From c30df8f2f62b57134f1ac73494f608d48121c79e Mon Sep 17 00:00:00 2001 From: gheber Date: Tue, 19 Apr 2016 20:14:41 -0500 Subject: [PATCH] Added Francis' changes. --- examples/11_Simplicial_Groups.ipynb | 367 ++++++++++++++++++---------- 1 file changed, 241 insertions(+), 126 deletions(-) diff --git a/examples/11_Simplicial_Groups.ipynb b/examples/11_Simplicial_Groups.ipynb index 81a7ee0..bbcaa7f 100644 --- a/examples/11_Simplicial_Groups.ipynb +++ b/examples/11_Simplicial_Groups.ipynb @@ -18,7 +18,7 @@ "\n", "`grml`, an object of type `SIMPLICIAL-MRPH`, defining in the underlying simplicial set $S$, the group operation as a simplicial morphism from $S \\times S$ onto $S$, compatible with the face and degeneracy operators in $S$, i.e. the $\\partial$'s and $\\eta$'s operators are also group morphisms. In dimension $n$, the neutral element is assumed to be the $n$-th degeneracy of the base point of the underlying simplicial set.\n", "\n", - "`grin`, an object of type `SIMPLICIAL-MRPH`, defining the inverse of an element of the Kan simplicial set w.r.t. the preceding group law.\n", + "`grin`, an object of type `SIMPLICIAL-MRPH`, defining the inverse of an element of the Kan simplicial set with respect to the preceding group law.\n", "\n", "A printing method has been associated to the class `SIMPLICIAL GROUP` and the external representation of an instance is a string like `[K`*n* `Simplicial-Group]`, where *n* is the number plate of the Kenzo object.\n", "\n", @@ -43,7 +43,7 @@ "\n", "defined with keyword parameters and returning an instance of the class `SIMPLICIAL-GROUP`. The keyword arguments *cmpr*, *basis*, *bspn*, *face*, *face*$*$, *intr-bndr*, *bndr-strt*, *intr-dgnl* and *dgnl-strt* are the arguments provided to build the underlying simplicial set using the function `build-smst`. Let us call it $S$. As usual, an adequate comment list must be provided for the parameter `:orgn`. The only two new arguments are:\n", "\n", - "- *sintr-grml*, a lisp function defining the group operation $S \\times S \\longrightarrow S$. The function `build-smgr` uses this lisp function to build a simplicial morphism of degree 0 between the cartesian product of the newly created simplicial set $S$ and itself. This new simplicial morphism is the value of the slot `grml` of the simplicial group instance.\n", + "- *sintr-grml*, a lisp function defining the group operation $S \\times S \\longrightarrow S$. The function `build-smgr` uses this lisp function to build a simplicial morphism of degree 0 between the cartesian product of the newly created simplicial set $S$ and itself. This new simplicial morphism is the value of the slot `grml` of the cartesian square of the simplicial group instance.\n", "- *sintr-grin*, a lisp function defining the inverse w.r.t the preceding group law of an element of $S$. The function `build-smgr` uses this lisp function to build a simplicial morphism of degree 0 between $S$ and itself. This new simplicial morphism is the value of the slot `grin` of the simplicial group instance.\n", "\n", "After a call to `build-smgr`, the simplicial group instance is pushed onto the list of previously constructed ones (`*smgr-list*`). The simplicial group with Kenzo identification $n$, may be retrieved in the `*smgr-list*`, by a call to the function `sgmr` as `(sgmr` *n*`)`. The list `*smgr-list*` may be cleared by the function `cat-init`.