physics/functional-derivative-to-fdv

Level

AuthoringFaithfulCorpusEquivEvery profile applies this rule; its output remains suitable for authoring.

Fidelity

renderPreserves rendering under the reference renderer.

Package

physics

Source

physics/authoring/derivative_to_short/functional_derivative_to_fdv.rs (opens in new tab)

Triggers

\fderivative, \functionalderivative commands

Eliminates

\fderivative, \functionalderivative commands

Produces

\fdv command

Rewrite patterns#

1. fderivative-two-args\fderivative{#1}{#2}\fdv{#1}{#2}
2. fderivative-star\fderivative*{#1}{#2}\fdv*{#1}{#2}
3. fderivative-order\fderivative[#1]{#2}{#3}\fdv[#1]{#2}{#3}
4. fderivative-single-arg\fderivative{#1}\fdv{#1}
5. functionalderivative-two-args\functionalderivative{#1}{#2}\fdv{#1}{#2}
6. functionalderivative-star\functionalderivative*{#1}{#2}\fdv*{#1}{#2}
7. functionalderivative-order\functionalderivative[#1]{#2}{#3}\fdv[#1]{#2}{#3}
8. functionalderivative-single-arg\functionalderivative{#1}\fdv{#1}

Examples#

Each example shows this rule applied in isolation. A complete normalization profile may make additional changes.

\functionalderivative{S[\phi]}{\phi(x)}=0

\fdv{S[\phi]}{\phi(x)}=0

\fderivative{\Gamma[J]}{J(y)}=\phi(y)

\fdv{\Gamma[J]}{J(y)}=\phi(y)

\fderivative*{S}{\phi}

\fdv*{S}{\phi}

\fderivative[n]{S}{\phi}

\fdv[n]{S}{\phi}

\fderivative{\phi} S[\phi]

\fdv{\phi} S[\phi]

\functionalderivative*{S}{\phi}

\fdv*{S}{\phi}

Related rules#

Downstream rules#

• physics/fdv-to-frac-delta Expand fdv forms to explicit delta-based derivative fractions.

Same family#

• physics/derivative-to-dv Collapse derivative to the compact dv command.
• physics/partial-derivative-to-pdv Collapse long partial derivative names to the pdv command.
• physics/vectorarrow-to-va Collapse vectorarrow to the short va helper.
• physics/vectorbold-to-vb Collapse vectorbold to the short vb helper.
• physics/vectorunit-to-vu Collapse vectorunit to the short vu helper.
• physics/dv-to-frac-d Expand dv forms to explicit d-based derivative fractions.
• physics/fdv-to-frac-delta Expand fdv forms to explicit delta-based derivative fractions.
• physics/pdv-to-frac-partial Expand pdv forms to explicit partial-derivative fractions.
• physics/va-to-vec-mathbf Canonicalize va to an explicit vec-wrapped mathbf form.
• physics/vb-to-mathbf Canonicalize vb to an explicit mathbf wrapper.
• physics/vu-to-hat-mathbf Canonicalize vu to an explicit hat-wrapped mathbf form.

Notes#

Alias rewrite: fderivative, functionalderivative, and fdv share the same physics Derivative handler and argspec, so star, optional order, and one-argument forms are preserved by renaming the command.

Disable this rule#

TransformEngine(profile="corpus", disable_rules=["physics/functional-derivative-to-fdv"])

new TransformEngine({ profile: 'corpus', disableRules: ['physics/functional-derivative-to-fdv'] })

Open in Playground