "(homology m23xm23 0 8)" ] }, { @@ -790,24 +241,13 @@ }, { "cell_type": "code", - "execution_count": 13, + "execution_count": null, "metadata": { "collapsed": false }, - "outputs": [ - { - "data": { - "text/plain": [ - "[K38 Abelian-Simplicial-Group]" - ] - }, - "execution_count": 13, - "metadata": {}, - "output_type": "execute_result" - } - ], + "outputs": [], "source": [ - "(cat:def kz1 (cat:k-z 1))" + "(def kz1 (k-z 1))" ] }, { @@ -820,66 +260,24 @@ }, { "cell_type": "code", - "execution_count": 14, + "execution_count": null, "metadata": { "collapsed": false }, - "outputs": [ - { - "data": { - "text/plain": [ - "\n", - "----------------------------------------------------------------------{CMBN 4}\n", - "<1 * >\n", - "<1 * >\n", - "<1 * >\n", - "<1 * >\n", - "<1 * >\n", - "------------------------------------------------------------------------------\n" - ] - }, - "execution_count": 14, - "metadata": {}, - "output_type": "execute_result" - } - ], + "outputs": [], "source": [ - "(cat:cprd kz1 4 '(2 3 4 5))" + "(cprd kz1 4 '(2 3 4 5))" ] }, { "cell_type": "code", - "execution_count": 15, + "execution_count": null, "metadata": { "collapsed": false }, - "outputs": [ - { - "data": { - "text/plain": [ - "\n", - "----------------------------------------------------------------------{CMBN 6}\n", - "<1 * (1 2 3 4 5 6)>\n", - "<-1 * (1 3 2 4 5 6)>\n", - "<1 * (1 3 4 2 5 6)>\n", - "<-1 * (1 3 4 5 2 6)>\n", - "<1 * (1 3 4 5 6 2)>\n", - "<1 * (3 1 2 4 5 6)>\n", - "<-1 * (3 1 4 2 5 6)>\n", - "<1 * (3 1 4 5 2 6)>\n", - "<-1 * (3 1 4 5 6 2)>\n", - "<1 * (3 4 1 2 5 6)>\n", - "... ...\n", - "------------------------------------------------------------------------------\n" - ] - }, - "execution_count": 15, - "metadata": {}, - "output_type": "execute_result" - } - ], + "outputs": [], "source": [ - "(cat:aprd kz1 6 (cat:tnpr 2 '(1 2) 4 '(3 4 5 6)))" + "(aprd kz1 6 (tnpr 2 '(1 2) 4 '(3 4 5 6)))" ] }, { @@ -893,103 +291,24 @@ }, { "cell_type": "code", - "execution_count": 16, + "execution_count": null, "metadata": { "collapsed": false }, - "outputs": [ - { - "data": { - "text/plain": [ - "[K64 Abelian-Simplicial-Group]" - ] - }, - "execution_count": 16, - "metadata": {}, - "output_type": "execute_result" - } - ], + "outputs": [], "source": [ - "(cat:def k-z2-2 (cat:k-z2 2))" + "(def k-z2-2 (k-z2 2))" ] }, { "cell_type": "code", - "execution_count": 17, + "execution_count": null, "metadata": { "collapsed": false }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "\n", - "Computing boundary-matrix in dimension 4.\n", - "Rank of the source-module : 2.\n", - "\n", - "\n", - ";; Clock -> 2015-12-29, 1h 11m 1s.\n", - "Computing the boundary of the generator 1/2 (dimension 4) :\n", - "<> \n", - "End of computing.\n", - "\n", - "\n", - ";; Clock -> 2015-12-29, 1h 11m 1s.\n", - "Computing the boundary of the generator 2/2 (dimension 4) :\n", - "<> \n", - "End of computing.\n", - "\n", - "\n", - "Computing boundary-matrix in dimension 5.\n", - "Rank of the source-module : 3.\n", - "\n", - "\n", - ";; Clock -> 2015-12-29, 1h 11m 1s.\n", - "Computing the boundary of the generator 1/3 (dimension 5) :\n", - "<> \n", - "End of computing.\n", - "\n", - "\n", - ";; Clock -> 2015-12-29, 1h 11m 1s.\n", - "Computing the boundary of the generator 2/3 (dimension 5) :\n", - "<> \n", - "End of computing.\n", - "\n", - "\n", - ";; Clock -> 2015-12-29, 1h 11m 1s.\n", - "Computing the boundary of the generator 3/3 (dimension 5) :\n", - "<> \n", - "End of computing.\n", - "\n", - "\n", - "\n", - "\n", - "Homology in dimension 4 :\n", - "\n", - "\n", - "Component Z/4Z\n", - "\n", - "\n", - "---done---\n", - "\n", - ";; Clock -> 2015-12-29, 1h 11m 1s.\n", - "\n" - ] - }, - { - "data": { - "text/plain": [ - "NIL" - ] - }, - "execution_count": 17, - "metadata": {}, - "output_type": "execute_result" - } - ], + "outputs": [], "source": [ - "(cat:homology k-z2-2 4)" + "(homology k-z2-2 4)" ] }, { @@ -1002,246 +321,35 @@ }, { "cell_type": "code", - "execution_count": 18, + "execution_count": null, "metadata": { "collapsed": false }, - "outputs": [ - { - "data": { - "text/plain": [ - "[K174 Simplicial-Set]" - ] - }, - "execution_count": 18, - "metadata": {}, - "output_type": "execute_result" - } - ], + "outputs": [], "source": [ - "(cat:def s3 (cat:sphere 3))" + "(def s3 (sphere 3))" ] }, { "cell_type": "code", - "execution_count": 19, + "execution_count": null, "metadata": { "collapsed": false }, - "outputs": [ - { - "data": { - "text/plain": [ - "[K191 Simplicial-Group]" - ] - }, - "execution_count": 19, - "metadata": {}, - "output_type": "execute_result" - } - ], + "outputs": [], "source": [ - "(cat:def o2s3 (cat:loop-space s3 2))" + "(def o2s3 (loop-space s3 2))" ] }, { "cell_type": "code", - "execution_count": 20, + "execution_count": null, "metadata": { "collapsed": false }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "\n", - "Computing boundary-matrix in dimension 4.\n", - "Rank of the source-module : 3.\n", - "\n", - "\n", - ";; Clock -> 2015-12-29, 1h 11m 1s.