Pointwise product
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The pointwise product of two functions is another function, obtained by multiplying the results of the two functions. If f and g are both functions with domain X and codomain Y, and elements of Y can be multiplied (for instance, Y could be some set of numbers), then the pointwise product of f and g is another function from X to Y which maps x ∈ X to f(x)g(x).
[edit] Generalization
If both f and g have as their domain all possible assignments of a set of discrete variables, then their pointwise product is a function whose domain is constructed by all possible assignments of the union of both sets. The value of each assignment is calculated as the product of the values of both functions given to each one the subset of the assignment that is in its domain.
For example, given the function f1() for the boolean variables p and q, and f2() for the boolean variables q and r, both with the range in R, the pointwise product of f1() and f2() is shown in the next table:
| p | q | r | f1(p, q) | f2(q, r) | pointwise product |
| T | T | T | 0.1 | 0.2 | 0.1 x 0.2 |
| T | T | F | 0.1 | 0.4 | 0.1 x 0.4 |
| T | F | T | 0.3 | 0.6 | 0.3 x 0.6 |
| T | F | F | 0.3 | 0.8 | 0.3 x 0.8 |
| F | T | T | 0.5 | 0.2 | 0.5 x 0.2 |
| F | T | F | 0.5 | 0.4 | 0.5 x 0.4 |
| F | F | T | 0.7 | 0.6 | 0.7 x 0.6 |
| F | F | F | 0.7 | 0.8 | 0.7 x 0.8 |
