Java 2

Week 2

Software Development Life Cycle, Steps 4-5

Fraction Class

4. Development (Coding)

Using IntelliJ, create a new Java project called "MathCalculators".
Select a preferred location on your device.

Select to create a Git repository
Select Maven as the build system.
Select or download JDK 25.
Select to add sample code.
Toggle open the advanced settings.
Set the GroupId to edu.kirkwood
Leave the ArtifactId as the default.

IntelliJ Project Setup

IntelliJ has built-in AI tools that you can agree to their terms. You can remove it from the sidebar if you don't plan to use it.
- For assignments, I only want you to submit code that was taught in class. If you use AI, please write comments next to untaught lines explaining their purpose.

pom.xml

The pom.xml (Project Object Model) file is the core configuration file in a Maven project. It contains all the essential information and instructions needed to build, manage, and deploy a project.
We will use this file regularly in later lessons.
Close the pom.xml file.

Main.java

A Main.java file is automatically created.
To run code, press Shift + F10 or click one of the play icons.
Run debug mode by pressing Shift + F9 or clicking the bug icon.
When text is highlighted yellow, press Alt + Enter with your mouse at the highlighted text to see suggested fixes.
You may delete the Main.java file after you know that it works.

Fraction.java

Right-click the "edu.kirkwood" package and create a new package called "model".
Right-click the "model" package and create a new Java class called Fraction.java.
I prefer to add files to Git manually. When this prompt appears, I select "Don't ask again", and click "Cancel".

Note that file names in the project panel may be red. This red text does not mean the file has an error. It means that the file is not tracked by Git.
File names may also be brownish. This means the file is being ignored by Git, as specified in the .gitignore file.

Fraction.java

Create two private int instance variables, called numerator and denominator.
Right-click the file and choose "Generate". Add a default constructor that assigns 1 to the numerator and denominator.
Create a toString method that returns a string representation of the fraction in the format "numerator/denominator"

public class Fraction {
    private int numerator;
    private int denominator;

    public Fraction() {
        numerator = 1;
        denominator = 1;
    }

    public String toString() {
        return numerator + "/" + denominator;
    }
}

Fraction.java

Generate a parameterized constructor that has two int parameters, called numerator and denominator. Assign both parameters to the instance variables.
Generate a getNumerator and getDenominator method.
Generate a setNumerator and setDenominator method.

public class Fraction {
    // code omitted

    public Fraction(int numerator, int denominator) {
        setNumerator(numerator);
        setDenominator(denominator);
    }

    public int getNumerator() {
        return numerator;
    }

    public void setNumerator(int numerator) {
        this.numerator = numerator;
    }

    public int getDenominator() {
        return denominator;
    }

    public void setDenominator(int denominator) {
        this.denominator = denominator;
    }


}

Fraction.java

Add other methods as shown in the class diagram we created last week, but don't implement any code yet.
The compareTo() method requires the Comparable interface to be implemented.
The equals() and hashCode() methods are generated by IntelliJ.

package edu.kirkwood.model;

public class Fraction implements Comparable<Fraction> {
    // Code omitted

    @Override
    public int compareTo(Fraction o) {
        return 0;
    }
    
    @Override
    public boolean equals(Object o) {
        if (o == null || getClass() != o.getClass()) return false;
        Fraction fraction = (Fraction) o;
        return numerator == fraction.numerator && denominator == fraction.denominator;
    }

    @Override
    public int hashCode() {
        return Objects.hash(numerator, denominator);
    }

    public static int gcd(int a, int b) {
        return 0;
    }

    public static int lcm(int a, int b) {
        return 0;
    }

    public void simplify() {

    }

    public String toMixedNumber() {
        return "";
    }

    public Fraction add(Fraction other) {
        return null;
    }

    public Fraction subtract(Fraction other) {
        return null;
    }

    public Fraction multiply(Fraction other) {
        return null;
    }

    public Fraction divide(Fraction other) {
        return null;
    }
}

Static vs Non-Static Methods

Static methods are called like this:
- Fraction.gcd(15, 6); // 3
- Fraction.lcm(15, 6); // 30
- lcm(15, 6) // "Fraction" can be omitted if called inside the Fraction class.
These methods are static because they are not related to a single Fraction object. Input parameters a and b do not refer to numerator and denominator
These methods could go in the Helpers class if you think you will use it for other applications.

