0th pass version of solver? #11

New Issue

glen · 2024-01-22T22:37:23Z

glen commented

2024-01-22 22:37:23 +00:00

Per discussion with @Vectornaut today:

A potential specification for an initial toy solver is one that would allow specifications like "A is a point," "B is a plane", and "C and D are incident", where two points would be identical if incident, and perhaps the same for planes, or perhaps incident planes are simply non-parallel ones -- unclear. (A point and plane are incident if one contains the other.) Then the solver would return (presumably rational) coordinates for each object that satisfy the constraints.

However, the difficulty is that if all we have are such constraints, then there is always a trivial solution of making all points be the origin and all planes be the xy plane. So to make this a non-trivial exercise, perhaps we need in addition one or more of the following:

To return some sort of description of all solutions
To return the solution closest in some sense to specified coordinates for all of the points (and perhaps also the planes)
Add constraints of the form "A and B are not incident" (or at least that two points are distinct)
Add constraints of the form "The coordinates of A are such-and-such rational numbers."

There may be other reasonable changes to get beyond the trivial solver.

Per discussion with @Vectornaut today: A potential specification for an initial toy solver is one that would allow specifications like "A is a point," "B is a plane", and "C and D are incident", where two points would be identical if incident, and perhaps the same for planes, or perhaps incident planes are simply non-parallel ones -- unclear. (A point and plane are incident if one contains the other.) Then the solver would return (presumably rational) coordinates for each object that satisfy the constraints. However, the difficulty is that if all we have are such constraints, then there is always a trivial solution of making all points be the origin and all planes be the xy plane. So to make this a non-trivial exercise, perhaps we need in addition one or more of the following: * To return some sort of description of all solutions * To return the solution closest in some sense to specified coordinates for all of the points (and perhaps also the planes) * Add constraints of the form "A and B are not incident" (or at least that two points are distinct) * Add constraints of the form "The coordinates of A are such-and-such rational numbers." There may be other reasonable changes to get beyond the trivial solver.

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