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