Difference between revisions of "Coefficients Command"

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(Autogenerated from properties)
(:{{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 }})
 
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<noinclude>{{Manual Page|version=5.0}}</noinclude>{{command|cas=true|function}}
<noinclude>{{Manual Page|version=4.0}}</noinclude>
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;Coefficients( <Polynomial> )
{{command|function}}
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: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>.
;Coefficients[ <Polynomial> ]
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:{{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>}}
:{{description}}
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:{{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> ]
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;Coefficients( <Conic> )
:{{description}}
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: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>
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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'').
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::{{example|1= Given <code>line: 3x + 2y - 2 = 0</code>:
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::*<code>x(line)</code> returns 3
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::*<code>y(line)</code> returns 2
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::*<code>z(line)</code> returns -2}} }}
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==CAS Syntax==
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;Coefficients( <Polynomial> )
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:Yields the list of all coefficients of the polynomial in the main variable.
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:{{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>}}
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;Coefficients( <Polynomial>, <Variable> )
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:Yields the list of all coefficients of the polynomial in the given variable.
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:{{example| 1=<div>
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:* <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>
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:* <code><nowiki>Coefficients(a^3 - 3 a^2 + 3 a, x)</nowiki></code> yields {''a''³ - 3 ''a''² + 3 ''a''}.</div>}}

Latest revision as of 09:00, 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}.
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