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# Array _ NCPolynomialRing -- create a word from an array

- Operator: _
- Usage:
    `w = a_R`
- Inputs:
  - a, an array, In the form [i_1,...i_k] where 0 < i_j< d+1, where d is the number of generators of R;
  - R, an instance of the type NCPolynomialRing,
- Outputs:
  - w, an instance of the type NCRingElement, The element of R corresponding to R_(i_1)*...R_(i_k);

## Description

This method allows to create a monomial in a free associative algebra $R$. It follows the same convention of wordFormat. Let $Lt_1,\dots, Lt_d$ be the generators of $R$, then an array of integers $[i_1,\dots, i_k]$ such that $0<i_l<d+1, \forall 1\leq l\leq k$ yields the element $$Lt_{i_1} Lt_{i_2}\cdot\dots\cdot Lt_{i_{k-1}} Lt_{i_k}$$ of $R$.

    i1 : d = 5;

    i2 : R = wordAlgebra(d); -- create a free associative algebra over Lt_1,..., Lt_d

    i3 : a = new Array from for i from 1 to d list i; -- The array [1,...,d]

    i4 : f = a_R  -- The word associated to a

    o4 = Lt Lt Lt Lt Lt
           1  2  3  4  5

    o4 : R

    i5 : g = product gens R -- The word Lt_1*...Lt_d

    o5 = Lt Lt Lt Lt Lt
           1  2  3  4  5

    o5 : R

    i6 : f === product gens R

    o6 = true

## See also

- wordAlgebra -- create a free algebra over a given alphabet
- wordFormat -- display a tensor in word notation

## Ways to use this method:

- Array _ NCPolynomialRing -- create a word from an array

The source of this document is in /build/macaulay2-88fgJW/macaulay2-1.25.11+ds/M2/Macaulay2/packages/PathSignatures/documentation.m2:159:0.