physics/partial-derivative-to-pdv

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/partial_derivative_to_pdv.rs (opens in new tab)

Triggers

\partialderivative, \pderivative commands

Eliminates

\partialderivative, \pderivative commands

Produces

\pdv command

Rewrite patterns#

1. partialderivative-two-args\partialderivative{#1}{#2}\pdv{#1}{#2}
2. partialderivative-star\partialderivative*{#1}{#2}\pdv*{#1}{#2}
3. partialderivative-order\partialderivative[#1]{#2}{#3}\pdv[#1]{#2}{#3}
4. partialderivative-single-arg\partialderivative{#1}\pdv{#1}
5. partialderivative-three-args\partialderivative{#1}{#2}{#3}\pdv{#1}{#2}{#3}
6. pderivative-two-args\pderivative{#1}{#2}\pdv{#1}{#2}
7. pderivative-star\pderivative*{#1}{#2}\pdv*{#1}{#2}
8. pderivative-order\pderivative[#1]{#2}{#3}\pdv[#1]{#2}{#3}
9. pderivative-single-arg\pderivative{#1}\pdv{#1}
10. pderivative-three-args\pderivative{#1}{#2}{#3}\pdv{#1}{#2}{#3}

Examples#

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

J=\pderivative{f}{x}+\pderivative{g}{y}

J=\pdv{f}{x}+\pdv{g}{y}

\partialderivative{T}{z}=0

\pdv{T}{z}=0

\partialderivative*{f}{x}

\pdv*{f}{x}

\partialderivative[n]{f}{x}

\pdv[n]{f}{x}

\partialderivative{x} f(x,y)

\pdv{x} f(x,y)

\partialderivative{f}{x}{y}

\pdv{f}{x}{y}

Related rules#

Downstream rules#

• physics/pdv-to-frac-partial Expand pdv forms to explicit partial-derivative fractions.

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/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: partialderivative, pderivative, and pdv share the same physics Derivative handler and argspec, so star, optional order, one-argument, and mixed-partial forms are preserved by renaming the command. The optional order branch is intentionally represented with two braced arguments because MathJax ignores that order when more derivative variables are supplied.

Disable this rule#

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

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

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