// Place your snippets for latex here. Each snippet is defined under a snippet name and has a prefix, body and 
	// description. The prefix is what is used to trigger the snippet and the body will be expanded and inserted. Possible variables are:
	// $1, $2 for tab stops, $0 for the final cursor position, and ${1:label}, ${2:another} for placeholders. Placeholders with the 
	// same ids are connected.
	// Example:
	// "Print to console": {
	// 	"prefix": "log",
	// 	"body": [
	// 		"console.log('$1');",
	// 		"$2"
	// 	],
	// 	"description": "Log output to console"
	// }

	
	{
		"PlusMinus": {
		  "prefix": "+-",
		  "body": "\\pm",
		  "description": "Plus or Minus Symbol"
		},
		"MinusPlus": {
		  "prefix": "-+",
		  "body": "\\mp",
		  "description": "Minus or Plus Symbol"
		},
		"RightArrow": {
		  "prefix": "->",
		  "body": "\\rightarrow",
		  "description": "Right Arrow"
		},
		"ThreeDots": {
		  "prefix": "...",
		  "body": "\\dots",
		  "description": "Ellipsis"
		},
		"ColonEquals": {
		  "prefix": ":=",
		  "body": "\\coloneqq",
		  "description": "Colon Equals"
		},
		"DoubleColon": {
		  "prefix": "::",
		  "body": "\\dblcolon",
		  "description": "Double Colon"
		},
		"MuchLessThan": {
		  "prefix": "<<",
		  "body": "\\ll",
		  "description": "Much Less Than"
		},
		"LessThanOrEqual": {
		  "prefix": "<=",
		  "body": "\\leq",
		  "description": "Less Than or Equal"
		},
		"GreaterThanOrEqual": {
		  "prefix": ">=",
		  "body": "\\geq",
		  "description": "Greater Than or Equal"
		},
		"DoubleRightArrow": {
		  "prefix": "=>",
		  "body": "\\Rightarrow",
		  "description": "Double Right Arrow"
		},
		"GreaterGreater": {
		  "prefix": ">>",
		  "body": "\\gg",
		  "description": "Much Greater Than"
		},
			"Alpha": {
			  "prefix": "Alpha",
			  "body": "A",
			  "description": "Greek Capital Alpha"
			},
			"Beta": {
			  "prefix": "Beta",
			  "body": "B",
			  "description": "Greek Capital Beta"
			},
			"Lambda": {
			  "prefix": "Lambda",
			  "body": "L",
			  "description": "Greek Capital Lambda"
			},
			"Omega": {
			  "prefix": "Omega",
			  "body": "\\Omega",
			  "description": "Greek Capital Omega"
			},
			"Pi": {
			  "prefix": "Pi",
			  "body": "P",
			  "description": "Greek Capital Pi"
			},
			"Sigma": {
			  "prefix": "Sigma",
			  "body": "S",
			  "description": "Greek Capital Sigma"
			},
			"Delta": {
			  "prefix": "Delta",
			  "body": "\\Delta",
			  "description": "Greek Capital Delta"
			},
		"ApproxEqual": {
		  "prefix": "approx",
		  "body": "\\approx",
		  "description": "Approximately Equal"
		},
		"Congruent": {
		  "prefix": "congru",
		  "body": "\\equiv",
		  "description": "Congruence"
		},
		"Union": {
		  "prefix": "cup",
		  "body": "\\cup",
		  "description": "Union"
		},
		"Intersection": {
		  "prefix": "cap",
		  "body": "\\cap",
		  "description": "Intersection"
		},
		"RealPart": {
		  "prefix": "Re",
		  "body": "\\Re",
		  "description": "Real Part Symbol"
		},
		"ImaginaryPart": {
		  "prefix": "Im",
		  "body": "\\Im",
		  "description": "Imaginary Part Symbol"
		},
		"SigmaLower": {
		  "prefix": "sigma",
		  "body": "\\sigma",
		  "description": "Lowercase Sigma"
		},
		"Psi": {
		  "prefix": "Psi",
		  "body": "\\Psi",
		  "description": "Greek Capital Psi"
		},
		"Bigotimes": {
		  "prefix": "bigotimes",
		  "body": "\\bigotimes",
		  "description": "Tensor Product"
		},
		"Cdot": {
		  "prefix": "cdot",
