Difference between revisions of "Polynomial Command"
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<noinclude>{{Manual Page|version=5.0}}</noinclude>{{command|function}} | <noinclude>{{Manual Page|version=5.0}}</noinclude>{{command|function}} | ||
− | ;Polynomial | + | ;Polynomial( <Function> ) |
:Yields the expanded polynomial function. | :Yields the expanded polynomial function. | ||
:{{Example|1=<code>Polynomial[(x - 3)^2]</code> yields ''x<sup>2</sup> - 6x + 9''. }} | :{{Example|1=<code>Polynomial[(x - 3)^2]</code> yields ''x<sup>2</sup> - 6x + 9''. }} | ||
− | ;Polynomial | + | ;Polynomial( <List of Points> ) |
:Creates the interpolation polynomial of degree ''n-1'' through the given ''n'' points. | :Creates the interpolation polynomial of degree ''n-1'' through the given ''n'' points. | ||
:{{Example|1=<code>Polynomial[{(1, 1), (2, 3), (3, 6)}]</code> yields ''0.5 x<sup>2</sup> + 0.5 x''. }} | :{{Example|1=<code>Polynomial[{(1, 1), (2, 3), (3, 6)}]</code> yields ''0.5 x<sup>2</sup> + 0.5 x''. }} | ||
==CAS Syntax== | ==CAS Syntax== | ||
− | ;Polynomial | + | ;Polynomial( <Function> ) |
:Expands the function and writes it as a polynomial in x (grouping the coefficients). | :Expands the function and writes it as a polynomial in x (grouping the coefficients). | ||
:{{Example|1=<code>Polynomial[(x - 3)^2 + (a + x)^2]</code> yields ''2 x<sup>2</sup> + (2a - 6) x + a<sup>2</sup> + 9''. }} | :{{Example|1=<code>Polynomial[(x - 3)^2 + (a + x)^2]</code> yields ''2 x<sup>2</sup> + (2a - 6) x + a<sup>2</sup> + 9''. }} | ||
− | ;Polynomial | + | ;Polynomial( <Function>, <Variable> ) |
:Expands the function and writes it as a polynomial in the variable (grouping the coefficients). | :Expands the function and writes it as a polynomial in the variable (grouping the coefficients). | ||
:{{Example|1=<code>Polynomial[(x - 3)^2 + (a + x)^2, a]</code> yields ''a<sup>2</sup> + 2 x a + 2 x<sup>2</sup> - 6 x + 9''. }} | :{{Example|1=<code>Polynomial[(x - 3)^2 + (a + x)^2, a]</code> yields ''a<sup>2</sup> + 2 x a + 2 x<sup>2</sup> - 6 x + 9''. }} |
Revision as of 17:15, 7 October 2017
- Polynomial( <Function> )
- Yields the expanded polynomial function.
- Example:
Polynomial[(x - 3)^2]
yields x2 - 6x + 9.
- Polynomial( <List of Points> )
- Creates the interpolation polynomial of degree n-1 through the given n points.
- Example:
Polynomial[{(1, 1), (2, 3), (3, 6)}]
yields 0.5 x2 + 0.5 x.
CAS Syntax
- Polynomial( <Function> )
- Expands the function and writes it as a polynomial in x (grouping the coefficients).
- Example:
Polynomial[(x - 3)^2 + (a + x)^2]
yields 2 x2 + (2a - 6) x + a2 + 9.
- Polynomial( <Function>, <Variable> )
- Expands the function and writes it as a polynomial in the variable (grouping the coefficients).
- Example:
Polynomial[(x - 3)^2 + (a + x)^2, a]
yields a2 + 2 x a + 2 x2 - 6 x + 9.