Sysquake User Manual 2 Sysquake User Manual ©1999-2016, Calerga Sàrl Copyright 1999-2016, Calerga Sàrl. No part of this publication may be reproduced, transmitted or stored in any form or by any means including electronic, mechanical, recording or oth- erwise, without the express written permission of Calerga Sàrl. The information provided in this manual is for reference and information use only, and Calerga assumes no responsibility or liability for any inaccu- racies or errors that may appear in this documentation. Improvements to Sysquake brought by minor releases are described in the electronic documen- tation; please read the file ReadMe for a summary. Sysquake, Calerga, the Calerga logo, and icons are copyrighted and are protected under the Swiss and international laws. Copying this software for any reason beyond archival purposes is a violation of copyright, and violators may be subject to civil and criminal penalties. Sysquake, LME, and Calerga are trademarks of Calerga Sàrl. All other trademarks are the property of their respective owners. Sysquake User Manual, December 2016. Calerga Sàrl, La Tour-de-Peilz, Switzerland. Most of the material in Sysquake User Manual has first been written as a set of XHTML files, with lots of cross-reference links. Since (X)HTML is not very well suited for printing, it has been converted to LATEX with the help of a home-made conversion utility. Additional XML tags have been used to benefit from LATEX features: e.g. raster images have been replaced with EPS images, equations have been converted from text to real mathematic notation, and a table of contents and an index have been added. The same method has been used to create the material for the help command. Thanks to the make utility, the whole process is completely automatic. This system has proved to be very flexible to maintain three useful formats in parallel: two for on-line help, and one for high-quality printing. World Wide Web: http://www.calerga.com E-mail: [email protected] Mail: Calerga Sàrl Ch. des Murs Blancs 25 1814 La Tour-de-Peilz Switzerland Typesetting: 2016-12-27 Contents 1 Introduction 7 1.1 Introduction . 7 1.2 How Sysquake can be used . 8 2 Registration 13 2.1 Where SQ_Reg.key is located . 13 2.2 Remark . 14 2.3 What’s in the Serial Number . 14 3 Getting Started with Sysquake 17 3.1 First steps . 17 3.2 Files . 18 3.3 Manipulation modes . 19 3.4 Menus . 21 3.5 Command-Line Interface . 32 3.6 Interruption Key . 32 3.7 Memory . 32 3.8 Extensions . 33 3.9 Preference Files . 33 3.10 Environment Variables . 34 4 SQ Files 35 4.1 PID_ct.sq . 35 4.2 PID_dt.sq . 38 4.3 RST_ct.sq . 40 4.4 RST_dt.sq . 47 4.5 LQR_ct.sq . 53 4.6 filter.sq . 55 4.7 id_par.sq . 58 4.8 id_npar.sq . 60 5 Introduction to LME 63 5.1 Simple operations . 65 5.2 Complex Numbers . 66 5.3 Vectors and Matrices . 68 4 Sysquake User Manual ©1999-2016, Calerga Sàrl 5.4 Polynomials . 71 5.5 Strings . 72 5.6 Variables . 73 5.7 Loops and Conditional Execution . 73 5.8 Functions . 74 5.9 Local and Global Variables . 76 6 SQ Script Tutorial 79 6.1 Displaying a Plot . 79 6.2 Adding Interactivity . 81 7 SQ Script Reference 83 8 SQ File Tutorial 87 8.1 Displaying a Plot . 88 8.2 Adding Interactivity . 93 8.3 Menu Entries . 95 8.4 More about graphic ID . 98 8.5 Saving Data . 101 9 SQ File Reference 103 9.1 SQ Files . 103 9.2 SQ Data Files and Input/Output Handlers . 127 9.3 Error Messages . 130 9.4 Advanced Features of SQ Files . 131 10LME Reference 143 10.1 Program format . 143 10.2 Function Call . 145 10.3 Named input arguments . 145 10.4 Command syntax . 146 10.5 Libraries . 146 10.6 Types . 147 10.7 Input and Output . 157 10.8 Error Messages . 158 10.9 Character Set . 163 10.10 Formatted text . 164 10.11 List of Commands, Functions, and Operators . 169 10.12 Variable Assignment and Subscripting . 183 10.13 Programming Constructs . 190 10.14 Debugging Commands . 207 10.15 Profiler . 214 10.16 Miscellaneous Functions . 216 10.17 Sandbox Function . 245 10.18 Help Function . 247 10.19 Operators . 250 10.20 Mathematical Functions . 280 Contents 5 10.21 Linear Algebra . 337 10.22 Array Functions . 384 10.23 Triangulation Functions . 423 10.24 Integer Functions . 430 10.25 Non-Linear Numerical Functions . 433 10.26 String Functions . 455 10.27 Quaternions . 483 10.28 List Functions . 493 10.29 Structure Functions . 497 10.30 Object Functions . 504 10.31 Logical Functions . 509 10.32 Dynamical System Functions . 519 10.33 Input/Output Functions . 528 10.34 File System Functions . 545 10.35 Path Manipulation Functions . 547 10.36 XML Functions . 549 10.37 Search Path Function . 557 10.38 Time Functions . 558 10.39 Date Functions . 561 10.40 Threads . 563 10.41 Parallel . 568 10.42 Sysquake Graphics . 580 10.43 Remarks on graphics . 583 10.44 Base Graphical Functions . 587 10.45 3D Graphics . 624 10.46 Graphics for Dynamical Systems . 638 10.47 Sysquake Graphical Functions . 672 10.48 Dialog Functions . 692 10.49 Sysquake Miscellaneous Functions . 697 11Libraries 703 11.1 stdlib . 704 11.2 stat . 715 11.3 probdist . 725 11.4 polynom . 730 11.5 ratio . 740 11.6 bitfield . 742 11.7 filter . 748 11.8 lti . 758 11.9 lti (graphics) . 790 11.10 sigenc . 797 11.11 wav . 803 11.12 date . 804 11.13 constants . ..