expression.transpose.ipynb

Kernel: Python 3

expression.transpose

Reverse all the concatenations, and transpose the labels.

Preconditions:

• None

Properties:

• involution

See also:

• automaton.transpose

• expression.transposition

Examples

import vcsn
c = vcsn.context('law_char(abc), seriesset<law_char(xyz), b>')
c

$\{a, b, c\}^*\to\mathsf{Series}[\{x, y, z\}^*\to\mathbb{B}]$

r = c.expression('(<x>a+<xyz>(abc))*')
r

$\left( \left\langle \mathit{x} \right\rangle \,\mathit{a} + \left\langle \mathit{xyz} \right\rangle \,\left(\mathit{abc}\right)\right)^{*}$

r.transpose()

$\left( \left\langle \mathit{x} \right\rangle \,\mathit{a} + \left\langle \mathit{zyx} \right\rangle \,\left(\mathit{cba}\right)\right)^{*}$

assert(r.transpose().transpose() == r)

transpose and transposition should not be confused. The former completely rewrites the expression, while the latter only wraps it in a syntactic transposition operator:

r = c.expression('<xyz>(abc)')
r

$\left\langle \mathit{xyz} \right\rangle \,\left(\mathit{abc}\right)$

r.transpose()

$\left\langle \mathit{zyx} \right\rangle \,\left(\mathit{cba}\right)$

r.transposition()

$\left( \left\langle \mathit{xyz} \right\rangle \,\left(\mathit{abc}\right)\right)^{T}$