symmetric-tensor-index

Index operations for symmetric tensors (aka multinomials). In a r-th order symmetric tensor over a d-dimensional vector spaces, we can think of the indices in 3 different ways:

As a tensor index (ie an array of length r with values of length d)
As a polynomial degree (ie an array of length d with values up to r)
Or a flattened array index (a scalar number between 0 and (d + r - 1) choose r )

The code in this library can be used to convert between these indices. For more details see:

http://0fps.wordpress.com/2011/08/30/multidimensional-taylor-series-and-symmetric-tensors/

Install

npm install symmetric-tensor-index

API

var sym = require("symmetric-tensor-index")

`sym.nextTensor(rank, dimension, seq[, index])`

Finds the index of the next entry in the tensor.

rank is the rank of the tensor
dimension is the dimension of the tensor
seq is the tensor index
index is the array index (optional)

Returns The next array index. seq is updated in place.

`sym.tensorToDegree(rank, dimension, seq[, result])`

Converts a tensor index to a degree index

rank rank of the tensor
dimension dimension of vector space
seq is the tensor index
result (optional) gets the resulting computation

Returns result

`sym.tensorToArray(rank, dimension, seq)`

Converts a tensor index to an array index

rank rank of the tensor
dimension dimension of vector space
seq is the tensor index

Returns The array index of the tensor entry

`sym.degreeToTensor(rank, dimension, degrees[, result])`

Converts a degree index to a tensor index

rank rank of the tensor
dimension dimension of vector space
degrees is the degree index
result is the result (optional)

Returns result

`sym.degreeToArray(rank, dimension, degrees)`

Converts a degree index to an array index

rank rank of the tensor
dimension dimension of vector space
degrees is the degree index

Returns The array index of the degree sequence

Package detail