extract a coefficient of a polynomial
coeff(p, x, n)
polynomial in x
The coeff function extracts the coefficient of x^n in the polynomial p.
If the third argument is omitted, it is determined by looking at the second argument. Thus coeff(p, x^n) is equivalent to coeff(p, x, n) for n <> 0.
The cases of the second argument being a number or a product are disallowed since they do not make sense.
The related functions lcoeff, tcoeff, and coeffs extract the leading coefficient, trailing coefficient and all the coefficients of p in x respectively.
The coeff command is thread-safe as of Maple 15.
For more information on thread safety, see index/threadsafe.
p ≔ 2⁢x2+3⁢y3−5:
coeff(p, x^n) is equivalent to coeff(p, x, n) for n<>0.
To find the constant term of the equation, let the exponent of x be zero.
The command coeff works with any variable.
However, the following form is not allowed:
r ≔ x2+4⁢x−6⁢x⁢y+9
Error, invalid input: coeff received x*y, which is not valid for its 2nd argument, x
A more difficult example: the polynomial does not need to be expanded for coeff(p, x^n) to work.
q ≔ 3⁢a⁢x+12+sin⁡a⁢x2⁢y−y2⁢x+x−a
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