The AddMultiple function performs the operation  placing the output in a new object, or in C, depending on calling sequence. All of A, B, and C must be mod m Matrices or Vectors, and mult must be a scalar.

The first calling sequence returns a new mod m Matrix or Vector for the result with the specified ordering, order, or the ordering of the input objects A and B.

Note: If A and B have different ordering, order must be specified.

The second calling sequence places the output of the computation into C, returning NULL.

Note: The parameter C can be the same Matrix or Vector as A or B as long as the operation is performed with direct overlap.  For example, if A and C are the same Matrix, the operation involving the entry  must have the result going to .

The multiplier, mult, is an optional parameter.  However, if it is not specified, it is assumed to be 1. The multiplier must be in the range .  This function can be used to perform Matrix or Vector subtraction by the selection of . This is coded efficiently, that is, without multiplication.

If specified, the optional keyword 'sparse', is only applicable if the multiplier is not  or  and the datatype is a hardware datatype.  It indicates that the algorithm checks for zero entries before performing multiplications. This typically provides an efficiency gain if matrices have 10% or more entries in B equal to zero. This is not implemented for the integer datatype, as it typically provides very little gain.

Note: In cases for which sparse does not apply but has been specified, the option is ignored.

The AddMultiple function allows the use of sub-Matrix and sub-Vector specifications for both input and output Matrices or Vectors. For example, the function can be used to add a row of a Matrix to a row Vector, placing the result in the column of another Matrix.

Note: If the used portion of A or B, and C overlap, but not directly, the behavior of AddMultiple is undefined.

This command is part of the LinearAlgebra[Modular] package, so it can be used in the form AddMultiple(..) only after executing the command with(LinearAlgebra[Modular]).  However, it can always be used in the form LinearAlgebra[Modular][AddMultiple](..).