\n", @@ -74,7 +74,7 @@ "\n", "Let us recall the notion of classifying space in the framework of simplicial sets and in the particular case of discrete groups. Given a discrete group $\\cal G$, we know that we may build a simplicial set $K({\\cal G}, 1)$; in dimension $n$, we have $(K({\\cal G}, 1))_n = {\\cal G}^n$, the simplices or *bar objects* being conventionally represented as sequences of elements of $\\cal G$:\n", "$$ [g_1 \\mid g_2 \\mid \\ldots \\mid g_n]. $$\n", - "The base point is the void bar object $[\\ ]$. Let us note the group law multiplicatively.\n", + "The base point is the void bar object $[\\ ]$, the only vertex of $K(\\mathcal{G},1)$. Let us note the group law multiplicatively.\n", "\n", "The face operators are defined as follows:\n", "$$\n", @@ -103,16 +103,17 @@ "`k-z-1` *[Function]*\n", "> Build the simplicial group $K(\\mathbb{Z},1)$. In this simplicial group, a simplex in dimension $n$ is mathematically represented by a sequence of integers, known as a *bar* object:\n", "$$ [a_1 \\mid a_2 \\mid \\ldots \\mid a_n]. $$\n", + "Such a simplex of $K(\\mathbb{Z},1)$ is really, mathematically speaking, a *bar* object, but exceptionally is not implemented as a `bar` structure object, as it will be the rule later for arbitrary *classifying spaces*.\n", "The group operation inherits the additive law of $\\mathbb{Z}$:\n", "$$[a_1 \\mid \\cdots \\mid a_n] + [b_1 \\mid \\cdots \\mid b_n] = [a_1+b_1 \\mid \\cdots \\mid a_n+b_n]$$\n", "and the inverse of $[a_1 \\mid \\ldots \\mid a_n]$ is $[-a_1 \\mid \\ldots \\mid -a_n]. $\n", "In `Kenzo`, a non-degenerate simplex of $K(\\mathbb{Z},1)$ in dimension $n$ will be simply a list of $n$ non-null integers. The underlying simplicial set is locally effective and its base point is `NIL`, i.e the void bar object\n", - "$[\\ ]$. To be coeherent with the general policy of `Kenzo`, a degenerate simplex must be represented by\n", - "an abstract simplex of the form `(:absm` *dgop* `.` *gmsm*`)` where *gmsm* is a non-degenerate simplex, here a list of non-null integers. But, for the computations in the simplicial group, the general form of a bar object, including 0, is more natural and more convenient. Consequently, two conversion functions are provided (see below).\n", + "$[\\ ]$. To be coherent with the general policy of `Kenzo`, a degenerate simplex must be represented by\n", + "an abstract simplex of the form `#S(ABSM :dgop` *n* `:gmsm` *list*`)` where *gmsm* is a non-degenerate simplex, here a list of non-null integers. But, for the computations in the simplicial group, the general form of a bar object, including an arbitrary number of 0's, is more natural and more convenient. Consequently, two conversion functions are provided (see below).\n", "\n", "`k-z2-1` *[Function]*\n", "> Build the simplicial group $K(\\mathbb{Z}_2,1)$. Mathematically, in dimension $n$, the only non-degenerate simplex is\n", - "a sequence of $n$ 1's. But one may show that as simplicial set, $K(\\mathbb{Z}_2,1)$ is isomorphic to $P^\\infty \\mathbb{R}$ which may be built by the statement `(R-proj-space)`. This is the representation adopted in `Kenzo`. In dimension $n$, this simplicial set has only one non-degenerate simplex, namely the integer $n$. The formulas for the faces of this non-degenerate simplex $n$ collapse to:\n", + "a sequence of $n$ 1's. But one may show that as simplicial set, $K(\\mathbb{Z}_2,1)$ is isomorphic to $P^\\infty \\mathbb{R}$ which may be built by the statement `(R-proj-space)`. This is the representation adopted in `Kenzo`. In dimension $n$, this simplicial set has only one non-degenerate simplex, namely the integer $n$. The formulas for the faces of one non-degenerate simplex conventionally represented by the integer $n$ become:\n", "$$\n", "\\begin{aligned}\n", "\\partial_0 n & = & n-1, \\\\\n", @@ -125,10 +126,10 @@ "provided.