\n", - "Computing the boundary of the generator 1/3 (dimension 4) :\n", - "<>][3 <>]>> \n", - "End of computing.\n", - "\n", - "\n", - ";; Clock -> 2015-12-29, 1h 11m 1s.\n", - "Computing the boundary of the generator 2/3 (dimension 4) :\n", - "<>][1 <>]>> \n", - "End of computing.\n", - "\n", - "\n", - ";; Clock -> 2015-12-29, 1h 11m 1s.\n", - "Computing the boundary of the generator 3/3 (dimension 4) :\n", - "<>][1 <>][1 <>][1 <>]>> \n", - "End of computing.\n", - "\n", - "\n", - "Computing boundary-matrix in dimension 5.\n", - "Rank of the source-module : 5.\n", - "\n", - "\n", - ";; Clock -> 2015-12-29, 1h 11m 1s.\n", - "Computing the boundary of the generator 1/5 (dimension 5) :\n", - "<>]>> \n", - "End of computing.\n", - "\n", - "\n", - ";; Clock -> 2015-12-29, 1h 11m 1s.\n", - "Computing the boundary of the generator 2/5 (dimension 5) :\n", - "<>][1 <>][3 <>]>> \n", - "End of computing.\n", - "\n", - "\n", - ";; Clock -> 2015-12-29, 1h 11m 1s.\n", - "Computing the boundary of the generator 3/5 (dimension 5) :\n", - "<>][3 <>][1 <>]>> \n", - "End of computing.\n", - "\n", - "\n", - ";; Clock -> 2015-12-29, 1h 11m 1s.\n", - "Computing the boundary of the generator 4/5 (dimension 5) :\n", - "<>][1 <>][1 <>]>> \n", - "End of computing.\n", - "\n", - "\n", - ";; Clock -> 2015-12-29, 1h 11m 1s.\n", - "Computing the boundary of the generator 5/5 (dimension 5) :\n", - "<>][1 <>][1 <>][1 <>][1 <>]>> \n", - "End of computing.\n", - "\n", - "\n", - "\n", - "\n", - "Homology in dimension 4 :\n", - "\n", - "\n", - "Component Z/3Z\n", - "\n", - "Component Z/2Z\n", - "\n", - "\n", - "---done---\n", - "\n", - ";; Clock -> 2015-12-29, 1h 11m 1s.\n", - "\n", - "\n", - "Computing boundary-matrix in dimension 5.\n", - "Rank of the source-module : 5.\n", - "\n", - "\n", - ";; Clock -> 2015-12-29, 1h 11m 1s.\n", - "Computing the boundary of the generator 1/5 (dimension 5) :\n", - "<>]>> \n", - "End of computing.\n", - "\n", - "\n", - ";; Clock -> 2015-12-29, 1h 11m 1s.\n", - "Computing the boundary of the generator 2/5 (dimension 5) :\n", - "<>][1 <>][3 <>]>> \n", - "End of computing.\n", - "\n", - "\n", - ";; Clock -> 2015-12-29, 1h 11m 1s.\n", - "Computing the boundary of the generator 3/5 (dimension 5) :\n", - "<>][3 <>][1 <>]>> \n", - "End of computing.\n", - "\n", - "\n", - ";; Clock -> 2015-12-29, 1h 11m 1s.\n", - "Computing the boundary of the generator 4/5 (dimension 5) :\n", - "<>][1 <>][1 <>]>> \n", - "End of computing.\n", - "\n", - "\n", - ";; Clock -> 2015-12-29, 1h 11m 1s.\n", - "Computing the boundary of the generator 5/5 (dimension 5) :\n", - "<>][1 <>][1 <>][1 <>][1 <>]>> \n", - "End of computing.\n", - "\n", - "\n", - "Computing boundary-matrix in dimension 6.\n", - "Rank of the source-module : 8.\n", - "\n", - "\n", - ";; Clock -> 2015-12-29, 1h 11m 1s.\n", - "Computing the boundary of the generator 1/8 (dimension 6) :\n", - "<>][5 <>]>> \n", - "End of computing.\n", - "\n", - "\n", - ";; Clock -> 2015-12-29, 1h 11m 1s.\n", - "Computing the boundary of the generator 2/8 (dimension 6) :\n", - "<>][3 <>]>> \n", - "End of computing.\n", - "\n", - "\n", - ";; Clock -> 2015-12-29, 1h 11m 1s.\n", - "Computing the boundary of the generator 3/8 (dimension 6) :\n", - "<>][1 <>]>> \n", - "End of computing.\n", - "\n", - "\n", - ";; Clock -> 2015-12-29, 1h 11m 1s.\n", - "Computing the boundary of the generator 4/8 (dimension 6) :\n", - "<>][1 <>][1 <>][3 <>]>> \n", - "End of computing.\n", - "\n", - "\n", - ";; Clock -> 2015-12-29, 1h 11m 1s.\n", - "Computing the boundary of the generator 5/8 (dimension 6) :\n", - "<>][1 <>][3 <>][1 <>]>> \n", - "End of computing.\n", - "\n", - "\n", - ";; Clock -> 2015-12-29, 1h 11m 1s.\n", - "Computing the boundary of the generator 6/8 (dimension 6) :\n", - "<>][3 <>][1 <>][1 <>]>> \n", - "End of computing.\n", - "\n", - "\n", - ";; Clock -> 2015-12-29, 1h 11m 1s.\n", - "Computing the boundary of the generator 7/8 (dimension 6) :\n", - "<>][1 <>][1 <>][1 <>]>> \n", - "End of computing.\n", - "\n", - "\n", - ";; Clock -> 2015-12-29, 1h 11m 1s.\n", - "Computing the boundary of the generator 8/8 (dimension 6) :\n", - "<>][1 <>][1 <>][1 <>][1 <>][1 <>]>> \n", - "End of computing.\n", - "\n", - "\n", - "\n", - "\n", - "Homology in dimension 5 :\n", - "\n", - "\n", - "Component Z/3Z\n", - "\n", - "Component Z/2Z\n", - "\n", - "\n", - "---done---\n", - "\n", - ";; Clock -> 2015-12-29, 1h 11m 1s.