Added Francis' changes.
This commit is contained in:
gheber
parent
3e17919559
commit
c30df8f2f6
@ -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"
|
||||
"(<AbSm - (3 6)> <AbSm 0 (3 6)> <AbSm 1 (3 6)> <AbSm 1-0 (3 6)> <AbSm 2 (3 6)> <AbSm 2-0 (3 6)> <AbSm 2-1 (3 6)> <AbSm 2-1-0 (3 6)>)"
|
||||
]
|
||||
},
|
||||
"execution_count": 23,
|
||||
@ -689,40 +683,119 @@
|
||||
}
|
||||
],
|
||||
"source": [
|
||||
"#|\n",
|
||||
"labsms ==>\n",
|
||||
"\n",
|
||||
"(<AbSm - (3 6)> <AbSm 0 (3 6)> <AbSm 1 (3 6)>\n",
|
||||
" <AbSm 1-0 (3 6)> <AbSm 2 (3 6)> <AbSm 2-0 (3 6)>\n",
|
||||
" <AbSm 2-1 (3 6)> <AbSm 2-1-0 (3 6)>)\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",
|
||||
"(<AbSm - (3 6)> <AbSm 0 (3 6)> <AbSm 1 (3 6)>\n",
|
||||
" <AbSm 1-0 (3 6)> <AbSm 2 (3 6)> <AbSm 2-0 (3 6)>\n",
|
||||
" <AbSm 2-1 (3 6)> <AbSm 2-1-0 (3 6)>)\n",
|
||||
"\n",
|
||||
"labsms2 ==>\n",
|
||||
"\n",
|
||||
"(<AbSm - 0> <AbSm - 1> <AbSm - 2> <AbSm - 3>\n",
|
||||
" <AbSm 0 0> <AbSm 0 1> <AbSm 0 2> <AbSm 0 3>\n",
|
||||
" <AbSm 1-0 0> <AbSm 1-0 1> <AbSm 1-0 2> <AbSm 1-0 3>)\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",
|
||||
"(<AbSm - 0> <AbSm - 1> <AbSm - 2> <AbSm - 3>\n",
|
||||
" <AbSm 0 0> <AbSm 0 1> <AbSm 0 2> <AbSm 0 3>\n",
|
||||
" <AbSm 1-0 0> <AbSm 1-0 1> <AbSm 1-0 2> <AbSm 1-0 3>)\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": [
|
||||
"(<AbSm - (3 6)> <AbSm 0 (3 6)> <AbSm 1 (3 6)> <AbSm 1-0 (3 6)> <AbSm 2 (3 6)> <AbSm 2-0 (3 6)> <AbSm 2-1 (3 6)> <AbSm 2-1-0 (3 6)>)"
|
||||
]
|
||||
},
|
||||
"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": [
|
||||
"(<AbSm - 0> <AbSm - 1> <AbSm - 2> <AbSm - 3> <AbSm 0 0> <AbSm 0 1> <AbSm 0 2> <AbSm 0 3> <AbSm 1-0 0> <AbSm 1-0 1> ...)"
|
||||
]
|
||||
},
|
||||
"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": [
|
||||
"(<AbSm - 0> <AbSm - 1> <AbSm - 2> <AbSm - 3> <AbSm 0 0> <AbSm 0 1> <AbSm 0 2> <AbSm 0 3> <AbSm 1-0 0> <AbSm 1-0 1> ...)"
|
||||
]
|
||||
},
|
||||
"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: #<FUNCTION K-Z-1-FACE>\n",
|
||||
"11. KFLL: #<CLOSURE (FLET CAT::RSLT :IN CAT::SMGR-KFLL-INTR) {100561DD8B}>\n",
|
||||
"11. KFLL: #<CLOSURE (FLET CAT::RSLT :IN CAT::SMGR-KFLL-INTR) {100579D84B}>\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 @@
|
||||
"<TnPr (1 2) (7 8 9)>"
|
||||
]
|
||||
},
|
||||
"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: #<FUNCTION K-Z-1-FACE>\n",
|
||||
"11. KFLL: #<CLOSURE (FLET CAT::RSLT :IN CAT::SMGR-KFLL-INTR) {100561DD8B}>\n",
|
||||
"11. KFLL: #<CLOSURE (FLET CAT::RSLT :IN CAT::SMGR-KFLL-INTR) {100579D84B}>\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",
|
||||
" #<SB-INT:SIMPLE-STYLE-WARNING \"The variable ~S is defined but never used.\" {10063368B3}>\n"
|
||||
" #<SB-INT:SIMPLE-STYLE-WARNING \"The variable ~S is defined but never used.\" {10067FD4A3}>\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": [
|
||||
"#<CLOSURE (LAMBDA (DEGR ABAR) :IN BAR-INTR-VRTC-DFFR) {1006FEDBBB}>"
|
||||
]
|
||||
},
|
||||
"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 @@
|
||||
"<<Abar[3 (1 2)][3 (-1 -2)][3 (3 4)]>>"
|
||||
]
|
||||
},
|
||||
"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": [
|
||||
"#<CLOSURE (LAMBDA (DEGR ABAR) :IN BAR-INTR-HRZN-DFFR) {10071670DB}>"
|
||||
]
|
||||
},
|
||||
"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 @@
|
||||
"<<Abar[5 (7 11 4 -9)][4 (8 3 2)][5 (-1 -2 -3 -4)]>>"
|
||||
]
|
||||
},
|
||||
"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"
|
||||
}
|
||||
|
||||
Loading…
Reference in New Issue
Block a user