\n", "\n", "`z-bar-absm` *bar* *[Function]*\n", - "> Transform a general mathematical bar object *bar* of $K(\\mathbb{Z}, 1)$, represented by a list of integers (including 0's), into a valid abstract simplex (an object of type `ABSM`), `(:absm` *dgop* `.` *gmsm*`)`, where *gmsm* is a sequence of non-null integers representing a non-degenerate bar object of $K(\\mathbb{Z},1)$ and *dgop* a coded sequence of degeneracy operators $\\eta_i$'s.\n", + "> Transform a general mathematical bar object *bar* of $K(\\mathbb{Z}, 1)$, represented by a list of integers (including 0's), into a valid abstract simplex (an object of type `ABSM`), `#S(ABSM :dgop` *n* `:gmsm` *list*`)`, where *gmsm* is a sequence of non-null integers representing a non-degenerate bar object of $K(\\mathbb{Z},1)$ and *dgop* a coded sequence of degeneracy operators $\\eta_i$'s.\n", "\n", "`z-absm-bar` *absm* *[Function]*\n", - "> Transform the abstract simplex *absm*, `(:absm` *dgop* `.` *gmsm*`)`, where *gmsm* is a sequence of non-null integers representing a nondegenerate bar object of $K(\\mathbb{Z},1)$ and *dgop* a coded sequence of degeneracy operators, into a list of integers representing a bar object, degenerate or not, of $K(\\mathbb{Z},1)$, for more convenience in the internal computations or for more clarity in external printing.\n", + "> Transform the abstract simplex *absm*, `#S(ABSM :dgop` *n* `:gmsm` *list*`)`, where *gmsm* is a sequence of non-null integers representing a nondegenerate bar object of $K(\\mathbb{Z},1)$ and *dgop* a coded sequence of degeneracy operators, into a list of integers representing a bar object, degenerate or not, of $K(\\mathbb{Z},1)$, for more convenience in the internal computations or for more clarity in external printing.\n", "\n", "`z2-bar-absm` *bar* *[Function]*\n", "> Function analogous to `z-bar-absm` but for $K(\\mathbb{Z}_2, 1)$.\n", @@ -209,7 +210,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "Let us build the list of the four faces and by suppressing successively, each face one after the other in this list, let us verify that we have always a Kan hat (we recall that the lisp function `remove`, works on a copy of the list, i.e. the argument `hat` is not modified). In the forth statement, we verify the property of minimality of this special simplicial group." + "Let us build the list of the four faces and by suppressing successively, each face one after the other in this list, let us verify that we have always a Kan horn (we recall that the lisp function `remove`, works on a copy of the list, i.e. the argument `hat` is not modified). In the forth statement, we verify the property of minimality of this special simplicial group." ] }, { @@ -536,7 +537,7 @@ } ], "source": [ - "(grml KZ2 4 (crpr 0 * 0 *))" + "(grml KZ2 4 (crpr 0 4 0 4))" ] }, { @@ -670,17 +671,10 @@ "collapsed": false }, "outputs": [ - { - "name": "stderr", - "output_type": "stream", - "text": [ - "Warning: no evaluable input\n" - ] - }, { "data": { "text/plain": [ - "NIL" + "( )" ] }, "execution_count": 23, @@ -689,40 +683,119 @@ } ], "source": [ - "#|\n", - "labsms ==>\n", - "\n", - "( \n", - " \n", - " )\n", - "\n", - "(mapcar #'z-absm-bar labsms) ==>\n", - "\n", - "((3 6) (0 3 6) (3 0 6) (0 0 3 6) (3 6 0) (0 3 0 6) (3 0 0 6) (0 0 0 3 6))\n", - "\n", - "(mapcar #'z-bar-absm *) ==>\n", - "\n", - "( \n", - " \n", - " )\n", - "\n", - "labsms2 ==>\n", - "\n", - "( \n", - " \n", - " )\n", - "\n", - "(mapcar #'z2-absm-bar labsms2) ==>\n", - "\n", - "(NIL (1) (1 1) (1 1 1) (0) (0 1) (0 1 1) (0 1 1 1) (0 0) (0 0 1) (0 0 1 1)\n", - " (0 0 1 1 1))\n", - "\n", - "(mapcar #'z2-bar-absm *) ==>\n", - "\n", - "( \n", - " \n", - " )\n", - "|#" + "(def labsms (mapcar #'(lambda (n) (absm n '(3 6))) '(0 1 2 3 4 5 6 7)))" + ] + }, + { + "cell_type": "code", + "execution_count": 24, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "((3 6) (0 3 6) (3 0 6) (0 0 3 6) (3 6 0) (0 3 0 6) (3 0 0 6) (0 0 0 3 6))" + ] + }, + "execution_count": 24, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "(mapcar #'z-absm-bar labsms)" + ] + }, + { + "cell_type": "code", + "execution_count": 25, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "( )" + ] + }, + "execution_count": 25, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "(mapcar #'z-bar-absm *)" + ] + }, + { + "cell_type": "code", + "execution_count": 26, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "( ...)" + ] + }, + "execution_count": 26, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "(def labsms2 (append (mapcar #'(lambda (n) (absm 0 n)) '(0 1 2 3))\n", + " (mapcar #'(lambda (n) (absm 1 n)) '(0 1 2 3))\n", + " (mapcar #'(lambda (n) (absm 3 n)) '(0 1 2 3))))" + ] + }, + { + "cell_type": "code", + "execution_count": 27, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "(NIL (1) (1 1) (1 1 1) (0) (0 1) (0 1 1) (0 1 1 1) (0 0) (0 0 1) ...)" + ] + }, + "execution_count": 27, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "(mapcar #'z2-absm-bar labsms2)" + ] + }, + { + "cell_type": "code", + "execution_count": 28, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "( ...)" + ] + }, + "execution_count": 28, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "(mapcar #'z2-bar-absm *)" ] }, { @@ -741,7 +814,7 @@ }, { "cell_type": "code", - "execution_count": 23, + "execution_count": 29, "metadata": { "collapsed": false }, @@ -752,7 +825,7 @@ "[K1 Abelian-Simplicial-Group]" ] }, - "execution_count": 23, + "execution_count": 29, "metadata": {}, "output_type": "execute_result" } @@ -763,7 +836,7 @@ }, { "cell_type": "code", - "execution_count": 24, + "execution_count": 30, "metadata": { "collapsed": false }, @@ -785,7 +858,7 @@ "8. APRD: \"unbound\"\n", "9. CPRD: [K5 Morphism (degree 0): K1 -> K3]\n", "10. FACE: #\n", - "11. KFLL: #\n", + "11. KFLL: #\n", "12. GRML: [K11 Simplicial-Morphism K6 -> K1]\n", "13. GRIN: [K12 Simplicial-Morphism K1 -> K1]\n", "\n", @@ -798,7 +871,7 @@ "NIL" ] }, - "execution_count": 24, + "execution_count": 30, "metadata": {}, "output_type": "execute_result" } @@ -819,7 +892,7 @@ }, { "cell_type": "code", - "execution_count": 25, + "execution_count": 31, "metadata": { "collapsed": false }, @@ -830,7 +903,7 @@ "" ] }, - "execution_count": 25, + "execution_count": 31, "metadata": {}, "output_type": "execute_result" } @@ -841,7 +914,7 @@ }, { "cell_type": "code", - "execution_count": 26, + "execution_count": 32, "metadata": { "collapsed": false }, @@ -864,7 +937,7 @@ "------------------------------------------------------------------------------\n" ] }, - "execution_count": 26, + "execution_count": 32, "metadata": {}, "output_type": "execute_result" } @@ -882,7 +955,7 @@ }, { "cell_type": "code", - "execution_count": 