\n", - "\n" - ] - }, - { - "data": { - "text/plain": [ - "NIL" - ] - }, - "execution_count": 20, - "metadata": {}, - "output_type": "execute_result" - } - ], + "outputs": [], "source": [ - "(cat:homology o2s3 4 6)" + "(homology o2s3 4 6)" ] }, { @@ -1253,24 +361,13 @@ }, { "cell_type": "code", - "execution_count": 21, + "execution_count": null, "metadata": { "collapsed": false }, - "outputs": [ - { - "data": { - "text/plain": [ - "[K179 Simplicial-Group]" - ] - }, - "execution_count": 21, - "metadata": {}, - "output_type": "execute_result" - } - ], + "outputs": [], "source": [ - "(cat:def os3 (cat:loop-space s3))" + "(def os3 (loop-space s3))" ] }, { @@ -1282,24 +379,13 @@ }, { "cell_type": "code", - "execution_count": 22, + "execution_count": null, "metadata": { "collapsed": false }, - "outputs": [ - { - "data": { - "text/plain": [ - "<>" - ] - }, - "execution_count": 22, - "metadata": {}, - "output_type": "execute_result" - } - ], + "outputs": [], "source": [ - "(cat:def L1 (cat:loop3 0 's3 1))" + "(def L1 (loop3 0 's3 1))" ] }, { @@ -1311,24 +397,13 @@ }, { "cell_type": "code", - "execution_count": 23, + "execution_count": null, "metadata": { "collapsed": false }, - "outputs": [ - { - "data": { - "text/plain": [ - ">>" - ] - }, - "execution_count": 23, - "metadata": {}, - "output_type": "execute_result" - } - ], + "outputs": [], "source": [ - "(cat:def null-simp (cat:absm 3 cat:+null-loop+))" + "(def null-simp (absm 3 +null-loop+))" ] }, { @@ -1340,25 +415,14 @@ }, { "cell_type": "code", - "execution_count": 24, + "execution_count": null, "metadata": { "collapsed": false }, - "outputs": [ - { - "data": { - "text/plain": [ - "[K435 Simplicial-Set]" - ] - }, - "execution_count": 24, - "metadata": {}, - "output_type": "execute_result" - } - ], + "outputs": [], "source": [ - "(cat:def dos3 (cat:disk-pasting os3 3 ' \n", - " (list L1 null-simp L1 null-simp)))" + "(def dos3 (disk-pasting os3 3 '\n", + " (list L1 null-simp L1 null-simp)))" ] }, { @@ -1370,94 +434,13 @@ }, { "cell_type": "code", - "execution_count": 25, + "execution_count": null, "metadata": { "collapsed": false }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "\n", - "Computing boundary-matrix in dimension 2.\n", - "Rank of the source-module : 1.\n", - "\n", - "\n", - ";; Clock -> 2015-12-29, 1h 11m 1s.\n", - "Computing the boundary of the generator 1/1 (dimension 2) :\n", - "<> \n", - "End of computing.\n", - "\n", - "\n", - "Computing boundary-matrix in dimension 3.\n", - "Rank of the source-module : 1.\n", - "\n", - "\n", - ";; Clock -> 2015-12-29, 1h 11m 1s.\n", - "Computing the boundary of the generator 1/1 (dimension 3) :\n", - " \n", - "End of computing.\n", - "\n", - "\n", - "\n", - "\n", - "Homology in dimension 2 :\n", - "\n", - "\n", - "Component Z/2Z\n", - "\n", - "\n", - "---done---\n", - "\n", - ";; Clock -> 2015-12-29, 1h 11m 1s.\n", - "\n", - "\n", - "Computing boundary-matrix in dimension 3.\n", - "Rank of the source-module : 1.\n", - "\n", - "\n", - ";; Clock -> 2015-12-29, 1h 11m 1s.\n", - "Computing the boundary of the generator 1/1 (dimension 3) :\n", - " \n", - "End of computing.\n", - "\n", - "\n", - "Computing boundary-matrix in dimension 4.\n", - "Rank of the source-module : 1.\n", - "\n", - "\n", - ";; Clock -> 2015-12-29, 1h 11m 1s.\n", - "Computing the boundary of the generator 1/1 (dimension 4) :\n", - "<> \n", - "End of computing.\n", - "\n", - "\n", - "\n", - "\n", - "Homology in dimension 3 :\n", - "\n", - "\n", - "\n", - "---done---\n", - "\n", - ";; Clock -> 2015-12-29, 1h 11m 1s.\n", - "\n" - ] - }, - { - "data": { - "text/plain": [ - "NIL" - ] - }, - "execution_count": 25, - "metadata": {}, - "output_type": "execute_result" - } - ], + "outputs": [], "source": [ - "(cat:homology dos3 2 4)" + "(homology dos3 2 4)" ] }, { @@ -1469,325 +452,24 @@ }, { "cell_type": "code", - "execution_count": 26, + "execution_count": null, "metadata": { "collapsed": false }, - "outputs": [ - { - "data": { - "text/plain": [ - "[K453 Simplicial-Group]" - ] - }, - "execution_count": 26, - "metadata": {}, - "output_type": "execute_result" - } - ], + "outputs": [], "source": [ - "(cat:def odos3 (cat:loop-space dos3))" + "(def odos3 (loop-space dos3))" ] }, { "cell_type": "code", - "execution_count": 27, + "execution_count": null, "metadata": { "collapsed": false }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "\n", - "Computing boundary-matrix in dimension 5.\n", - "Rank of the source-module : 14.\n", - "\n", - "\n", - ";; Clock -> 2015-12-29, 1h 11m 1s.\n", - "Computing the boundary of the generator 1/14 (dimension 5) :\n", - "<>]>> \n", - "End of computing.\n", - "\n", - "\n", - ";; Clock -> 2015-12-29, 1h 11m 1s.\n", - "Computing the boundary of the generator 2/14 (dimension 5) :\n", - "<][3 <>]>> \n", - "End of computing.\n", - "\n", - "\n", - ";; Clock -> 2015-12-29, 1h 11m 1s.\n", - "Computing the boundary of the generator 3/14 (dimension 5) :\n", - "<>][2 ]>> \n", - "End of computing.\n", - "\n", - "\n", - ";; Clock -> 2015-12-29, 1h 11m 1s.\n", - "Computing the boundary of the generator 4/14 (dimension 5) :\n", - "<>][1 <>][3 <>]>> \n", - "End of computing.\n", - "\n", - "\n", - ";; Clock -> 2015-12-29, 1h 11m 1s.\n", - "Computing the boundary of the generator 5/14 (dimension 5) :\n", - "<>][2 ][2 ]>> \n", - "End of computing.\n", - "\n", - "\n", - ";; Clock -> 2015-12-29, 1h 11m 1s.\n", - "Computing the boundary of the generator 6/14 (dimension 5) :\n", - "<>][3 <>][1 <>]>> \n", - "End of computing.\n", - "\n", - "\n", - ";; Clock -> 2015-12-29, 1h 11m 1s.\n", - "Computing the boundary of the generator 7/14 (dimension 5) :\n", - "<][1 <>][2 ]>> \n", - "End of computing.