Difference between revisions of "Coefficients Command"

Revision as of 13:20, 27 March 2013

Coefficients[ <Polynomial> ]: Yields the list of all coefficients \{a_k,a_{k-1},\ldots,a_1, a_0\} of the polynomial a_kx^k+a_{k-1}x^{k-1}+\cdots+a_1x+a_0.; Example:
Coefficients[x^3 - 3 x^2 + 3 x] yields {1, -3, 3, 0}, the list of all coefficients of x^3 - 3 x^2 + 3 x.

Coefficients[ <Conic> ]: Returns the list \{a, b, c, d, e, f\} for conics in standard form: a\cdot x^2 + b\cdot y^2 + c + d\cdot x\cdot y + e\cdot x + f\cdot y = 0

Hint: For a line in implicit form l: ax + by + c = 0 it is possible to obtain the coefficients using the syntax x(l), y(l), z(l).

Example: Given l: 3x + 2y - 2 = 0:

x(l) returns 3,

y(l) returns 2 and

z(l) returns -2.

Coefficients[ <Polynomial> ]: Yields the list of all coefficients of the polynomial in the main variable.; Example:
Coefficients[x^3 - 3 x^2 + 3 x] yields {1, -3, 3, 0}, the list of all coefficients of x^3 - 3 x^2 + 3 x.

Coefficients[ <Polynomial>, <Variable> ]

Yields the list of all coefficients of the polynomial in the given variable.

Example:

Coefficients[a^3 - 3 a^2 + 3 a, a] yields {1, -3, 3, 0}, the list of all coefficients of a^3 - 3 a^2 + 3 a, and
Coefficients[a^3 - 3 a^2 + 3 a, x] yields \{a^3 - 3 a^2 + 3 a\}.

@@ Line 2: / Line 2: @@
 {{command|cas=true|function}}
 ;Coefficients[ <Polynomial> ]
-:Yields the list of all coefficients of the polynomial.
+:Yields the list of all coefficients  <math>\{a_k,a_{k-1},\ldots,a_1, a_0\}</math>  of the polynomial  <math>a_kx^k+a_{k-1}x^{k-1}+\cdots+a_1x+a_0</math>.
 :{{example| 1=<div><code><nowiki>Coefficients[x^3 - 3 x^2 + 3 x]</nowiki></code> yields ''{1, -3, 3, 0}'', the list of all coefficients of <math>x^3 - 3 x^2 + 3 x</math>.</div>}}
 ;Coefficients[ <Conic> ]
-:It returns list <math>\{a, b, c, d, e, f\}</math> for conics in standard form:<br><hr>
+:Returns the list <math>\{a, b, c, d, e, f\}</math> for conics in standard form: <math>a\cdot x^2  +  b\cdot y^2 +  c + d\cdot x\cdot y +  e\cdot x  +  f\cdot y  =  0</math>
-:<center><small><math>a\cdot x^2  +  b\cdot y^2 +  c + d\cdot x\cdot y +  e\cdot x  +  f\cdot y  =  0</math></small></center><hr>
 :{{hint|1=For a line in implicit form <math>l: ax + by + c = 0</math> it is possible to obtain the coefficients using the syntax <math>x(l), y(l), z(l)</math>.