Static vs Non-Static Methods

Non-static methods are called like this
- Fraction f1 = new Fraction(15, 6);
- f1.simplify(); // 5/2
- f1.toMixedNumber(); // 2 1/2
- f1.getNumerator(); // 5
- f1.getDenominator(); // 2
- Fraction f2 = new Fraction(1, 3);
- f1.add(f2); // 2 5/6

Javadoc Comments

Add Javadoc comments to the class and each method.
For your next assignment, I would appreciate if you hand-typed at least two Javadoc comments. You can then use AI to generate the remainder—but be sure to proofread them.

package edu.kirkwood.model;

/**
 * Represents a fraction with an integer numerator and denominator.
 * This class provides methods for fraction arithmetic, simplification,
 * and comparison.
 */
public class Fraction implements Comparable<Fraction> {
    private int numerator;
    private int denominator;

    /**
     * Default constructor.
     * Initializes a new fraction to 1/1.
     */
    public Fraction() {
        this.numerator = 1;
        this.denominator = 1;
    }

    /**
     * Constructs a fraction with a specified numerator and denominator.
     *
     * @param numerator   the numerator of the fraction
     * @param denominator the denominator of the fraction
     */
    public Fraction(int numerator, int denominator) {
        this.numerator = numerator;
        this.denominator = denominator;
    }

    /**
     * Gets the numerator of the fraction.
     *
     * @return the numerator
     */
    public int getNumerator() {
        return numerator;
    }

    /**
     * Sets the numerator of the fraction.
     *
     * @param numerator the new numerator
     */
    public void setNumerator(int numerator) {
        this.numerator = numerator;
    }

    /**
     * Gets the denominator of the fraction.
     *
     * @return the denominator
     */
    public int getDenominator() {
        return denominator;
    }

    /**
     * Sets the denominator of the fraction.
     *
     * @param denominator the new denominator
     * @throws ArithmeticException if the denominator is zero
     */
    public void setDenominator(int denominator) {
        this.denominator = denominator;
    }

    /**
     * Returns a string representation of the fraction in the format "numerator/denominator".
     *
     * @return a string representation of the fraction
     */
    @Override
    public String toString() {
    	// Implementation needed
        return "";
    }

    /**
     * Compares this fraction to another fraction.
     *
     * @param o the other Fraction to be compared.
     * @return a negative integer, zero, or a positive integer.
     */
    @Override
    public int compareTo(Fraction o) {
        // Implementation needed
        return 0;
    }
    
    /**
     * Determines if two fraction objects are the same
     *
     * @param o the other object to be compared.
     * @return a boolean true is both objects are the same, false otherwise
     */
    @Override
    public boolean equals(Object o) {
        if (o == null || getClass() != o.getClass()) return false;
        Fraction fraction = (Fraction) o;
        return numerator == fraction.numerator && denominator == fraction.denominator;
    }

	/**
     * This method is supported for the benefit of hash tables such as HashMap and HashSet.
     *
     * @return an integer representing a hash code value for this object.
     */
    @Override
    public int hashCode() {
        return Objects.hash(numerator, denominator);
    }

    /**
     * Calculates the greatest common divisor (GCD) of two integers.
     *
     * @param a the first integer
     * @param b the second integer
     * @return the greatest common divisor of a and b
     */
    public static int gcd(int a, int b) {
        // Implementation needed
        return 0;
    }

    /**
     * Calculates the least common multiple (LCM) of two integers.
     *
     * @param a the first integer
     * @param b the second integer
     * @return the least common multiple of a and b
     */
    public static int lcm(int a, int b) {
        // Implementation needed
        return 0;
    }

    /**
     * Simplifies this fraction to its lowest terms by dividing the numerator
     * and denominator by their greatest common divisor.
     */
    public void simplify() {
        // Implementation needed
    }

