File:Bird horner rule 6789.pdf
Original file (1,062 × 618 pixels, file size: 39 KB, MIME type: application/pdf)
Captions
Summary
[edit]DescriptionBird horner rule 6789.pdf |
English: Computation example for Horner's rule from Bird.1989, Lemma 1, p.125 lf. Our example uses integer numbers with binary addition ("") and multiplication (""), of which only their distributivity, and the left-neutrality of wrt. is used. In particular, none of the operations need to be associative. The Horner operation is defined from and . |
Date | |
Source | Own work |
Author | Jochen Burghardt |
Other versions | File:Bird horner rule 456789.pdf — File:Bird horner rule 456789 svg.svg — File:Bird horner rule 56789.pdf — File:Bird horner rule 56789 svg.svg — File:Bird horner rule 6789.pdf — File:Bird horner rule 6789 svg.svg |
(General explanations applying to all similar images, including the LaTeX source code of the used file "bird_Preamble.tex" can be found at the description page of File:Bird foldl map fusion.pdf.)
LaTeX source code
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\documentclass[12pt]{article}
\setlength{\unitlength}{1mm}
\usepackage[pdftex]{color}
\usepackage{amssymb}
\usepackage[paperwidth=180mm,paperheight=105mm]{geometry}
\setlength{\topmargin}{-36mm}
\setlength{\textwidth}{180mm}
\setlength{\textheight}{105mm}
\setlength{\oddsidemargin}{-23mm}
\setlength{\parindent}{0cm}
\pagestyle{empty}
\include{bird_Preamble}
\begin{document}
\begin{picture}(175,100)
%\put(0,0){\makebox(0,0){$+$}}
%\put(175,100){\makebox(0,0){$+$}}
%
\put(120.000,95.000){\makebox(0.000,0.000)[bl]{{$\List{6\,7\,8\,9}$}}}%
\put(120.000,65.000){\makebox(0.000,0.000)[br]{{$\List{\List{6\,7\,8\,9}\,\List{7\,8\,9}\,\List{8\,9}\,\List{9}\,\Nil}$}}}%
\put(120.000,35.000){\makebox(0.000,0.000)[br]{{$\List{(((1\*6)\*7)\*8)\*9\,((1\*7)\*8)\*9\,(1\*8)\*9\,1\*9\,1}$}}}%
\put(120.000,5.000){\makebox(0.000,0.000)[br]{{$\A{((((0+\B{(((1\*6)\*7)\*8)\*9})+\B{((1\*7)\*8)\*9})+\B{(1\*8)\*9})+\B{1\*9})+\B{1}}$}}}%
\put(130.000,5.000){\makebox(0.000,0.000)[bl]{{$\A{(((1\otimes \B{6})\otimes \B{7})\otimes \B{8})\otimes \B{9}}$}}}%
\put(125.000,6.000){\makebox(0.000,0.000)[b]{{$\mathbf{=}$}}}%
%
\thicklines
%
\textcolor{cFct}{\put(120.000,92.000){\vector(-2,-1){40.000}}}%
\textcolor{cFct}{\put(99.000,82.000){\makebox(0.000,0.000)[br]{$\tails$}}}%
%
\textcolor{cFct}{\put(80.000,62.000){\vector(0,-1){20.000}}}%
\textcolor{cFct}{\put(78.000,52.000){\makebox(0.000,0.000)[br]{$\map \; (\foldl \; (*) \; 1)$}}}%
%
\textcolor{cFct}{\put(80.000,32.000){\vector(0,-1){20.000}}}%
\textcolor{cFct}{\put(78.000,22.000){\makebox(0.000,0.000)[br]{$\foldl \; (+) \; 0$}}}%
%
\textcolor{cFct}{\put(135.000,92.000){\vector(0,-1){80.000}}}%
\textcolor{cFct}{\put(137.000,52.000){\makebox(0.000,0.000)[bl]{$\foldl \; (\otimes) \; 1$}}}%
%
\textcolor{bCmt}{\put(147.000,12.000){\makebox(0.000,0.000)[bl]{\rule{24mm}{16mm}}}}%
\textcolor{cCmt}{\put(148.000,13.000){\makebox(0.000,0.000)[bl]{%
\shortstack[r]{where $x \otimes y$\\is defined as\\$x \* y + 1$}}}}%
% validate:
% 6*7*8*9 + 7*8*9 + 8*9 + 9 + 1 = 3610
% (((1*6+1)*7+1)*8+1)*9+1 = 3610
\end{picture}
\end{document}
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Licensing
[edit]- You are free:
- to share – to copy, distribute and transmit the work
- to remix – to adapt the work
- Under the following conditions:
- attribution – You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.
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Date/Time | Thumbnail | Dimensions | User | Comment | |
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current | 13:54, 25 September 2019 | 1,062 × 618 (39 KB) | Jochen Burghardt (talk | contribs) | User created page with UploadWizard |
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Software used | TeX |
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Conversion program | pdfTeX-1.40.18 |
Encrypted | no |
Page size | 510.236 x 297.638 pts |
Version of PDF format | 1.5 |