refactor: Move NonlinearSolvePolyAlgorithm to Base #279

Job	Run time
downgrade (1.10, core)	8m 58s
downgrade (1.10, downstream)	8m 41s
test (core, 1.10, ubuntu-latest)	8m 41s
downgrade (1.10, wrappers)	8m 57s
test (core, 1.10, macos-latest)	9m 0s
test (core, 1.10, windows-latest)	11m 23s
test (core, 1, ubuntu-latest)	16m 13s
test (core, 1, macos-latest)	14m 18s
test (core, 1, windows-latest)	20m 43s
test (downstream, 1.10, ubuntu-latest)	8m 39s
test (downstream, 1.10, macos-latest)	5m 49s
test (downstream, 1.10, windows-latest)	11m 19s
test (downstream, 1, ubuntu-latest)	16m 56s
test (downstream, 1, macos-latest)	11m 39s
test (downstream, 1, windows-latest)	19m 55s
test (wrappers, 1.10, ubuntu-latest)	8m 39s
test (wrappers, 1.10, macos-latest)	6m 56s
test (wrappers, 1.10, windows-latest)	11m 55s
test (wrappers, 1, ubuntu-latest)	17m 3s
test (wrappers, 1, macos-latest)	13m 28s
test (wrappers, 1, windows-latest)	21m 13s
	4h 20m 25s

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