27, + "execution_count": 33, "metadata": { "collapsed": false }, @@ -904,7 +977,7 @@ "8. APRD: [K26 Morphism (degree 0): K3 -> K1]\n", "9. CPRD: [K5 Morphism (degree 0): K1 -> K3]\n", "10. FACE: #\n", - "11. KFLL: #\n", + "11. KFLL: #\n", "12. GRML: [K11 Simplicial-Morphism K6 -> K1]\n", "13. GRIN: [K12 Simplicial-Morphism K1 -> K1]\n", "\n", @@ -917,7 +990,7 @@ "NIL" ] }, - "execution_count": 27, + "execution_count": 33, "metadata": {}, "output_type": "execute_result" } @@ -952,7 +1025,7 @@ }, { "cell_type": "code", - "execution_count": 28, + "execution_count": 34, "metadata": { "collapsed": false }, @@ -963,7 +1036,7 @@ "[K1 Abelian-Simplicial-Group]" ] }, - "execution_count": 28, + "execution_count": 34, "metadata": {}, "output_type": "execute_result" } @@ -974,7 +1047,7 @@ }, { "cell_type": "code", - "execution_count": 29, + "execution_count": 35, "metadata": { "collapsed": false }, @@ -985,7 +1058,7 @@ "[K27 Chain-Complex]" ] }, - "execution_count": 29, + "execution_count": 35, "metadata": {}, "output_type": "execute_result" } @@ -996,7 +1069,7 @@ }, { "cell_type": "code", - "execution_count": 30, + "execution_count": 36, "metadata": { "collapsed": false }, @@ -1007,7 +1080,7 @@ "[K29 Chain-Complex]" ] }, - "execution_count": 30, + "execution_count": 36, "metadata": {}, "output_type": "execute_result" } @@ -1025,7 +1098,7 @@ }, { "cell_type": "code", - "execution_count": 31, + "execution_count": 37, "metadata": { "collapsed": false }, @@ -1035,7 +1108,7 @@ "output_type": "stream", "text": [ "SIMPLE-STYLE-WARNING: \n", - " #\n" + " #\n" ] }, { @@ -1044,7 +1117,7 @@ "[K31 Morphism (degree 0): K27 -> K29]" ] }, - "execution_count": 31, + "execution_count": 37, "metadata": {}, "output_type": "execute_result" } @@ -1069,7 +1142,7 @@ }, { "cell_type": "code", - "execution_count": 32, + "execution_count": 38, "metadata": { "collapsed": false }, @@ -1080,7 +1153,7 @@ "T" ] }, - "execution_count": 32, + "execution_count": 38, "metadata": {}, "output_type": "execute_result" } @@ -1091,7 +1164,7 @@ }, { "cell_type": "code", - "execution_count": 33, + "execution_count": 39, "metadata": { "collapsed": false }, @@ -1105,7 +1178,7 @@ "------------------------------------------------------------------------------\n" ] }, - "execution_count": 33, + "execution_count": 39, "metadata": {}, "output_type": "execute_result" } @@ -1123,7 +1196,7 @@ }, { "cell_type": "code", - "execution_count": 34, + "execution_count": 40, "metadata": { "collapsed": false }, @@ -1134,7 +1207,7 @@ "[K26 Morphism (degree 0): K3 -> K1]" ] }, - "execution_count": 34, + "execution_count": 40, "metadata": {}, "output_type": "execute_result" } @@ -1145,7 +1218,7 @@ }, { "cell_type": "code", - "execution_count": 35, + "execution_count": 41, "metadata": { "collapsed": false }, @@ -1156,7 +1229,7 @@ "[K32 Morphism (degree 0): K1 -> K1]" ] }, - "execution_count": 35, + "execution_count": 41, "metadata": {}, "output_type": "execute_result" } @@ -1167,7 +1240,7 @@ }, { "cell_type": "code", - "execution_count": 36, + "execution_count": 42, "metadata": { "collapsed": false }, @@ -1178,7 +1251,7 @@ "[K33 Morphism (degree 0): K29 -> K3]" ] }, - "execution_count": 36, + "execution_count": 42, "metadata": {}, "output_type": "execute_result" } @@ -1189,7 +1262,7 @@ }, { "cell_type": "code", - "execution_count": 37, + "execution_count": 43, "metadata": { "collapsed": false }, @@ -1200,7 +1273,7 @@ "[K34 Morphism (degree 0): K27 -> K3]" ] }, - "execution_count": 