physics/pdv-to-frac-partial

Level

AuthoringFaithfulCorpusEquivFaithful, Corpus, and Equiv apply this rule.

Fidelity

renderPreserves rendering under the reference renderer.

Package

physics

Source

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

Triggers

\pdv command

Eliminates

\pdv command

Produces

\frac, \flatfrac commands; \partial character

Rewrite patterns#

1. pdv-two-argument\pdv{#1}{#2}\frac{\partial #1}{\partial #2}
2. pdv-operator\pdv{#1}\frac{\partial}{\partial #1}
3. pdv-order\pdv[#1]{#2}{#3}\frac{\partial^{#1} #2}{\partial #3^{#1}}
4. pdv-mixed-partial\pdv{#1}{#2}{#3}\frac{\partial^{2} #1}{\partial #2 \partial #3}
5. pdv-star\pdv*{#1}{#2}\flatfrac{\partial #1}{\partial #2}

Examples#

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

\lambda=\pdv{f}{x}

\lambda=\frac{\partial f}{\partial x}

\pdv{x} f

\frac{\partial}{\partial x} f

\pdv[2]{f}{x}

\frac{\partial^{2} f}{\partial x^{2}}

\pdv{f}{x}{y}

\frac{\partial^{2} f}{\partial x \partial y}

\pdv*{f}{x}

\flatfrac{\partial f}{\partial x}

Related rules#

Upstream rules#

• physics/partial-derivative-to-pdv Collapse long partial derivative names to the pdv 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/fdv-to-frac-delta Expand fdv forms to explicit delta-based 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 partial derivative, one-argument operator form, optional [n] order, mixed partial third braced group, and star branch. For MathJax physics, a third braced group makes the numerator order depend on the number of denominator variables and ignores the optional [n] order; that combined form is intentionally not represented as a separate rewrite pattern here.

Disable this rule#

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

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

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