Difference between revisions of "Coefficients Command"

Latest revision as of 10:00, 25 September 2019

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.

Note: There's a special mode (for non-polynomials) for the output of the fitting commands eg if f(x) = FitExp(l1) then Coefficients(f) will return the calculated parameters

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}.

@@ Line 1: / Line 1: @@
-<noinclude>{{Manual Page|version=4.2}}</noinclude>
+<noinclude>{{Manual Page|version=5.0}}</noinclude>{{command|cas=true|function}}
-{{command|cas=true|function}}
+;Coefficients( <Polynomial> )
-;Coefficients[ <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>.
-:Yields the list of all coefficients of the polynomial.
+:{{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>}}
-:{{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>}}
+:{{note|1=There's a special mode (for non-polynomials) for the output of the fitting commands eg if <code>f(x) = FitExp(l1)</code> then <code>Coefficients(f)</code> will return the calculated parameters  }}
-;Coefficients[ <Conic> ]
+;Coefficients( <Conic> )
-:It returns list <math>\{a, b, c, d, e, f\}</math> for conics in standard form:<br><hr>
+:Returns the list of the coefficients ''a'', ''b'', ''c'', ''d'', ''e'', ''f'' of a conic 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>
+:{{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>:
-:{{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>.
+::*<code>x(line)</code> returns 3
-::{{example|1= Given <code>l: 3x + 2y - 2 = 0</code>:
+::*<code>y(line)</code> returns 2
-:::<code>x(''l'')</code> returns 3,
+::*<code>z(line)</code> returns -2}} }}
-:::<code>y(''l'')</code> returns 2 and
-:::<code>z(''l'')</code> returns -2.}} }}
 ==CAS Syntax==
-;Coefficients[ <Polynomial> ]
+;Coefficients( <Polynomial> )
 :Yields the list of all coefficients of the polynomial in the main variable.
-:{{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>}}
+:{{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[ <Polynomial>, <Variable> ]
+;Coefficients( <Polynomial>, <Variable> )
 :Yields the list of all coefficients of the polynomial in the given variable.
 :{{example| 1=<div>
-:* <code><nowiki>Coefficients[a^3 - 3 a^2 + 3 a, a]</nowiki></code> yields ''{1, -3, 3, 0}'', the list of all coefficients of <math>a^3 - 3 a^2 + 3 a</math>, and
+:* <code><nowiki>Coefficients(a^3 - 3 a^2 + 3 a, a)</nowiki></code> yields ''{1, -3, 3, 0}'', the list of all coefficients of <math>a^3 - 3 a^2 + 3 a</math>
-:* <code><nowiki>Coefficients[a^3 - 3 a^2 + 3 a, x]</nowiki></code> yields <math>\{a^3 - 3 a^2 + 3 a\}</math>.</div>}}
+:* <code><nowiki>Coefficients(a^3 - 3 a^2 + 3 a, x)</nowiki></code> yields {''a''³ - 3 ''a''² + 3 ''a''}.</div>}}

Difference between revisions of "Coefficients Command"

Latest revision as of 10:00, 25 September 2019

Coefficients

Command Categories (All commands)

CAS Syntax