A mostly complete recreation of https://github.com/gillescastel/latex-snippets/ in vscode snippet syntax

latex.json

{
  "Begin/End": {
    "prefix": ["beg"],
    "body": ["\\begin{$1}", "  $0", "\\end{$1}"]
  },
  "ldots": {    
    "prefix": ["..."],
    "body": ["\\ldots"]
  },
  "Table environment": {    
    "prefix": ["table"],
    "body": [
      "\\begin{table}",
      "  \\centering",
      "  \\caption{$1}",
      "  \\label{tab:$2}",
      "  \\begin{tabular}{$3}",
      "    $0",
      "  \\end{tabular}",
      "\\end{table}"
    ]
  },
  "Enumerate": {
    "prefix": ["enum"],
    "body": ["\\begin{enumerate}", "  \\item $0", "\\end{enumerate}"]
  },
  "Itemize": {
    "prefix": ["item"],
    "body": ["\\begin{itemize}", "  \\item $0", "\\end{itemize}"]
  },
  "Desciption": {
    "prefix": ["desc"],
    "body": ["\\begin{description}", "  \\item[$1] $0", "\\end{description}"]
  },
  "Package": {    
    "prefix": ["pac"],
    "body": ["\\usepackage[${1:options}]{${2:package}}$0"]
  },
  "implies": {    
    "prefix": ["=>"],
    "body": ["\\implies"]
  },
  "implied by": {    
    "prefix": ["=<"],
    "body": ["\\impliedby"]
  },
  "iif": {    
    "prefix": ["iff"],
    "body": ["\\iff"]
  },
  "inline math": {    
    "prefix": ["im"],
    "body": ["$$1$$0"]
  },
  "display math": {    
    "prefix": ["dm"],
    "body": ["\\[", "  $1", "\\] $0"]
  },
  "fraction": {    
    "prefix": ["//"],
    "body": ["\\frac{$1}{$2}$0"]
  },
  "align": {
    "prefix": ["align"],
    "body": [
      "\\begin{align*}",
	    "    $1",
      ".\\end{align*}"
    ]
  },
  "aligned equals": {    
    "prefix": ["=="],
    "body": ["&="]
  },
  "!=": {
    "prefix": ["!="],
    "body": ["\\neq"]
  },
  "ceil": {    
    "prefix": ["ceil"],
    "body": ["\\left\\lceil $1 \\right\\rceil $0"]
  },
  "floor": {
    "prefix": ["floor"],
    "body": ["\\left\\lfloor $1 \\right\\rfloor $0"]
  },
  "pmat": {
    "prefix": ["pmat"],
    "body": ["\\left\\lfloor $1 \\right\\rfloor$0"]
  },
  "bmat": {
    "prefix": ["bmat"],
    "body": ["\\begin{pmatrix} $1 \\end{pmatrix} $0"]
  },
  "()": {
    "prefix": ["()"],
    "body": ["\\left( ${1:${VISUAL}} \\right) $0"]
  },
  "()": {
    "prefix": ["lr"],
    "body": ["\\left( ${1:${VISUAL}} \\right) $0"]
  },
  "()": {
    "prefix": ["lr("],
    "body": ["\\left( ${1:${VISUAL}} \\right) $0"]
  },
  "| |": {
    "prefix": ["lr|"],
    "body": ["\\left| ${1:${VISUAL}} \\right| $0"]
  },
  "{}": {
    "prefix": ["lr{"],
    "body": ["\\left\\{ ${1:${VISUAL}} \\right\\} $0"]
  },
  "{}": {
    "prefix": ["lrb"],
    "body": ["\\left\\{ ${1:${VISUAL}} \right\\} $0"]
  },
  "[]": {
    "prefix": ["lr["],
    "body": ["\\left[ ${1:${VISUAL}} \\right] $0"]
  },
  "< >": {
    "prefix": ["lra"],
    "body": ["\\left<${1:${VISUAL}} \\right>$0"]
  },
  "conjugate": {
    "prefix": ["conj"],
    "body": ["\\overline{$1}$0"]
  },
  "sum": {
    "prefix": ["sum"],
    "body": ["\\sum_{n=${1:1}}^{${2:\\infty}} ${3:a_n z^n}"]
  },
  "taylor": {
    "prefix": ["taylor"],
    "body": ["\\sum_{${1:k}=${2:0}}^{${3:\\infty}} ${4:c_$1} (x-a)^$1 $0"]
  },
  "limit": {
    "prefix": ["limit"],
    "body": ["\\sum_{n=${1:1}}^{${2:\\infty}} ${3:a_n z^n}"]
  },
  "limsup": {
    "prefix": ["limsup"],
    "body": ["\\limsup_{${1:n} \\to ${2:\\infty}} "]
  },
  "product": {
    "prefix": ["prod"],
    "body": ["\\prod_{${1:n=${2:1}}}^{${3:\\infty}} ${4} $0"]
  },
  "d/dx": {
    "prefix": ["part"],
    "body": ["\\frac{\\partial ${1:V}}{\\partial ${2:x}} $0"]
  },
  "sqrt": {
    "prefix": ["sqr"],
    "body": ["\\sqrt{$1} $0"]
  },
  "squared": {
    "prefix": ["sq"],
    "body": ["^2"]
  },
  "cubed": {
    "prefix": ["cb"],
    "body": ["^3"]
  },
  "td": {
    "prefix": ["to the ... power"],
    "body": ["^{$1}$0"]
