coeff - Maple Help

coeff

extract a coefficient of a polynomial

 Calling Sequence coeff(p, x) coeff(p, x, n) coeff(p, x^n)

Parameters

 p - polynomial in x x - variable (expression) n - (optional) integer

Description

 • 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.

Examples

 > $p≔2{x}^{2}+3{y}^{3}-5:$

coeff(p, x^n) is equivalent to coeff(p, x, n) for n<>0.

 > $\mathrm{coeff}\left(p,x,2\right)$
 ${2}$ (1)
 > $\mathrm{coeff}\left(p,{x}^{2}\right)$
 ${2}$ (2)

To find the constant term of the equation, let the exponent of x be zero.

 > $\mathrm{coeff}\left(p,x,0\right)$
 ${3}{}{{y}}^{{3}}{-}{5}$ (3)

The command coeff works with any variable.

 > $\mathrm{coeff}\left(p,{y}^{3}\right)$
 ${3}$ (4)

However, the following form is not allowed:

 > $r≔{x}^{2}+4x-6xy+9$
 ${r}{≔}{{x}}^{{2}}{-}{6}{}{x}{}{y}{+}{4}{}{x}{+}{9}$ (5)
 > $\mathrm{coeff}\left(r,xy\right)$

A more difficult example: the polynomial does not need to be expanded for coeff(p, x^n) to work.

 > $q≔3a{\left(x+1\right)}^{2}+\mathrm{sin}\left(a\right){x}^{2}y-{y}^{2}x+x-a$
 ${q}{≔}{3}{}{a}{}{\left({x}{+}{1}\right)}^{{2}}{+}{\mathrm{sin}}{}\left({a}\right){}{{x}}^{{2}}{}{y}{-}{{y}}^{{2}}{}{x}{+}{x}{-}{a}$ (6)
 > $\mathrm{coeff}\left(q,x\right)$
 ${-}{{y}}^{{2}}{+}{6}{}{a}{+}{1}$ (7)
 > $\mathrm{expand}\left(q\right)$
 ${3}{}{a}{}{{x}}^{{2}}{+}{6}{}{a}{}{x}{+}{2}{}{a}{+}{\mathrm{sin}}{}\left({a}\right){}{{x}}^{{2}}{}{y}{-}{{y}}^{{2}}{}{x}{+}{x}$ (8)