		  "body": "\\cdot",
		  "description": "Centered Dot"
		},
		"DeltaLower": {
		  "prefix": "delta",
		  "body": "\\delta",
		  "description": "Lowercase Delta"
		},
		
			"DoubleP": {
			  "prefix": "doubleP",
			  "body": "\\mathbb{P}",
			  "description": "Double P Symbol"
			},
			"DoubleF": {
			  "prefix": "doubleF",
			  "body": "\\mathbb{F}",
			  "description": "Double F Symbol"
			},
			"Double1": {
			  "prefix": "double1",
			  "body": "\\mathbb{1}",
			  "description": "Double 1 Symbol"
			},
			"DoubleDot": {
			  "prefix": "doubledot",
			  "body": "\\ddot{}",
			  "description": "Double Dot"
			},
			"DoubleUpTack": {
			  "prefix": "doubleuptack",
			  "body": "\\top",
			  "description": "Double Up Tack"
			},
			"EAA": {
			  "prefix": "eaa",
			  "body": "\\mathcal{A}",
			  "description": "Calligraphic A"
			},
			"EBB": {
			  "prefix": "ebb",
			  "body": "\\mathfrak{B}",
			  "description": "Fraktur B"
			},
			"Eff": {
			  "prefix": "eff",
			  "body": "\\mathfrak{F}",
			  "description": "Fraktur F"
			},
			"Ell": {
			  "prefix": "ell",
			  "body": "\\ell",
			  "description": "Ell Symbol"
			},
			"EmptySet": {
			  "prefix": "emptyset",
			  "body": "\\emptyset",
			  "description": "Empty Set Symbol"
			},
			"EPP": {
			  "prefix": "epp",
			  "body": "\\mathcal{P}",
			  "description": "Calligraphic P"
			},
			"Epsilon": {
			  "prefix": "epsilon",
			  "body": "\\epsilon",
			  "description": "Greek Epsilon"
			},
			"FrakturM": {
			  "prefix": "frakturM",
			  "body": "\\mathfrak{M}",
			  "description": "Fraktur M"
			},
			"Gamma": {
			  "prefix": "gamma",
			  "body": "\\gamma",
			  "description": "Lowercase Greek Gamma"
			},
			"Hdots": {
			  "prefix": "hdots",
			  "body": "\\cdots",
			  "description": "Horizontal Dots"
			},
			"IdentityMatrix": {
			  "prefix": "identitymatrix",
			  "body": "\\mathbb{I}",
			  "description": "Identity Matrix"
			},
			"Implies": {
			  "prefix": "implies",
			  "body": "\\Rightarrow",
			  "description": "Implies (Right Arrow)"
			},	
			"Eta": {
			  "prefix": "eta",
			  "body": "\\eta",
			  "description": "Lowercase Greek Eta"
			},
			"Exists": {
			  "prefix": "exists",
			  "body": "\\exists",
			  "description": "Existential Quantifier"
			},
			"Floor": {
			  "prefix": "floor",
			  "body": "\\lfloor \\rfloor",
			  "description": "Floor Function"
			},
			"ForAll": {
			  "prefix": "forall",
			  "body": "\\forall",
			  "description": "Universal Quantifier"
			},
			"In": {
			  "prefix": "in",
			  "body": "\\in",
			  "description": "Element Of"
			},
			"Infty": {
			  "prefix": "infty",
			  "body": "\\infty",
			  "description": "Infinity Symbol"
			},
			"Integral_symbol": {
			  "prefix": "int",
			  "body": "\\int",
			  "description": "Integral Symbol"
			},
			"LambdaLower": {
			  "prefix": "lambda",
			  "body": "\\lambda",
			  "description": "Lowercase Lambda"
			},
			"MathD": {
			  "prefix": "mathD",
			  "body": "\\mathbb{D}",
			  "description": "Double D (mathbb)"
			},
			"MathE": {
			  "prefix": "mathE",
			  "body": "\\mathbb{E}",
			  "description": "Double E (mathbb)"
			},
			"MathN": {
			  "prefix": "mathN",
			  "body": "\\mathbb{N}",
			  "description": "Double N (Natural Numbers)"
			},
			"MathP": {
			  "prefix": "mathP",
			  "body": "\\mathbb{P}",
			  "description": "Double P"
			},
			"MathC": {
				"prefix": "mathC",
				"body": "\\mathbb{C}",
