expression.is_valid

Whether all the starred sub-expressions have a constant-term that admits a star value.

Postconditions:

expression.constant_term does not throw an exception.

Examples

The following funtion will help display the result of is_valid.



In [1]:

    
import vcsn
from IPython.display import Latex

def valid(ctx, *rs):
    eqs = []
    for r in rs:
        r = ctx.expression(r)
        eqs.append(r'{0} &: \mathrm{{{1}}}'
                   .format(r.format('latex'),
                           "valid" if r.is_valid() else "invalid"))
    return Latex(r'''\begin{{aligned}}
        {0}
    \end{{aligned}}'''.format(r'\\'.join(eqs)))









    



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

In $\mathbb{B}$ all the values have a star-power, so expressions are always valid.



In [2]:

    
b = vcsn.context('lal_char(ab), b')
valid(b, '\e*')









    Out[2]:





\begin{aligned}
        {\varepsilon}^{*} &: \mathrm{valid}
    \end{aligned}

In $\mathbb{Z}$, $0$ is the only weight that admit a star.



In [3]:

    
z = vcsn.context('lal_char(ab), z')
valid(z, '(<0>\e)*', '(<1>\e)*', '(<42>\e)*')









    Out[3]:





\begin{aligned}
        \varepsilon &: \mathrm{valid}\\{\varepsilon}^{*} &: \mathrm{invalid}\\\left( \left\langle 42 \right\rangle \,\varepsilon\right)^{*} &: \mathrm{invalid}
    \end{aligned}

In $\mathbb{Q}$ (and $\mathbb{R}$), only weights $w$ such that $|w| < 1$ admit a star.



In [4]:

    
q = vcsn.context('lal_char(ab), q')
valid(q, '(<1/2>\e)*', '(<99/100>\e)*', '(<-99/100>\e)*', '(<101/100>\e)*', '(<-101/100>\e)*')









    Out[4]:





\begin{aligned}
        \left( \left\langle \frac{1}{2} \right\rangle \,\varepsilon\right)^{*} &: \mathrm{valid}\\\left( \left\langle \frac{99}{100} \right\rangle \,\varepsilon\right)^{*} &: \mathrm{valid}\\\left( \left\langle \frac{-99}{100} \right\rangle \,\varepsilon\right)^{*} &: \mathrm{valid}\\\left( \left\langle \frac{101}{100} \right\rangle \,\varepsilon\right)^{*} &: \mathrm{invalid}\\\left( \left\langle \frac{-101}{100} \right\rangle \,\varepsilon\right)^{*} &: \mathrm{invalid}
    \end{aligned}