Difference between revisions of "Coefficients Command"

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

Revision as of 10:49, 1 October 2015


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 of the coefficients a, b, c, d, e, f of a conic 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 line: 3x + 2y - 2 = 0:
x(line) returns 3
y(line) returns 2
z(line) returns -2

CAS Syntax

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 {a³ - 3 a² + 3 a}.
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