				"description": "Double C"
			  },
			"MathQ": {
			  "prefix": "mathQ",
			  "body": "\\mathbb{Q}",
			  "description": "Double Q (Rational Numbers)"
			},
			"MathR": {
			  "prefix": "mathR",
			  "body": "\\mathbb{R}",
			  "description": "Double R (Real Numbers)"
			},
			"MathZ": {
			  "prefix": "mathZ",
			  "body": "\\mathbb{Z}",
			  "description": "Double Z (Integers)"
			},
			"Mu": {
			  "prefix": "mu",
			  "body": "\\mu",
			  "description": "Lowercase Mu"
			},
			"Nabla": {
			  "prefix": "nabla",
			  "body": "\\nabla",
			  "description": "Nabla Symbol"
			},
			"Limit": {
			  "prefix": "limit",
			  "body": "\\lim_{n \\to \\infty}",
			  "description": "Limit Expression"
			},
			"Lrhar": {
			  "prefix": "lrhar",
			  "body": "\\leftrightarrow",
			  "description": "Left Right Arrow"
			},
			"Mapsto": {
			  "prefix": "mapsto",
			  "body": "\\mapsto",
			  "description": "Maps To"
			},
			"Norm": {
			  "prefix": "norm",
			  "body": "\\lVert $1 \\rVert",
			  "description": "Norm (Double Bar)"
			},
			"NotIn": {
			  "prefix": "notin",
			  "body": "\\notin",
			  "description": "Not In (Set Membership)"
			},
			"Nu": {
			  "prefix": "nu",
			  "body": "\\nu",
			  "description": "Lowercase Nu"
			},
			"Ohm": {
			  "prefix": "ohm",
			  "body": "\\Omega",
			  "description": "Ohm (Capital Omega)"
			},
			"OmegaLower": {
			  "prefix": "omega",
			  "body": "\\omega",
			  "description": "Lowercase Omega"
			},
			"Partial": {
			  "prefix": "partial",
			  "body": "\\partial",
			  "description": "Partial Derivative"
			},
			"Perp": {
			  "prefix": "perp",
			  "body": "\\perp",
			  "description": "Perpendicular Symbol"
			},
			"PhiLower": {
			  "prefix": "phi",
			  "body": "\\phi",
			  "description": "Lowercase Phi"
			},
			"PiLower": {
			  "prefix": "pi",
			  "body": "\\pi",
			  "description": "Lowercase Pi"
			},
			"PropTo": {
			  "prefix": "propto",
			  "body": "\\propto",
			  "description": "Proportional To Symbol"
			},
				"QuadraticFormula": {
				  "prefix": "quadratic",
				  "body": "x = \\frac{-b \\pm \\sqrt{b^2 - 4ac}}{2a}",
				  "description": "Quadratic Formula"
				},
				"Rho": {
				  "prefix": "rho",
				  "body": "\\rho",
				  "description": "Lowercase Rho"
				},
				"Rond": {
				  "prefix": "rond",
				  "body": "\\bigcirc",
				  "description": "Rond (Big Circle)"
				},
				"ScriptB": {
				  "prefix": "scriptB",
				  "body": "\\mathcal{B}",
				  "description": "Script B"
				},
				"ScriptC": {
				  "prefix": "scriptC",
				  "body": "\\mathscr{C}",
				  "description": "Script C"
				},
				"ScriptE": {
				  "prefix": "scriptE",
				  "body": "\\mathscr{E}",
				  "description": "Script E"
				},
				"ScriptF": {
				  "prefix": "scriptF",
				  "body": "\\mathscr{F}",
				  "description": "Script F"
				},
				"ScriptL": {
				  "prefix": "scriptL",
				  "body": "\\mathscr{L}",
				  "description": "Script L"
				},
				"ScriptM": {
				  "prefix": "scriptM",
				  "body": "\\mathcal{M}",
				  "description": "Script M"
				},
				"ScriptP": {
				  "prefix": "scriptP",
				  "body": "\\mathscr{P}",
				  "description": "Script P"
				},			
				"Space": {
				  "prefix": "space",
				  "body": "\\quad",
				  "description": "Space (Quad)"
				},
				"Sqrt": {
				  "prefix": "sqrt",
				  "body": "\\sqrt{$1}",
				  "description": "Square Root"
				},
				"Sub": {
				  "prefix": "sub",
				  "body": "\\subset",
				  "description": "Subset"
				},
				"SubsetEq": {
				  "prefix": "subseteq",
				  "body": "\\subseteq",
				  "description": "Subset Equal"
				},
				"SupsetEq": {
				  "prefix": "supseteq",
				  "body": "\\supseteq",
				  "description": "Supset Equal"
				},
				"Sum": {
				  "prefix": "sum",
				  "body": "\\sum",
				  "description": "Summation"
				},
				"Tau": {
				  "prefix": "tau",
				  "body": "\\tau",
				  "description": "Lowercase Tau"
				},
				"ThetaLower": {
				  "prefix": "theta",
				  "body": "\\theta",
				  "description": "Lowercase Theta"
				},
				"Tild": {
				  "prefix": "tild",
				  "body": "\\sim",
				  "description": "Tilde"
				},
				"Times": {
				  "prefix": "times",
				  "body": "\\times",
				  "description": "Multiplication (Times)"
				},
				"Und": {
				  "prefix": "und",
				  "body": "-",
				  "description": "Underscore"
				},
				"UnderArrow": {
				  "prefix": "underarrow",
				  "body": "\\underset{\\rightarrow}{\\text{$1}}",
				  "description": "Under Arrow"
				},
				"UnderBrace": {
				  "prefix": "underbrace",
				  "body": "\\underbrace{$1}",
				  "description": "Underbrace"
				},
				"UpArrow": {
				  "prefix": "uparrow",
				  "body": "\\uparrow",
				  "description": "Up Arrow"
				},
				"Varepsilon": {
				  "prefix": "varepsilon",
				  "body": "\\varepsilon",
				  "description": "Variant Epsilon"
				},
				"Varphi": {
				  "prefix": "varphi",
				  "body": "\\varphi",
				  "description": "Variant Phi"
				},
				"Vartheta": {
				  "prefix": "vartheta",
				  "body": "\\vartheta",
				  "description": "Variant Theta"
				},
				"Vbar": {
				  "prefix": "vbar",
				  "body": "|",
				  "description": "Vertical Bar"
				},
				"Vdots": {
				  "prefix": "vdots",
				  "body": "\\vdots",
				  "description": "Vertical Dots"
				},
				"Vec": {
				  "prefix": "vec",
				  "body": "\\vec{$1}",
				  "description": "Vector Symbol"
				},
				"MapsTo": {
				  "prefix": "|->",
				  "body": "\\mapsto",
				  "description": "Maps To (Arrow)"
				},
				"ApproximatelyEqual": {
				  "prefix": "~=",
				  "body": "\\approx",
				  "description": "Approximately Equal"
				},
				"Equiv": {
				  "prefix": "equiv",
				  "body": "\\Leftrightarrow",
				  "description": "Equivalence (Leftrightarrow)"
				},
				"Brace": {
				  "prefix": "brace",
				  "body": "\\left\\{$1\\right\\}",
				  "description": "Brace with content"
				},
			
				"Ceil": {
				  "prefix": "ceil",
				  "body": "\\lceil $1 \\rceil",
				  "description": "Ceil function"
				},
				"Integral": {
				  "prefix": "integral",
				  "body": "\\int_{$1}^{$2}",
				  "description": "Integral"
				},
					"alpha": {
					  "prefix": "alpha",
					  "body": "\\alpha",
					  "description": "Lowercase Greek Alpha"
					},
					"beta": {
					  "prefix": "beta",
					  "body": "\\beta",
					  "description": "Lowercase Greek Beta"
					},
					"gamma": {
					  "prefix": "gamma",
					  "body": "\\gamma",
					  "description": "Lowercase Greek Gamma"
					},
					"delta": {
					  "prefix": "delta",
					  "body": "\\delta",
					  "description": "Lowercase Greek Delta"
					},
					"epsilon": {
					  "prefix": "epsilon",
					  "body": "\\epsilon",
					  "description": "Lowercase Greek Epsilon"
					},
					"zeta": {
					  "prefix": "zeta",
					  "body": "\\zeta",
					  "description": "Lowercase Greek Zeta"
					},
					"eta": {
