refactor: Move NonlinearSolvePolyAlgorithm to Base #277

Job	Run time
downgrade (1.10, core)	16m 27s
test (core, 1.10, ubuntu-latest)	16m 23s
downgrade (1.10, downstream)	8m 27s
test (core, 1.10, macos-latest)	12m 16s
downgrade (1.10, wrappers)	10m 3s
test (core, 1.10, windows-latest)	26m 8s
test (core, 1, ubuntu-latest)	28m 2s
test (core, 1, macos-latest)	19m 18s
test (core, 1, windows-latest)	41m 13s
test (downstream, 1.10, ubuntu-latest)	8m 13s
test (downstream, 1.10, macos-latest)	5m 18s
test (downstream, 1.10, windows-latest)	10m 57s
test (downstream, 1, ubuntu-latest)	17m 10s
test (downstream, 1, macos-latest)	12m 22s
test (downstream, 1, windows-latest)	20m 56s
test (wrappers, 1.10, ubuntu-latest)	9m 31s
test (wrappers, 1.10, macos-latest)	6m 17s
test (wrappers, 1.10, windows-latest)	13m 57s
test (wrappers, 1, ubuntu-latest)	19m 4s
test (wrappers, 1, macos-latest)	12m 23s
test (wrappers, 1, windows-latest)	23m 12s
	5h 37m 37s

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