\n", - "\n", - "\n", - ";; Clock -> 2015-12-29, 1h 11m 1s.\n", - "Computing the boundary of the generator 8/14 (dimension 5) :\n", - "<][2 ][1 <>]>> \n", - "End of computing.\n", - "\n", - "\n", - ";; Clock -> 2015-12-29, 1h 11m 1s.\n", - "Computing the boundary of the generator 9/14 (dimension 5) :\n", - "<>][1 <>][1 <>]>> \n", - "End of computing.\n", - "\n", - "\n", - ";; Clock -> 2015-12-29, 1h 11m 1s.\n", - "Computing the boundary of the generator 10/14 (dimension 5) :\n", - "<>][1 <>][1 <>][2 ]>> \n", - "End of computing.\n", - "\n", - "\n", - ";; Clock -> 2015-12-29, 1h 11m 1s.\n", - "Computing the boundary of the generator 11/14 (dimension 5) :\n", - "<>][1 <>][2 ][1 <>]>> \n", - "End of computing.\n", - "\n", - "\n", - ";; Clock -> 2015-12-29, 1h 11m 1s.\n", - "Computing the boundary of the generator 12/14 (dimension 5) :\n", - "<>][2 ][1 <>][1 <>]>> \n", - "End of computing.\n", - "\n", - "\n", - ";; Clock -> 2015-12-29, 1h 11m 1s.\n", - "Computing the boundary of the generator 13/14 (dimension 5) :\n", - "<][1 <>][1 <>][1 <>]>> \n", - "End of computing.\n", - "\n", - "\n", - ";; Clock -> 2015-12-29, 1h 11m 1s.\n", - "Computing the boundary of the generator 14/14 (dimension 5) :\n", - "<>][1 <>][1 <>][1 <>][1 <>]>> \n", - "End of computing.\n", - "\n", - "\n", - "Computing boundary-matrix in dimension 6.\n", - "Rank of the source-module : 26.\n", - "\n", - "\n", - ";; Clock -> 2015-12-29, 1h 11m 1s.\n", - "Computing the boundary of the generator 1/26 (dimension 6) :\n", - "<>][5 <>]>> \n", - "End of computing.\n", - "\n", - "\n", - ";; Clock -> 2015-12-29, 1h 11m 1s.\n", - "Computing the boundary of the generator 2/26 (dimension 6) :\n", - "<>][3 <>]>> \n", - "End of computing.\n", - "\n", - "\n", - ";; Clock -> 2015-12-29, 1h 11m 1s.\n", - "Computing the boundary of the generator 3/26 (dimension 6) :\n", - "<>][1 <>]>> \n", - "End of computing.\n", - "\n", - "\n", - ";; Clock -> 2015-12-29, 1h 11m 1s.\n", - "Computing the boundary of the generator 4/26 (dimension 6) :\n", - "<>][2 ][3 <>]>> \n", - "End of computing.\n", - "\n", - "\n", - ";; Clock -> 2015-12-29, 1h 11m 1s.\n", - "Computing the boundary of the generator 5/26 (dimension 6) :\n", - "<>][3 <>][2 ]>> \n", - "End of computing.\n", - "\n", - "\n", - ";; Clock -> 2015-12-29, 1h 11m 1s.\n", - "Computing the boundary of the generator 6/26 (dimension 6) :\n", - "<][1 <>][3 <>]>> \n", - "End of computing.\n", - "\n", - "\n", - ";; Clock -> 2015-12-29, 1h 11m 1s.\n", - "Computing the boundary of the generator 7/26 (dimension 6) :\n", - "<][2 ][2 ]>> \n", - "End of computing.\n", - "\n", - "\n", - ";; Clock -> 2015-12-29, 1h 11m 1s.\n", - "Computing the boundary of the generator 8/26 (dimension 6) :\n", - "<][3 <>][1 <>]>> \n", - "End of computing.\n", - "\n", - "\n", - ";; Clock -> 2015-12-29, 1h 11m 1s.\n", - "Computing the boundary of the generator 9/26 (dimension 6) :\n", - "<>][1 <>][2 ]>> \n", - "End of computing.\n", - "\n", - "\n", - ";; Clock -> 2015-12-29, 1h 11m 1s.\n", - "Computing the boundary of the generator 10/26 (dimension 6) :\n", - "<>][2 ][1 <>]>> \n", - "End of computing.\n", - "\n", - "\n", - ";; Clock -> 2015-12-29, 1h 11m 1s.\n", - "Computing the boundary of the generator 11/26 (dimension 6) :\n", - "<>][1 <>][1 <>][3 <>]>> \n", - "End of computing.\n", - "\n", - "\n", - ";; Clock -> 2015-12-29, 1h 11m 1s.\n", - "Computing the boundary of the generator 12/26 (dimension 6) :\n", - "<>][1 <>][2 ][2 ]>> \n", - "End of computing.\n", - "\n", - "\n", - ";; Clock -> 2015-12-29, 1h 11m 1s.\n", - "Computing the boundary of the generator 13/26 (dimension 6) :\n", - "<>][1 <>][3 <>][1 <>]>> \n", - "End of computing.\n", - "\n", - "\n", - ";; Clock -> 2015-12-29, 1h 11m 1s.\n", - "Computing the boundary of the generator 14/26 (dimension 6) :\n", - "<>][2 ][1 <>][2 ]>> \n", - "End of computing.\n", - "\n", - "\n", - ";; Clock -> 2015-12-29, 1h 11m 1s.\n", - "Computing the boundary of the generator 15/26 (dimension 6) :\n", - "<>][2 ][2 ][1 <>]>> \n", - "End of computing.\n", - "\n", - "\n", - ";; Clock -> 2015-12-29, 1h 11m 1s.\n", - "Computing the boundary of the generator 16/26 (dimension 6) :\n", - "<>][3 <>][1 <>][1 <>]>> \n", - "End of computing.\n", - "\n", - "\n", - ";; Clock -> 2015-12-29, 1h 11m 1s.\n", - "Computing the boundary of the generator 17/26 (dimension 6) :\n", - "<][1 <>][1 <>][2 ]>> \n", - "End of computing.\n", - "\n", - "\n", - ";; Clock -> 2015-12-29, 1h 11m 1s.\n", - "Computing the boundary of the generator 18/26 (dimension 6) :\n", - "<][1 <>][2 ][1 <>]>> \n", - "End of computing.\n", - "\n", - "\n", - ";; Clock -> 2015-12-29, 1h 11m 1s.\n", - "Computing the boundary of the generator 19/26 (dimension 6) :\n", - "<][2 ][1 <>][1 <>]>> \n", - "End of computing.\n", - "\n", - "\n", - ";; Clock -> 2015-12-29, 1h 11m 1s.\n", - "Computing the boundary of the generator 20/26 (dimension 6) :\n", - "<>][1 <>][1 <>][1 <>]>> \n", - "End of computing.\n", - "\n", - "\n", - ";; Clock -> 2015-12-29, 1h 11m 1s.