diff --git a/README.md b/README.md
index 74d00b6..536fe98 100644
--- a/README.md
+++ b/README.md
@@ -8,7 +8,7 @@
 [![CI](https://github.com/Leedehai/typst-physics/actions/workflows/ci.yml/badge.svg)](https://github.com/Leedehai/typst-physics/actions/workflows/ci.yml)
 [![Latest release](https://img.shields.io/github/v/release/Leedehai/typst-physics.svg?color=gold)][latest-release]
 
-Available in the collection of [Typst packages](https://typst.app/docs/packages/): `#import "@preview/physica:0.9.0": *`
+Available in the collection of [Typst packages](https://typst.app/docs/packages/): `#import "@preview/physica:0.9.1": *`
 
 > physica _noun_.
 > * Latin, study of nature
@@ -17,7 +17,8 @@ This [Typst](https://typst.app) package provides handy typesetting utilities for
 natural sciences, including:
 * Braces,
 * Vectors and vector fields,
-* Matrices, including Jacobian and Hessian, interpreting `..^T` as transpose,
+* Matrices, including Jacobian and Hessian,
+* Smartly render `..^T` as transpose and `..^+` as dagger (conjugate transpose),
 * Dirac braket notations,
 * Common math functions,
 * Differentials and derivatives, including partial derivatives of mixed orders with automatic order summation,
@@ -32,7 +33,7 @@ See the [manual](https://github.com/Leedehai/typst-physics/blob/master/physica-m
 
 A larger [demo.typ](https://github.com/Leedehai/typst-physics/blob/master/demo.typ):
 
-![demo-larger](https://github.com/Leedehai/typst-physics/assets/18319900/af4fcf6c-5da3-48d1-a7a7-59053f808db5)
+![demo-larger](https://github.com/Leedehai/typst-physics/assets/18319900/75b94ef8-cc98-434f-be5f-bfac1ef6aef9)
 
 ## Using physica in your Typst document
 
@@ -49,21 +50,21 @@ compiler locally, it downloads packages on-demand and caches them on-disk, see
 
 ```typst
 // Style 1
-#import "@preview/physica:0.9.0": *
+#import "@preview/physica:0.9.1": *
 
 $ curl (grad f), tensor(T, -mu, +nu), pdv(f,x,y,[1,2]) $
 ```
 
 ```typst
 // Style 2
-#import "@preview/physica:0.9.0": curl, grad, tensor, pdv
+#import "@preview/physica:0.9.1": curl, grad, tensor, pdv
 
 $ curl (grad f), tensor(T, -mu, +nu), pdv(f,x,y,[1,2]) $
 ```
 
 ```typst
 // Style 3
-#import "@preview/physica:0.9.0"
+#import "@preview/physica:0.9.1"
 
 $ physica.curl (physica.grad f), physica.tensor(T, -mu, +nu), physica.pdv(f,x,y,[1,2]) $
 ```
diff --git a/demo.typ b/demo.typ
index f5b38f0..bbf1856 100644
--- a/demo.typ
+++ b/demo.typ
@@ -11,7 +11,7 @@ A^T, curl vb(E) = - pdv(vb(B), t),
 quad
 tensor(Lambda,+mu,-nu) = dmat(1,RR),
 quad
-dd(x,y),
+f(x,y) dd(x,y),
 quad
 dd(vb(x),y,[3]),
 quad
diff --git a/physica-manual.pdf b/physica-manual.pdf
index 55daa9b..e9adc21 100644
Binary files a/physica-manual.pdf and b/physica-manual.pdf differ
diff --git a/physica-manual.typ b/physica-manual.typ
index 45cbad2..1740625 100644
--- a/physica-manual.typ
+++ b/physica-manual.typ
@@ -2,7 +2,7 @@
 // This document is shared under the Creative Commons BY-ND 4.0 license.
 #import "physica.typ": *
 
-#let version = "0.9.0"
+#let version = "0.9.1"
 
 #set document(
   title: [physica-manual.typ],
@@ -61,7 +61,7 @@ This manual itself was generated using the Typst CLI and the `physica` package,
 With `typst`'s #linkurl("package management", "https://github.com/typst/packages"):
 
 ```typst
-#import "@preview/physica:0.9.0": *
+#import "@preview/physica:0.9.1": *
 
 $ curl (grad f), pdv(,x,y,z,[2,k]), tensor(Gamma,+k,-i,-j) = pdv(vb(e_i),x^j)vb(e^k) $
 ```
@@ -165,7 +165,7 @@ All symbols need to be used in *math mode* `$...$`.
   [`TT`],
   [],
   [`v^TT, A^TT` #sym.arrow $v^TT, A^TT$],
-  [transpose, also see\ @matrix-tranpose],
+  [transpose, also see\ @matrix-transpose],
 
