Objects and operator implementing the exterior algebra.
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| class | Manicore::ExteriorBasis< l, d > |
| | Class to handle the exterior algebra basis. More...
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| class | Manicore::ComplBasis< l, d > |
| | Return a mapping from the basis of l-forms in dimension d to the basis of (d-l)-forms. More...
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| struct | Manicore::Compute_pullback< l, d1, d2 > |
| | Generic pullback computation. More...
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| struct | Manicore::Compute_pullback< 0, d1, d2 > |
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| struct | Manicore::Compute_pullback< 1, d1, d2 > |
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| struct | Manicore::Compute_pullback< d, d, d > |
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| struct | Manicore::Compute_pullback< 1, 1, 1 > |
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| struct | Manicore::Compute_pullback< 2, 2, 3 > |
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| struct | Manicore::Compute_pullback< 2, 3, 2 > |
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| struct | Manicore::Compute_pullback< 2, 3, 3 > |
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| struct | Manicore::Compute_ExtGram< l > |
| | Wrapper for the \(L^2\) product on the exterior algebra. More...
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| struct | Manicore::Monomial_powers< d > |
| | Generate a basis of monomial powers of degree r. More...
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| struct | Manicore::Koszul_full< l, d > |
| | Koszul operator from \(\mathcal{P}_r\Lambda^l(\mathbb{R}^d)\) to \(\mathcal{P}_{r+1}\Lambda^{l-1}(\mathbb{R}^d)\). More...
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| struct | Manicore::Diff_full< l, d > |
| | Differential operator from \(\mathcal{P}_r\Lambda^l(\mathbb{R}^d)\) to \(\mathcal{P}_{r-1}\Lambda^{l+1}(\mathbb{R}^d)\). More...
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| struct | Manicore::Initialize_exterior_module< d > |
| | Initialize every class related to the polynomial degree r. More...
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| template<typename V , typename Derived > |
| double | Manicore::Compute_partial_det (const V &a1, const V &a2, const Eigen::MatrixBase< Derived > &A) |
| | Generic determinant computation. More...
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| constexpr size_t | Manicore::Dimension::ExtDim (size_t l, size_t d) |
| | Dimension of the exterior algebra \(\Lambda^l(\mathbb{R}^d)\). More...
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| constexpr size_t | Manicore::Dimension::PolyDim (int r, size_t d) |
| | Dimension of \(\mathcal{P}_r(\mathbb{R}^d)\). More...
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| constexpr size_t | Manicore::Dimension::HDim (int r, size_t d) |
| | Dimension of homogeneous polynomials \( \mathcal{H}_r(\mathbb{R}^d)\). More...
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| constexpr size_t | Manicore::Dimension::PLDim (int r, size_t l, size_t d) |
| | Dimension of \(\mathcal{P}_r\Lambda^l(\mathbb{R}^d)\). More...
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| constexpr size_t | Manicore::Dimension::kHDim (int r, size_t l, size_t d) |
| | Dimension of the image of Koszul on homogeneous polynomials \( \kappa\mathcal{H}_r\Lambda^l(\mathbb{R}^d)\). More...
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| constexpr size_t | Manicore::Dimension::dHDim (int r, size_t l, size_t d) |
| | Dimension of the image of d on homogeneous polynomials \( d\mathcal{H}_r\Lambda^l(\mathbb{R}^d)\). More...
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| constexpr size_t | Manicore::Dimension::kPLDim (int r, size_t l, size_t d) |
| | Dimension of the image of Koszul on polynomials \( \kappa \mathcal{P}_r\Lambda^l(\mathbb{R}^d)\). More...
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| constexpr size_t | Manicore::Dimension::dPLDim (int r, size_t l, size_t d) |
| | Dimension of the image of d on polynomials \( d \mathcal{P}_r\Lambda^l(\mathbb{R}^d)\). More...
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| constexpr size_t | Manicore::Dimension::PLtrimmedDim (int r, size_t l, size_t d) |
| | Dimension of trimmed polynomial spaces \( \mathcal{P}_r^{-}\Lambda^l(\mathbb{R}^d)\). More...
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Objects and operator implementing the exterior algebra.
◆ Compute_partial_det()
template<typename V , typename Derived >
| double Manicore::Compute_partial_det |
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const V & |
a1, |
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const V & |
a2, |
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const Eigen::MatrixBase< Derived > & |
A |
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Generic determinant computation.
The first two arguments should be the list of indexes to use, and the last the matrix This function returns the determinant of the partial matrix
◆ dHDim()
| constexpr size_t Manicore::Dimension::dHDim |
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int |
r, |
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size_t |
l, |
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size_t |
d |
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constexpr |
Dimension of the image of d on homogeneous polynomials \( d\mathcal{H}_r\Lambda^l(\mathbb{R}^d)\).
◆ dPLDim()
| constexpr size_t Manicore::Dimension::dPLDim |
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int |
r, |
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size_t |
l, |
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size_t |
d |
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constexpr |
Dimension of the image of d on polynomials \( d \mathcal{P}_r\Lambda^l(\mathbb{R}^d)\).
◆ ExtDim()
| constexpr size_t Manicore::Dimension::ExtDim |
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size_t |
l, |
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size_t |
d |
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constexpr |
Dimension of the exterior algebra \(\Lambda^l(\mathbb{R}^d)\).
◆ HDim()
| constexpr size_t Manicore::Dimension::HDim |
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int |
r, |
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size_t |
d |
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constexpr |
Dimension of homogeneous polynomials \( \mathcal{H}_r(\mathbb{R}^d)\).
◆ kHDim()
| constexpr size_t Manicore::Dimension::kHDim |
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int |
r, |
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size_t |
l, |
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size_t |
d |
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constexpr |
Dimension of the image of Koszul on homogeneous polynomials \( \kappa\mathcal{H}_r\Lambda^l(\mathbb{R}^d)\).
◆ kPLDim()
| constexpr size_t Manicore::Dimension::kPLDim |
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int |
r, |
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size_t |
l, |
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size_t |
d |
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constexpr |
Dimension of the image of Koszul on polynomials \( \kappa \mathcal{P}_r\Lambda^l(\mathbb{R}^d)\).
◆ PLDim()
| constexpr size_t Manicore::Dimension::PLDim |
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int |
r, |
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size_t |
l, |
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size_t |
d |
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constexpr |
Dimension of \(\mathcal{P}_r\Lambda^l(\mathbb{R}^d)\).
◆ PLtrimmedDim()
| constexpr size_t Manicore::Dimension::PLtrimmedDim |
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int |
r, |
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size_t |
l, |
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size_t |
d |
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constexpr |
Dimension of trimmed polynomial spaces \( \mathcal{P}_r^{-}\Lambda^l(\mathbb{R}^d)\).
◆ PolyDim()
| constexpr size_t Manicore::Dimension::PolyDim |
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int |
r, |
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size_t |
d |
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constexpr |
Dimension of \(\mathcal{P}_r(\mathbb{R}^d)\).
