expression.transpose

Reverse all the concatenations, and transpose the labels.

Preconditions:

None

Properties:

involution

Examples



In [1]:

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









    



:0: FutureWarning: IPython widgets are experimental and may change in the future.






    














    Out[1]:





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



In [2]:

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









    Out[2]:





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



In [3]:

    
r.transpose()









    Out[3]:





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



In [4]:

    
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:



In [5]:

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









    Out[5]:





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



In [6]:

    
r.transpose()









    Out[6]:





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



In [7]:

    
r.transposition()









    Out[7]:





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