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Kernel: Python 3

expression.difference(exp)

expression % exp

Restricting an expression to the words not accepted by the second. In other words:

$$ (\mathsf{E} \% \mathsf{F})(u) = \begin{cases} \mathsf{E}(u) & \text{if $\mathsf{F}(u) \ne 0$} \ 0 & \text{otherwise} \end{cases} $$

Preconditions:

  • None

Caveat:

  • The name difference is wrong, and will certainly be changed in the future.

  • If the second argument is not Boolean, because we determinize it, the process might loop for ever.

See also:

Examples

In the following example, we map every non empty word on {a,b}\{a, b\} to 22 with the exception of words that are repetitions of abab or of baba.

import vcsn
ctx = vcsn.context('lal_char, q')
exp = lambda e: ctx.expression(e)
e = exp('<2>[ab]{+}') % exp('(ab+ba)*')
e

⟨2⟩ ((a+b) (a+b)∗)&(a b+b a)∗c \left\langle 2 \right\rangle \,\left(\left(a + b\right) \, \left(a + b\right)^{*}\right) \& {\left(a \, b + b \, a\right)^{*}}^{c}

e.shortest(len = 4)

⟨2⟩a⊕⟨2⟩b⊕⟨2⟩aa⊕⟨2⟩bb⊕⟨2⟩aaa⊕⟨2⟩aab⊕⟨2⟩aba⊕⟨2⟩abb⊕⟨2⟩baa⊕⟨2⟩bab⊕⟨2⟩bba⊕⟨2⟩bbb⊕⟨2⟩aaaa⊕⟨2⟩aaab⊕⟨2⟩aaba⊕⟨2⟩aabb⊕⟨2⟩abaa⊕⟨2⟩abbb⊕⟨2⟩baaa⊕⟨2⟩babb⊕⟨2⟩bbaa⊕⟨2⟩bbab⊕⟨2⟩bbba⊕⟨2⟩bbbb\left\langle 2\right\rangle \mathit{a} \oplus \left\langle 2\right\rangle \mathit{b} \oplus \left\langle 2\right\rangle \mathit{aa} \oplus \left\langle 2\right\rangle \mathit{bb} \oplus \left\langle 2\right\rangle \mathit{aaa} \oplus \left\langle 2\right\rangle \mathit{aab} \oplus \left\langle 2\right\rangle \mathit{aba} \oplus \left\langle 2\right\rangle \mathit{abb} \oplus \left\langle 2\right\rangle \mathit{baa} \oplus \left\langle 2\right\rangle \mathit{bab} \oplus \left\langle 2\right\rangle \mathit{bba} \oplus \left\langle 2\right\rangle \mathit{bbb} \oplus \left\langle 2\right\rangle \mathit{aaaa} \oplus \left\langle 2\right\rangle \mathit{aaab} \oplus \left\langle 2\right\rangle \mathit{aaba} \oplus \left\langle 2\right\rangle \mathit{aabb} \oplus \left\langle 2\right\rangle \mathit{abaa} \oplus \left\langle 2\right\rangle \mathit{abbb} \oplus \left\langle 2\right\rangle \mathit{baaa} \oplus \left\langle 2\right\rangle \mathit{babb} \oplus \left\langle 2\right\rangle \mathit{bbaa} \oplus \left\langle 2\right\rangle \mathit{bbab} \oplus \left\langle 2\right\rangle \mathit{bbba} \oplus \left\langle 2\right\rangle \mathit{bbbb}

The operator % is also supported in the syntax of rational expressions:

exp('<2>[ab]{+}%(ab+ba)*')

⟨2⟩ ((a+b) (a+b)∗)&(a b+b a)∗c \left\langle 2 \right\rangle \,\left(\left(a + b\right) \, \left(a + b\right)^{*}\right) \& {\left(a \, b + b \, a\right)^{*}}^{c}