37, + "execution_count": 43, "metadata": {}, "output_type": "execute_result" } @@ -1218,7 +1291,7 @@ }, { "cell_type": "code", - "execution_count": 38, + "execution_count": 44, "metadata": { "collapsed": false }, @@ -1229,7 +1302,7 @@ "[K35 Morphism (degree 0): K27 -> K1]" ] }, - "execution_count": 38, + "execution_count": 44, "metadata": {}, "output_type": "execute_result" } @@ -1240,7 +1313,7 @@ }, { "cell_type": "code", - "execution_count": 39, + "execution_count": 45, "metadata": { "collapsed": false }, @@ -1251,7 +1324,7 @@ "[K37 Morphism (degree 0): K27 -> K1]" ] }, - "execution_count": 39, + "execution_count": 45, "metadata": {}, "output_type": "execute_result" } @@ -1262,7 +1335,7 @@ }, { "cell_type": "code", - "execution_count": 40, + "execution_count": 46, "metadata": { "collapsed": false }, @@ -1273,7 +1346,7 @@ "[K38 Morphism (degree 0): K27 -> K1]" ] }, - "execution_count": 40, + "execution_count": 46, "metadata": {}, "output_type": "execute_result" } @@ -1284,7 +1357,7 @@ }, { "cell_type": "code", - "execution_count": 41, + "execution_count": 47, "metadata": { "collapsed": false }, @@ -1297,7 +1370,7 @@ "------------------------------------------------------------------------------\n" ] }, - "execution_count": 41, + "execution_count": 47, "metadata": {}, "output_type": "execute_result" } @@ -1308,7 +1381,7 @@ }, { "cell_type": "code", - "execution_count": 42, + "execution_count": 48, "metadata": { "collapsed": false }, @@ -1321,7 +1394,7 @@ "------------------------------------------------------------------------------\n" ] }, - "execution_count": 42, + "execution_count": 48, "metadata": {}, "output_type": "execute_result" } @@ -1334,12 +1407,12 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "The resulting combination of the rather simple double tensor product has yet 140 terms:" + "It happens the resulting combination of the rather simple double tensor product has 140 terms:" ] }, { "cell_type": "code", - "execution_count": 43, + "execution_count": 49, "metadata": { "collapsed": false }, @@ -1363,7 +1436,7 @@ "------------------------------------------------------------------------------\n" ] }, - "execution_count": 43, + "execution_count": 49, "metadata": {}, "output_type": "execute_result" } @@ -1374,7 +1447,7 @@ }, { "cell_type": "code", - "execution_count": 44, + "execution_count": 50, "metadata": { "collapsed": false }, @@ -1385,7 +1458,7 @@ "140" ] }, - "execution_count": 44, + "execution_count": 50, "metadata": {}, "output_type": "execute_result" } @@ -1405,7 +1478,7 @@ }, { "cell_type": "code", - "execution_count": 45, + "execution_count": 51, "metadata": { "collapsed": false }, @@ -1416,7 +1489,7 @@ "[K1 Abelian-Simplicial-Group]" ] }, - "execution_count": 45, + "execution_count": 51, "metadata": {}, "output_type": "execute_result" } @@ -1427,7 +1500,29 @@ }, { "cell_type": "code", - "execution_count": 46, + "execution_count": 52, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "#" + ] + }, + "execution_count": 52, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "(def d-vert (bar-intr-vrtc-dffr (dffr kz1)))" + ] + }, + { + "cell_type": "code", + "execution_count": 53, "metadata": { "collapsed": false }, @@ -1440,19 +1535,18 @@ "------------------------------------------------------------------------------\n" ] }, - "execution_count": 46, + "execution_count": 53, "metadata": {}, "output_type": "execute_result" } ], "source": [ - "(def d-vert (bar-intr-vrtc-dffr (dffr kz1)))\n", "(funcall d-vert 