Difference between revisions of "LocusEquation Command"

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<noinclude>{{Manual Page|version=4.2}}[[Category:Manual (official)|{{PAGENAME}}]]</noinclude>
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<noinclude>{{Manual Page|version=5.0}}[[Category:Manual (official)|{{PAGENAME}}]]</noinclude>
 
{{command|function}}
 
{{command|function}}
;LocusEquation[ <Locus> ]
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;LocusEquation( <Locus> )
 
:Calculates the equation of a Locus and plots this as an Implicit Curve.
 
:Calculates the equation of a Locus and plots this as an Implicit Curve.
;LocusEquation[ <Point Creating Locus Line Q>, <Point P> ]
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;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.
 
:Calculates the equation of a Locus by using inputs tracer point ''Q'' and mover point ''P'', and plots this as an Implicit Curve.
{{example| 1=<div>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 <code><nowiki>LocusEquation[Q,P]</nowiki></code> will find and plot the exact equation of the locus.</div>}}
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:{{example| 1=<div>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 <code><nowiki>LocusEquation(Q,P)</nowiki></code> will find and plot the exact equation of the locus.</div>}}
{{Note| See also [[Locus Command|Locus]] command.}}
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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.
* 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]
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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—i.e. a line through ''B'' and C''.}}
* If the locus is too complicated then it will return 'undefined'.
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{{Notes|1=<div>
* 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.}}
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*The Locus must be made from a Point (not from a Slider)
 
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*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.)
{{betamanual|version=5.0|1=
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*If the locus is too complicated then it will return 'undefined'.
{{Note|1=
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*If there is no locus then the implicit curve is the empty set 0=1.
In GeoGebra 5 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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*If the locus is the whole plane then the implicit curve is the equation 0=0.
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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.
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*Further informations and examples on [https://www.geogebra.org/m/KZVzqVEM geogebra.org]. A [https://www.geogebra.org/m/mbXQuvUV collection of implicit locus examples] is also available.
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*See also [[Locus Command|Locus]] command and [https://github.com/kovzol/gg-art-doc/tree/master/pdf/english.pdf GeoGebra Automated Reasoning Tools: A Tutorial].</div>}}

Latest revision as of 08:41, 18 September 2019


LocusEquation( <Locus> )
Calculates the equation of a Locus and plots this as an Implicit Curve.
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.
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—i.e. a line through B and C.
Notes:
  • The Locus must be made from a Point (not from a Slider)
  • 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'.
  • If there is no locus then the implicit curve is the empty set 0=1.
  • If the locus is the whole plane then the implicit curve is the equation 0=0.
  • The calculation is done using Gröbner bases, so sometimes extra branches of the curve will appear that were not in the original locus.
  • Further informations and examples on geogebra.org. A collection of implicit locus examples is also available.
  • See also Locus command and GeoGebra Automated Reasoning Tools: A Tutorial.
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