    /**
     * Converts this fraction to a mixed number string representation (e.g., "1 2/3").
     * If the fraction is a proper fraction, it returns the fraction itself.
     *
     * @return a string representation of the fraction as a mixed number
     */
    public String toMixedNumber() {
        // Implementation needed
        return "";
    }

    /**
     * Adds another fraction to this fraction.
     *
     * @param other the fraction to add
     * @return a new Fraction object representing the sum
     */
    public Fraction add(Fraction other) {
        // Implementation needed
        return null;
    }

    /**
     * Subtracts another fraction from this fraction.
     *
     * @param other the fraction to subtract
     * @return a new Fraction object representing the difference
     */
    public Fraction subtract(Fraction other) {
        // Implementation needed
        return null;
    }

    /**
     * Multiplies this fraction by another fraction.
     *
     * @param other the fraction to multiply by
     * @return a new Fraction object representing the product
     */
    public Fraction multiply(Fraction other) {
        // Implementation needed
        return null;
    }

    /**
     * Divides this fraction by another fraction.
     *
     * @param other the fraction to divide by (the divisor)
     * @return a new Fraction object representing the quotient
     * @throws IllegalArgumentException if the divisor is zero
     */
    public Fraction divide(Fraction other) {
        // Implementation needed
        return null;
    }
}

Javadoc Comments

Click the IntelliJ menu icon, select the Tools menu, and select "Generate Javadoc..."
Set the Output directory to be a "docs" folder inside the project's root folder.
Click the blue "Generate" button.
An HTML file will open in your default browser. Click the "Fraction" class link to view the documentation.
When we push our code to GitHub, we will display the contents of the docs folder as a live webpage.

GitHub Setup

Create a new private respository on GitHub titled something like "Java2MathCalculators". Copy the URL.
Open the Terminal in IntelliJ. Enter this command:
git remote add origin <paste-your-url>
Go to the Commit tab. Disable the "Analyze Code" feature in the Settings pop-out.
Check all of the boxes under "Changes" and "Unversioned Files".
Type a commit message like "Created Fraction class".
Press the "Commit and Push" button.
Review the files committed, then press "Push".
View the files on GitHub.
Add "mlhaus" as a collaborator under the Settings tab.

Fraction Class Diagram

Fraction
- int numerator - int denominator
+ Fraction() + Fraction(int numerator, int denominator) + getNumerator() :: int + setNumerator(int numerator) :: void + getDenominator() :: int + setDenominator(int denominator) :: void + toString() :: String + compareTo(Fraction other) :: int + equals(Object other) :: boolean + hashCode() :: int + gcd(int a, int b) :: int + lcm(int a, int b) :: int + simplify() :: void + toMixedNumber() :: String + add(Fraction other) :: Fraction + subtract(Fraction other) :: Fraction + multiply(Fraction other) :: Fraction + divide(Fraction other) :: Fraction

Fraction

- int numerator
- int denominator

+ Fraction()
+ Fraction(int numerator, int denominator)
+ getNumerator() :: int
+ setNumerator(int numerator) :: void
+ getDenominator() :: int
+ setDenominator(int denominator) :: void
+ toString() :: String
+ compareTo(Fraction other) :: int
+ equals(Object other) :: boolean
+ hashCode() :: int
+ gcd(int a, int b) :: int
+ lcm(int a, int b) :: int
+ simplify() :: void
+ toMixedNumber() :: String
+ add(Fraction other) :: Fraction
+ subtract(Fraction other) :: Fraction
+ multiply(Fraction other) :: Fraction
+ divide(Fraction other) :: Fraction

Compare the work we have done with the UML class diagram from the Week 1 slide presentation.
Try uploading a screenshot of the class diagram (or Mermaid syntax) to an AI tool, asking it to write the Java class with unimplemented methods and Javadoc comments.

