`expression``.multiply`

This function is overloaded, it supports three different 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.

Preconditions:

min <= max
None

Examples



In [1]:

    
import vcsn
ctx = vcsn.context('law_char, q')
def exp(e):
    return ctx.expression(e)

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') # Two one-letter words









    Out[5]:





$\mathit{a} \, \mathit{b}$



In [6]:

    
exp('ab') # One two-letter word









    Out[6]:





$\mathit{ab}$



In [7]:

    
exp('(a)(b)') # Two one-letter words









    Out[7]:





$\mathit{a} \, \mathit{b}$

Repeated Multiplication

Instead of a.multiply(3), you may write a ** 3. Beware that a * 3 actually denotes a.right_mult(3).



In [8]:

    
exp('ab') ** 3









    Out[8]:





$\left(\mathit{ab}\right) \, \left(\mathit{ab}\right) \, \left(\mathit{ab}\right)$



In [9]:

    
exp('a*') * 3









    Out[9]:





$ \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 [10]:

    
exp('ab') ** -1









    Out[10]:





$\left(\mathit{ab}\right)^{*}$



In [11]:

    
exp('ab').star()









    Out[11]:





$\left(\mathit{ab}\right)^{*}$

Sums of Repeated Multiplications

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



In [12]:

    
exp('ab') ** (2, 2)









    Out[12]:





$\left(\mathit{ab}\right) \, \left(\mathit{ab}\right)$



In [13]:

    
exp('ab') ** (2, 4)









    Out[13]:





$\left(\mathit{ab}\right) \, \left(\mathit{ab}\right) \, \left(\varepsilon + \mathit{ab} + \left(\mathit{ab}\right) \, \left(\mathit{ab}\right)\right)$



In [14]:

    
exp('ab') ** (-1, 2)









    Out[14]:





$\varepsilon + \mathit{ab} + \left(\mathit{ab}\right) \, \left(\mathit{ab}\right)$



In [15]:

    
exp('ab') ** (2, -1)









    Out[15]:





$\left(\mathit{ab}\right) \, \left(\mathit{ab}\right) \, \left(\mathit{ab}\right)^{*}$

expression.multiply

Examples

Simple Multiplication

Repeated Multiplication

Sums of Repeated Multiplications

`expression``.multiply`