  We present systematic constructions of tensor-network wavefunctions for
bosonic symmetry protected topological (SPT) phases respecting both onsite and
spatial symmetries. From the classification point of view, our results show
that in spatial dimensions $d=1,2,3$, the cohomological bosonic SPT phases
protected by a general symmetry group $SG$ involving onsite and spatial
symmetries are classified by the cohomology group $H^{d+1}(SG,U(1))$, in which
both the time-reversal symmetry and mirror reflection symmetries should be
treated as anti-unitary operations. In addition, for every SPT phase protected
by a discrete symmetry group and some SPT phases protected by continous
symmetry groups, generic tensor-network wavefunctions can be constructed which
would be useful for the purpose of variational numerical simulations. As a
by-product, our results demonstrate a generic connection between rather
conventional symmetry enriched topological phases and SPT phases via an anyon
condensation mechanism.
