Difference between revisions of "Prove Command"

Latest revision as of 19:36, 8 April 2024

Prove( <Boolean Expression> ): Returns whether the given boolean expression is true or false in general.

Normally, GeoGebra decides whether a boolean expression is true or not by using numerical computations. However, the Prove command uses symbolic methods to determine whether a statement is true or false in general. If GeoGebra cannot determine the answer, the result is undefined.

Example:

We define three free points, A=(1,2), B=(3,4), C=(5,6). The command AreCollinear(A,B,C) yields true, since a numerical check is used on the current coordinates of the points. Using Prove(AreCollinear(A,B,C)) you will get false as an answer, since the three points are not collinear in general, i.e. when we change the points.

Example:

Let us define a triangle with vertices A, B and C, and define D=MidPoint(B,C), E=MidPoint(A,C), p=Line(A,B), q=Line(D,E). Now both p∥q and Prove(p∥q) yield true, since a midline of a triangle will always be parallel to the appropriate side. See also interactive version of this example.

@@ Line 1: / Line 1: @@
-<noinclude>{{Manual Page|version=5.0}}</noinclude>{{betamanual|version=5.0}}
+<noinclude>{{Manual Page|version=5.0}}</noinclude>{{command|logical}}
-{{command|logical}}
+;Prove( <Boolean Expression> ): Returns whether the given boolean expression is true or false in general.
-{{warning|This GeoGebra command is heavily under construction. Expect to encounter various problems when trying it out. The syntax or the output of this command may be subject to change.}}
+Normally, GeoGebra decides whether a [[Boolean_values|boolean expression]] is true or not by using numerical computations. However, the Prove command uses [[w:Symbolic_computation|symbolic methods]] to determine whether a statement is ''true'' or ''false'' in general. If GeoGebra cannot determine the answer, the result is ''undefined''.
-;Prove[ <Boolean Expression> ]: Returns if the result of the automated proof is true or false in general.
+{{example| 1=<div>We define three free points, <code><nowiki>A=(1,2)</nowiki></code>, <code><nowiki>B=(3,4)</nowiki></code>, <code><nowiki>C=(5,6)</nowiki></code>. The command <code><nowiki>AreCollinear(A,B,C)</nowiki></code> yields ''true'', since a numerical check is used on the current coordinates of the points. Using <code><nowiki>Prove(AreCollinear(A,B,C))</nowiki></code> you will get ''false'' as an answer, since the three points are not collinear in general, i.e. when we change the points.</div>}}
-Normally GeoGebra decides if a [[Manual:Boolean_values|boolean expression]] is true or not by using numerical computation. With the Prove command it is also possible to check a statement using [[w:Symbolic_computation|symbolic computation]] to determine whether the result is ''true'' or ''false'' in general. If the calculations cannot determine the answer, the result is ''undefined''.
+{{example| 1=<div>Let us define a triangle with vertices ''A'', ''B'' and ''C'', and define <code><nowiki>D=MidPoint(B,C)</nowiki></code>, <code><nowiki>E=MidPoint(A,C)</nowiki></code>, <code><nowiki>p=Line(A,B)</nowiki></code>, <code><nowiki>q=Line(D,E)</nowiki></code>. Now both <code><nowiki>p∥q</nowiki></code> and <code><nowiki>Prove(p∥q)</nowiki></code> yield ''true'', since a midline of a triangle will always be parallel to the appropriate side. See also [https://www.geogebra.org/m/vhZETdtd interactive version of this example].
-{{example| 1=<div>We define three free points, <code><nowiki>A=(1,2)</nowiki></code>, <code><nowiki>B=(3,4)</nowiki></code>, <code><nowiki>C=(5,6)</nowiki></code>. Now <code><nowiki>AreCollinear[A,B,C]</nowiki></code> yields ''true'', since a numerical check is used for this single case, but <code><nowiki>Prove[AreCollinear[A,B,C]]</nowiki></code> yields ''false'', since the three points are in general not collinear, when we drag the free points.</div>}}
+</div>}}
-{{example| 1=<div>Let us define a triangle with vertices ''A'', ''B'' and ''C'', and define <code><nowiki>D=MidPoint[B,C]</nowiki></code>, <code><nowiki>E=MidPoint[A,C]</nowiki></code>, <code><nowiki>p=Line[A,B]</nowiki></code>, <code><nowiki>q=Line[D,E]</nowiki></code>. Now both <code><nowiki>p∥q</nowiki></code> and <code><nowiki>Prove[p∥q]</nowiki></code> yield ''true'', since a midline of a triangle will always be parallel to the appropriate side.</div>}}
+{{Note| See also [[ProveDetails Command|ProveDetails]] command, [[Boolean values|Boolean values]], [https://github.com/kovzol/gg-art-doc/tree/master/pdf/english.pdf GeoGebra Automated Reasoning Tools: A Tutorial] and [http://dev.geogebra.org/trac/wiki/TheoremProving technical details of the algorithms].}}
-{{Note| See also [[Manual:ProveDetails_Command|ProveDetails]] command and [[Manual:Boolean_values|Boolean values]].}}

Difference between revisions of "Prove Command"

Latest revision as of 19:36, 8 April 2024

Prove

Command Categories (All commands)