code: def spaces(request):
      factors, default_point_type = request.param
      request.cls.space = ProductManifold(
          factors=factors,
          default_point_type=default_point_type,
          equip=False,
      )
  
file_path: geomstats/tests/tests_geomstats/test_geometry/test_product_manifold.py
imports: import pytest
  from geomstats.geometry.euclidean import Euclidean
  from geomstats.geometry.hyperboloid import Hyperboloid
  from geomstats.geometry.hypersphere import Hypersphere
  from geomstats.geometry.product_manifold import ProductManifold
  from geomstats.geometry.siegel import Siegel
  from geomstats.geometry.special_orthogonal import SpecialOrthogonal
  from geomstats.test.parametrizers import DataBasedParametrizer
  from geomstats.test_cases.geometry.product_manifold import ProductManifoldTestCase
  from geomstats.test_cases.geometry.riemannian_metric import RiemannianMetricTestCase
  from .data.product_manifold import ProductManifoldTestData, ProductRiemannianMetricTestData
label_desc: Use image node_id 1 for calling a global function with example usage: spaces(request) without return types