\n", - "Computing the boundary of the generator 21/26 (dimension 6) :\n", - "<>][1 <>][1 <>][1 <>][2 ]>> \n", - "End of computing.\n", - "\n", - "\n", - ";; Clock -> 2015-12-29, 1h 11m 1s.\n", - "Computing the boundary of the generator 22/26 (dimension 6) :\n", - "<>][1 <>][1 <>][2 ][1 <>]>> \n", - "End of computing.\n", - "\n", - "\n", - ";; Clock -> 2015-12-29, 1h 11m 1s.\n", - "Computing the boundary of the generator 23/26 (dimension 6) :\n", - "<>][1 <>][2 ][1 <>][1 <>]>> \n", - "End of computing.\n", - "\n", - "\n", - ";; Clock -> 2015-12-29, 1h 11m 1s.\n", - "Computing the boundary of the generator 24/26 (dimension 6) :\n", - "<>][2 ][1 <>][1 <>][1 <>]>> \n", - "End of computing.\n", - "\n", - "\n", - ";; Clock -> 2015-12-29, 1h 11m 1s.\n", - "Computing the boundary of the generator 25/26 (dimension 6) :\n", - "<][1 <>][1 <>][1 <>][1 <>]>> \n", - "End of computing.\n", - "\n", - "\n", - ";; Clock -> 2015-12-29, 1h 11m 1s.\n", - "Computing the boundary of the generator 26/26 (dimension 6) :\n", - "<>][1 <>][1 <>][1 <>][1 <>][1 <>]>> \n", - "End of computing.\n", - "\n", - "\n", - "\n", - "\n", - "Homology in dimension 5 :\n", - "\n", - "\n", - "Component Z/2Z\n", - "\n", - "Component Z/2Z\n", - "\n", - "Component Z/2Z\n", - "\n", - "Component Z/2Z\n", - "\n", - "Component Z/2Z\n", - "\n", - "Component Z/2Z\n", - "\n", - "Component Z\n", - "\n", - "\n", - "---done---\n", - "\n", - ";; Clock -> 2015-12-29, 1h 11m 1s.\n", - "\n" - ] - }, - { - "data": { - "text/plain": [ - "NIL" - ] - }, - "execution_count": 27, - "metadata": {}, - "output_type": "execute_result" - } - ], + "outputs": [], "source": [ - "(cat:homology odos3 5)" + "(homology odos3 5)" ] }, { @@ -1799,90 +481,46 @@ }, { "cell_type": "code", - "execution_count": 28, + "execution_count": null, "metadata": { "collapsed": false }, - "outputs": [ - { - "data": { - "text/plain": [ - "NIL" - ] - }, - "execution_count": 28, - "metadata": {}, - "output_type": "execute_result" - } - ], + "outputs": [], "source": [ - "(typep s3 'cat:kan)" + "(typep s3 'kan)" ] }, { "cell_type": "code", - "execution_count": 29, + "execution_count": null, "metadata": { "collapsed": false }, - "outputs": [ - { - "data": { - "text/plain": [ - "T" - ] - }, - "execution_count": 29, - "metadata": {}, - "output_type": "execute_result" - } - ], + "outputs": [], "source": [ - "(typep os3 'cat:kan)" + "(typep os3 'kan)" ] }, { "cell_type": "code", - "execution_count": 30, + "execution_count": null, "metadata": { "collapsed": false }, - "outputs": [ - { - "data": { - "text/plain": [ - "T" - ] - }, - "execution_count": 30, - "metadata": {}, - "output_type": "execute_result" - } - ], + "outputs": [], "source": [ - "(typep os3 'cat:simplicial-group)" + "(typep os3 'simplicial-group)" ] }, { "cell_type": "code", - "execution_count": 31, + "execution_count": null, "metadata": { "collapsed": false }, - "outputs": [ - { - "data": { - "text/plain": [ - "NIL" - ] - }, - "execution_count": 31, - "metadata": {}, - "output_type": "execute_result" - } - ], + "outputs": [], "source": [ - "(typep os3 'cat:ab-simplicial-group)" + "(typep os3 'ab-simplicial-group)" ] }, { @@ -1894,54 +532,24 @@ }, { "cell_type": "code", - "execution_count": 32, + "execution_count": null, "metadata": { "collapsed": false }, - "outputs": [ - { - "data": { - "text/plain": [ - "<>" - ] - }, - "execution_count": 32, - "metadata": {}, - "output_type": "execute_result" - } - ], + "outputs": [], "source": [ - "(cat:def L2 (cat:loop3 0 's3 2))" + "(def L2 (loop3 0 's3 2))" ] }, { "cell_type": "code", - "execution_count": 33, + "execution_count": null, "metadata": { "collapsed": false }, - "outputs": [ - { - "data": { - "text/plain": [ - "\n", - "----------------------------------------------------------------------{CMBN 4}\n", - "<1 * <>>\n", - "<-1 * <>>\n", - "<1 * <>>\n", - "<1 * <>>\n", - "<-1 * <>>\n", - "<1 * <>>\n", - "------------------------------------------------------------------------------\n" - ] - }, - "execution_count": 33, - "metadata": {}, - "output_type": "execute_result" - } - ], + "outputs": [], "source": [ - "(cat:def square (cat:aprd os3 4 (cat:tnpr 2 L2 2 L2)))" + "(def square (aprd os3 4 (tnpr 2 L2 2 L2)))" ] }, { @@ -1954,24 +562,13 @@ }, { "cell_type": "code", - "execution_count": 34, + "execution_count": null, "metadata": { "collapsed": false }, - "outputs": [ - { - "data": { - "text/plain": [ - "<>" - ] - }, - "execution_count": 34, - "metadata": {}, - "output_type": "execute_result" - } - ], + "outputs": [], "source": [ - "(cat:def L4 (cat:gnrt (second (cat:cmbn-list square))))" + "(def L4 (gnrt (second (cmbn-list square))))" ] }, { @@ -1983,24 +580,13 @@ }, { "cell_type": "code", - "execution_count": 35, + "execution_count": null, "metadata": { "collapsed": false }, - "outputs": [ - { - "data": { - "text/plain": [ - "(>> >> >> >>)" - ] - }, - "execution_count": 35, - "metadata": {}, - "output_type": "execute_result" - } - ], + "outputs": [], "source": [ - "(cat:def hat (mapcar #'(lambda (i) (cat:face os3 i 4 l4)) '(1 2 3 4)))" + "(def hat (mapcar #'(lambda (i) (face os3 i 4 l4)) '(1 2 3 4)))" ] }, { @@ -2012,66 +598,33 @@ }, { "cell_type": "code", - "execution_count": 36, + "execution_count": null, "metadata": { "collapsed": false }, - "outputs": [ - { - "data": { - "text/plain": [ - ">>" - ] - }, - "execution_count": 36, - "metadata": {}, - "output_type": "execute_result" - } - ], + "outputs": [], "source": [ - "(cat:def kan-simplex (cat:kfll os3 0 4 hat))" + "(def kan-simplex (kfll os3 0 4 hat))" ] }, { "cell_type": "code", - "execution_count": 37, + "execution_count": null, "metadata": { "collapsed": false }, - "outputs": [ - { - "data": { - "text/plain": [ - ">>" - ] - }, - "execution_count": 37, - "metadata": {}, - "output_type": "execute_result" - } - ], + "outputs": [], "source": [ - "(cat:face os3 2 4 kan-simplex)" + "(face os3 2 4 kan-simplex)" ] }, { "cell_type": "code", - "execution_count": 38, + "execution_count": null, "metadata": { "collapsed": false }, - "outputs": [ - { - "data": { - "text/plain": [ - ">>" - ] - }, - "execution_count": 38, - "metadata": {}, - "output_type": "execute_result" - } - ], + "outputs": [], "source": [ "(second hat)" ] @@ -2085,99 +638,35 @@ }, { "cell_type": "code", - "execution_count": 39, + "execution_count": null, "metadata": { "collapsed": false }, - "outputs": [ - { - "data": { - "text/plain": [ - "[K598 Simplicial-Set]" - ] - }, - "execution_count": 39, - "metadata": {}, - "output_type": "execute_result" - } - ], + "outputs": [], "source": [ - "(cat:def cls-os3 (cat:classifying-space os3))" + "(def cls-os3 (classifying-space os3))" ] }, { "cell_type": "code", - "execution_count": 40, + "execution_count": null, "metadata": { "collapsed": false }, - "outputs": [ - { - "data": { - "text/plain": [ - "NIL" - ] - }, - "execution_count": 40, - "metadata": {}, - "output_type": "execute_result" - } - ], + "outputs": [], "source": [ - "(typep cls-os3 'cat:simplicial-group)" + "(typep cls-os3 'simplicial-group)" ] }, { "cell_type": "code", - "execution_count": 41, + "execution_count": null, "metadata": { "collapsed": false }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "\n", - "Computing boundary-matrix in dimension 4.\n", - "Rank of the source-module : 0.\n", - "\n", - "\n", - "Computing boundary-matrix in dimension 5.\n", - "Rank of the source-module : 1.\n", - "\n", - "\n", - ";; Clock -> 2015-12-29, 1h 11m 2s.\n", - "Computing the boundary of the generator 1/1 (dimension 5) :\n", - "<>]>> \n", - "End of computing.\n", - "\n", - "\n", - "\n", - "\n", - "Homology in dimension 4 :\n", - "\n", - "\n", - "\n", - "---done---\n", - "\n", - ";; Clock -> 2015-12-29, 1h 11m 2s.\n", - "\n" - ] - }, - { - "data": { - "text/plain": [ - "NIL" - ] - }, - "execution_count": 41, - "metadata": {}, - "output_type": "execute_result" - } - ], + "outputs": [], "source": [ - "(cat:homology cls-os3 4)" + "(homology cls-os3 4)" ] }, { @@ -2191,24 +680,13 @@ }, { "cell_type": "code", - "execution_count": 42, + "execution_count": null, "metadata": { "collapsed": false }, - "outputs": [ - { - "data": { - "text/plain": [ - "[K729 Cohomology-Class on K1 of degree 3]" - ] - }, - "execution_count": 42, - "metadata": {}, - "output_type": "execute_result" - } - ], + "outputs": [], "source": [ - "(cat:def ch3 (cat:chml-clss m23 3))" + "(def ch3 (chml-clss m23 3))" ] }, { @@ -2220,24 +698,13 @@ }, { "cell_type": "code", - "execution_count": 43, + "execution_count": null, "metadata": { "collapsed": false }, - "outputs": [ - { - "data": { - "text/plain": [ - "[K730 Fibration K1 -> K64]" - ] - }, - "execution_count": 43, - "metadata": {}, - "output_type": "execute_result" - } - ], + "outputs": [], "source": [ - "(cat:def f3 (cat:z2-whitehead m23 ch3))" + "(def f3 (z2-whitehead m23 ch3))" ] }, { @@ -2249,24 +716,13 @@ }, { "cell_type": "code", - "execution_count": 44, + "execution_count": null, "metadata": { "collapsed": false }, - "outputs": [ - { - "data": { - "text/plain": [ - "[K736 Simplicial-Set]" - ] - }, - "execution_count": 44, - "metadata": {}, - "output_type": "execute_result" - } - ], + "outputs": [], "source": [ - "(cat:def x4 (cat:fibration-total f3))" + "(def x4 (fibration-total f3))" ] }, { @@ -2278,142 +734,13 @@ }, { "cell_type": "code", - "execution_count": 45, + "execution_count": null, "metadata": { "collapsed": false }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "\n", - "Computing boundary-matrix in dimension 3.\n", - "Rank of the source-module : 2.\n", - "\n", - "\n", - ";; Clock -> 2015-12-29, 1h 11m 2s.\n", - "Computing the boundary of the generator 1/2 (dimension 3) :\n", - ">> \n", - "End of computing.\n", - "\n", - "\n", - ";; Clock -> 2015-12-29, 1h 11m 2s.\n", - "Computing the boundary of the generator 2/2 (dimension 3) :\n", - ">> \n", - "End of computing.\n", - "\n", - "\n", - "Computing boundary-matrix in dimension 4.\n", - "Rank of the source-module : 3.\n", - "\n", - "\n", - ";; Clock -> 2015-12-29, 1h 11m 2s.