cosmetic changes

Author: MikaelSlevinsky

examples/disk.jl

@@ -8,7 +8,7 @@
 # We analyze the function on an $N\times M$ tensor product grid defined by:
 # ```math
 # \begin{aligned}
-# r_n & = \cos\left[(n+\tfrac{1}{2})\pi/2N],\quad{\rm for} 0\le n < N,\quad{\rm and}\\
+# r_n & = \cos\left[(n+\tfrac{1}{2})\pi/2N\right],\quad{\rm for} 0\le n < N,\quad{\rm and}\\
 # \theta_m & = 2\pi m/M,\quad{\rm for}\quad 0\le m < M;
 # \end{aligned}
 # ```

examples/padua.jl

@@ -7,12 +7,14 @@ using FastTransforms
 # We define the Padua points and extract Cartesian components:
 N = 15
 pts = paduapoints(N)
-x = pts[:,1];
-y = pts[:,2];
+x = pts[:,1]
+y = pts[:,2]
+nothing #hide
 
 # We take the Padua transform of the function:
 f = (x,y) -> exp(x + cos(y))
-f̌ = paduatransform(f.(x , y));
+f̌ = paduatransform(f.(x , y))
+nothing #hide
 
 # and use the coefficients to create an approximation to the function $f$:
 f̃ = (x,y) -> begin

examples/spinweighted.jl

@@ -5,7 +5,7 @@
 # ```
 # for some $k\in\mathbb{R}^3$ and where $r\in\mathbb{S}^2$, using spin-$0$ spherical harmonics.
 #
-# It applies $\dh$, the spin-raising operator,
+# It applies ð, the spin-raising operator,
 # both on the spin-$0$ coefficients as well as the original function,
 # followed by a spin-$1$ analysis to compare coefficients.
 #
@@ -36,13 +36,13 @@ P = plan_spinsph2fourier(F, 0)
 # And an FFTW Fourier analysis plan on $\mathbb{S}^2$:
 PA = plan_spinsph_analysis(F, 0)
 
-# Its spin-0 spherical harmonic coefficients are:
+# Its spin-$0$ spherical harmonic coefficients are:
 U⁰ = P\(PA*F)
 
 # We can check its $L^2(\mathbb{S}^2)$ norm against an exact result:
 norm(U⁰) ≈ sqrt(4π)
 
-# Spin can be incremented by applying $\dh$, either on the spin-$0$ coefficients:
+# Spin can be incremented by applying ð, either on the spin-$0$ coefficients:
 U¹c = zero(U⁰)
 for n in 1:N-1
     U¹c[n, 1] = sqrt(n*(n+1))*U⁰[n+1, 1]

examples/triangle.jl

@@ -11,7 +11,7 @@
 # We analyze $f(x,y)$ on an $N\times M$ mapped tensor product grid defined by:
 # ```math
 # \begin{aligned}
-# x & = (1+u)/2,\quad{\rm and}\quad y = (1-u)*(1+v)/4,\quad {\rm where:}\\
+# x & = (1+u)/2,\quad{\rm and}\quad y = (1-u)(1+v)/4,\quad {\rm where:}\\
 # u_n & = \cos\left[(n+\tfrac{1}{2})\pi/N\right],\quad{\rm for}\quad 0\le n < N,\quad{\rm and}\\
 # v_m & = \cos\left[(m+\tfrac{1}{2})\pi/M\right],\quad{\rm for}\quad 0\le m < M;
 # \end{aligned}