Difference between revisions of "Coefficients Command"
From GeoGebra Manual
m |
m (fixed example format/indentation) |
||
Line 1: | Line 1: | ||
− | <noinclude>{{Manual Page|version=5.0}}</noinclude>{{command|cas=true|function}};Coefficients[ <Polynomial> ] | + | <noinclude>{{Manual Page|version=5.0}}</noinclude>{{command|cas=true|function}} |
+ | ;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 <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>}} | ||
Line 6: | Line 7: | ||
:{{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 10:51, 2 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 3y(line)
returns 2z(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 aCoefficients[a^3 - 3 a^2 + 3 a, x]
yields {a³ - 3 a² + 3 a}.