[
"apply operator to bra",
"apply operator to ket",
"X cross both sides by",
"X dot both sides",
"add X to both sides",
"add zero to LHS",
"add zero to RHS",
"apply divergence",
"apply gradient to scalar function",
"assume N dimensions",
"both sides cross X",
"both sides dot X",
"boundary condition for expr",
"claim LHS equals RHS",
"combine like terms",
"conjugate both sides",
"conjugate function X",
"conjugate transpose both sides",
"declare assumption",
"declare final expr",
"declare guess solution",
"declare identity",
"declare initial expr",
"differentiate with respect to",
"distribute conjugate to factors",
"distribute conjugate transpose to factors",
"divide both sides by",
"evaluate definite integral",
"expand LHS",
"expand RHS",
"expand integrand",
"expand magnitude to conjugate",
"factor out X",
"factor out X from LHS",
"factor out X from RHS",
"function is even",
"function is odd",
"indefinite integral over",
"indefinite integrate LHS over",
"indefinite integration",
"indefinite integrate RHS over",
"integrate over from to",
"make expr power",
"multiply LHS by unity",
"multiply RHS by unity",
"multiply both sides by",
"normalization condition",
"partially differentiate with respect to",
"raise both sides to power",
"replace curl with LeviCevita summation contravariant",
"replace scalar with vector",
"replace summation notation with vector notation",
"select imaginary parts",
"select real parts",
"simplify",
"solve for X",
"change variable X to Y",
"subtract X from both sides",
"sum exponents",
"sum exponents LHS",
"sum exponents RHS",
"swap LHS with RHS",
"take curl of both sides",
"multiply expr 1 by expr 2",
"substitute LHS of expr 1 into expr 2",
"substitute RHS of expr 1 into expr 2",
"LHS of expr 1 equals LHS of expr 2",
"RHS of expr 1 equals RHS of expr 2",
"subtract expr 1 from expr 2",
"add expr 1 to expr 2",
"expr 1 is true under condition expr 2",
"claim expr 1 equals expr 2",
"apply function to both sides of expression",
"expr 1 is equivalent to expr 2 under the condition",
"substitute LHS of two expressions into expr",
"substitute LHS of three expressions into expr",
"substitute LHS of four expressions into expr",
"substitute LHS of five expressions into expr",
"substitute LHS of six expressions into expr",
"change two variables in expr",
"change three variables in expr",
"change four variables in expr",
"change five variables in expr",
"change six variables in expr",
"square root both sides",
"divide expr 1 by expr 2",
"separate two vector components",
"separate three vector components",
"separate vector into two trigonometric ratios",
"boundary condition",
"maximum of expr",
"integrate",
"replace constant with value",
"drop non-dominant term"
]