Difference between revisions of "Coefficients Command"
From GeoGebra Manual
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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''). | :{{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 10:49, 1 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}.