Difference between revisions of "Coefficients Command"
From GeoGebra Manual
| Line 6: | Line 6: | ||
;Coefficients[ <Conic> ] | ;Coefficients[ <Conic> ] | ||
:Returns the list <math>\{a, b, c, d, e, f\}</math> for conics 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> | :Returns the list <math>\{a, b, c, d, e, f\}</math> for conics 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 <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>. | |
| − | :{{ | ||
::{{example|1= Given <code>l: 3x + 2y - 2 = 0</code>: | ::{{example|1= Given <code>l: 3x + 2y - 2 = 0</code>: | ||
| − | :::<code>x(''l'')</code> returns 3 | + | :::<code>x(''l'')</code> returns 3 |
| − | :::<code>y(''l'')</code> returns 2 | + | :::<code>y(''l'')</code> returns 2 |
| − | :::<code>z(''l'')</code> returns -2 | + | :::<code>z(''l'')</code> returns -2}} }} |
| − | |||
==CAS Syntax== | ==CAS Syntax== | ||
;Coefficients[ <Polynomial> ] | ;Coefficients[ <Polynomial> ] | ||
| Line 20: | Line 18: | ||
:Yields the list of all coefficients of the polynomial in the given variable. | :Yields the list of all coefficients of the polynomial in the given variable. | ||
:{{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 <math>\{a^3 - 3 a^2 + 3 a\}</math>.</div>}} | :* <code><nowiki>Coefficients[a^3 - 3 a^2 + 3 a, x]</nowiki></code> yields <math>\{a^3 - 3 a^2 + 3 a\}</math>.</div>}} | ||
Revision as of 15:13, 27 March 2013
- 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 \{a, b, c, d, e, f\} for conics 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 3y(l)returns 2z(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 \{a^3 - 3 a^2 + 3 a\}.
