/usr/include/trilinos/ is in libtrilinos-piro-dev 12.10.1-3.
This file is owned by root:root, with mode 0o755.
..
/usr/include/trilinos/Makefile.export.Piro
/usr/include/trilinos/Piro_ConfigDefs.hpp
/usr/include/trilinos/Piro_Epetra_AdaptiveSolutionManager.hpp
/usr/include/trilinos/Piro_Epetra_InvertMassMatrixDecorator.hpp
/usr/include/trilinos/Piro_Epetra_LOCAAdaptiveSolver.hpp
/usr/include/trilinos/Piro_Epetra_LOCASolver.hpp
/usr/include/trilinos/Piro_Epetra_MatrixFreeDecorator.hpp
/usr/include/trilinos/Piro_Epetra_NECoupledModelEvaluator.hpp
/usr/include/trilinos/Piro_Epetra_NOXSolver.hpp
/usr/include/trilinos/Piro_Epetra_NewmarkSolver.hpp
/usr/include/trilinos/Piro_Epetra_PerformAnalysis.hpp
/usr/include/trilinos/Piro_Epetra_PerformSolve.hpp
/usr/include/trilinos/Piro_Epetra_RythmosSolver.hpp
/usr/include/trilinos/Piro_Epetra_SensitivityOperator.hpp
/usr/include/trilinos/Piro_Epetra_SolverFactory.hpp
/usr/include/trilinos/Piro_Epetra_StokhosMPSolver.hpp
/usr/include/trilinos/Piro_Epetra_StokhosNOXObserver.hpp
/usr/include/trilinos/Piro_Epetra_StokhosSolver.hpp
/usr/include/trilinos/Piro_Epetra_StokhosSolverFactory.hpp
/usr/include/trilinos/Piro_Epetra_TrapezoidRuleSolver.hpp
/usr/include/trilinos/Piro_Epetra_VelocityVerletSolver.hpp
/usr/include/trilinos/Piro_InvertMassMatrixDecorator.hpp
/usr/include/trilinos/Piro_InvertMassMatrixDecorator_Def.hpp
/usr/include/trilinos/Piro_LOCAAdaptiveSolver.hpp
/usr/include/trilinos/Piro_LOCAAdaptiveSolver_Def.hpp
/usr/include/trilinos/Piro_LOCASolver.hpp
/usr/include/trilinos/Piro_LOCASolver_Def.hpp
/usr/include/trilinos/Piro_MatrixFreeDecorator.hpp
/usr/include/trilinos/Piro_MatrixFreeDecorator_Def.hpp
/usr/include/trilinos/Piro_MatrixFreeLinearOp.hpp
/usr/include/trilinos/Piro_MatrixFreeLinearOp_Def.hpp
/usr/include/trilinos/Piro_NOXSolver.hpp
/usr/include/trilinos/Piro_NOXSolver_Def.hpp
/usr/include/trilinos/Piro_ObserverBase.hpp
/usr/include/trilinos/Piro_ObserverToLOCASaveDataStrategyAdapter.hpp
/usr/include/trilinos/Piro_ObserverToRythmosIntegrationObserverAdapter.hpp
/usr/include/trilinos/Piro_ObserverToRythmosIntegrationObserverAdapter_Def.hpp
/usr/include/trilinos/Piro_PerformAnalysis.hpp
/usr/include/trilinos/Piro_PerformSolve.hpp
/usr/include/trilinos/Piro_PerformSolve_Def.hpp
/usr/include/trilinos/Piro_Provider.hpp
/usr/include/trilinos/Piro_ProviderBase.hpp
/usr/include/trilinos/Piro_ProviderHelpers.hpp
/usr/include/trilinos/Piro_RythmosNOX_RowSumUpdater.hpp
/usr/include/trilinos/Piro_RythmosSolver.hpp
/usr/include/trilinos/Piro_RythmosSolver_Def.hpp
/usr/include/trilinos/Piro_RythmosStepControlFactory.hpp
/usr/include/trilinos/Piro_RythmosStepperFactory.hpp
/usr/include/trilinos/Piro_SolutionObserverBase.hpp
/usr/include/trilinos/Piro_SolverFactory.hpp
/usr/include/trilinos/Piro_SolverFactory_Def.hpp
/usr/include/trilinos/Piro_SteadyStateSolver.hpp
/usr/include/trilinos/Piro_SteadyStateSolver_Def.hpp
/usr/include/trilinos/Piro_StratimikosUtils.hpp
/usr/include/trilinos/Piro_TransientDecorator.hpp
/usr/include/trilinos/Piro_TrapezoidRuleSolver.hpp
/usr/include/trilinos/Piro_TrapezoidRuleSolver_Def.hpp
/usr/include/trilinos/Piro_ValidPiroParameters.hpp
/usr/include/trilinos/Piro_VelocityVerletSolver.hpp
/usr/include/trilinos/Piro_VelocityVerletSolver_Def.hpp
/usr/include/trilinos/Piro_Version.hpp
/usr/include/trilinos/Piro_config.hpp