   [`vectorbold(`_content_`)`],
   [`vb`],
@@ -234,7 +234,7 @@ All symbols need to be used in *math mode* `$...$`.
   [`TT`],
   [],
   [`v^TT, A^TT` #sym.arrow $v^TT, A^TT$],
-  [transpose, also see\ @matrix-tranpose],
+  [transpose, also see\ @matrix-transpose],
 
   [#builtin([`mat(`...`)`])],
   [],
@@ -591,6 +591,15 @@ Functions: `differential(`\*_args_, \*\*_kwargs_`)`, abbreviated as `dd(`...`)`.
 - named _kwargs_:
   - `d`: the differential symbol [default: `upright(d)`].
   - `p`: the product symbol connecting the components [default: `none`].
+  - `compact`: only effective if `p` is `none`. If `#true`, will remove the TeXBook-advised thin spaces between the d-units [default: `#false`].
+
+TeXBook advises _[f]ormulas involving calculus look best when an extra thin space
+appears before dx or dy or d whatever_ (Chapter 18 p.168), and this package
+heeds this advice. If you don't want the spaces between the d-units, you may
+pass a `compact:#true` argument: $dd(r,theta) "vs." dd(r,theta,compact:#true)$ (compact).
+// https://github.com/typst/typst/issues/147 advocates for set rules for
+// non built-in functions. When that's implemented, user can do a
+// #set dd(compact: true) to set this param for all dd() invocations.
 
 *Order assignment algorithm:*
 - If there is no order number or order array, all variables has order 1.
@@ -607,8 +616,8 @@ Functions: `differential(`\*_args_, \*\*_kwargs_`)`, abbreviated as `dd(`...`)`.
   column-gutter: 2em,
 
   [
-    *(1)* #hl(`dd(f), dd(x,y)`) \
-    $ dd(f), dd(x,y) $
+    *(1)* #hl(`dd(f), f(r,theta) dd(r,theta)`) \
+    $ dd(f), f(r,theta) dd(r,theta) $
   ],
   [
     *(2)* #hl(`dd(x,3), dd(f,[k]), dd(f,[k],d:delta)`) \
@@ -619,8 +628,8 @@ Functions: `differential(`\*_args_, \*\*_kwargs_`)`, abbreviated as `dd(`...`)`.
     $ dd(f,2), dd(vb(x),t,[3,]) $
   ],
   [
-    *(4)* #hl(`dd(x,y,[2,3]), dd(x,y,z,[2,3])`) \
-    $ dd(x,y,[2,3]), dd(x,y,z,[2,3]) $
+    *(4)* #hl(`dd(x,y), dd(x,y,[2,3]), dd(x,y,z,[2,3])`) \
+    $ dd(x,y), dd(x,y,[2,3]), dd(x,y,z,[2,3]) $
   ],
   [
     *(5)* #hl(`dd(x, y, z, [[1,1],rho+1,n_1])`) \
@@ -756,68 +765,157 @@ Function: `partialderivative(`_f_, \*_args_, \*\*_kwargs_`)`, abbreviated as `pd
 *(11)* #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 $
 
-== Miscellaneous
+== Special show rules
 
 #v(1em)
 
-=== Reduced Planck constant (hbar)
+=== Matrix transpose with superscript T <matrix-transpose>
 
 #v(1em)
 
-In the default font, the Typst built-in symbol `planck.reduce` $planck.reduce$ looks a bit off: on letter "h" there is a slash instead of a horizontal bar, contrary to the symbol's colloquial name "h-bar". This package offers `hbar` to render the symbol in the familiar form: $hbar$. Contrast:
+Matrix transposition can be simply written as `..^T`, just like handwriting,
+and the only superscript `T` will be formatted properly to represent
+transposition instead of a normal capital letter $T$.
 
-#table(
-  columns: (auto, auto, auto, auto, auto),
-  align: horizon,
-  column-gutter: 1em,
-  stroke: none,
+This $square.stroked.dotted^T => square.stroked.dotted^TT$
+conversion is disabled if the base is either
+- a `limits(...)` or `scripts(...)` element, or
+- an integration symbol $integral$ or vertical bar $|$, or
+- an equation or `lr(...)` element whose last child is one of the above.
 
