R8POLY
Polynomials with R8 Coefficients

R8POLY is a Python library which contains a number of utilities for polynomials with R8 coefficients, that is, using double precision or 64 bit real arithmetic.

Licensing:

The computer code and data files made available on this web page are distributed under the GNU LGPL license.

Languages:

R8POLY is available in a C++ version and a C version and a FORTRAN90 version and a MATLAB version and a Python version.

Related Data and Programs:

LEGENDRE_PRODUCT_POLYNOMIAL, a Python library which defines Legendre product polynomials, creating a multivariate polynomial as the product of univariate Legendre polynomials.

MONOMIAL, a Python library which enumerates, lists, ranks, unranks and randomizes multivariate monomials in a space of M dimensions, with total degree less than N, equal to N, or lying within a given range.

POLYNOMIAL, a Python library which adds, multiplies, differentiates, evaluates and prints multivariate polynomials in a space of M dimensions.

Source Code:

• r8_sign.py, returns the sign of an R8.
• r82poly2_print.py, prints a second order polynomial in two variables;
• r82poly2_type.py, analyzes a second order polynomial in two variables.
• r82poly2_type_print.py, prints the meaning of the output from R82POLY2_TYPE.
• r8mat_inverse_3d.py, computes the inverse of a 3 by 3 R8MAT;
• r8mat_print.py, prints an R8MAT;
• r8mat_print_some.py, prints some of an R8MAT;
• r8poly_degree.py, returns the degree of a polynomial;
• r8poly_deriv.py, returns the derivative of a polynomial;
• r8poly_lagrange_0.py, evaluates the Lagrange factor at a point;
• r8poly_lagrange_1.py, evaluates the first derivative of the Lagrange factor at a point;
• r8poly_lagrange_2.py, evaluates the second derivative of the Lagrange factor at a point;
• r8poly_lagrange_coef.py, returns the coefficients of a Lagrange polynomial;
• r8poly_lagrange_factor.py, evaluates the polynomial Lagrange factor at a point;
• r8poly_lagrange_val.py, evaluates the IPOL-th Lagrange polynomial;
• r8poly_order.py, returns the order of a polynomial.
• r8poly_print.py, prints a polynomial;
• r8poly_shift.py, adjusts the coefficients of a polynomial for a new argument.
• r8poly_value.py, evaluates a polynomial using a naive method;
• r8poly_value_horner.py, evaluates a polynomial using Horner's method;
• r8poly_value_2d.py, evaluates a polynomial of X and Y of total degree M, using a coefficient ordering that begins with the constant term.
• r8poly_values_horner.py, evaluates a polynomial, using Horner's method.
• r8poly2_ex.py, finds the extremal point of a parabola determined by three points.
• r8poly2_ex2.py, finds the extremal point of a parabola determined by three points.
• r8poly2_root.py, returns the two roots of a quadratic polynomial.
• r8poly2_rroot.py, returns the real parts of the two roots of a quadratic polynomial.
• r8poly2_val.py, evaluates a parabola defined by three data values.
• r8poly2_val_f.py
• r8poly2_val2.py, evaluates a parabolic interpolant through tabular data.
• r8poly3_root.py, returns the three roots of a cubic polynomial.
• r8poly4_root.py, returns the four roots of a quartic polynomial.
• r8vec_even.py, returns an R8VEC of N values evenly spaced between given limits;
• r8vec_even_select.py, returns the I-th of N evenly spaced values;
• r8vec_is_distinct.py, is true if all entries of an R8VEC are distinct;
• r8vec_linspace.py, returns an R8VEC of values evenly spaced between given limits.
• r8vec_print.py, prints an R8VEC;
• r8vec_transpose_print.py, prints the "transpose" of an R8VEC.
• roots_to_r8poly.py, converts polynomial roots to polynomial coefficients;
• timestamp.py, prints the current YMDHMS date as a timestamp;

Examples and Tests:

• r8poly_test.py, runs all the tests;
• r8poly_test.txt, the output file;

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