Difference between revisions of "Solve Command"
From GeoGebra Manual
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:*<code><nowiki>Solve[{x = 4 x + y , y + x = 2}, {x, y}]</nowiki></code> yields ''<nowiki>( x = -1, y = 3 )</nowiki>'', the sole solution of ''x = 4x + y'' and ''y + x = 2'' | :*<code><nowiki>Solve[{x = 4 x + y , y + x = 2}, {x, y}]</nowiki></code> yields ''<nowiki>( x = -1, y = 3 )</nowiki>'', the sole solution of ''x = 4x + y'' and ''y + x = 2'' | ||
:*<code><nowiki>Solve[{2a^2 + 5a + 3 = b, a + b = 3}, {a, b}]</nowiki></code> yields ''{{a = 0, b = 3}, {a = -3, b = 6}}''.</div>}} | :*<code><nowiki>Solve[{2a^2 + 5a + 3 = b, a + b = 3}, {a, b}]</nowiki></code> yields ''{{a = 0, b = 3}, {a = -3, b = 6}}''.</div>}} | ||
+ | ;Solve[ <Equation>, <Variable> , <List of assumptions>] | ||
+ | :Solves an equation for a given unknown variable with the list of assumptions and returns a list of all solutions. | ||
+ | :{{examples|1=<div> | ||
+ | :*<code><nowiki>Solve[u *x < a,x, u>0]</nowiki></code> yields ''<nowiki>{x < a / u}</nowiki>'', the sole solution of ''u *x < a'' assuming that ''u>0'' | ||
+ | :*<code><nowiki>Solve[u *x < a,x, {u<0, a<0}]</nowiki></code> yields ''{x > a / u}''.</div>}} | ||
{{note|1= | {{note|1= | ||
* The right hand side of equations (in any of the above syntaxes) can be omitted. If the right hand side is missing, it is treated as 0. | * The right hand side of equations (in any of the above syntaxes) can be omitted. If the right hand side is missing, it is treated as 0. | ||
− | * Sometimes you need to do some manipulation to allow the automatic solver to work, for example <code> Solve[TrigExpand[sin(5/4 π + x) - cos(x - 3/4 π) = sqrt(6) * cos(x) - sqrt(2)]] </code>.}} | + | * Sometimes you need to do some manipulation to allow the automatic solver to work, for example <code> Solve[TrigExpand[sin(5/4 π + x) - cos(x - 3/4 π) = sqrt(6) * cos(x) - sqrt(2)]] </code>. |
+ | * For piecewise-defined functions, you will need to use [[NSolve Command|NSolve]]}} | ||
;Solve[ <List of Parametric Equations>, <List of Variables> ] | ;Solve[ <List of Parametric Equations>, <List of Variables> ] | ||
:Solves a set of parametric equations for a given set of unknown variables and returns a list of all solutions. | :Solves a set of parametric equations for a given set of unknown variables and returns a list of all solutions. | ||
:{{example|1=<div> | :{{example|1=<div> | ||
:*<code><nowiki>Solve[{(x, y) = (3, 2) + t*(5, 1), (x, y) = (4, 1) + s*(1, -1)}, {x, y, t, s}]</nowiki></code> yields ''<nowiki>{{x = 3, y = 2, t = 0, s = -1}}</nowiki>''.</div>}} | :*<code><nowiki>Solve[{(x, y) = (3, 2) + t*(5, 1), (x, y) = (4, 1) + s*(1, -1)}, {x, y, t, s}]</nowiki></code> yields ''<nowiki>{{x = 3, y = 2, t = 0, s = -1}}</nowiki>''.</div>}} | ||
− | {{note| | + | {{note|See also [[Solutions Command|Solutions]], [[NSolve Command|NSolve]] and [[CSolve Command|CSolve]] commands.}} |
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Revision as of 12:01, 5 October 2015
CAS Syntax
- Solve[ <Equation in x> ]
- Solves a given equation for the main variable and returns a list of all solutions.
- Example:
Solve[x^2 = 4x]
yields {x = 4, x = 0}, the solutions of x2 = 4x.
- Solve[ <Equation>, <Variable> ]
- Solves an equation for a given unknown variable and returns a list of all solutions.
- Example:
Solve[x * a^2 = 4a, a]
yields {a = \frac{4}{x}, a = 0}, the solutions of xa2 = 4a.
- Solve[ <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:
Solve[{x = 4 x + y , y + x = 2}, {x, y}]
yields ( x = -1, y = 3 ), the sole solution of x = 4x + y and y + x = 2Solve[{2a^2 + 5a + 3 = b, a + b = 3}, {a, b}]
yields {{a = 0, b = 3}, {a = -3, b = 6}}.
- Solve[ <Equation>, <Variable> , <List of assumptions>]
- Solves an equation for a given unknown variable with the list of assumptions and returns a list of all solutions.
- Examples:
Solve[u *x < a,x, u>0]
yields {x < a / u}, the sole solution of u *x < a assuming that u>0Solve[u *x < a,x, {u<0, a<0}]
yields {x > a / u}.
Note:
- The right hand side of equations (in any of the above syntaxes) can be omitted. If the right hand side is missing, it is treated as 0.
- Sometimes you need to do some manipulation to allow the automatic solver to work, for example
Solve[TrigExpand[sin(5/4 π + x) - cos(x - 3/4 π) = sqrt(6) * cos(x) - sqrt(2)]]
. - For piecewise-defined functions, you will need to use NSolve
- Solve[ <List of Parametric Equations>, <List of Variables> ]
- Solves a set of parametric equations for a given set of unknown variables and returns a list of all solutions.
- Example:
Solve[{(x, y) = (3, 2) + t*(5, 1), (x, y) = (4, 1) + s*(1, -1)}, {x, y, t, s}]
yields {{x = 3, y = 2, t = 0, s = -1}}.