* element to the element
* described by the vertices.
*
- * For example, if
- * dim==spacedim==2, then the
- * alternating form is a scalar
- * (because spacedim-dim=0) and
- * its value equals $\mathbf
- * v_1\wedge \mathbf v_2=\mathbf
- * v_1\cdot\mathbf v_2$. If
- * dim==spacedim==3, then the
- * result is again a scalar with
- * value $\mathbf v_1\wedge
- * \mathbf v_2 \wedge \mathbf v_3
- * = (\mathbf v_1\times \mathbf
- * v_2)\cdot \mathbf v_3$, where
- * $\mathbf v_1, \mathbf v_2,
- * \mathbf v_3$ are the images of
- * the unit vectors at a vertex
- * of the unit dim-dimensional
- * cell under transformation to
- * the dim-dimensional cell in
- * spacedim-dimensional space. In
- * both cases, i.e. for dim==2 or
- * 3, the result happens to equal
- * the determinant of the
- * Jacobian of the mapping from
- * reference cell to cell in real
- * space. Note that it is the
- * actual determinant, not its
- * absolute value as often used
- * in transforming integrals from
- * one coordinate system to
- * another. In particular, if the
- * object specified by the
- * vertices is a parallelogram
- * (i.e. a linear transformation
- * of the reference cell) then
- * the computed values are the
- * same at all vertices and equal
- * the (signed) area of the cell;
- * similarly, for
- * parallel-epipeds, it is the
- * volume of the cell.
+ * For example, if dim==spacedim==2, then
+ * the alternating form is a scalar
+ * (because spacedim-dim=0) and its value
+ * equals $\mathbf v_1\wedge \mathbf
+ * v_2=\mathbf v_1^\perp \cdot\mathbf
+ * v_2$, where $\mathbf v_1^\perp$ is a
+ * vector that is rotated to the right by
+ * 90 degrees from $\mathbf v_1$. If
+ * dim==spacedim==3, then the result is
+ * again a scalar with value $\mathbf
+ * v_1\wedge \mathbf v_2 \wedge \mathbf
+ * v_3 = (\mathbf v_1\times \mathbf
+ * v_2)\cdot \mathbf v_3$, where $\mathbf
+ * v_1, \mathbf v_2, \mathbf v_3$ are the
+ * images of the unit vectors at a vertex
+ * of the unit dim-dimensional cell under
+ * transformation to the dim-dimensional
+ * cell in spacedim-dimensional space. In
+ * both cases, i.e. for dim==2 or 3, the
+ * result happens to equal the
+ * determinant of the Jacobian of the
+ * mapping from reference cell to cell in
+ * real space. Note that it is the actual
+ * determinant, not its absolute value as
+ * often used in transforming integrals
+ * from one coordinate system to
+ * another. In particular, if the object
+ * specified by the vertices is a
+ * parallelogram (i.e. a linear
+ * transformation of the reference cell)
+ * then the computed values are the same
+ * at all vertices and equal the (signed)
+ * area of the cell; similarly, for
+ * parallel-epipeds, it is the volume of
+ * the cell.
*
* This function is used in order to
* determine how distorted a cell is (see