# PetscDTAltVStar
Apply a power of the Hodge star operator, which maps k-forms to (N-k) forms, to a k-form 
## Synopsis
```
#include "petscdt.h" 
PetscErrorCode PetscDTAltVStar(PetscInt N, PetscInt k, PetscInt pow, const PetscReal *w, PetscReal *starw)
```

## Input Parameters

- ***N -*** the dimension of the vector space, N >= 0
- ***k -*** the degree k of the k-form w, 0 <= k <= N
- ***pow -*** the number of times to apply the Hodge star operator: pow < 0 indicates that the inverse of the Hodge star operator should be applied |pow| times.
- ***w -*** a k-form, size [N choose k]



## Output Parameter

- ***starw = (star)^pow w.  Each degree of freedom of a k-*** form is associated with a subset S of k coordinates of the N dimensional vector space: the Hodge start operator (star) maps that degree of freedom to the degree of freedom associated with S', the complement of S, with a sign change if the permutation of coordinates {S[0], ... S[k-1], S'[0], ... S'[N-k- 1]} is an odd permutation.  This implies (star)^2 w = (-1)^{k(N-k)} w, and (star)^4 w = w.





## See Also
 `PetscDTAltV`, `PetscDTAltVPullback()`, `PetscDTAltVPullbackMatrix()`

## Level
intermediate

## Location
<A HREF="PETSC_DOC_OUT_ROOT_PLACEHOLDER/src/dm/dt/interface/dtaltv.c.html#PetscDTAltVStar">src/dm/dt/interface/dtaltv.c</A>


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