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This example program doesn't actually do anything; these comments 
This example program doesn't actually do anything; these comments 
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list the Unicode characters that you can use in Diderot. 
list the Unicode characters that you can use in Diderot. 
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After each character is the LaTeX equivalent, which might be 
With each character we give the Unicode code point and name, the LaTeX equivalent (might be 
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useful for Diderot programs in LaTeX documents, and other comments. 
useful for Diderot programs in LaTeX documents), and other comments. 
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#### π means Pi, as in 
Our basic philosophy behind indicating mathematical values and operators 
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in the most idiomatic way possible is similar to principles previously 
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articulated by other computer scientists. 
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> First, we want to establish the idea that a computer language is not 
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> just a way of getting a computer to perform operations but rather that 
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> it is a novel formal medium for expressing ideas about methodology. 
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> Thus, programs must be written for people to read, and only 
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> incidentally for machines to execute.  Abelson & Sussman & Sussman, 
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> Structure and Interpretation of Computer Programs (1985) 
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> Let us change our traditional attitude to the construction of 
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> programs: instead of imagining that our main task is to instruct a 
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> computer what to do, let us concentrate rather on explaining to humans 
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> what we want the computer to do.  Donald Knuth, Literate Programming (1984) 
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These statements predate Unicode development, but that does not 
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undermine their continued relevance for Diderot or for programming in general. 
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See https://en.wikipedia.org/wiki/Unicode_input for information about 
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how best to input unicode in your OS. Or, copy and paste from this file. 
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#### π means pi, as in 
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real rad = degrees*π/180; 
real rad = degrees*π/180; 
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* Unicode: U+03C0 (Greek Small Letter Pi) 
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* LaTeX: `\pi` 
* LaTeX: `\pi` 
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* This is currently the only finite real constant in Diderot. 
* This is currently the only finite real constant in Diderot. 
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#### ∞ means Infinity, as in 
#### ∞ means infinity, as in 
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output real out = ∞; 
output real out = ∞; 
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* Unicode: U+221E (Infinity) 
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* LaTeX: `\infty` 
* LaTeX: `\infty` 
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* The above line of code is how the output of maximumintensity projection might be intialized; 
* The above line of code is how the output of maximumintensity projection might be intialized; 
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from then on subsequent use might be like `out = max(out, F(pos))`. 
from then on subsequent use might be like `out = max(out, F(pos))`. 
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#### ⊛ means convolution, as in 
#### ⊛ means convolution, as in 
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field#2(3)[] F = bspln3 ⊛ image("img.nrrd"); 
field#2(3)[] F = bspln3 ⊛ image("img.nrrd"); 
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* Unicode: U+229B (Circled Asterisk Operator) 
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* LaTeX: `\circledast` is probably typical, but `\varoast` (with `\usepackage{stmaryrd}`) 
* LaTeX: `\circledast` is probably typical, but `\varoast` (with `\usepackage{stmaryrd}`) 
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is slightly more legible 
is slightly more legible 
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* This commutes; you could also write `image("img.nrrd") ⊛ bspln3`. 
* This commutes; you could also write `image("img.nrrd") ⊛ bspln3`. 
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#### × means cross product, as in 
#### × means cross product, as in 
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vec3 camU = normalize(camN × camUp); 
vec3 camU = normalize(camN × camUp); 
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* Unicode: U+00D7 (Multiplication Sign) 
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* LaTeX: `\times` 
* LaTeX: `\times` 
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* As the crossproduct, this is only defined for `vec3` variables. 
* As the crossproduct, this is only defined for `vec3` variables. 
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It also works for the curl of a vector field; see below. 
It also works for the curl of a vector field; see below. 
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#### ⊗ means tensor product, as in 
#### ⊗ means tensor product, as in 
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tensor[3,3] Proj = identity[3]  norm⊗norm 
tensor[3,3] Proj = identity[3]  norm⊗norm 
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* Unicode: U+2297 (Circled Times) 
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* LaTeX: `\otimes`. 
* LaTeX: `\otimes`. 
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* As an operator on coordinate vectors, this is typically called the outer product. 
* As an operator on coordinate vectors, this is typically called the outer product. 
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It is also used to define the Jacobian of a vector field; see below. 
It is also used to define the Jacobian of a vector field; see below. 
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#### • means dot product and matrix multiplication, as in 
#### • means dot product and matrix multiplication, as in 
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real ld = norm • lightDir; 
real ld = norm • lightDir; 
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* Unicode: U+2022 (Bullet) 
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* LaTeX: `\bullet`, which is more consistently visible than 
* LaTeX: `\bullet`, which is more consistently visible than 
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the `\cdot` that more typical for dot products. 
the `\cdot` that more typical for dot products. 
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* The meaning of `•` is really (in tensorspeak) "contract out the 
* The meaning of `•` is really (in tensorspeak) "contract out the 
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field#1(3)[] divergence = ∇•V; 
field#1(3)[] divergence = ∇•V; 
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field#2(2)[2] U = ...; 
field#2(2)[2] U = ...; 
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field#1(2)[] vort = ∇×U; 
field#1(2)[] vort = ∇×U; 
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* Unicode: U+2207 (Nabla) 
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* LaTeX: `\nabla`. 
* LaTeX: `\nabla`. 
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* See above for the different uses of `∇`. Note that `∇×` applied to a 2D vector field 
* See above for the different uses of `∇`. Note that `∇×` applied to a 2D vector field 
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gives you a scalar, but `∇×` applied to a 3D vector field gives you another 3D vector field. 
gives you a scalar, but `∇×` applied to a 3D vector field gives you another 3D vector field. 