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poly
Polynomial definition from given roots or coefficients, or characteristic to a square matrix.
Syntax
p = poly(vec, vname) p = poly(vec, vname, "roots"|"coeff") Pc = poly(matNN, vname)
Arguments
- vname
a string: the symbolic variable name of the polynomial. Allowed characters are the same as for variables names (see naming rules).
- vec
scalar, vector, or non-square matrix of real or complex numbers.
- flag "roots" (default) | "coeff" (or "r" | "c")
Indicates what numbers in
vec
represent."roots"
is the default value.Shortcuts can be used:
"r"
for"roots"
, and"c"
for"coeff"
.- p
Polynomial with given roots or coefficients and symbolic variable name.
- matNN
Square matrix of real or complex numbers.
- Pc
Characteristic polynomial of the given square matrix, =
det(x*eye() - matNN)
, with the symbolic variablex = poly(0,vname)
.
Description
- When a vector or non-square matrix
vec
is provided, p = poly(vec, "x", "roots")
orp = poly(vec, "x")
is the polynomial whose roots are thevec
components, and"x"
is the name of its variable.degree(p)==length(vec)
poly()
androots()
are then inverse functions of each other.- Infinite roots give null highest degree coefficients.
In this case, the actual degree of
p
is smaller thanlength(vec)
. For instance,poly([-%inf -1 2 %inf ], "x")
yields(x-2)(x+1)
whose degree is 2.
The simple expression
x=poly(0,"x")
defines the elementaryp(x)=x
, which then can be used with usual operators +, -, *, / and simple functions likesum()
.Scilab provides 3 predefined elementary polynomials%s
,%z
, and$
. The last one is mainly used as symbolic value of last index (of a range).poly(vec, "x", "coeff")
builds the polynomial with symbol"x"
whose coefficients in order of increasing degree arevec
components (vec(1)
is the constant term of the polynomial). Null high order coefficients (appended tovec
) are ignored.Conversely,coeff(p)
returns the coefficients of a given polynomial.
- When a square matrix
matNN
is provided, poly(matNN, vname)
returns its characteristic polynomial of symbolic variablevname
, i.e.p
is set todet(x*eye() - matNN)
, withx = poly(0,vname)
.
Examples
Building a polynomial of given coefficients:
// Direct building: x = poly(0, "x"); p = 1 - x + 2*x^3 // With poly(): p2 = poly([1 -1 0 2], "x", "coeff") // With null high order coefficients p3 = poly([2 0 -3 zeros(1,8)], "y", "coeff")
--> p = 1 - x + 2*x^3 p = 3 1 -x +2x --> p2 = poly([1 -1 0 2], "x", "coeff") p2 = 3 1 -x +2x --> p3 = poly([2 0 -3 zeros(1,8)], "y", "coeff") p3 = 2 2 -3y
Building a polynomial of given roots:
// Direct building: x = poly(0,"x"); p = (1-x)^2 * (2+x) // With poly(): p2 = poly([1 1 -2], "x") // With infinite roots p3 = poly([%inf -1 2 %inf -%inf], "x")
--> p = (1-x)^2 * (2+x) p = 3 2 -3x +x --> p2 = poly([1 1 -2], "x") p2 = 3 2 -3x +x --> p3 = poly([%inf -1 2 %inf -%inf], "x") p3 = 2 -2 -x +x
Characteristic polynomial of a square matrix:
A = [1 2 ; 3 -4] poly(A, "x")
--> A = [1 2 ; 3 -4] A = 1. 2. 3. -4. --> poly(A, "x") ans = 2 -10 +3x +x
See also
- inv_coeff — constrói uma matriz de polinômios a partir de seus coeficientes
- coeff — coeficientes de matrizes de polinômios
- roots — raízes de polinômios
- varn — variável simbólica de polinômios ou de frações racionais
- horner — avaliação polinomial/racional
- %s — A variable used to define polynomials.
- %z — A variable used to define polynomials.
- rational — razão de polinômios
- rlist — definição de função racional do Scilab
History
Versão | Descrição |
5.5.0 | The only values allowed for the third argument are "roots", "coeff", "c" and "r". |
6.0.0 | The name of the symbolic variable is no longer limited to 4 characters. It can include some extended UTF-8 characters. |
6.0.2 | With the "coeff" method, null high order coefficients are now ignored. |
Report an issue | ||
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