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Updated notebook.

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Gerd Heber 2016-01-10 18:06:15 -05:00
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examples/Chapter1.ipynb
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@ -165,8 +165,8 @@
"\n", "\n",
"### Representation of a combination\n", "### Representation of a combination\n",
"\n", "\n",
"A combination is represented internally in the system by a list having the following general form:\n", "A combination is represented internally in the system by a structure having the following general form:\n",
"$$\\texttt{(:cmbn degree}\\quad(\\lambda_1\\cdot\\sigma_1)\\dots(\\lambda_k\\cdot\\sigma_k)\\texttt{)}$$\n", "$$\\#\\texttt{S(CMBN}\\quad\\texttt{DEGREE P}\\quad\\texttt{LIST (}\\texttt{(}\\lambda_1\\cdot\\sigma_1\\texttt{)}\\dots\\texttt{(}\\lambda_k\\cdot\\sigma_k\\texttt{)))}$$\n",
"and containing\n", "and containing\n",
"\n", "\n",
"1. The degree of the combination corresponding to the index $p\\in\\mathbb{Z}$ of the group $C_p$ to which this combination belongs.\n", "1. The degree of the combination corresponding to the index $p\\in\\mathbb{Z}$ of the group $C_p$ to which this combination belongs.\n",
@ -174,7 +174,14 @@
"\n", "\n",
"This choice of representation implaies that only homogeneous combinations will be considered. A type $\\texttt{CMBN}$ and a printing method are provided with this internal representation. The external form of a combination is shown in the examples.\n", "This choice of representation implaies that only homogeneous combinations will be considered. A type $\\texttt{CMBN}$ and a printing method are provided with this internal representation. The external form of a combination is shown in the examples.\n",
"\n", "\n",
"### Ordering the generators" "### Ordering the generators\n",
"\n",
"In order to speed up the execution of algorithms involving combinations, the list of pairs $(\\lambda_i.\\sigma_i)$ is ordered by an adequate ordering function (ex: the lexicographical ordering n the symbols). For programming convenience, an enumerated type $\\texttt{CMPR}$ has been defined:\n",
"```lisp\n",
"(deftype cmpr() '(member :less :equal :greater))\n",
"```\n",
"A number of macros, functions and methods have been defined on usual sets (symbols, numbers, lists, etc.) taking their value in the set $\\texttt{[:less, :equal, :greater]}$. Of course, the user may define its own function for a particular case.\n",
"The functions $\\texttt{f-cmpr}$, $\\texttt{s-cmpr}$, and $\\texttt{l-cmpr}$ can be used to compare various couples of common items."
] ]
}, },
{ {
@ -329,7 +336,9 @@
"cell_type": "markdown", "cell_type": "markdown",
"metadata": {}, "metadata": {},
"source": [ "source": [
"### Functions handling combinations" "### Functions handling combinations\n",
"\n",
"The software provides a set of functions, methods, and macros to create or modify combinations."
] ]
}, },
{ {