There is no single universal meaning for the double dot operator (..). Its meaning depends on the language or notation around it: in Db2 SQL it invokes a method, in one GTA3script grammar it marks an inclusive character range, and in continuum mechanics double-dot symbols denote tensor contractions. Check the expression’s context before interpreting it.
How to identify which double dot you are seeing
Look at the notation surrounding the two periods. A value followed by .. and a method name points to Db2; quoted character terminals around .. point to the GTA3script grammar; tensor symbols with indices point to continuum mechanics. These are different operations, not interchangeable definitions of one operator.
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| Context | Typical notation | Meaning | Result |
|---|---|---|---|
| Db2 SQL structured types | subject..method(arguments) |
Invokes a method on a structured-type value | The method’s return value |
| GTA3script grammar | 'A'..'Z' |
Inclusive range of characters between two terminals | Grammar alternatives |
| Continuum mechanics | Tensor symbols with double-dot contraction notation | Contracts dyadic tensors over indices | A scalar in the cited definitions |
What .. means in Db2
In Db2 11.1, the double-dot operator invokes a method on a value of a user-defined structured type. The subject’s static type, or one of its supertypes, must provide the named method. Db2 resolves the method using its name and the argument types. IBM shows the form subject-expression..method-name(arguments) in its method invocation documentation.
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Db2 specifies high precedence and left-to-right association. For example, a..b..c + x..y..z is interpreted as ((a..b)..c) + ((x..y)..z).
Null handling is also specific to Db2: a null subject passed to a system-generated mutator causes an error with SQLSTATE 2202D. Other method calls on null subjects are not executed and yield null. These rules should not be generalized to other uses of ...
Rank #2
What .. means in the GTA3script grammar
The GTA3script specification uses a variation of EBNF, a notation for describing grammar rules. There, two dots between terminal characters define the inclusive range of characters between them. Its example, digit := '0'..'9' ;, describes the allowed digit characters; it is not a runtime arithmetic range operation. See the GTA3script specification.
What double-dot notation means in tensor formulas
In the cited continuum-mechanics text, double-dot contractions reduce dyadic tensors to a scalar, but the index arrangement matters. The horizontal form is Aij ·· Bij = AijBji; the vertical form is Aij : Bij = AijBij. The horizontal contraction pairs the indices in the second tensor in reversed order, while the vertical form pairs them in the same order. As a result, the two values can differ for nonsymmetric dyadics.
Rank #3
The same text notes that the horizontal contraction is zero when one dyadic is symmetric and the other is antisymmetric. It defines the dyadic norm using the vertical contraction. Because notation and typesetting can vary, retain the source’s symbols and index convention when reading or writing a formula. The definitions appear in the excerpt from Essentials of Continuum Framework.
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What to check when you encounter ..
- Identify the programming language, grammar specification, or mathematical field.
- Read a short span of the expression: a method name, quoted terminals, or indexed tensor symbols usually reveal the context.
- Do not assume two periods always mean a range, method call, or mathematical contraction; the surrounding notation determines the meaning.
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