-  [Typst's `planck.reduce`],
-  [$ E = planck.reduce omega $],
-  [$ (pi G^2) / (planck.reduce c^4) $],
-  [$ A e^(frac(i(p x - E t), planck.reduce)) $],
-  [$ i planck.reduce pdv(,t) psi = -frac(planck.reduce^2, 2m) laplacian psi $],
+If you really want to:
+- print a transpose explicitly: use symbol `TT`: `A^TT` $=> A^TT$;
+- print a superscript letter $T$: use `scripts(T)`: `2^scripts(T)` $=> 2^scripts(T)$.
 
-  [this package's `hbar`],
-  [$ E = hbar omega $],
-  [$ (pi G^2) / (hbar c^4) $],
-  [$ A e^(frac(i(p x - E t), hbar)) $],
-  [$ i hbar pdv(,t) psi = -frac(hbar^2, 2m) laplacian psi $],
+This feature needs to be enabled explicitly through a _show rule_.
+```typ
+#show: super-T-as-transpose
+(A B)^T = B^T A^T
+```
+
+If you only want to enable it within a content block's scope, you may do
+```typ
+#[
+  #show: super-T-as-transpose // Enabled from here till the end of block.
+  (A B)^T = B^T A^T
+]
+```
+
+#align(center, [*Examples*])
+
+#show: super-T-as-transpose  // Necessary!
+
+#grid(
+  columns: (auto, auto),
+  row-gutter: 1em,
+  column-gutter: 2em,
+
+  [
+    *(1)* #hl(`(U V_n W')^T = W'^T V_n^T U^T`) \
+    $ (U V_n W')^T = W'^T V_n^T U^T  $
+  ],
+  [
+    *(2)* #hl(`vec(a, b)^T, mat(a, b; c, d)^T`) \
+    $ vec(a, b)^T, mat(a, b; c, d)^T $
+  ],
+  [
+    *(3)* #hl(`limits(sum)^T, scripts(e)^T`) \
+    $ limits(sum)^T, scripts(e)^T $
+  ],
+  [
+    *(4)* #hl(`integral_0^T, abs(a)^T, eval(F(t))^T_0`) \
+    $ integral_0^T, abs(a)^T, eval(F(t))^T_0 $
+  ],
 )
 
-=== Matrix transpose <matrix-tranpose>
+=== Matrix dagger with superscript +
 
-#v(1em)
+The conjugate transpose, also known as the Hermitian transpose, transjugate, or
+adjoint, of a complex matrix $A$ is performed by first transposing and then
+complex-conjugating each matrix element. It is often denoted as $A^*$,
+$A^upright(sans(H))$, and sometimes with a dagger symbol:
+`A^dagger` $=> A^dagger$.
+
+Writing `..^dagger` often visually clutters an equation in the source code form.
+Therefore, the package offers the ability to write `..^+` instead.
 
-Matrix transposition can be simply written as `..^T`, where the `T` will be
-formatted properly to represent transposition instead of a normal letter $T$.
-This conversion is disabled if the base is integral symbol.
+This $square.stroked.dotted^+ => square.stroked.dotted^dagger$ conversion is
+disabled if the base is either
+- a `limits(...)` or `scripts(...)` element, or
+- an equation or `lr(...)` element whose last child is one of the above.
 
-To enable this feature, users need to first import this and call
+This feature needs to be enabled explicitly through a _show rule_.
 ```typ
-#import "...(this physica package)...": super-T-as-transpose
-#show: super-T-as-transpose
+#show: super-plus-as-dagger
+U^+U = U U^+ = I
+```
+
+If you only want to enable it within a content block's scope (e.g. you want
+to have $square.stroked.dotted^+$ for ions or Moore–Penrose inverse outside the
+block), you may do
+```typ
+#[
+  #show: super-plus-as-dagger // Enabled from here till the end of block.
+  U^+U = U U^+ = I
+]
 ```
 
 #align(center, [*Examples*])
 
-#show: super-T-as-transpose  // Necessary!
+#show: super-plus-as-dagger  // Necessary!
 
