Difference between revisions of "Polynomial Command"

Latest revision as of 14:05, 9 February 2024

Polynomial( <Function> ): Yields the expanded polynomial function.; Example: Polynomial((x - 3)^2) yields x² - 6x + 9.

Example: Polynomial(f(x,y)=y^2+(x+y)^2) yields x²+2xy+2x².

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.

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.

@@ Line 1: / Line 1: @@
-<noinclude>{{Manual Page|version=4.2}}</noinclude>
+<noinclude>{{Manual Page|version=5.0}}</noinclude>{{command|function}}
-{{command|function}}
+;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(f(x,y)=y^2+(x+y)^2)</code> yields ''x<sup>2</sup>+2xy+2x<sup>2</sup>''. }}
+;Polynomial( &lt;List of 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''. }}
-; Polynomial[Function]: Yields the expanded polynomial function.
+==CAS Syntax==
-: {{Example|1=<code>Polynomial[(x - 3)^2]</code> yields ''x<sup>2</sup> - 6x + 9''. }}
+;Polynomial( <Function> )
-; Polynomial[List of n points]: Creates the interpolation polynomial of degree ''n-1'' through the given ''n'' points.
+: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''. }}
+;Polynomial( <Function>, <Variable> )
+: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''. }}