Difference between revisions of "Coefficients Command"

Revision as of 17:45, 29 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

Note: 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
Coefficients[a^3 - 3 a^2 + 3 a, x] yields \{a^3 - 3 a^2 + 3 a\}.

@@ Line 7: / Line 7: @@
 :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>
 :{{note|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>.
-::{{example|1= Given <code>l: 3x + 2y - 2 = 0</code>:
+::{{example|1= Given <code>l: 3x + 2y - 2 = 0</code>: <code>x(l)</code> returns 3, <code>y(l)</code> returns 2, and <code>z(l)</code> returns -2}} }}
-:::<code>x(''l'')</code> returns 3
-:::<code>y(''l'')</code> returns 2
-:::<code>z(''l'')</code> returns -2}} }}
 ==CAS Syntax==
 ;Coefficients[ <Polynomial> ]