Editing Ambiguity (section)

=== Expressions ===
Ambiguous expressions often appear in physical and mathematical texts.
It is common practice to omit multiplication signs in mathematical expressions. Also, it is common to give the same name to a variable and a function, for example, {{nowrap|<math>f=f(x)</math>.}} Then, if one sees {{nowrap|<math>f=f(y+1)</math>,}} there is no way to distinguish whether it means <math>f=f(x)</math> '''multiplied''' by {{nowrap|<math>(y+1)</math>,}} or function <math>f</math> '''evaluated''' at argument equal to {{nowrap|<math>(y+1)</math>.}} In each case of use of such notations, the reader is supposed to be able to perform the deduction and reveal the true meaning.

Creators of algorithmic languages try to avoid ambiguities. Many algorithmic languages ([[C++]] and [[Fortran]]) require the character * as a symbol of multiplication. The [[Wolfram Language]] used in [[Mathematica]] allows the user to omit the multiplication symbol, but requires square brackets to indicate the argument of a function; square brackets are not allowed for grouping of expressions. Fortran, in addition, does not allow use of the same name (identifier) for different objects, for example, function and variable; in particular, the expression <math>f = f(x)</math> is qualified as an error.

The order of operations may depend on the context. In most [[programming language]]s, the operations of division and multiplication have equal priority and are executed from left to right. Until the last century, many editorials assumed that multiplication is performed first, for example, <math>a/bc</math> is interpreted as {{nowrap|<math>a/(bc)</math>;}} in this case, the insertion of parentheses is required when translating the formulas to an algorithmic language. In addition, it is common to write an argument of a function without parenthesis, which also may lead to ambiguity.
In the [[scientific journal]] style, one uses roman letters to denote elementary functions, whereas variables are written using italics.
For example, in mathematical journals the expression <math>s i n</math> does not denote the [[sine function]], but the product of the three variables {{nowrap|<math>s</math>,}} {{nowrap|<math>i</math>,}} {{nowrap|<math>n</math>,}} although in the informal notation of a slide presentation it may stand for {{nowrap|<math>\sin</math>.}}

Commas in multi-component subscripts and superscripts are sometimes omitted; this is also potentially ambiguous notation.
For example, in the notation {{nowrap|<math>T_{mnk}</math>,}} the reader can only infer from the context whether it means a single-index object, taken with the subscript equal to product of variables {{nowrap|<math>m</math>,}} <math>n</math> and {{nowrap|<math>k</math>,}} or it is an indication to a trivalent [[tensor]].