weight.multiply.ipynb

Kernel: Python 3

weight.multiply

This function is overloaded, it supports these signatures:

• weight.multiply(w)

  The product of two weights.

• weight.multiply(num)

  The repeated multiplication (power) of a weight with itself. Exponent -1 denotes the infinity.

• weight.multiply((min, max))

  The sum of repeated multiplications of an expression: w.multiply((2,4)) = $w^2 + w^3 + w^4$. When min = -1, it denotes 0, when max = -1, it denotes the infinity.

Preconditions:

• min <= max

Examples

import vcsn
weight = vcsn.context('law_char, q').weight

Simple Multiplication

Instead of a.multiply(b), you may write a * b.

weight('1/2') * weight('3')

$\frac{3}{2}$

weight('1/2').multiply(weight('3'))

$\frac{3}{2}$

Repeated Multiplication

Instead of w.multiply(3), you may write w ** 3.

half = weight('1/2')
half ** 3

$\frac{1}{8}$

half ** 0

$1$

Use the exponent -1 to mean infinity. Alternatively, you may invoke w.star instead of w ** -1.

half ** -1

$2$

half.star()

$2$

Sums of Repeated Multiplications

Instead of w.multiply((2, 4)), you may write w ** (2, 4). Again, use exponent max = -1 to denotes infinity.

half ** (2, 2)

$\frac{1}{4}$

half ** (2, 4)

$\frac{7}{16}$

half ** 2 + half ** 3 + half ** 4

$\frac{7}{16}$

half ** (0, 2)

$\frac{7}{4}$

half ** (1, -1)

$1$