polynomial.ldivide.ipynb

Kernel: Python 3

polynomial.ldivide(poly)

polynomial//poly

A polynomial which denotes the left-quotient of both polynomials. Makes more sense when the labels can be words. Beware that the notation lhs // rhs is somewhat misleading, and corresponds to lhs \ rhs, i.e. lhs is the divisor, and rhs the dividend.

Preconditions:

• the division is valid

See also:

• automaton.ldivide

• expression.ldivide

Examples

import sys
import vcsn
ctx = vcsn.context('law, q')
poly = lambda p: ctx.polynomial(p)
poly('ab') // poly('abc')

$\mathit{c}$

The division must be valid.

try:
    poly('c') // poly('abc')
except RuntimeError as e:
    print(e, file=sys.stderr)

{abc}*: ldivide: invalid arguments: c, abc

poly('a+b') // poly('aa+ab+ba+bb')

$\mathit{a} \oplus \mathit{b}$

poly('<2>\e') // poly('a+<2>b')

$\left\langle \frac{1}{2}\right\rangle \mathit{a} \oplus \mathit{b}$