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DifferentialAlgebra[Tools][ToJet] - rewrite in jet notation a mathematical expression written in function notation
DifferentialAlgebra[Tools][FromJet] - rewrite in function notation a mathematical expression written in jet notation
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Calling Sequence
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ToJet(expr, DepVars, notation = ...)
FromJet(expr, DepVars, differentiationnotation = ...)
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Parameters
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expr
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algebraic expression or equation
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DepVars
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function or list of functions indicating the dependent variables of the problem
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differentiationnotation = ...
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(optional) can be diff (default), Diff, or D; specifies the derivative notation to return
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notation = ...
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(optional) can be jet (default), tjet, diff, or Diff; specifies the jet notation to return
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Description
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The ToJet and FromJet commands rewrite mathematical expressions back and forth using jet and function notation respectively.
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For ToJet, the option notation can be used to select the jet notation. The possible values are jet and tjet, respectively corresponding to the notations jetvariables and jetvariableswithbrackets explained in the help page of the equivalent PDEtools[ToJet] command.
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For FromJet, the option differentiationnotation can be used to select the notation used for derivatives. The possible values are diff, Diff and D, explained in the help page of the equivalent PDEtools[FromJet] command.
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Examples
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![[ToJet, FromJet]](/support/helpjp/helpview.aspx?si=8710/file05739/math141.png)
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![DepVars := [u(x, t), v(t), w(y)]](/support/helpjp/helpview.aspx?si=8710/file05739/math145.png)
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![DepVars := [u(x, t), v(t), w(y)]](/support/helpjp/helpview.aspx?si=8710/file05739/math148.png)
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The following is  in jet notation
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![jet_PDE := u[x]*v*w+u[t]*v*w[y]+u*v[t]*w[y]](/support/helpjp/helpview.aspx?si=8710/file05739/math166.png)
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This is  in tjet notation, or jet notation with brackets
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![tjet_PDE := u[x]*v[]*w[]+u[t]*v[]*w[y]+u[]*v[t]*w[y]](/support/helpjp/helpview.aspx?si=8710/file05739/math179.png)
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You can express jet_PDE and tjet_PDE in function notation, using diff, Diff, or D for expression the derivatives. By default diff notation is used.
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)(x, t)*v(t)*w(y)+(D[2](u))(x, t)*v(t)*(D(w))(y)+u(x, t)*(D(v))(t)*(D(w))(y)](/support/helpjp/helpview.aspx?si=8710/file05739/math214.png)
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