find the subspace of vectors (or 1-forms) whose interior product with a given list of 1-forms (or vectors) vanishes
a list of vectors or a list of 1-forms
(optional) a list of 1-forms if S is a list of vectors or a list of vectors if S is a list of 1-forms
Let S be a list of 1-forms and T a list of vectors. Then Annihilator(S, T) calculates the subspace of vectors X in the span of T such that alpha(X) = 0 for all alpha in S.
Let S be a list of vectors and T a list of 1-forms. Then Annihilator(S, T) calculates the subspace of 1-forms alpha in the span of T such that alpha(X) = 0 for all X in S.
If the optional argument T is not given, then T is taken to be the standard basis for the tangent space or cotangent space for the manifold M on which the elements of S are defined.
This command is part of the DifferentialGeometry package, and so can be used in the form Annihilator(...) only after executing the command with(DifferentialGeometry). It can always be used in the long form DifferentialGeometry:-Annihilator.
Calculate the annihilator of the set of 1-forms S1 relative to subspaces T1, T2, and the full tangent space.
S1 ≔ dx,dy
T1 ≔ D_x,D_y,D_z
T2 ≔ D_x,D_y
Calculate the annihilator of the set of vectors S2 and S3.
S2 ≔ D_y
S3 ≔ evalDG⁡D_x−2⁢D_y+D_z,D_y+3⁢D_z−D_w
A3 ≔ Annihilator⁡S3
Let us check this result.
Download Help Document