Difference between revisions of "Coefficients Command"
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:{{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> ] | ||
| − | : | + | :It returns list <math>\{a, b, c, d, e, f\}</math> for conics in standard form:<br><hr> |
| − | + | :<center><small><math>a\cdot x^2 + b\cdot y^2 + c + d\cdot x\cdot y + e\cdot x + f\cdot y = 0</math></small></center><hr> | |
:{{hint|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>. | :{{hint|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>. | ||
| Line 13: | Line 13: | ||
:::<code>y(''l'')</code> returns 2 and | :::<code>y(''l'')</code> returns 2 and | ||
:::<code>z(''l'')</code> returns -2.}} }} | :::<code>z(''l'')</code> returns -2.}} }} | ||
| − | |||
==CAS Syntax== | ==CAS Syntax== | ||
Revision as of 21:19, 17 November 2012
- Coefficients[ <Polynomial> ]
- Yields the list of all coefficients of the polynomial.
- 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> ]
- It returns 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
Hint: 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 a, andCoefficients[a^3 - 3 a^2 + 3 a, x]yields \{a^3 - 3 a^2 + 3 a\}.
