tensorArray -- k-th level component of a tensor.

Usage:

sk = tensorArray(s,k)

sk = s@k

L = tensorArray(s)
Inputs:
- s, an instance of the type NCRingElement,
- k, an integer, The level to extract;
Outputs:
- sk, a list, The k-th level of s, as a multi-dimensional array;
- L, a list, The list of all levels of s, as multi-dimensional arrays;

Description

Returns the $k$-level component of a tensor as multi-dimensional array, represented by a nested List.

i1 : R = QQ[t];

i2 : X = polyPath({t,t^2});

i3 : sig(X,2)@2 -- signature matrix at depth 2

       1  2    1  1
o3 = {{-, -}, {-, -}}
       2  3    3  2

o3 : List

i4 : A = sig(X,3)@3 -- third level signature as multi-dimensional array

        1  1    1   4       1   2     1  1
o4 = {{{-, -}, {-, --}}, {{--, --}, {--, -}}}
        6  4    6  15      12  15    10  6

o4 : List

i5 : i = 0; j = 0; k = 0;

i8 : A#i#j#k == (Lt_(i+1)*Lt_(j+1)*Lt_(k+1))@(sig(X, 3)) --The coefficient of (Lt_1)^3 in sig(X, 3)

o8 = true

If the integer $k$ is not provided, returns a list of all non trivial levels (in nested list form).

i9 : L = tensorArray(sig(X, 3))

                                   1  1    1   4       1   2     1  1
o9 = {{0, 0}, {{0, 0}, {0, 0}}, {{{-, -}, {-, --}}, {{--, --}, {--, -}}}}
                                   6  4    6  15      12  15    10  6

o9 : List

i10 : L#2 == A

o10 = true

Ways to use tensorArray:

tensorArray(NCRingElement)
tensorArray(NCRingElement,ZZ)

For the programmer

The object tensorArray is a method function.

The source of this document is in PathSignatures/documentation.m2:159:0.

tensorArray -- k-th level component of a tensor.

Description

See also

Ways to use tensorArray:

For the programmer