Difference between revisions of "Coefficients Command"
From GeoGebra Manual
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<noinclude>{{Manual Page|version=5.0}}</noinclude>{{command|cas=true|function}} | <noinclude>{{Manual Page|version=5.0}}</noinclude>{{command|cas=true|function}} | ||
| − | ;Coefficients | + | ;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>}} | ||
| − | ;Coefficients | + | ;Coefficients( <Conic> ) |
: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> | :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 ''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''). | ||
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::*<code>z(line)</code> returns -2}} }} | ::*<code>z(line)</code> returns -2}} }} | ||
==CAS Syntax== | ==CAS Syntax== | ||
| − | ;Coefficients | + | ;Coefficients( <Polynomial> ) |
:Yields the list of all coefficients of the polynomial in the main variable. | :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 | + | ;Coefficients( <Polynomial>, <Variable> ) |
: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 {''a''³ - 3 ''a''² + 3 ''a''}.</div>}} | :* <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 17:17, 7 October 2017
- 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}.
