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Make differential operators in partialderivative(pdv) customizable #36

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Nov 1, 2024
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Make differential operators in partialderivative(pdv) customizable #36

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13 changes: 11 additions & 2 deletions physica-manual.typ
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Original file line number Diff line number Diff line change
Expand Up @@ -753,6 +753,7 @@ Function: `partialderivative(`_f_, \*_args_, \*\*_kwargs_`)`, abbreviated as `pd
- _f_: the function, which can be `#none` or omitted,
- positional _args_: the variable names, *optionally* followed by an order number e.g. `2`, or an order array e.g. `[2,3]`, `[k]`, `[m n, lambda+1]`.
- named _kwargs_:
- `d`: the differential symbol [default: `diff`].
- `s`: the "slash" separating the numerator and denominator [default: `none`], by default it produces the normal fraction form $pdv(f,x)$. The most common non-default is `slash` or simply `\/`, so as to create a flat form $pdv(f,x,s:\/)$ that fits inline.
- `total`: the user-specified total order.
- If it is absent, then (1) if the orders assigned to all variables are numeric, the total order number will be *automatically computed*; (2) if non-number symbols are present, computation will be attempted with minimum effort, and a user override with argument `total` may be necessary.
Expand Down Expand Up @@ -802,17 +803,25 @@ Function: `partialderivative(`_f_, \*_args_, \*\*_kwargs_`)`, abbreviated as `pd
*(8)* #hl(`pdv(phi,x,y,z,tau, [2,2,2,1])`) \
$ pdv(phi,x,y,z,tau, [2,2,2,1]) $
],
[
[
*(9)* #hl(`pdv(,x,y,z,t,[1,xi,2,eta+2])`) \
$ pdv(,x,y,z,t,[1,xi,2,eta+2]) $
],
[
*(10)* #hl(`pdv(,x,y,z,[xi n,n-1],total:(xi+1)n)`) \
$ pdv(,x,y,z,[xi n,n-1],total:(xi+1)n) $
],
[
*(11)* #hl(`pdv(S, phi.alt, phi.alt, d:delta)`) \
$ pdv(S, phi.alt, phi.alt, d:delta) $
],
[
*(12)* #hl(`pdv(W[J], J^mu (x) J^nu (y), d:delta)`) \
$ pdv(W[J], J^mu (x) J^nu (y), d:delta) $
]
)

*(11)* #hl(`integral_V dd(V) (pdv(cal(L), phi) - diff_mu (pdv(cal(L), (diff_mu phi)))) = 0`) \
*(13)* #hl(`integral_V dd(V) (pdv(cal(L), phi) - diff_mu (pdv(cal(L), (diff_mu phi)))) = 0`) \
$ integral_V dd(V) (pdv(cal(L), phi) - diff_mu (pdv(cal(L), (diff_mu phi)))) = 0 $

== Special show rules
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10 changes: 6 additions & 4 deletions physica.typ
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Expand Up @@ -693,22 +693,24 @@
__bare_minimum_effort_symbolic_add(orders)
}

let d = kwargs.at("d", default: $diff$)

let lowers = ()
for i in range(var_num) {
let var = args.at(1 + i) // 1st element is the function name, skip
let order = orders.at(i)
if order == [1] {
lowers.push($diff#var$)
lowers.push($#d#var$)
} else {
let varorder = __combine_var_order(var, order)
lowers.push($diff#varorder$)
lowers.push($#d#varorder$)
}
}

let upper = if total_order != 1 and total_order != [1] { // number or Content
if f == none { $diff^#total_order$ } else { $diff^#total_order#f$ }
if f == none { $#d^#total_order$ } else { $#d^#total_order#f$ }
} else {
if f == none { $diff$ } else { $diff #f$ }
if f == none { $#d$ } else { $#d #f$ }
}

let display(num, denom, slash) = {
Expand Down
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