`.`  operator for noncommutative or dot product multiplication

Description


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The '.' operator performs noncommutative or dot product multiplication on its arguments.


If A and B are numbers (including complex and extended numerics such as infinity and undefined), then A . B = A*B.


If A and B are Vectors with the same orientation (i.e., both are row Vectors or both are column Vectors), then A . B is computed by using LinearAlgebra[DotProduct].


If A and B are Arrays, their product is computed as componentwise multiplication using zip. If A and B do not have the same dimensions, extra entries are ignored.


Arguments that are not of type Matrix, Vector, constant, or Array are ignored, and A . B remains unevaluated.

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Calls to '.' such as A . B . C call `.`(A, B, C).


In this case, the process is repeated on the (transformed) arguments until no such argument pairs remain.

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The dot operator is leftassociative.

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Note: In Maple, '.' can be interpreted as a decimal point (for example, ), as part of a range operator (for example, ), or as the (noncommutative) multiplication operator. To distinguish between these three circumstances, Maple uses the following rule.


Any dot that is not part of a range operator (more than one '.' in a row) and not part of a number is interpreted as the noncommutative multiplication operator.


Note that the interpretation of the phrase "not part of a number" depends on whether you are using 1D or 2D input mode. In 1D input mode, interpretation proceeds from left to right, and a dot following a number will be interpreted as a decimal point unless that number already contains a decimal point. In 2D input mode, interpretation is carried out on the expression as a whole, and because spaces and juxtaposition can be interpreted as multiplication, a dot which is immediately preceded or followed by a number is always interpreted as a decimal point.


For example, in 1D input mode, 3.4 is a number, 3. 4 is an error and 3 .4 and 3 . 4 return 12. 3. .4 is 12. and 3..4 is a range.


In 2D input mode, 3.4 is a number, 3. 4 and 3 .4 are errors and 3 . 4 returns 12. 3. .4 is an error and 3..4 is again a range. (All of the errors shown by these examples are due to the rule that a number cannot appear as the righthand operand of an implicit multiplication operation. In such cases, use of explicit multiplication ( * ) can avoid the error. See also 2D Math Details for more information.)



Thread Safety


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The `.` operator is threadsafe as of Maple 15.



Examples


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If the dimensions of the Arrays are not the same, extra entries are ignored by the dot operator.
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