\n", - "Computing the boundary of the generator 1/3 (dimension 4) :\n", - ">> \n", - "End of computing.\n", - "\n", - "\n", - ";; Clock -> 2015-12-29, 1h 11m 2s.\n", - "Computing the boundary of the generator 2/3 (dimension 4) :\n", - ">> \n", - "End of computing.\n", - "\n", - "\n", - ";; Clock -> 2015-12-29, 1h 11m 2s.\n", - "Computing the boundary of the generator 3/3 (dimension 4) :\n", - ">> \n", - "End of computing.\n", - "\n", - "\n", - "\n", - "\n", - "Homology in dimension 3 :\n", - "\n", - "\n", - "\n", - "---done---\n", - "\n", - ";; Clock -> 2015-12-29, 1h 11m 2s.\n", - "\n", - "\n", - "Computing boundary-matrix in dimension 4.\n", - "Rank of the source-module : 3.\n", - "\n", - "\n", - ";; Clock -> 2015-12-29, 1h 11m 2s.\n", - "Computing the boundary of the generator 1/3 (dimension 4) :\n", - ">> \n", - "End of computing.\n", - "\n", - "\n", - ";; Clock -> 2015-12-29, 1h 11m 2s.\n", - "Computing the boundary of the generator 2/3 (dimension 4) :\n", - ">> \n", - "End of computing.\n", - "\n", - "\n", - ";; Clock -> 2015-12-29, 1h 11m 2s.\n", - "Computing the boundary of the generator 3/3 (dimension 4) :\n", - ">> \n", - "End of computing.\n", - "\n", - "\n", - "Computing boundary-matrix in dimension 5.\n", - "Rank of the source-module : 4.\n", - "\n", - "\n", - ";; Clock -> 2015-12-29, 1h 11m 2s.\n", - "Computing the boundary of the generator 1/4 (dimension 5) :\n", - ">> \n", - "End of computing.\n", - "\n", - "\n", - ";; Clock -> 2015-12-29, 1h 11m 2s.\n", - "Computing the boundary of the generator 2/4 (dimension 5) :\n", - ">> \n", - "End of computing.\n", - "\n", - "\n", - ";; Clock -> 2015-12-29, 1h 11m 2s.\n", - "Computing the boundary of the generator 3/4 (dimension 5) :\n", - ">> \n", - "End of computing.\n", - "\n", - "\n", - ";; Clock -> 2015-12-29, 1h 11m 2s.\n", - "Computing the boundary of the generator 4/4 (dimension 5) :\n", - ">> \n", - "End of computing.\n", - "\n", - "\n", - "\n", - "\n", - "Homology in dimension 4 :\n", - "\n", - "\n", - "Component Z/2Z\n", - "\n", - "\n", - "---done---\n", - "\n", - ";; Clock -> 2015-12-29, 1h 11m 2s.\n", - "\n" - ] - }, - { - "data": { - "text/plain": [ - "NIL" - ] - }, - "execution_count": 45, - "metadata": {}, - "output_type": "execute_result" - } - ], + "outputs": [], "source": [ - "(cat:homology x4 3 5)" + "(homology x4 3 5)" ] }, { @@ -2425,328 +752,46 @@ }, { "cell_type": "code", - "execution_count": 46, + "execution_count": null, "metadata": { "collapsed": false }, - "outputs": [ - { - "data": { - "text/plain": [ - "[K817 Cohomology-Class on K802 of degree 4]" - ] - }, - "execution_count": 46, - "metadata": {}, - "output_type": "execute_result" - } - ], + "outputs": [], "source": [ - "(cat:def ch4 (cat:chml-clss x4 4))" + "(def ch4 (chml-clss x4 4))" ] }, { "cell_type": "code", - "execution_count": 47, + "execution_count": null, "metadata": { "collapsed": false }, - "outputs": [ - { - "data": { - "text/plain": [ - "[K832 Fibration K736 -> K818]" - ] - }, - "execution_count": 47, - "metadata": {}, - "output_type": "execute_result" - } - ], + "outputs": [], "source": [ - "(cat:def f4 (cat:z2-whitehead x4 ch4))" + "(def f4 (z2-whitehead x4 ch4))" ] }, { "cell_type": "code", - "execution_count": 48, + "execution_count": null, "metadata": { "collapsed": false }, - "outputs": [ - { - "data": { - "text/plain": [ - "[K838 Simplicial-Set]" - ] - }, - "execution_count": 48, - "metadata": {}, - "output_type": "execute_result" - } - ], + "outputs": [], "source": [ - "(cat:def x5 (cat:fibration-total f4))" + "(def x5 (fibration-total f4))" ] }, { "cell_type": "code", - "execution_count": 49, + "execution_count": null, "metadata": { "collapsed": false }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "\n", - "Computing boundary-matrix in dimension 4.\n", - "Rank of the source-module : 4.\n", - "\n", - "\n", - ";; Clock -> 2015-12-29, 1h 11m 2s.\n", - "Computing the boundary of the generator 1/4 (dimension 4) :\n", - ">> <>]>>> \n", - "End of computing.\n", - "\n", - "\n", - ";; Clock -> 2015-12-29, 1h 11m 2s.\n", - "Computing the boundary of the generator 2/4 (dimension 4) :\n", - ">> <>> \n", - "End of computing.\n", - "\n", - "\n", - ";; Clock -> 2015-12-29, 1h 11m 2s.\n", - "Computing the boundary of the generator 3/4 (dimension 4) :\n", - ">> <>> \n", - "End of computing.\n", - "\n", - "\n", - ";; Clock -> 2015-12-29, 1h 11m 2s.\n", - "Computing the boundary of the generator 4/4 (dimension 4) :\n", - ">> <>> \n", - "End of computing.\n", - "\n", - "\n", - "Computing boundary-matrix in dimension 5.\n", - "Rank of the source-module : 7.\n", - "\n", - "\n", - ";; Clock -> 2015-12-29, 1h 11m 2s.\n", - "Computing the boundary of the generator 1/7 (dimension 5) :\n", - ">> <>]>>> \n", - "End of computing.\n", - "\n", - "\n", - ";; Clock -> 2015-12-29, 1h 11m 2s.\n", - "Computing the boundary of the generator 2/7 (dimension 5) :\n", - ">> <>]>>> \n", - "End of computing.\n", - "\n", - "\n", - ";; Clock -> 2015-12-29, 1h 11m 2s.\n", - "Computing the boundary of the generator 3/7 (dimension 5) :\n", - ">> <>]>>> \n", - "End of computing.