 #grid(
-  columns: (50%, 50%),
+  columns: (auto, auto),
   row-gutter: 1em,
   column-gutter: 2em,
 
   [
-    *(1)* #hl(`(A_n B_n)^T = B_n^T A_n^T`) \
-    $ (A_n B_n)^T = B_n^T A_n^T $
+    *(1)* #hl(`U^+U = U U^+ = I`) \
+    $ U^+U = U U^+ = I  $
+  ],
+  [
+    *(2)* #hl(`mat(1+i,1;2-i,1)^+ = mat(1-i,2+i;1,1)`) \
+    $ mat(1+i,1;2-i,1)^+ = mat(1-i,2+i;1,1) $
+  ],
+  [
+    *(3)* #hl(`limits(N)^+, scripts(N)^+`) \
+    $ limits(N)^+, scripts(N)^+ $
   ],
   [
-    *(2)* #hl(`integral_0^T A^T f(x) dif x`) \
-    $ integral_0^T A^T f(x) dif x $
+    *(4)* #hl(`#let eq = $scripts(N)$; eq^+`) \
+    $ #let eq = $scripts(N)$; eq^+ $
   ],
 )
 
+== Miscellaneous
+
+#v(1em)
+
+=== Reduced Planck constant (hbar)
+
+#v(1em)
+
+In the default font, the Typst built-in symbol `planck.reduce` $planck.reduce$ looks a bit off: on letter "h" there is a slash instead of a horizontal bar, contrary to the symbol's colloquial name "h-bar". This package offers `hbar` to render the symbol in the familiar form: $hbar$. Contrast:
+
+#table(
+  columns: (auto, auto, auto, auto, auto),
+  align: horizon,
+  column-gutter: 1em,
+  stroke: none,
+
+  [Typst's `planck.reduce`],
+  [$ E = planck.reduce omega $],
+  [$ (pi G^2) / (planck.reduce c^4) $],
+  [$ A e^(frac(i(p x - E t), planck.reduce)) $],
+  [$ i planck.reduce pdv(,t) psi = -frac(planck.reduce^2, 2m) laplacian psi $],
+
+  [this package's `hbar`],
+  [$ E = hbar omega $],
+  [$ (pi G^2) / (hbar c^4) $],
+  [$ A e^(frac(i(p x - E t), hbar)) $],
+  [$ i hbar pdv(,t) psi = -frac(hbar^2, 2m) laplacian psi $],
+)
+
 === Tensors
 
 #v(1em)
@@ -1054,6 +1152,8 @@ Function: `BMEsymadd([`...`])`.
   [$BMEsymadd([2a+1,xi,b+1,a xi + 2b+a,2b+1])$],
 )
 
+#pagebreak()
+
 = Acknowledgement
 
 #v(1em)
@@ -1063,10 +1163,13 @@ Huge thanks to these LATEX packages, for lighting the way of physics typesetting
 - `derivatives` by Simon Jensen,
 - `tensor` by Philip G. Ratcliffe et al.
 
-#v(2em)
+#pagebreak()
 
-#align(bottom, text(8pt)[
+= License
 
-#sym.copyright Copyright 2023 Leedehai. The document is shared under Creative Commons Attribution-NoDerivatives 4.0 license (#linkurl("CC BY-ND 4.0", "https://creativecommons.org/licenses/by-nd/4.0/legalcode")).
+Source code:
+#sym.copyright Copyright 2023 Leedehai. See the license
+#linkurl("here", "https://github.com/Leedehai/typst-physics/blob/master/LICENSE.txt").
 
-])
+The document:
+Creative Commons Attribution-NoDerivatives 4.0 license (#linkurl("CC BY-ND 4.0", "https://creativecommons.org/licenses/by-nd/4.0/legalcode")).
diff --git a/physica.typ b/physica.typ
index ebc798a..4b78249 100644
--- a/physica.typ
+++ b/physica.typ
@@ -151,7 +151,11 @@
 
 #let vecrow(..content) = $lr(( #content.pos().join([,]) ))$
 
-// Prefer using super-T-as-transpose()
+// Prefer using super-T-as-transpose() found below.
+//
+// Note Unicode U+1D40 (#str.from-unicode(7488)) is kinda ugly, and that
+// glyph is in the superscript position already so users could not write
+// the habitual "A^TT".
 #let TT = $sans(upright(T))$
 