classDiagram
    class Fraction {
        - int numerator
        - int denominator
        + Fraction()
        + Fraction(int numerator, int denominator)
        + getNumerator(): int
        + setNumerator(int numerator): void
        + getDenominator(): int
        + setDenominator(int denominator): void
        + toString() : String
        + compareTo(Fraction other) : int
        + equals(Object other) : boolean
        + hashCode() : int
        + simplify() : void
        + gcd(int a, int b): int
        + toMixedNumberString() : String
        + add(Fraction other) : Fraction
        + subtract(Fraction other) : Fraction
        + multiply(Fraction other) : Fraction
        + divide(Fraction other) : Fraction
    }

GitHub Setup

Run this command if your project is not set up with Git.
- git init -b main
Run this command if your project's default branch is not "main".
- git checkout -b main
Run these commands in the terminal one at a time
- git remote add origin <https://github.com/your-username/your-repo-name.git>
- git add .
- git commit -m "Started Fraction calculator, September XX"
- git push origin main
If you get a srcrefspec error, run this command:
- git checkout -b main
Add "mlhaus" as a collaborator.

6. Deployment

When you created the project, you were asked to check the "Create Git respository" button.
Note the tab in the menu bar displays "main". If it does not, you need to initialize your project with Git. Open the Terminal tab and enter this command:
git init -b main
If the menu bar displays "master", run this command:
git checkout -b main

GitHub Setup

Create a new private repository on GitHub. Title the repository "Java-Calculators". Copy the URL.
In IntelliJ, enter this command in the terminal:
git remote add origin https://github.com/YOUR-USERNAME/java-calculators.git
Click the Commit icon. Click the gear icon and uncheck the "Analyze Code" and "Check TODO" boxes.
Check all boxes to add changes and unversioned files.
- Alternatively, you could enter this command.
  git add .
Write a commit message. The message should be a short description of what you recently accomplished.
Click "Commit"—don't click "Commit and Push".
- Alternatively, you could enter this command.
  git commit -m "Your message"

GitHub Setup

If a "Line Separators Warning" message displays, check the "Don't warn again" box and click "Fix and Commit".
Note that the files are no longer red in the project panel.
From the previous slide, if you get a warning saying your name or username are not set in Git, run these terminal commands.
git config --global user.name "YOUR FULL NAME"
git config --global user.email "YOUR EMAIL ADDRESS"
Click the Git menu that says "main" and click "Push".
Verify that your main branch is being pushed to the origin's (GitHub's) main branch. Verify the files that are being pushed.
The first time you push, you will need to sign into GitHub.

Mac Users Only

When signing in with your GitHub password, you may get an error saying you need to use a personal access token.
Click "Log In with Token".
Click "Generate".
Log in to your GitHub account.
You will be on a screen to generate a new personal access token. The note should be pre-filled with "IntelliJ IDEA GitHub integration plugin".
Set the expiration date to be after the semester ends (or Never).
Select the Repo check box.
Click Generate Token and copy the token that is generated.
Paste the token as the password in the IntelliJ GitHub popup.
In the Terminal app, enter this command so you only have to enter the token once.
git config --global credential.helper cache

GitHub Setup

Refresh your GitHub repository page to see the changes.
As you add more code, commit regularly. Please change commit messages each time to something short and descriptive. Only push to GitHub when your work is ready to grade.
Student To-do:
- Click the "Settings" tab
- Choose Access > Collaborators, and click "Add people".
- Type "mlhaus" and select the instructor's profile. The instructor will grade all assignments via GitHub.
Instructor To-do:
- Click the "Settings" tab, then set the visibility to public so students can access it.
- Copy and paste a link to the course content so students always have access to demo code.

GitHub Setup

Click the "Settings" tab.
Click the "Pages" button.
Set the source to "Deploy from a branch".
Select the "main" branch.
Set the folder to "/docs".
Click Save.
Click the "Code" tab.
Click the gear icon next to the "About" section.
Check the box to add your github.io URL. Make sure "/docs" is at the end. Click the link to see your live documentation website.