\n", - "\n", - "\n", - ";; Clock -> 2015-12-29, 1h 11m 2s.\n", - "Computing the boundary of the generator 4/7 (dimension 5) :\n", - ">> <>> \n", - "End of computing.\n", - "\n", - "\n", - ";; Clock -> 2015-12-29, 1h 11m 2s.\n", - "Computing the boundary of the generator 5/7 (dimension 5) :\n", - ">> <>> \n", - "End of computing.\n", - "\n", - "\n", - ";; Clock -> 2015-12-29, 1h 11m 2s.\n", - "Computing the boundary of the generator 6/7 (dimension 5) :\n", - ">> <>> \n", - "End of computing.\n", - "\n", - "\n", - ";; Clock -> 2015-12-29, 1h 11m 2s.\n", - "Computing the boundary of the generator 7/7 (dimension 5) :\n", - ">> <>> \n", - "End of computing.\n", - "\n", - "\n", - "\n", - "\n", - "Homology in dimension 4 :\n", - "\n", - "\n", - "\n", - "---done---\n", - "\n", - ";; Clock -> 2015-12-29, 1h 11m 2s.\n", - "\n", - "\n", - "Computing boundary-matrix in dimension 5.\n", - "Rank of the source-module : 7.\n", - "\n", - "\n", - ";; Clock -> 2015-12-29, 1h 11m 2s.\n", - "Computing the boundary of the generator 1/7 (dimension 5) :\n", - ">> <>]>>> \n", - "End of computing.\n", - "\n", - "\n", - ";; Clock -> 2015-12-29, 1h 11m 2s.\n", - "Computing the boundary of the generator 2/7 (dimension 5) :\n", - ">> <>]>>> \n", - "End of computing.\n", - "\n", - "\n", - ";; Clock -> 2015-12-29, 1h 11m 2s.\n", - "Computing the boundary of the generator 3/7 (dimension 5) :\n", - ">> <>]>>> \n", - "End of computing.\n", - "\n", - "\n", - ";; Clock -> 2015-12-29, 1h 11m 2s.\n", - "Computing the boundary of the generator 4/7 (dimension 5) :\n", - ">> <>> \n", - "End of computing.\n", - "\n", - "\n", - ";; Clock -> 2015-12-29, 1h 11m 2s.\n", - "Computing the boundary of the generator 5/7 (dimension 5) :\n", - ">> <>> \n", - "End of computing.\n", - "\n", - "\n", - ";; Clock -> 2015-12-29, 1h 11m 2s.\n", - "Computing the boundary of the generator 6/7 (dimension 5) :\n", - ">> <>> \n", - "End of computing.\n", - "\n", - "\n", - ";; Clock -> 2015-12-29, 1h 11m 2s.\n", - "Computing the boundary of the generator 7/7 (dimension 5) :\n", - ">> <>> \n", - "End of computing.\n", - "\n", - "\n", - "Computing boundary-matrix in dimension 6.\n", - "Rank of the source-module : 14.\n", - "\n", - "\n", - ";; Clock -> 2015-12-29, 1h 11m 2s.\n", - "Computing the boundary of the generator 1/14 (dimension 6) :\n", - ">> <>]>>> \n", - "End of computing.\n", - "\n", - "\n", - ";; Clock -> 2015-12-29, 1h 11m 2s.\n", - "Computing the boundary of the generator 2/14 (dimension 6) :\n", - ">> <>]>>> \n", - "End of computing.\n", - "\n", - "\n", - ";; Clock -> 2015-12-29, 1h 11m 2s.\n", - "Computing the boundary of the generator 3/14 (dimension 6) :\n", - ">> <>]>>> \n", - "End of computing.\n", - "\n", - "\n", - ";; Clock -> 2015-12-29, 1h 11m 2s.\n", - "Computing the boundary of the generator 4/14 (dimension 6) :\n", - ">> <>][3 <>]>>> \n", - "End of computing.\n", - "\n", - "\n", - ";; Clock -> 2015-12-29, 1h 11m 2s.\n", - "Computing the boundary of the generator 5/14 (dimension 6) :\n", - ">> <>]>>> \n", - "End of computing.\n", - "\n", - "\n", - ";; Clock -> 2015-12-29, 1h 11m 2s.\n", - "Computing the boundary of the generator 6/14 (dimension 6) :\n", - ">> <>]>>> \n", - "End of computing.\n", - "\n", - "\n", - ";; Clock -> 2015-12-29, 1h 11m 2s.\n", - "Computing the boundary of the generator 7/14 (dimension 6) :\n", - ">> <>]>>> \n", - "End of computing.\n", - "\n", - "\n", - ";; Clock -> 2015-12-29, 1h 11m 2s.\n", - "Computing the boundary of the generator 8/14 (dimension 6) :\n", - ">> <>> \n", - "End of computing.\n", - "\n", - "\n", - ";; Clock -> 2015-12-29, 1h 11m 2s.\n", - "Computing the boundary of the generator 9/14 (dimension 6) :\n", - ">> <>> \n", - "End of computing.\n", - "\n", - "\n", - ";; Clock -> 2015-12-29, 1h 11m 2s.\n", - "Computing the boundary of the generator 10/14 (dimension 6) :\n", - ">> <>> \n", - "End of computing.\n", - "\n", - "\n", - ";; Clock -> 2015-12-29, 1h 11m 2s.\n", - "Computing the boundary of the generator 11/14 (dimension 6) :\n", - ">> <>> \n", - "End of computing.\n", - "\n", - "\n", - ";; Clock -> 2015-12-29, 1h 11m 2s.\n", - "Computing the boundary of the generator 12/14 (dimension 6) :\n", - ">> <>> \n", - "End of computing.\n", - "\n", - "\n", - ";; Clock -> 2015-12-29, 1h 11m 2s.\n", - "Computing the boundary of the generator 13/14 (dimension 6) :\n", - ">> <>> \n", - "End of computing.\n", - "\n", - "\n", - ";; Clock -> 2015-12-29, 1h 11m 2s.\n", - "Computing the boundary of the generator 14/14 (dimension 6) :\n", - ">> <>> \n", - "End of computing.\n", - "\n", - "\n", - "\n", - "\n", - "Homology in dimension 5 :\n", - "\n", - "\n", - "Component Z/4Z\n", - "\n", - "\n", - "---done---\n", - "\n", - ";; Clock -> 2015-12-29, 1h 11m 2s.\n", - "\n" - ] - }, - { - "data": { - "text/plain": [ - "NIL" - ] - }, - "execution_count": 49, - "metadata": {}, - "output_type": "execute_result" - } - ], + "outputs": [], "source": [ - "(cat:homology x5 4 6)" + "(homology x5 4 6)" ] }, {