Difference between revisions of "LocusEquation Command"

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(;LocusEquation[ <Boolean Expression>, <Free Point> ])
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:*The calculation is done using [[w:Gröbner_basis|Gröbner bases]], so sometimes extra branches of the curve will appear that were not in the original locus.}}
 
:*The calculation is done using [[w:Gröbner_basis|Gröbner bases]], so sometimes extra branches of the curve will appear that were not in the original locus.}}
  
{{betamanual|version=5.2|1=
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;LocusEquation[ <Boolean Expression>, <Free Point> ]
{{Note|1=
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:Calculates the locus of the free point such that the boolean condition is satisified
In GeoGebra 5.2 and above a remote web server may be used to perform the calculation (this can be disabled by using command line option <code><nowiki>--singularWS=enable:false</nowiki></code>).}}}}
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:{{example| 1= <code>LocusEquation[AreCollinear[A, B, C],A]</code> for free points A, B, C calculates the set of positions of A that make A, B and C collinear - ie a Line through B and C}}
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{{Notes|1=<div>
 
{{Notes|1=<div>
 
*Further informations and examples on [http://www.geogebra.org/student/b121563# GeoGebra]
 
*Further informations and examples on [http://www.geogebra.org/student/b121563# GeoGebra]
 
*See also [[Locus Command|Locus]] command.</div>}}
 
*See also [[Locus Command|Locus]] command.</div>}}

Revision as of 18:51, 12 March 2016


LocusEquation[ <Locus> ]
Calculates the equation of a Locus and plots this as an Implicit Curve.
Note: The Locus must be made from a Point (not from a Slider)
LocusEquation[ <Point Creating Locus Line Q>, <Point P> ]
Calculates the equation of a Locus by using inputs tracer point Q and mover point P, and plots this as an Implicit Curve.
Example:
Let us construct a parabola as a locus: Create free Points A and B, and Line d lying through them (this will be the directrix of the parabola). Create free point F for the focus. Now create P on Line d (the mover point), then create line p as a perpendicular line to d through P. Also create line b as perpendicular bisector of Line Segment FP. Finally, point Q (the point creating locus line) is to be created as intersection of Lines p and b. Now LocusEquation[Q,P] will find and plot the exact equation of the locus.
Notes:
  • Works only for a restricted set of geometric loci, i.e. using points, lines, circles, conics. [Rays and line segments will be treated as (infinite) lines]
  • If the locus is too complicated then it will return 'undefined'.
  • The calculation is done using Gröbner bases, so sometimes extra branches of the curve will appear that were not in the original locus.
LocusEquation[ <Boolean Expression>, <Free Point> ]
Calculates the locus of the free point such that the boolean condition is satisified
Example: LocusEquation[AreCollinear[A, B, C],A] for free points A, B, C calculates the set of positions of A that make A, B and C collinear - ie a Line through B and C


Notes:
  • Further informations and examples on GeoGebra
  • See also Locus command.
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