physics/fdv-to-frac-delta

Level

AuthoringFaithfulCorpusEquivFaithful, Corpus, and Equiv apply this rule.

Fidelity

renderPreserves rendering under the reference renderer.

Package

physics

Source

physics/faithful/derivative_expand/fdv_to_frac_delta.rs (opens in new tab)

Triggers

\fdv command

Eliminates

\fdv command

Produces

\frac, \flatfrac commands; \delta character

Rewrite patterns#

1. fdv-two-argument\fdv{#1}{#2}\frac{\delta #1}{\delta #2}
2. fdv-operator\fdv{#1}\frac{\delta}{\delta #1}
3. fdv-order\fdv[#1]{#2}{#3}\frac{\delta^{#1} #2}{\delta #3^{#1}}
4. fdv-star\fdv*{#1}{#2}\flatfrac{\delta #1}{\delta #2}

Examples#

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

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

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

\fdv{\phi(x)} S

\frac{\delta}{\delta \phi(x)} S

\fdv[2]{S}{\phi}

\frac{\delta^{2} S}{\delta \phi^{2}}

\fdv*{S}{\phi}

\flatfrac{\delta S}{\delta \phi}

Related rules#

Upstream rules#

• physics/functional-derivative-to-fdv Collapse long functional derivative names to the fdv command.

Same family#

• physics/derivative-to-dv Collapse derivative to the compact dv command.
• physics/functional-derivative-to-fdv Collapse long functional derivative names to the fdv 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/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#

Covers the two-argument functional derivative, one-argument operator form, optional [n] order, and star branch. The star branch follows MathJax physics by expanding to \flatfrac rather than \frac.

Disable this rule#

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

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

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