6.40.27 Product: product mul
The product command can find the products of elements of an
expression (see Section 6.40.27), the elements of a
list (see Section 6.40.27), the elements of the
columns of a matrix (see Section 6.45.6), and the term-by-term
(Hadamard) product of two matrices (see Section 6.45.8).
Product of values of an expression: product
The product command can find the product of the values of an
expression as the variable changes.
Here, mul is a synonym for product.
-
product takes four mandatory arguments and one
optional argument:
-
expr, an expression.
- x, the name of a variable.
- a and b, real numbers.
- Optionally p, a real number representing a step size. (By
default p=1).
- product(exprx,a,b ⟨
p⟩) returns the product of the values of
expr as x goes from a to b in steps of p.
This syntax is for compatibility with Maple.
Examples.
-
Input:
product(x^2+1,x,1,4)
or:
mul(x^2+1,x,1,4)
Output:
Indeed (12+1)·(22+1)·(32+1)·(42+1)=1700
- Input:
product(x^2+1,x,1,5,2)
or:
mul(x^2+1,x,1,5,2)
Output:
Indeed (12+1)·(32+1)·(52+1)=520
Product of elements of a list: product
The product command can find the products of elements of a
list.
For this, mul is a synonym for product.
-
product takes one mandatory and one optional argument:
-
L, a list of numbers.
- Optionally, L2, another list of numbers the same length
as L.
- product(L) returns the product of the elements of
L.
- product(L,L2) returns the term by term product
of the elements of L and L2.
(See also Section 6.45.8.)
Examples.
-
Input:
product([2,3,4])
or:
mul([2,3,4])
Output:
- Input:
product([[2,3,4],[5,6,7]])
Output:
- Input:
product([2,3,4],[5,6,7])
or:
mul([2,3,4],[5,6,7])
Output: