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CoefficientArrays

CoefficientArrays
gives the arrays of coefficients of the variables vars in the polynomials polys.
  • Any element of polys of the form is taken to correspond to the polynomial . »
  • CoefficientArrays takes all expressions in polys that match any of the to be variables.
  • The length of the list CoefficientArrays is one more than the total degree of polys.
  • The are sparse arrays with ranks .
  • The first element has the same length as the list polys.
  • If polys is a single polynomial rather than a list, is also not a list.
  • For nonlinear equations, the are not unique. CoefficientArrays by default assigns nonzero coefficients only to monomials where the variables appear in the same order as vars.
  • CoefficientArrays[polys, vars, Symmetric->True] makes all the symmetric in all their indices. The resulting arrays will generally be less sparse.
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Linear polynomial:
List of linear polynomials:
Nonlinear polynomials:
Polynomial equations:
The default coefficient of a quadratic form corresponding to is zero:
With True, CoefficientArrays gives symmetric arrays:
Convert linear equations to arrays suitable for LinearSolve:
The polynomial can be reconstructed by using Dot ():
The symmetric coefficient arrays correspond to vector derivatives at the origin:
CoefficientArrays gives a list of arrays of polynomial coefficients ordered by total degrees:
CoefficientList gives a tensor of the coefficients:
Use Coefficient to find the coefficient of :
In the position is concatenated with a s and b s ( and indicate the first and second variables):
In the coefficient of is the element at position :
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