The Polynomial Toolbox for MATLAB - DCE FEL ČVUT v Praze
The Polynomial Toolbox for MATLAB - DCE FEL ČVUT v Praze The Polynomial Toolbox for MATLAB - DCE FEL ČVUT v Praze
PolyX, Ltd E-mail: info@polyx.com Support: support@polyx.com Sales: sales@polyx.com Web www.polyx.com Tel. +420-603-844-561, +420-233-323-801 Fax +420-233-323-802 Jarni 4 Prague 6, 16000 Czech Republic Polynomial Toolbox 3.0 Manual © COPYRIGHT 2009 by PolyX, Ltd. The software described in this document is furnished under a license agreement. The software may be used or copied only under the terms of the license agreement. No part of this manual may be photocopied or reproduced in any form without prior written consent from PolyX, Ltd. Printing history: September 2009. First printing.
Contents 1 Quick Start ........................................................................................................ 8 Initialization .................................................................................................................... 8 Help ................................................................................................................................. 8 How to define a polynomial matrix .............................................................................. 9 Simple operations with polynomial matrices ............................................................. 10 Addition, subtraction and multiplication ........................................................ 10 Entrywise and matrix division ........................................................................ 11 Operations with fractions ................................................................................ 11 Concatenation and working with submatrices ................................................ 12 Coefficients and coefficient matrices .............................................................. 13 Conjugation and transposition ........................................................................ 13 Advanced operations and functions ........................................................................... 14 2 Polynomial matrices ....................................................................................... 16 Introduction .................................................................................................................. 16 Polynomials and polynomial matrices ........................................................................ 16 Entering polynomial matrices ..................................................................................... 16 The pol command ......................................................................................... 17 The Polynomial Matrix Editor ........................................................................ 17 The default indeterminate variable ................................................................. 17 Changing the default indeterminate variable .................................................. 18 Basic manipulations with polynomial matrices ......................................................... 19 Concatenation and working with submatrices ................................................ 19 Coefficients ..................................................................................................... 19 Degrees and leading coefficients .................................................................... 20 Constant, zero and empty matrices ................................................................. 21 Values ............................................................................................................. 21 Derivative and integral .................................................................................... 21 Arithmetic operations on polynomial matrices ......................................................... 22 Addition, subtraction and multiplication ........................................................ 22 Determinants, unimodularity and adjoints ...................................................... 23
- Page 4 and 5: Rank ..............................
- Page 6 and 7: Resampling of polynomials in z ....
- Page 8 and 9: 1 Quick Start Initialization Help E
- Page 10 and 11: Typing the name of the matrix P now
- Page 12 and 13: Concatenation and working with subm
- Page 14 and 15: ans = 1 0 0 1 s^2 s^3 1 - s 1 The c
- Page 16 and 17: 2 Polynomial matrices Introduction
- Page 18 and 19: Changing the default indeterminate
- Page 20 and 21: Degrees and leading coefficients R
- Page 22 and 23: 3 + 8s integral(F) ans = 2s + 1.5s^
- Page 24 and 25: isunimod(U) ans = 1 Also the adjoin
- Page 26 and 27: Bases and null spaces ans = 1 confi
- Page 28 and 29: If P( s) is square then its roots a
- Page 30 and 31: and simply type or or hurwitz(p) an
- Page 32 and 33: Least common multiple If the only c
- Page 34 and 35: Greatest common left divisor 0 -3 +
- Page 36 and 37: Dual concepts M = lrm(A,B) M = 0.32
- Page 38 and 39: 0 1 s^2 -s^3 -s 0 Reduced and canon
- Page 40 and 41: Another triangular form Hermite for
- Page 42 and 43: Invariant polynomials The entries a
- Page 44 and 45: Bézout equations Matrix polynomial
- Page 46 and 47: Factorizations returns X = Y = 0.25
- Page 48 and 49: zpplot(1-s^2), grid zpplot(1+2*s^2+
- Page 50 and 51: Spectral factorization zpplot(1+2*i
PolyX, Ltd<br />
E-mail: info@polyx.com<br />
Support: support@polyx.com<br />
Sales: sales@polyx.com<br />
Web www.polyx.com<br />
Tel. +420-603-844-561, +420-233-323-801<br />
Fax +420-233-323-802<br />
Jarni 4<br />
Prague 6, 16000<br />
Czech Republic<br />
<strong>Polynomial</strong> <strong>Toolbox</strong> 3.0 Manual<br />
© COPYRIGHT 2009 by PolyX, Ltd.<br />
<strong>The</strong> software described in this document is furnished under a license agreement.<br />
<strong>The</strong> software may be used or copied only under the terms of the license agreement.<br />
No part of this manual may be photocopied or reproduced in any <strong>for</strong>m without prior<br />
written consent from PolyX, Ltd.<br />
Printing history: September 2009. First printing.
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