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Catch constant solution paths#691

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PBrdng wants to merge 3 commits intomainfrom
patch-for-issue-647
Draft

Catch constant solution paths#691
PBrdng wants to merge 3 commits intomainfrom
patch-for-issue-647

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@PBrdng PBrdng commented Apr 7, 2026

This addresses #647

The bug is still not entirely clear to me. The updates in this PR fixes the problem in #647, but by addressing constant solution paths. This cannot be the reason as outlined below.

@PBrdng PBrdng mentioned this pull request Apr 7, 2026
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PBrdng commented Apr 8, 2026

The code that didnt work in #647 works at the current stage of this patch. However, before the patch

using HomotopyContinuation
@var x y
F = System([(y - 50) * (x - y)], variables = [y], parameters = [x])
solve(F, [50.0]; start_parameters = [-1.0], target_parameters = [-2.0])

also worked. So the reason cannot just be constant paths. The problem must be with 0 as start solution.
Notice: the following still fails:

using HomotopyContinuation
@var x y
F = System([y-x], variables = [y], parameters = [x])
solve(F, [1.0]; start_parameters = [1.0], target_parameters = [-2.0])

The reason seems to be that the WeightedNorm gives a second derivative of size 1e6 around y=0. This causes the step size to become essentially zero.

@PBrdng PBrdng marked this pull request as draft April 8, 2026 05:35
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