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

Ways to use this method:

Array _ NCPolynomialRing -- create a word from an array

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

Array _ NCPolynomialRing -- create a word from an array

Description

See also

Ways to use this method: