ZDD : Overview of ZDD Operators and Methods : * : Multiplication operator

3.2 * : Multiplication operator

Format

$zdd1$ * $zdd2$ $\rightarrow$ $zdd$

Description

Multiplication of $zdd1$ and $zdd2$ .

Consider its similarities with general polynomial, the only difference is when the same item is multiplied by itself, it does not become the power of 2. For instance, it is computed by the expression a*a=a.

Example

Example 1: Basic Example

> require 'zdd'
# a. Multiplication of constants.
# Weight is attached to sum of products term x by the expression x*c, the weight
# of each term in x is multiplied by c times.
# The computation is similar to general polynomial.
> a=ZDD::itemset('a')
> b=ZDD::itemset('b')
> c=ZDD::itemset('c')
> d=ZDD::itemset('d')
> (a*3).show
 3 a
> (-2*a).show
 - 2 a
> ((a+2*b+3*c)*4).show
 4 a + 8 b + 12 c

# b. Multiplication by 1 itemset
# Weight is attached to sum of products term y by the expression x*y,
# y is added to the weight of each term in x.
# However, note that the multiplication beteween same items is expressed as a*a=a.
> x=a+2*a*b+3*c
> x.show
 2 a b + a + 3 c
> (x*c).show
 2 a b c + a c + 3 c
> (x*b).show
 3 a b + 3 b c
> (4*x*a).show
 8 a b + 12 a c + 4 a

# c. Multiplication of 2 or more itemsets
# Multiplication of the sum of products x,y which is attached with weight is computed
# by the expression x*y,
# The operation enumerates all possible combinations on the two product terms.
# Like terms such as a,b itemset are multiplied.
# The resulting expression includes addition and subtraction operations between
# enumerated item sets.
> ((a+b)*(c+d)).show
 a c + a d + b c + b d
> ((a+b)*(b+c)).show
 a b + a c + b c + b
> ((a+b)*(a+b)).show
 2 a b + a + b
> ((a+b)*(a-b)).show
 a - b

See Also

/ :Division operator