Polynomial Coefficient Calculators

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Maths Polynomial Coefficient

Calculate polynomial coefficients from real roots or zeros, or from XZ data points.

To calculate the coeficients from real roots, the value of An (the nth order coefficient) must be included in order to calculate a unique set of polynomial coefficients. The coefficients are listed in the order A0, A1, A2....An where An is the coefficient for the nth power of x (x^n) etc... The calculation is only valid for polynomials with no imaginary roots, ie the number of real roots equals the polynomial order.

The polynomial value, slope and curvature are calculated at X. The maximum and minimum points (zero slope), and the points of inflection (zero curvature), can not be calculated unless all points are real numbers.

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CALCULATOR : Polynomial Coefficients From Real Roots Or Zeros [FREE] ±

Calculate polynomial coefficients from the polynomial roots.

Enter the roots as a comma separated list, or as separate points on each line. The roots can also be copied and pasted from a spreadsheet. The roots may be entered in any order. There are an infinite number of polynomials with the same roots, so the value of An (the nth order coefficient) must be included in order to calculate a unique set of polynomial coefficients. The coefficients are listed in the order A0, A1, A2....An where An is the coefficient for the nth power of x (x^n) etc... The calculation is only valid for polynomials with no imaginary roots, ie the number of real roots equals the polynomial order.

Use the Result Plot option to plot the polymomial value, slope and curvature versus X.

Tool Input

R : Polynomial Roots
An : Nth Coefficient Value
X : Input X Value

Tool Output

C : Polynomial Curvature At X
P : Polynomial Value At X
S : Polynomial Slope At X

CALCULATOR : Polynomial Coefficients And Interpolation From Data Points [FREE] ±

Calculate polynomial coefficients from all polynomial data points using matrix factorisation.

Enter data as comma separated pairs (X,Z), with each pair on a new line, or copy and past cells from a spreadsheet. The data should be in ascending order.

The polynomial value, slope and curvature are calculated at either the user defined X, the root or zero, the maximum or minimum, or the point of inflection. The maximum and minimum can only be calculated for polynomials of second order or greater. The point of inflection can only be calculated for polynomials of third order or greater. The root, maximum or minimum, or point of inflection must be real.

The user defined Xu value is used as the initial guess value for calculating the root and other points. Use the Result Plot option to plot the polymomial value, slope and curvature versus X, and to determine suitable guess values for Xu.

Tool Input

ptype : Polynomial Calculation Type
- Xu : User Defined X Value or Guess Value
Xdata : X Data Values
Zdata : Z Data Values

Tool Output

C : Polynomial Curvature At X
P : Polynomial Value At X
S : Polynomial Slope At X
X : X Value (Input, Root, Maximum or Minimum, Or Inflection Point)
cvg : Convergence (== 1)
|M| : Matrix Determinant (!= 0)