operator recordPolynomial
Record defining the data for a polynomial
Information
This record defines a polynomial, e.g., y = 2*x^2 + 3*x + 1. The general form is:
y = c[1]*x^n + c[2]*x^(n-1) + ... + c[n]*x + c[n+1];
In the record, the coefficients c[i] are stored. Usually, the record is not directly accessed. Instead, a polynomial is generated with the functions provided in the record such as Polynomial.base(..), Polynomial.fitting(..). Several functions are provided that operate on polynomials.
Components
| Type | Name | Default | Description |
|---|---|---|---|
| Real[:] | c | Polynomial coefficients (c[1]*x^n + ... c[n]*x + c[n+1]) |
Contents
| Name | Description |
|---|---|
 Examples | Package of examples to demonstrate the usage of polynomials |
| 'constructor' | Collection of operators to construct a Polynomial data record |
| '-' | Collection of operators for subtraction of polynomials |
| '+' | Add two polynomials (p1 + p2) |
| '*' | Multiply two polynomials (p1 * p2) |
| '/' | Divide two polynomials (p1 / p2) |
| '^' | Integer power of polynomial (p^n) |
| '==' | Check whether two polynomials are identical |
| 'String' | Transform Polynomial into a String representation |
| x | Generate a base polynomial y=x |
| fitting | Computes a Polynomial that fits a set of data points in a least-squares sense |
| degree | Return degree of polynomial |
| degree2 | Return degree of polynomial |
| plot | Plot polynomial y=p(x) |
| derivative | Derivative of Polynomial |
| integral | Indefinite integral of Polynomial |
| evaluate | Evaluate a Polynomial at a given (Real) abszissa value |
| evaluateMatrix | Evaluate a Polynomial with a matrix argument |
| evaluateComplex | Evaluate a Polynomial at a given (Complex) abszissa value |
| derivativeValue | Integral of polynomial p(x) from x_low to x_high |
| integralValue | Integral of polynomial p(x) from x_low to x_high |
| roots | Determine zeros of polynomial, i.e., points x with p(x)=0 |
| numberOfRoots | Determine number of roots of polynomial |
| rootsOfNonZeroHighestCoefficientPolynomial | Determine zeros of polynomial where highest coefficient of polynomial is not zero |
| evaluate_der | Evaluate derivative of polynomial at a given abszissa value |
| integralValue_der | Evaluate derivative of integral of polynomial p(x) from x_low to x_high, assuming only x_high as time-dependent (Leibniz rule) |
 Internal | Internal library of record Polynomial (should not be directly used by user) |