  },
  "tr": {
    "prefix": ["to the ... power"],
    "body": ["^{($1)}$0"]
  },
  "subscript": {
    "prefix": ["__"],
    "body": ["_{$1}$0"]
  },
  "infinity": {
    "prefix": ["ooo"],
    "body": ["\\infty"]
  },
  "<=": {
    "prefix": ["<="],
    "body": ["\\le"]
  },
  ">=": {
    "prefix": [">="],
    "body": ["\\ge"]
  },
  "exists": {
    "prefix": ["EE"],
    "body": ["\\exists"]
  },
  "forall": {
    "prefix": ["AA"],
    "body": ["\\forall"]
  },
  "xn": {
    "prefix": ["xn"],
    "body": ["x_{n}"]
  },
  "yn": {
    "prefix": ["yn"],
    "body": ["y_{n}"]
  },
  "xi": {
    "prefix": ["xi"],
    "body": ["x_{i}"]
  },
  "yi": {
    "prefix": ["yi"],
    "body": ["y_{i}"]
  },
  "xj": {
    "prefix": ["xj"],
    "body": ["x_{j}"]
  },
  "yj": {
    "prefix": ["yj"],
    "body": ["j_{j}"]
  },
  "xm": {
    "prefix": ["xm"],
    "body": ["x_{m}"]
  },
  "xp1": {
    "prefix": ["xp1"],
    "body": ["x_{n+1}"]
  },
  "l": {
    "prefix": ["lll"],
    "body": ["\\ell"]
  },
  "nabla": {
    "prefix": ["nabl"],
    "body": ["\\nabla"]
  },
  "cross": {
    "prefix": ["xx"],
    "body": ["\\times"]
  },
  "cdot": {
    "prefix": ["**"],
    "body": ["\\cdot"]
  },
  "abs": {
    "prefix": ["abs"],
    "body": ["|$1|$0"]
  },
  "intergral": {
    "prefix": ["dint"],
    "body": ["\\int_{${1:-\\infty}}^{${2:\\infty}} ${3} \\mathop{${4:dx}} $0"]
  },
  "->": {
    "prefix": ["to"],
    "body": ["\\to"]
  },
  "<->": {
    "prefix": ["lrarrow"],
    "body": ["\\leftrightarrow"]
  },
  "!>": {
    "prefix": ["mapsto"],
    "body": ["\\mapsto"]
  },
  "inverse": {
    "prefix": ["invs"],
    "body": ["^{-1}"]
  },
  "complement": {
    "prefix": ["compl"],
    "body": ["^{c}"]
  },
  "setminus": {
    "prefix": ["\\\\\\"],
    "body": ["\\setminus"]
  },
  ">>": {
    "prefix": [">>"],
    "body": ["\\gg"]
  },
  "<<": {
    "prefix": ["<<"],
    "body": ["\\ll"]
  },
  "~": {
    "prefix": ["~~"],
    "body": ["\\sim"]
  },
  "set": {
    "prefix": ["set"],
    "body": ["\\{$1\\} $0"]
  },
  "mid": {
    "prefix": ["||"],
    "body": ["\\mid"]
  },
  "subset": {
    "prefix": ["cc"],
    "body": ["\\subset"]
  },
  "not in": {
    "prefix": ["notin"],
    "body": ["\\not\\in"]
  },
  "in": {
    "prefix": ["inn"],
    "body": ["\\in"]
  },
  "N": {
    "prefix": ["NN"],
    "body": ["\\N"]
  },
  "cap": {
    "prefix": ["nn"],
    "body": ["\\cap"]
  },
  "cup": {
    "prefix": ["UU"],
    "body": ["\\cup"]
  },
  "big cup": {
    "prefix": ["uuu"],
    "body": ["\\bigcup_{${1:i \\in ${2: I}}} $0"]
  },
  "big cap": {
    "prefix": ["nnn"],
    "body": ["\\bigcap_{${1:i \\in ${2: I}}} $0"]
  },
  "empty set": {
    "prefix": ["OO"],
    "body": ["\\O"]
  },
  "R": {
    "prefix": ["RR"],
    "body": ["\\R"]
  },
  "Q": {
    "prefix": ["QQ"],
    "body": ["\\Q"]
  },
  "Z": {
    "prefix": ["ZZ"],
    "body": ["\\Z"]
  },
  "normal": {
    "prefix": ["<!"],
    "body": ["\\triangleleft"]
  },
  "<>": {
    "prefix": ["diamond"],
    "body": ["\\diamond"]
  },
  "text": {
    "prefix": ["tt"],
    "body": ["\\text{$1}$0"]
  },
  "cases": {
    "prefix": ["case"],
    "body": [
      "\\begin{cases}",
	    "    $1",
      ".\\end{cases}"
    ]
  },
  "SI": {
    "prefix": ["SI"],
    "body": ["\\SI{$1}{$2}"]
  },
  "Big function": {
    "prefix": ["bigfun"],
    "body": [
      "\\begin{align*}",
	    "    $1: $2 &\\longrightarrow $3 \\\\\\\\",
	    "    $4 &\\longmapsto $1($4) = $0",
      ".\\end{align*}"
    ]
  },
  "column vector": {
    "prefix": ["cvec"],
    "body": ["\\begin{pmatrix} ${1:x}_${2:1}\\\\\\\\ \\vdots\\\\\\\\ $1_${2:n} \\end{pmatrix}"]
  },
  "bar": {
    "prefix": ["bar"],
    "body": ["\\overline{$1}$0"]
  },
  "hat": {
    "prefix": ["hat"],
    "body": ["\\hat{$1}$0"]
  }
}