Difference between revisions of "NSolutions Command"

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(For non-polynomials you should always specify a starting value)
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<noinclude>{{Manual Page|version=4.2}}</noinclude><!-- -->
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<noinclude>{{Manual Page|version=5.0}}</noinclude><!-- -->{{command|geogebra}}
{{command|geogebra}}
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The following commands are only available in the [[File:Menu view cas.svg|link=|16px]] [[CAS View]].
==CAS Syntax==
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;NSolutions[ <Equation> ]
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;NSolutions( <Equation> )
 
:Attempts (numerically) to find a solution for the equation for the main variable.  For non-polynomials you should always specify a starting value (see below)
 
:Attempts (numerically) to find a solution for the equation for the main variable.  For non-polynomials you should always specify a starting value (see below)
:{{example|1=<br><code><nowiki>NSolutions[x^6 - 2x + 1=0]</nowiki></code> yields ''{0.51, 1}'' or ''{0.508660391642, 1}'' (the number of decimals depends on the choosen in [[Options Menu#Rounding|global rounding]])}}
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:{{example|1=<br><code><nowiki>NSolutions(x^6 - 2x + 1 = 0)</nowiki></code> yields ''{0.51, 1}'' or ''{0.508660391642, 1}'' (the number of decimals depends on the choosen in [[Options Menu#Rounding|global rounding]])}}
;NSolutions[ <Equation>, <Variable> ]
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;NSolutions( <Equation>, <Variable> )
 
:Attempts (numerically) to find a solution of the equation for the given unknown variable. For non-polynomials you should always specify a starting value (see below)
 
:Attempts (numerically) to find a solution of the equation for the given unknown variable. For non-polynomials you should always specify a starting value (see below)
:{{example|1=<div><code><nowiki>NSolutions[a^4 + 34a^3 = 34, a]</nowiki></code> yields '' {a =  -34.00086498588374, a = 0.9904738885574178}''.</div>}}
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:{{example|1=<div><code><nowiki>NSolutions(a^4 + 34a^3 = 34, a)</nowiki></code> yields '' {a =  -34.00086498588374, a = 0.9904738885574178}''.</div>}}
;NSolutions[ <Equation>, <Variable = starting value> ]
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;NSolutions( <Equation>, <Variable = starting value> )
 
:Finds numerically the list of solutions to the given equation for the given unknown variable with its starting value.
 
:Finds numerically the list of solutions to the given equation for the given unknown variable with its starting value.
 
:{{examples|1=<div>
 
:{{examples|1=<div>
:*<code><nowiki>NSolutions[cos(x) = x, x = 0]</nowiki></code> yields ''{0.74}''
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:*<code><nowiki>NSolutions(cos(x) = x, x = 0)</nowiki></code> yields ''{0.74}''
:*<code><nowiki>NSolutions[a^4 + 34a^3 = 34, a = 3]</nowiki></code> yields the list ''{-34, 0.99}''.</div>}}
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:*<code><nowiki>NSolutions(a^4 + 34a^3 = 34, a = 3)</nowiki></code> yields the list ''{0.99}''.</div>}}
;NSolutions[ <List of Equations>, <List of Variables> ]
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;NSolutions( &lt;List of Equations>, &lt;List of Variables> )
 
:Attempts (numerically) to find a solution of the set of equations for the given set of unknown variables.
 
:Attempts (numerically) to find a solution of the set of equations for the given set of unknown variables.
:{{example|1=<br><code><nowiki>NSolutions[{π / x = cos(x - 2y), 2 y - π = sin(x)}, {x = 3, y = 1.5}]</nowiki></code> yields the list ''{3.14, 1.57}''}}
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:{{example|1=<br><code><nowiki>NSolutions({pi / x = cos(x - 2y), 2 y - pi = sin(x)}, {x = 3, y = 1.5})</nowiki></code> yields the list ''{3.14, 1.57}''}}
 
{{note| 1=<br>
 
{{note| 1=<br>
 
* If you don't give a starting point like ''a=3'' or ''{x = 3, y = 1.5}''  the numerical algorithm may find it hard to find a solution (and giving a starting point doesn't guarantee that a solution will be found)
 
* If you don't give a starting point like ''a=3'' or ''{x = 3, y = 1.5}''  the numerical algorithm may find it hard to find a solution (and giving a starting point doesn't guarantee that a solution will be found)
 
* The number of decimals depends on the choosen in [[Options Menu#Rounding|global rounding]].
 
* The number of decimals depends on the choosen in [[Options Menu#Rounding|global rounding]].
* π is obtaind by pressing {{KeyCode|Alt + p}}.
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* NSolutions won't work for functions that are asymptotic to the x-axis. They can often be reformulated though.
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* NSolutions will work only if the function is continuous
 
* See also [[Solutions Command]] and [[NSolve Command]].
 
* See also [[Solutions Command]] and [[NSolve Command]].
 
}}
 
}}

Latest revision as of 18:57, 2 August 2019


The following commands are only available in the Menu view cas.svg CAS View.

NSolutions( <Equation> )
Attempts (numerically) to find a solution for the equation for the main variable. For non-polynomials you should always specify a starting value (see below)
Example:
NSolutions(x^6 - 2x + 1 = 0) yields {0.51, 1} or {0.508660391642, 1} (the number of decimals depends on the choosen in global rounding)
NSolutions( <Equation>, <Variable> )
Attempts (numerically) to find a solution of the equation for the given unknown variable. For non-polynomials you should always specify a starting value (see below)
Example:
NSolutions(a^4 + 34a^3 = 34, a) yields {a = -34.00086498588374, a = 0.9904738885574178}.
NSolutions( <Equation>, <Variable = starting value> )
Finds numerically the list of solutions to the given equation for the given unknown variable with its starting value.
Examples:
  • NSolutions(cos(x) = x, x = 0) yields {0.74}
  • NSolutions(a^4 + 34a^3 = 34, a = 3) yields the list {0.99}.
NSolutions( <List of Equations>, <List of Variables> )
Attempts (numerically) to find a solution of the set of equations for the given set of unknown variables.
Example:
NSolutions({pi / x = cos(x - 2y), 2 y - pi = sin(x)}, {x = 3, y = 1.5}) yields the list {3.14, 1.57}
Note:
  • If you don't give a starting point like a=3 or {x = 3, y = 1.5} the numerical algorithm may find it hard to find a solution (and giving a starting point doesn't guarantee that a solution will be found)
  • The number of decimals depends on the choosen in global rounding.
  • NSolutions won't work for functions that are asymptotic to the x-axis. They can often be reformulated though.
  • NSolutions will work only if the function is continuous
  • See also Solutions Command and NSolve Command.
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