tensor[lin_com] - linear combination of any number of tensor_types
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Calling Sequence
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lin_com(c1, T1, c2, T2, ...., cN, TN)
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Parameters
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c1, c2, c3, ..., cN
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algebraic coefficients in the linear combination to be formed
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T1, T2, T3, ..., TN
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tensor_types of identical characters and sharing the same space dimension
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Description
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This function forms the following linear combination of tensors:
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Each * represents a scalar multiplication and each + represents naturally a tensor addition.
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There is no limit on how many tensors to be summed; that is, N can be any positive integer.
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Any of the algebraic c's can be omitted, in which case it is by default substituted by 1.
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Simplification: This routine uses the `tensor/lin_com/simp` routine for simplification purposes. The simplification routine is applied to each component of result after it is computed. By default, `tensor/lin_com/simp` is initialized to the `tensor/simp` routine. It is recommended that the `tensor/lin_com/simp` routine be customized to suit the needs of the particular problem. It should be noted that `tensor/lin_com/simp` is used frequently as a simplifier by other routines. See ?tensor[simp] for a list of simplifiers used by each routine of the package.
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This function is part of the tensor package, and so can be used in the form lin_com(..) only after performing the command with(tensor) or with(tensor, lin_com). The function can always be accessed in the long form tensor[lin_com](..).
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Examples
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The following is the direct definitions of the tensor_types T1, T2, T3, without using the function tensor[create].
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Form the linear combination of some scalars:
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