Min

Command Summary

Returns the minimum of two elements or of a list.

Command Syntax

• for two numbers: min(x,y)
• for a list: min(list)
• comparing a number to each element of a list: min(x,list) or min(list,x)
• pairwise comparing two lists: min(list1,list2)

min(x,y) returns the smallest of the two numbers x and y. min(list) returns the smallest element of list. min(list1,list2) returns the pairwise minima of the two lists. min(list1,x) (equivalently, min(x,list1)) returns a list whose elements are the smaller of x or the corresponding element of the original list.

min(2,3)
     2
min({2,3,4})
     2
min({1,3},{4,2})
     {1 2}
min({1,3},2)
     {1 2}

Unlike relational operators, such as < and >, min( can also compare complex numbers. To do this, both arguments must be complex — either complex numbers or complex lists: min(2,i) will throw a ERR:DATA TYPE error even though min(2+0i,i) won't. In the case of complex numbers, the number with the smallest absolute value will be returned. When the two numbers have the same absolute value, the second one will be returned: min(i,-i) returns -i and min(-i,i) returns i.

Advanced Uses

min( can be used in Boolean comparisons to see if every value of a list is 1 (true) — useful because commands like If or While only deal with numbers, and not lists, but comparisons like L1=L2 return a list of values. In general, the behavior you want varies, and you will use the min( or max( functions accordingly.

Using min( will give you a strict test — only if every single value of a list is true will min( return true. For example, the following code will test if two lists are identical — they have the same exact elements — and print EQUAL in that case:

If dim(L1)=dim(L2
Then
If min(L1=L2
Disp "EQUAL
End

The first check, to see if the sizes are identical, is necessary because otherwise comparing the lists will return a ERR:DIM MISMATCH error.

Error Conditions

• ERR:DATA TYPE is thrown when comparing a real and a complex number. This can be avoided by adding 0i to the real number.
• Dimension Mismatch is thrown, when using min( with two lists, if they have different dimensions.

Related Commands

• max(
• sum(
• prod(