Difference between revisions of "Coefficients Command"
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{{command|cas=true|function}} | {{command|cas=true|function}} | ||
;Coefficients[ <Polynomial> ] | ;Coefficients[ <Polynomial> ] | ||
| − | :Yields the list of all coefficients <math> | + | :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>}} | :{{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> ] | ;Coefficients[ <Conic> ] | ||
| − | :Returns the list | + | :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> |
| − | :{{note|1=For a line in implicit form | + | :{{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>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}} }} | ::{{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}} }} | ||
==CAS Syntax== | ==CAS Syntax== | ||
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:{{example| 1=<div> | :{{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> | :* <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 | + | :* <code><nowiki>Coefficients[a^3 - 3 a^2 + 3 a, x]</nowiki></code> yields {''a''³ - 3 ''a''² + 3 ''a''}.</div>}} |
Revision as of 14:52, 6 February 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
l: 3x + 2y - 2 = 0:x(l)returns 3,y(l)returns 2, andz(l)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 aCoefficients[a^3 - 3 a^2 + 3 a, x]yields {a³ - 3 a² + 3 a}.
