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JetCalculus[ProjectionTransformation] - construct the canonical projection map between jet spaces of a fiber bundle
Calling Sequences
ProjectionTransformation(n, m)
Parameters
n - a non-negative integer, the order for the domain jet space
m - a non-negative integer, the order for the range jet space, m <= n
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Description
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Let E -> M a fiber bundle. Then ProjectionTransformation(n, m) defines the canonical projection map from J^n(E) to J^m(E).
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The command ProjectionTransformation is part of the DifferentialGeometry:-JetCalculus package. It can be used in the form ProjectionTransformation(...) only after executing the commands with(DifferentialGeometry) and with(JetCalculus), but can always be used by executing DifferentialGeometry:-JetCalculus:-ProjectionTransformation(...).
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Examples
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Example 1.
Define the 6-th order jet bundle J^6(E) for E = R^2 x R, with coordinates (x, y, u) -> (x, y).
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![DGsetup([x, y], [u], E, 6)](/support/helpjp/helpview.aspx?si=6564/file05764/math65.png)
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Define the canonical projection from J^6(E) to J^3(E).
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![PI1 := [x = x, y = y, u[] = u[], u[1] = u[1], u[2] = u[2], u[1, 1] = u[1, 1], u[1, 2] = u[1, 2], u[2, 2] = u[2, 2], u[1, 1, 1] = u[1, 1, 1], u[1, 1, 2] = u[1, 1, 2], u[1, 2, 2] = u[1, 2, 2], u[2, 2, 2] = u[2, 2, 2]]](/support/helpjp/helpview.aspx?si=6564/file05764/math80.png)
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E >
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| (2.3) |
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