 #let __vector(a, accent, be_bold) = {
@@ -461,7 +465,12 @@
   }
 
   let dsym = kwargs.at("d", default: $upright(d)$)
-  let prod = kwargs.at("p", default: none)
+  let compact = kwargs.at("compact", default: false)
+  // Why a very thin space is the default joiner: see TeXBook, Chapter 18.
+  // math.thin (1/6 em, thinspace in typography) is used to separate the
+  // differential with the preceding function, so to keep visual cohesion, the
+  // width of this joiner inside the differential shall be smaller.
+  let prod = kwargs.at("p", default: if compact { none } else { h(0.09em) })
 
   let difference = var_num - orders.len()
   while difference > 0 {
@@ -478,7 +487,8 @@
       arr.push($dsym#var$)
     }
   }
-  $#arr.join(prod)$
+  // Smart spacing, like Typst's built-in "dif" symbol. See TeXBook, Chapter 18.
+  $op(#arr.join(prod))$
 }
 #let dd = differential
 
@@ -635,9 +645,29 @@
 // Credit: Enivex in https://github.com/typst/typst/issues/355 was very helpful.
 #let hbar = (sym.wj, move(dy: -0.08em, strike(offset: -0.55em, extent: -0.05em, sym.planck)), sym.wj).join()
 
+// A show rule, should be used like:
+//   #show: super-T-as-transpose
+//   (A B)^T = B^T A^T
+// or in scope:
+//   #[
+//     #show: super-T-as-transpose
+//     (A B)^T = B^T A^T
+//   ]
 #let super-T-as-transpose(document) = {
   show math.attach: elem => {
-    if elem.base != [∫] and elem.at("t", default: none) == [T] {
+    let __eligible(e) = {
+      if e.func() == math.limits or e.func() == math.scripts { return false }
+      if e.func() == math.lr {
+        let last = e.at("body").at("children").at(-1)
+        return __eligible(last)
+      }
+      if e.func() == math.equation {
+        return __eligible(e.at("body"))
+      }
+      (e != [∫]) and (e != [|]) and (e != sym.bar.v.double)
+    }
+
+    if __eligible(elem.base) and elem.at("t", default: none) == [T] {
       $attach(elem.base, t: TT, b: elem.at("b", default: #none))$
     } else {
       elem
@@ -647,6 +677,38 @@
   document
 }
 
+// A show rule, should be used like:
+//   #show: super-plus-as-dagger
+//   U^+U = U U^+ = I
+// or in scope:
+//   #[
+//     #show: super-plus-as-dagger
+//     U^+U = U U^+ = I
+//   ]
+#let super-plus-as-dagger(document) = {
+  show math.attach: elem => {
+    let __eligible(e) = {
+      if e.func() == math.limits or e.func() == math.scripts { return false }
+      if e.func() == math.lr {
+        let last = e.at("body").at("children").at(-1)
+        return __eligible(last)
+      }
+      if e.func() == math.equation {
+        return __eligible(e.at("body"))
+      }
+      true
+    }
+
+    if __eligible(elem.base) and elem.at("t", default: none) == [+] {
+      $attach(elem.base, t: dagger, b: elem.at("b", default: #none))$
+    } else {
+      elem
+    }
+  }
+
+  document
+}
+
 #let tensor(T, ..sink) = {
   let args = sink.pos()
 
diff --git a/typst.toml b/typst.toml
index 45259ff..c666474 100644
--- a/typst.toml
+++ b/typst.toml
@@ -1,6 +1,6 @@
 [package]
 name = "physica"
-version = "0.9.0"
+version = "0.9.1"
 description = "Neat derivative, differential, field, matrix, braket, tensor, hbar, etc."
 authors = ["Leedehai"]
 repository = "https://github.com/Leedehai/typst-physics"
@@ -8,9 +8,10 @@ keywords = [
   "physics", "mathematics", "brace", "set", "product", "evaluate", "restrict",
   "integral", "gradient", "divergence", "curl", "vector", "field", "laplacian",
   "matrix", "determinant", "diagonal", "identity", "Jacobian", "Hessian",
-  "Dirac", "braket", "differential", "derivative", "partial", "dv", "odv",
-  "pdv", "Planck", "hbar", "tensor", "isotope", "signal", "electromagnetism",
-  "mechanics", "quantum", "relativity", "imaginary", "notation",
+  "transpose", "Dirac", "braket", "differential", "derivative", "partial",
+  "dv", "odv", "pdv", "Planck", "hbar", "tensor", "isotope", "signal",
+  "electromagnetism", "mechanics", "quantum", "relativity", "imaginary",
+  "notation",
 ]
 compiler = "0.10.0"
 exclude = ["*.pdf", "*.py"]