coefficient of (multivariate) expression
coeftayl(expr, eqn, k)
equation of the form x=α where x is a name (univariate case) or list (multivariate case)
non-negative integer (univariate case) or a list of non-negative integers (multivariate case)
This function computes a coefficient in the (multivariate) Taylor series representation of expr without forming the series (it uses differentiation and substitution). Often, expr is a polynomial.
The one-variable and several-variable cases are distinguished by the types of the input parameters.
UNIVARIATE CASE: x is a name and k a non-negative integer.
In this case, the value returned is the coefficient of x−αk in the Taylor series expansion of expr about x=α. This is equivalent to executing coeff⁡taylor⁡expr,x=α,k+1,x−α,k but it is more efficient (because only a single term is computed).
MULTIVARIATE CASE: x is a nonempty list x1,…,xv of indeterminates appearing in expr and α is a list α1,…,αv specifying the point of expansion with respect to the given indeterminates; k is a list k1,…,kv of non-negative integers corresponding to elements in x and α.
In this case, the value returned is the coefficient of the term specified by the monomial
in the multivariate Taylor series expansion of expr about the point x=α. If k is the list of zeros then the value returned is the value resulting from substituting x=α into expr.
p ≔ 2⁢x2+3⁢y3−5
q ≔ 3⁢a⁢x+12+sin⁡a⁢x2⁢y−y2⁢x+x−a
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