polynomial.split.ipynb

Kernel: Python 3

polynomial.split()

Split the expressions of a polynomial of rational expressions. In other words, when an expression is actually a sum of expressions, breaks it in smaller expressions, and return a polynomial of all these smaller expressions.

See also:

• expression.split

Examples

import vcsn
c = vcsn.context('expressionset<lal, q>, q')
c

$\mathsf{RatE}[\{\ldots\}\to\mathbb{Q}]\to\mathbb{Q}$

Beware that the following polynomial (admittedly badly displayed) is $\langle 2 \rangle \odot (a+b)$, not $\langle 2 \rangle \odot a \oplus b$: it contains a single expression, $a+b$.

p1 = c.polynomial('<2>a+b')
p1

$\left\langle 2\right\rangle a + b$

p1.split()

$\left\langle 2\right\rangle a \oplus \left\langle 2\right\rangle b$

p2 = c.polynomial('a+b(c+d)')
p2

$a + b \, \left(c + d\right)$

p2.split()

$a \oplus b \, \left(c + d\right)$

p1 + p2

$\left\langle 2\right\rangle a + b \oplus a + b \, \left(c + d\right)$

(p1 + p2).split()

$\left\langle 3\right\rangle a \oplus \left\langle 2\right\rangle b \oplus b \, \left(c + d\right)$