cyjax.polynomial.univariate_coefficients#

cyjax.polynomial.univariate_coefficients(poly, var)#

Polynomials for coefficients in each order for a single variable.

Given a multivariate polynomial poly, we single one variable (var) out and treat the others as constants. The coefficients of the single variate polynomial in var are then given by polynomials in the remaining “constant” variables. This function extracts the coefficients of the univariate polynomial in var in terms of polynomials in the remaining constant variables.

Example

>>> poly = 'z1**2 * z2 * x**2 + 3 * shift * (1 + x**2)'
>>> variables = ['x', 'z', 'shift']
>>> poly = Poly.from_sympy(poly, variables)
>>> coeff_polies = univariate_coefficients(poly, 'x')
>>> len(coeff_polies)  # degree in x is 2 so we get 3 coefficients
3
>>> print(coeff_polies[0])  # At degree x^2
Poly([z_1, z_2], shift) = 3*shift + z1**2*z2
>>> print(coeff_polies[1])  # At degree x^1
0.0
>>> print(coeff_polies[2])  # At degree x^0
Poly([z_1, z_2], shift) = 3*shift
Parameters:

  • poly (Poly) – multivariate polynomial.

  • var (Union[str, Symbol, ndarray[Any, dtype[Symbol]]]) – variable of interest.

Return type:

list[Poly]

Returns:

List of numerical values of instances of Poly, representing the coefficients of the polynomial in var.