Difference between revisions of "Solutions Command"

Revision as of 11:04, 12 October 2017

CAS Syntax

Solutions( <Equation> ): Solves a given equation for the main variable and returns a list of all solutions.; Example: Solutions(x^2 = 4x) yields {0, 4}, the solutions of x² = 4x.

Solutions( <Equation>, <Variable> ): Solves an equation for a given unknown variable and returns a list of all solutions.; Example: Solutions(x * a^2 = 4a, a) yields {\frac{4}{x},0}, the solutions of xa² = 4a.

Solutions( <List of Equations>, <List of Variables> )

Solves a set of equations for a given set of unknown variables and returns a list of all solutions.

Examples:

Solutions({x = 4 x + y , y + x = 2}, {x, y}) yields {{-1, 3}}, the sole solution of x = 4x + y and y + x = 2, displayed as \begin{pmatrix}-1&3\end{pmatrix}.
Solutions({2a^2 + 5a + 3 = b, a + b = 3}, {a, b}) yields {{-3, 6}, {0, 3}}, displayed as \begin{pmatrix}-3&6\\0&3\end{pmatrix}.

Note:

Sometimes you need to do some manipulation to allow the automatic solver to work, for example Solutions(TrigExpand(sin(5/4 π + x) - cos(x - 3/4 π) = sqrt(6) * cos(x) - sqrt(2)))
See also Solve Command.

@@ Line 1: / Line 1: @@
-<noinclude>{{Manual Page|version=4.0}}</noinclude>
+<noinclude>{{Manual Page|version=5.0}}</noinclude>{{command|geogebra}}
-{{command|CAS}}
+==CAS Syntax==
-;Solutions[ <Equation> ]
+;Solutions( <Equation> )
 :Solves a given equation for the main variable and returns a list of all solutions.
-:{{example|1=<div><code><nowiki>Solutions[x^2 = 4x]</nowiki></code> yields ''{4, 0}'', the solutions of ''x<sup>2</sup> = 4x''.</div>}}
+:{{example|1=<code><nowiki>Solutions(x^2 = 4x)</nowiki></code> yields ''{0, 4}'', the solutions of ''x<sup>2</sup> = 4x''.}}
-;Solutions[ <Equation>, <Variable> ]
+;Solutions( <Equation>, <Variable> )
-:Solves an equation for a given unknown variable and returns a list of all solution.
+:Solves an equation for a given unknown variable and returns a list of all solutions.
-:{{example|1=<div><code><nowiki>Solutions[x * a^2 = 4a, a]</nowiki></code> yields <math>\{\frac{4}{x},0\}</math>, the solutions of ''x a<sup>2</sup> = 4a''.</div>}}
+:{{example|1=<code><nowiki>Solutions(x * a^2 = 4a, a)</nowiki></code> yields {<math>\frac{4}{x},0</math>}, the solutions of ''xa<sup>2</sup> = 4a''.}}
-;Solutions[ <List of Equations>, <List of Variables> ]
+;Solutions( <List of Equations>, <List of Variables> )
 :Solves a set of equations for a given set of unknown variables and returns a list of all solutions.
-:{{example|1=<div>
+:{{examples|1=<div>
-:* <code><nowiki>Solutions[{x = 4 x + y , y + x = 2}, {x, y}]</nowiki></code> yields ''&#123;&#123;-1, 3&#125;&#125;'', the sole solution of ''x = 4x + y'' and ''y + x = 2'', displayed as <math>\begin{pmatrix}
+:* <code><nowiki>Solutions({x = 4 x + y , y + x = 2}, {x, y})</nowiki></code> yields ''&#123;&#123;-1, 3&#125;&#125;'', the sole solution of ''x = 4x + y'' and ''y + x = 2'', displayed as <math>\begin{pmatrix}-1&3\end{pmatrix}</math>.
--1&3
+:* <code><nowiki>Solutions({2a^2 + 5a + 3 = b, a + b = 3}, {a, b})</nowiki></code> yields ''&#123;&#123;-3, 6}, {0, 3&#125;&#125;'', displayed as <math>\begin{pmatrix}-3&6\\0&3\end{pmatrix}</math>.</div>}}
-\end{pmatrix}</math>.
+:{{note|1=
-:* <code><nowiki>Solutions[{2a^2 + 5a + 3 = b, a + b = 3}, {a, b}]</nowiki></code> yields ''&#123;&#123;0, 3}, {-3, 6&#125;&#125;'', displayed as <math>\begin{pmatrix}
+:* Sometimes you need to do some manipulation to allow the automatic solver to work, for example  <code> Solutions(TrigExpand(sin(5/4 π + x) - cos(x - 3/4 π) = sqrt(6) * cos(x) - sqrt(2))) </code>
-&3\\
+:* See also [[Solve Command]].}}
--3&6
-\end{pmatrix}</math>.</div>}}
-{{note|See also [[Solve Command]].}}

Difference between revisions of "Solutions Command"

Revision as of 11:04, 12 October 2017

Solutions

Command Categories (All commands)

CAS Syntax