For Markus and Miguel: Please, review it and correct it if necessary.

Since algebraic methods are going to be used to find the locus equation, any semi-algebraic element in the construction will be replaced by its algebraic analogue. This can result in locus equations corresponding to a superset of the sought locus.

If no information is added to an element, then for polynomial translation it will be considered as is (algebraic element). Furthermore, the resulting locus polynomials will not be flagged as a possible superset of the actual solution if all its elements are algebraic.

For example, given two points and a line, the resulting equation won't be flagged but, given two points and a segment instead of a line, it will.

On the other hand, if an element is not in the list, it won't be considered for translation (BTW, is there any word for the process better than translation?)

• New point (tested)
• Intersection point
  • IntersectConics (done, used in ex. B9, NOT the right graph)
    • No movingPath condition needed
  • IntersectLineConic (tested in ex. A8)
    • No movingPath condition needed
  • IntersectLineCubic
    • No movingPath condition needed
  • IntersectSingle (tested)
    • No movingPath condition needed
  • RootsPolynomial ?
    • ComplexRootsPolynomial ?
    • ExtremumPolynomial ?
    • IntersectPolynomialLine ?
    • IntersectPolynomials ?
    • TurningPolynomialPoint ?
  • Intersection
  • IntersectLines (tested in ex. A7 and B11)
    • No movingPath condition needed
  • PolygonOperation ?
  • RootNewton ??
    • IntersectFunctionLineNewton ??
    • IntersectFunctionsNewton ??
• Middle point (tested in ex. A4 et al.)
  • No movingPath condition needed
• Line
  • JoinPoints (tested in ex. A2)
  • Condition for PointOnPath on moving JointPoints (tested in example D1)
• Segment => Line
  • JoinPointsSegment (tested in ex. A4)
  • segment for one point and the length (tested)
  • Condition for PointOnPath on moving SEgmentPointLength
  • Condition for PointOnPath on moving JointPointsSegment (tested in example D2)
• Ray => Line
  • JoinPointsRay (tested in ex. B13)
  • Condition for PointOnPath on moving JoinPointsRay (tested in ex. D4)
• Perpendicular line
  • OrthoLinePointLine (tested in ex, A8)
  • Condition for PointOnPath on moving OrthoLinePointLine (tested)
• Parallel line
  • LinePointLine (tested in ex. B1)
  • Condition for PointOnPath on moving LinePointLine
• Perpendicular bisector
  • LineBisector (tested in ex. B1)
  • Condition for PointOnPath on moving LineBisector (tested)
  • LineBisectorSegment (done, included in ex. B2)
  • Condition for PointOnPath on moving LineBisectorSegment (tested)
• Angle bisector
  • AngularBisectorPoints (tested)
  • Condition for PointOnPath on moving AngularBisectorPoints
  • AngularBisectorLines (done)
  • Condition for PointOnPath on moving AngularBisectorLines
• Tangent line
  • TangentPoint (done)
  • Condition for PointOnPath on moving TangentPoint
• Polar
  • PolarLine (done)
  • Condition for PointOnPath on moving PolarLine
• Polygon (regular or not) => Union of segments => Union of lines.
  • Polygon (done)
  • PolygonRegular (done)
• Circles (given in any way)
  • CircleTwoPoints (tested)
  • Condition for PointOnPath on moving CircleTwoPoints (NOT implemented)
  • CirclePointRadius (tested)
  • Condition for PointOnPath on moving CirclePointRadius (NOT implemented)
  • CircleThreePoints (tested in ex. B16)
  • Condition for PointOnPath on moving CircleThreePoints (NOT implemented)
• Arc => circle
  • Semicircle (tested)
  • Condition for PointOnPath on moving Semicircle
  • ConicPartCircle (done)
  • ConicPartCircumcircle (done)
• Circular sector => Union of arc and two segments => Union of circle and two lines.
  • Look Up
• Conics
  • EllipseFociPoint (done, included in ex. B4)
  • Condition for PointOnPath on moving EllipseFociPoint (done, included in example D3)
  • HyperbolaFociPoint (done, inlcuded in ex. B5)
  • Condition for PointOnPath on moving HyperbolaFociPoint
  • ParabolaPointLine (done, included in ex. B6)
  • Condition for PointOnPath on moving ParabolaPointLine