Difference between revisions of "Coefficients Command"
From GeoGebra Manual
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(:{{note|1=There's a special mode (for non-polynomials) for the output of the fitting commands eg if <code>f(x) = FitExp(l1)</code> then <code>Coefficients(f)</code> will return the calculated parameters }}) |
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− | + | <noinclude>{{Manual Page|version=5.0}}</noinclude>{{command|cas=true|function}} | |
− | <noinclude>{{Manual Page|version= | + | ;Coefficients( <Polynomial> ) |
− | {{command|function}} | + | :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>. |
− | ;Coefficients | + | :{{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>}} |
− | :{{ | + | :{{note|1=There's a special mode (for non-polynomials) for the output of the fitting commands eg if <code>f(x) = FitExp(l1)</code> then <code>Coefficients(f)</code> will return the calculated parameters }} |
− | ;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> |
+ | :{{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>: | ||
+ | ::*<code>x(line)</code> returns 3 | ||
+ | ::*<code>y(line)</code> returns 2 | ||
+ | ::*<code>z(line)</code> returns -2}} }} | ||
+ | ==CAS Syntax== | ||
+ | ;Coefficients( <Polynomial> ) | ||
+ | :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>}} | ||
+ | ;Coefficients( <Polynomial>, <Variable> ) | ||
+ | :Yields the list of all coefficients of the polynomial in the given variable. | ||
+ | :{{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, x)</nowiki></code> yields {''a''³ - 3 ''a''² + 3 ''a''}.</div>}} |
Latest revision as of 10:00, 25 September 2019
- 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.
- Note: There's a special mode (for non-polynomials) for the output of the fitting commands eg if
f(x) = FitExp(l1)
thenCoefficients(f)
will return the calculated parameters - 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}.