0 (abar))" ] }, { "cell_type": "code", - "execution_count": 47, + "execution_count": 54, "metadata": { "collapsed": false }, @@ -1463,7 +1557,7 @@ "<>" ] }, - "execution_count": 47, + "execution_count": 54, "metadata": {}, "output_type": "execute_result" } @@ -1474,7 +1568,7 @@ }, { "cell_type": "code", - "execution_count": 48, + "execution_count": 55, "metadata": { "collapsed": false }, @@ -1496,7 +1590,7 @@ "------------------------------------------------------------------------------\n" ] }, - "execution_count": 48, + "execution_count": 55, "metadata": {}, "output_type": "execute_result" } @@ -1507,7 +1601,29 @@ }, { "cell_type": "code", - "execution_count": 49, + "execution_count": 56, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "#" + ] + }, + "execution_count": 56, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "(def d-hrz (bar-intr-hrzn-dffr (aprd kz1)))" + ] + }, + { + "cell_type": "code", + "execution_count": 57, "metadata": { "collapsed": false }, @@ -1531,13 +1647,12 @@ "------------------------------------------------------------------------------\n" ] }, - "execution_count": 49, + "execution_count": 57, "metadata": {}, "output_type": "execute_result" } ], "source": [ - "(def d-hrz (bar-intr-hrzn-dffr (aprd kz1)))\n", "(funcall d-hrz 9 abar0)" ] }, @@ -1550,7 +1665,7 @@ }, { "cell_type": "code", - "execution_count": 50, + "execution_count": 58, "metadata": { "collapsed": false }, @@ -1561,7 +1676,7 @@ "[K42 Chain-Complex]" ] }, - "execution_count": 50, + "execution_count": 58, "metadata": {}, "output_type": "execute_result" } @@ -1572,7 +1687,7 @@ }, { "cell_type": "code", - "execution_count": 51, + "execution_count": 59, "metadata": { "collapsed": false }, @@ -1596,7 +1711,7 @@ "------------------------------------------------------------------------------\n" ] }, - "execution_count": 51, + "execution_count": 59, "metadata": {}, "output_type": "execute_result" } @@ -1607,7 +1722,7 @@ }, { "cell_type": "code", - "execution_count": 52, + "execution_count": 60, "metadata": { "collapsed": false }, @@ -1620,7 +1735,7 @@ "------------------------------------------------------------------------------\n" ] }, - "execution_count": 52, + "execution_count": 60, "metadata": {}, "output_type": "execute_result" } @@ -1631,7 +1746,7 @@ }, { "cell_type": "code", - "execution_count": 53, + "execution_count": 61, "metadata": { "collapsed": false }, @@ -1642,7 +1757,7 @@ "<>" ] }, - "execution_count": 53, + "execution_count": 61, "metadata": {}, "output_type": "execute_result" } @@ -1653,7 +1768,7 @@ }, { "cell_type": "code", - "execution_count": 54, + "execution_count": 62, "metadata": { "collapsed": false }, @@ -1677,7 +1792,7 @@ "------------------------------------------------------------------------------\n" ] }, - "execution_count": 54, + "execution_count": 62, "metadata": {}, "output_type": "execute_result" } @@ -1688,7 +1803,7 @@ }, { "cell_type": "code", - "execution_count": 55, + "execution_count": 63, "metadata": { "collapsed": false }, @@ -1699,7 +1814,7 @@ "84" ] }, - "execution_count": 55, + "execution_count": 63, "metadata": {}, "output_type": "execute_result" } @@ -1710,7 +1825,7 @@ }, { "cell_type": "code", - "execution_count": 56, + "execution_count": 64, "metadata": { "collapsed": false }, @@ -1723,7 +1838,7 @@ "------------------------------------------------------------------------------\n" ] }, - "execution_count": 56, + "execution_count": 64, "metadata": {}, "output_type": "execute_result" }