					  "prefix": "eta",
					  "body": "\\eta",
					  "description": "Lowercase Greek Eta"
					},
					"theta": {
					  "prefix": "theta",
					  "body": "\\theta",
					  "description": "Lowercase Greek Theta"
					},
					"iota": {
					  "prefix": "iota",
					  "body": "\\iota",
					  "description": "Lowercase Greek Iota"
					},
					"kappa": {
					  "prefix": "kappa",
					  "body": "\\kappa",
					  "description": "Lowercase Greek Kappa"
					},
					"lambda": {
					  "prefix": "lambda",
					  "body": "\\lambda",
					  "description": "Lowercase Greek Lambda"
					},
					"mu": {
					  "prefix": "mu",
					  "body": "\\mu",
					  "description": "Lowercase Greek Mu"
					},
					"nu": {
					  "prefix": "nu",
					  "body": "\\nu",
					  "description": "Lowercase Greek Nu"
					},
					"xi": {
					  "prefix": "xi",
					  "body": "\\xi",
					  "description": "Lowercase Greek Xi"
					},
					"omicron": {
					  "prefix": "omicron",
					  "body": "o",  // no distinct symbol for lowercase omicron
					  "description": "Lowercase Greek Omicron"
					},
					"pi": {
					  "prefix": "pi",
					  "body": "\\pi",
					  "description": "Lowercase Greek Pi"
					},
					"rho": {
					  "prefix": "rho",
					  "body": "\\rho",
					  "description": "Lowercase Greek Rho"
					},
					"sigma": {
					  "prefix": "sigma",
					  "body": "\\sigma",
					  "description": "Lowercase Greek Sigma"
					},
					"tau": {
					  "prefix": "tau",
					  "body": "\\tau",
					  "description": "Lowercase Greek Tau"
					},
					"upsilon": {
					  "prefix": "upsilon",
					  "body": "\\upsilon",
					  "description": "Lowercase Greek Upsilon"
					},
					"phi": {
					  "prefix": "phi",
					  "body": "\\phi",
					  "description": "Lowercase Greek Phi"
					},
					"chi": {
					  "prefix": "chi",
					  "body": "\\chi",
					  "description": "Lowercase Greek Chi"
					},
					"psi": {
					  "prefix": "psi",
					  "body": "\\psi",
					  "description": "Lowercase Greek Psi"
					},
					"omega": {
					  "prefix": "omega",
					  "body": "\\omega",
					  "description": "Lowercase Greek Omega"
					},
						"Fraction": {
						  "prefix": "frac",
						  "body": [
							"\\frac{$1}{$2}"
						  ],
						  "description": "Fraction"
						},
						
							"Piecewise Function": {
							  "prefix": "brace",
							  "body": [
								"\\[",
								"  f(x) = \\begin{cases}",
								"    $1 & \\text{if $2}$ \\\\",
								"    $3 & \\text{otherwise}",
								"  \\end{cases}",
								"\\]"
							  ],
							  "description": "Piecewise function with two cases"
							},
						 "Textbf": {
						  "prefix": "textbf",
						  "body": [
							"\\textbf{$1}"
						  ],
						  "description": "Bold text"
						},
						"Dot": {
							"prefix": ".",
							"body": ".",
							"description": "dot"
							},
							"Brack": {
							"prefix": "brack",
							"body": "[\\![ $1 ]\\!]",
							"description": "brack"
							},
							
							"dagger": {
								"prefix": "dagger",
								"body": "\\dagger",
								"description": "Dagger symbol"
							},  
							"Underset": {
				  "prefix": "underset",
				  "body": "\\underset{$1}{$2}",
				  "description": "Under set"
				},
				"Setminus": {
					"prefix": "setminus",
					"body": "\\setminus",
					"description": "setminus"
				  },
				  "Mathrm": {
					"prefix": "mathrm",
					"body": "\\mathrm{$1}",
					"description": "mathrm"
				  }
			  }