28 | Tests and Conditionals |
Is 2+2 equal to 4? Let’s ask the Wolfram Language.
Test whether 2+2 is equal to 4:
2 + 2 == 4
Not surprisingly, testing whether 2+2 is equal to 4 gives True.
We can also test whether 2×2 is greater than 5. We do that using >.
Test whether 2×2 is greater than 5:
2*2 > 5
If[2 + 2 == 4, x, y]
If an element is less than 4, make it x, otherwise make it y:
If[# < 4, x, y] & /@ {1, 2, 3, 4, 5, 6, 7}
You can also test for less than or equal using ≤, which is typed as <=.
If an element is less than or equal to 4, make it x; otherwise, make it y:
If[# <= 4, x, y] & /@ {1, 2, 3, 4, 5, 6, 7}
This makes an element x only if it is equal to 4:
If[# == 4, x, y] & /@ {1, 2, 3, 4, 5, 6, 7}
You can test whether two things are not equal using ≠, which is typed as !=.
If an element is not equal to 4, make it x; otherwise, make it y:
If[# != 4, x, y] & /@ {1, 2, 3, 4, 5, 6, 7}
It’s often useful to select elements in a list that satisfy a test. You can do this by using Select, and giving your test as a pure function.
Select elements in the list that are greater than 3:
Select[{1, 2, 3, 4, 5, 6, 7}, # > 3 &]
Select elements that are between 2 and 5:
Select[{1, 2, 3, 4, 5, 6, 7}, 2 <= # <= 5 &]
Beyond size comparisons like <, > and ==, the Wolfram Language includes many other kinds of tests. Examples are EvenQ and OddQ, which test whether numbers are even or odd. (The “Q” indicates that the functions are asking a question.)
4 is an even number:
EvenQ[4]
Select even numbers from the list:
Select[{1, 2, 3, 4, 5, 6, 7, 8, 9}, EvenQ[#] &]
In this case, we don’t need the explicit pure function:
Select[{1, 2, 3, 4, 5, 6, 7, 8, 9}, EvenQ]
Select prime numbers:
Select[{1, 2, 3, 4, 5, 6, 7, 8, 9, 10}, PrimeQ]
Select elements of the list that are both even and greater than 2:
Select[{1, 2, 3, 4, 5, 6, 7}, EvenQ[#] && # > 2 &]
Select[{1, 2, 3, 4, 5, 6, 7}, EvenQ[#] || # > 4 &]
Select elements that are not either even or greater than 4:
Select[{1, 2, 3, 4, 5, 6, 7}, ! (EvenQ[#] || # > 4) &]
There are many other “Q functions” that ask various kinds of questions. LetterQ tests whether a string consists of letters.
The space between letters isn’t a letter; nor is “!”:
{LetterQ["a"], LetterQ["bc"], LetterQ["a b"], LetterQ["!"]}
Turn a string into a list of characters, then test which are letters:
LetterQ /@ Characters["30 is the best!"]
Select the characters that are letters:
Select[Characters["30 is the best!"], LetterQ]
Select letters that appear after position 10 in the alphabet:
Select[Characters["30 is the best!"],
LetterQ[#] && LetterNumber[#] > 10 &]
You can use Select to find words in English that are palindromes, meaning that they are the same if you reverse them.
Select[WordList[], StringReverse[#] == # &]
MemberQ tests whether something appears as an element, or member, of a list.
5 appears in the list {1, 3, 5, 7}:
MemberQ[{1, 3, 5, 7}, 5]
Select[Range[100], MemberQ[IntegerDigits[#], 2] &]
ImageInstanceQ is a machine-learning-based function that tests whether an image is an instance of a particular kind of thing, like a cat.
Test if an image is of a cat:
ImageInstanceQ[\!\(\*
GraphicsBox[
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