Index Raising / Lowering¶
Index raising and lowering utilities for tensors.
- gravica.indexing.raise_index_2d(metric, T_lower, which)¶
Raise one index of a rank-2 covariant tensor.
- Parameters:
metric (
MetricTensor)T_lower (
list[list[Expression]]) – \(T_{ab}\) as a 2D list.which (
int) – Which index to raise:0gives \(T^a{}_b = g^{ac}\,T_{cb}\),1gives \(T_a{}^b = g^{bc}\,T_{ac}\).
- Returns:
The mixed tensor as a 2D list.
- Return type:
list[list[Expression]]
- gravica.indexing.lower_index_2d(metric, T_upper, which)¶
Lower one index of a rank-2 contravariant tensor.
- Parameters:
metric (
MetricTensor)T_upper (
list[list[Expression]]) – \(T^{ab}\) as a 2D list.which (
int) – Which index to lower:0gives \(T_a{}^b = g_{ac}\,T^{cb}\),1gives \(T^a{}_b = g_{bc}\,T^{ac}\).
- Returns:
The mixed tensor as a 2D list.
- Return type:
list[list[Expression]]