if in formulas

• Iverson’s notation Iverson bracket

• [Iverson’s notation - Wikipedia https://ja.wikipedia.org/wiki/%E3%82%A2%E3%82%A4%E3%83%90%E3%83%BC%E3%82%BD%E3%83%B3%E3%81%AE%E8%A8%98%E6%B3% 95]

• ${\sum }_{x:0<x<N}f(x)={\sum }_{x}f(x)[0<x<N]$

• Personally, I didn’t like Kronecker’s delta and indicator functions because they were hard to read, but I thought this notation was nice because it didn’t make it too hard to read.

  • When neither True nor False has a non-zero value, it is easier to read if it is written in pieces rather than put together (B below).
    • A: $(x<0?-1:1)$
    • B: $-1[x<0]+1[x\ge 0]$
    • C: $1-2[x<0]$
    • D: $-1{\delta }_{x<0}+1{\delta }_{x\ge 0}$
    • E: $1-2{\delta }_{x<0}$

• Two notes on notation - Donald E. Knuth

  • $[k\mathrm{even}][k\mathrm{odd}][k\mathrm{prime}][k\mathrm{divedes}n]$

• Kronecker delta

• [Kronecker’s Delta - Wikipedia https://ja.wikipedia.org/wiki/%E3%82%AF%E3%83%AD%E3%83%8D%E3%83%83%E3%82%AB%E3%83%BC%E3%81%AE%E3%83%87%E3%83% AB%E3%82%BF]

• indicator function

• Directive function - Wikipedia

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