# Coefficients Command

##### Command Categories (All commands)

Coefficients[ <Polynomial> ]
Yields the list of all coefficients \mathrm{\mathsf{ a_k,a_{k-1},\ldots,a_1, a_0 }} of the polynomial \mathrm{\mathsf{ 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 \mathrm{\mathsf{ 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: \mathrm{\mathsf{ 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 3
• y(line) returns 2
• z(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 \mathrm{\mathsf{ 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 \mathrm{\mathsf{ a^3 - 3 a^2 + 3 a }}
• Coefficients[a^3 - 3 a^2 + 3 a, x] yields {a³ - 3 a² + 3 a}.
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