Difference between revisions of "Solutions Command"
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:Solves a set of equations for a given set of unknown variables and returns a list of all solutions. | :Solves a set of equations for a given set of unknown variables and returns a list of all solutions. | ||
:{{examples|1=<div> | :{{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} | + | :* <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>. |
| − | -1&3 | + | :* <code><nowiki>Solutions[{2a^2 + 5a + 3 = b, a + b = 3}, {a, b}]</nowiki></code> yields ''{{0, 3}, {-3, 6}}'', displayed as <math>\begin{pmatrix}0&3\\-3&6\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 ''{{0, 3}, {-3, 6}}'', 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> |
| − | 0&3\\ | + | :* See also [[Solve Command]].}} |
| − | -3&6 | ||
| − | \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 14:58, 27 August 2014
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 {4, 0}, 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 {{0, 3}, {-3, 6}}, displayed as \begin{pmatrix}0&3\\-3&6\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
