# expression.multiply¶

This function is overloaded, it supports these signatures:

• expression.multiply(exp)

The product (i.e., the concatenation) of two expressions: a.multiply(b) => ab.

• expression.multiply(num)

The repeated multiplication (concatenation) of an expression with itself: a.multiply(3) => aaa. Exponent -1 denotes the infinity: the Kleene star.

• expression.multiply((min,max))

The sum of repeated multiplications of an expression: a.multiply((2,4)) => aa+aaa+aaaa. When min = -1, it denotes 0, when max = -1, it denotes the infinity.

Preconditions:

• min <= max

## Examples¶

In [1]:
import vcsn
exp = vcsn.context('law_char, q').expression


### Simple Multiplication¶

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

In [2]:
exp('a*b') * exp('ab*')

Out[2]:
${\mathit{a}}^{*} \, \mathit{b} \, \mathit{a} \, {\mathit{b}}^{*}$

Of course, trivial identities are applied.

In [3]:
exp('<2>a') * exp('<3>\e')

Out[3]:
$\left\langle 6 \right\rangle \,\mathit{a}$
In [4]:
exp('<2>a') * exp('\z')

Out[4]:
$\emptyset$

In the case of word labels, adjacent words are not fused: concatenation of two expressions behaves as if the expressions were parenthetized. Pay attention to the space between $a$ and $b$ below, admittedly too discreet.

In [5]:
(exp('a') * exp('b')).SVG() # Two one-letter words

Out[5]:
In [6]:
exp('ab').SVG() # One two-letter word

Out[6]:
In [7]:
exp('(a)(b)').SVG() # Two one-letter words

Out[7]:

### Repeated Multiplication¶

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

In [8]:
exp('ab') ** 3

Out[8]:
$\left(\mathit{ab}\right)^{3}$
In [9]:
exp('ab') ** 0

Out[9]:
$\varepsilon$

Beware that a * 3 actually denotes a.rweight(3).

In [10]:
exp('a*') * 3

Out[10]:
$\left\langle 3 \right\rangle \,{\mathit{a}}^{*}$

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

In [11]:
exp('ab') ** -1

Out[11]:
$\left(\mathit{ab}\right)^{*}$
In [12]:
exp('ab').star()

Out[12]:
$\left(\mathit{ab}\right)^{*}$

### Sums of Repeated Multiplications¶

Instead of a.multiply((2, 4)), you may write a ** (2, 4). Again, use exponent -1 to mean infinity.

In [13]:
exp('ab') ** (2, 2)

Out[13]:
$\left(\mathit{ab}\right)^{2}$
In [14]:
exp('ab') ** (2, 4)

Out[14]:
$\left(\mathit{ab}\right)^{2} \, \left(\varepsilon + \mathit{ab} + \left(\mathit{ab}\right)^{2}\right)$
In [15]:
exp('ab') ** (-1, 2)

Out[15]:
$\varepsilon + \mathit{ab} + \left(\mathit{ab}\right)^{2}$
In [16]:
exp('ab') ** (2, -1)

Out[16]:
$\left(\mathit{ab}\right)^{2} \, \left(\mathit{ab}\right)^{*}$