return a univariate polynomial from a Vector of coefficients - Maple Help

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PolynomialTools[FromCoefficientVector] - return a univariate polynomial from a Vector of coefficients

PolynomialTools[FromCoefficientList] - return a univariate polynomial from list of coefficients

 Calling Sequence FromCoefficientList(L, x, opts) FromCoefficientVector(L, x, opts)

Parameters

 L - list of coefficients x - name for the polynomial variable opts - (optional) equations of the form option=value (see below)

Description

 • The FromCoefficientList(L, x) calling sequence returns a polynomial in x from a list of coefficients.
 • The FromCoefficientVector(L, x) calling sequence returns a polynomial in x from a vector of coefficients.
 • These are inverse commands to CoefficientList and CoefficientVector.
 • FromCoefficientVector is written to handle sparse Vector inputs efficiently.

Examples

 > $\mathrm{with}\left(\mathrm{PolynomialTools}\right):$
 > $\mathrm{FromCoefficientList}\left(\left[1,-1,2,3\right],x\right)$
 ${3}{}{{x}}^{{3}}{+}{2}{}{{x}}^{{2}}{-}{x}{+}{1}$ (1)
 > $\mathrm{FromCoefficientList}\left(\left[1,-1,2,3\right],x,\mathrm{form}=\mathrm{horner}\right)$
 ${x}{}\left({-}{1}{+}{x}{}\left({2}{+}{3}{}{x}\right)\right){+}{1}$ (2)
 > $\mathrm{FromCoefficientList}\left(\left[1,0,0,2,0\right],x,\mathrm{termorder}=\mathrm{reverse}\right)$
 ${{x}}^{{4}}{+}{2}{}{x}$ (3)
 > $\mathrm{FromCoefficientVector}\left(⟨{y}^{3},-{y}^{2},y-2,1⟩,x\right)$
 ${{y}}^{{3}}{-}{{y}}^{{2}}{}{x}{+}\left({y}{-}{2}\right){}{{x}}^{{2}}{+}{{x}}^{{3}}$ (4)
 > $\mathrm{FromCoefficientList}\left(\left[\right],x\right)$
 ${0}$ (5)
 > $\mathrm{FromCoefficientVector}\left(\mathrm{CoefficientVector}\left(0,x\right),x\right)$
 ${0}$ (6)

Most vector shapes will be handled efficiently

 > $\mathrm{v1}:=\mathrm{Vector}\left(500000001,\mathrm{shape}={\mathrm{unit}}_{300}\right):$
 > $\mathrm{FromCoefficientVector}\left(\mathrm{v1},x\right)$
 ${{x}}^{{300}}$ (7)
 > $\mathrm{v2}:=\mathrm{Vector}\left(200000001,\mathrm{shape}={\mathrm{scalar}}_{50000,a}\right):$
 > $\mathrm{FromCoefficientVector}\left(\mathrm{v2},x\right)$
 ${a}{}{{x}}^{{50000}}$ (8)
 > $\mathrm{v3}:=\mathrm{Vector}\left(10,\mathrm{shape}={\mathrm{constant}}_{{b}^{2}-1}\right):$
 > $\mathrm{FromCoefficientVector}\left(\mathrm{v3},x\right)$
 $\left({{b}}^{{2}}{-}{1}\right){}\left({{x}}^{{9}}{+}{{x}}^{{8}}{+}{{x}}^{{7}}{+}{{x}}^{{6}}{+}{{x}}^{{5}}{+}{{x}}^{{4}}{+}{{x}}^{{3}}{+}{{x}}^{{2}}{+}{x}{+}{1}\right)$ (9)
 > $\mathrm{v4}:=\mathrm{Vector}\left(1000000001,\left\{1=5,1000000001=1\right\},\mathrm{storage}=\mathrm{sparse}\right):$
 > $\mathrm{FromCoefficientVector}\left(\mathrm{v4},x\right)$
 ${{x}}^{{1000000000}}{+}{5}$ (10)