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
Typing the name of the matrix P now results in Polynomial matrix in s: 2-by-2, degree: 3 P = Matrix coefficient at s^0 : 1 0 0 1 Matrix coefficient at s^1 : 1 0 0 2 Matrix coefficient at s^2 : 0 1 0 1 Matrix coefficient at s^3 : 0 0 2 0 Simple operations with polynomial matrices Addition, subtraction and multiplication In the Polynomial Toolbox polynomial matrices are objects for which all standard operations are defined. Define the polynomial matrices P = [ 1+s 2; 3 4], Q = [ s^2 1-s; s^3 1] P = Q = 1 + s 2 3 4 s^2 1-s s^3 1 The sum and product of P and Q follow easily: S = P+Q S = R = P*Q 1 + s + s^2 3 - s 3 + s^3 5
Entrywise and matrix division Operations with fractions R = s^2 + 3s^3 3 - s^2 3s^2 + 4s^3 7 - 3s Entrywise division of polynomial matrices P and Q yields a fraction T = P./Q results in T = 1 + s 2 ----- ----- s^2 1 - s 3 4 --- - s^3 1 Right matrix division gets a fraction U = P/Q U = 1 PQ 1 + s 2 / s^2 1 - s 3 4 / s^3 1 Left matrix division gets a fraction V = Q\P U = 1 Q P s^2 1 - s \ 1 + s 2 s^3 1 \ 3 4 Polynomial fractions may also enter arithmetic operations, possibly mixed with numbers or polynomials such as or 2*U ans = 2 + 2s 4 / s^2 1 - s 6 8 / s^3 1 P+T ans =
- Page 2 and 3: PolyX, Ltd E-mail: info@polyx.com S
- 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 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
- Page 52 and 53: Non-symmetric factorization or 1 0
- Page 54 and 55: Transformation to Kronecker canonic
- Page 56 and 57: common roots (including roots at in
- Page 58 and 59: Derivatives and integrals ans = ans
Typing the name of the matrix<br />
P<br />
now results in<br />
<strong>Polynomial</strong> matrix in s: 2-by-2, degree: 3<br />
P =<br />
Matrix coefficient at s^0 :<br />
1 0<br />
0 1<br />
Matrix coefficient at s^1 :<br />
1 0<br />
0 2<br />
Matrix coefficient at s^2 :<br />
0 1<br />
0 1<br />
Matrix coefficient at s^3 :<br />
0 0<br />
2 0<br />
Simple operations with polynomial matrices<br />
Addition,<br />
subtraction and<br />
multiplication<br />
In the <strong>Polynomial</strong> <strong>Toolbox</strong> polynomial matrices are objects <strong>for</strong> which all standard<br />
operations are defined.<br />
Define the polynomial matrices<br />
P = [ 1+s 2; 3 4], Q = [ s^2 1-s; s^3 1]<br />
P =<br />
Q =<br />
1 + s 2<br />
3 4<br />
s^2 1-s<br />
s^3 1<br />
<strong>The</strong> sum and product of P and Q follow easily:<br />
S = P+Q<br />
S =<br />
R = P*Q<br />
1 + s + s^2 3 - s<br />
3 + s^3 5
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