5. Testing

In IntelliJ, right-click the Fraction class title and choose "Show Context Options" then "Create Test".
JUnit 5 will be pre-selected, click the "Fix" button if shown.
Check the "setUp/@Before" box.
Click the check boxes next to all of the methods.
- Click one method name, press Ctrl + A, press the spacebar
The FractionTest class is successfully added to the tests folder.
Fully-qualified annotations ("@org.junit.jupiter.api.BeforeEach" and "@org.junit.jupiter.api.Test") only need to be @BeforeEach and @Test.
- If your annotations are fully-qualified press Ctrl + R to open the find and replace menu.
- Replace all references of "@org.junit.jupiter.api." with "@".
- Add an import statement for @BeforeEach and @Test.

BeforeEach Methods

Some Unit Tests require a default instance of the class.
The setUp method can be used to instantiate that object needed for each test.
Create two new Fraction objects as a private instance variables.
Instantiate the Fraction objects in the setUp method.
We want to keep our code DRY (Don't Repeat Yourself). If we don't use the setUp method we will have to instantiate a Fraction object inside of every single test method.

private Fraction f1;
private Fraction f2;

@BeforeEach
void setUp() {
    f1 = new Fraction();
    f2 = new Fraction(2, 3);
}

Run the tests to fail

Study the fail method from JUnit's Assertions class.
If you run the tests now, it should say all tests passed and you will see green checkmarks next to the method names in the bottom-left corner. We actually want all tests to fail by default.
Highlight a set of curly brackets on one of the tests.
- Press Ctrl+Cmd+G (Mac) or Shift+Ctrl+Alt+J (Windows) to select all occurrences.
- Use the arrow keys to position the cursors inside the curly brackets and type a fail method.
  fail();
  - This is a static method from the Assertions class of JUnit.
Run the FractionTest class again to see that all tests failed. You will see orange X's next to the method names.

Test the Getters and toString

Study the assertEquals methods from JUnit's Assertions class.
Write tests for all of the getters and toString.
- You should test all getter methods before setter methods so you can safely use the getter methods to verify that the setter methods work correctly.
- When using the assertEquals method the first argument is the expected value and the second argument is the actual value.
- The actual value will always come from a getter method.

@Test
void getNumerator() {
    assertEquals(1, f1.getNumerator());
    assertEquals(2, f2.getNumerator());
}

@Test
void getDenominator() {
    assertEquals(1, f1.getDenominator());
    assertEquals(3, f2.getDenominator());
}

@Test
void testToString() {
    assertEquals("1/1", f1.toString());
    assertEquals("2/3", f2.toString());
}

Test the Setters

Next, we will write tests for all of the setters
For setNumerator, set a positive, 0, and negative value. Call the getNumerator and toString methods to ensure equality.
For setDenominator, set a positive and negative value. Call the getDenominator and toString methods to ensure equality.
The denominator negative test will fail because "1/-3" will be returned instead of "-1/3" as I want.
An optional third parameter can be used for a message.

@Test
void setNumeratorPostive() {
    // Act
    f1.setNumerator(3);
    // Assert
    assertEquals(3, f1.getNumerator());
    assertEquals("3/1", f1.toString());
}

@Test
void setNumeratorZero() {
    // Act
    f1.setNumerator(0);
    // Assert
    assertEquals(0, f1.getNumerator());
    assertEquals("0/1", f1.toString());
}

@Test
void setNumeratorNegative() {
    // Act
    f1.setNumerator(-3);
    // Assert
    assertEquals(-3, f1.getNumerator());
    assertEquals("-3/1", f1.toString());
}

@Test
void setDenominatorPostive() {
    // Act
    f1.setDenominator(3);
    // Assert
    assertEquals(3, f1.getDenominator());
    assertEquals("1/3", f1.toString());
}

@Test
void setDenominatorNegative() {
    // Act
    f1.setDenominator(-3);
    // Assert
    assertEquals(-3, f1.getDenominator());
    assertEquals("-1/3", f1.toString());
}

@Test
void setNumeratorAndDenominatorNegative() {
    // Act
    f1.setNumerator(-3);
    f1.setDenominator(-3);
    // Assert
    assertEquals("3/3", f1.toString());
}

Test Exceptions

Because the denominator cannot be 0, we use assertThrows.
The first argument is the type of Exception you expect to be thrown, in this case ArithmeticException.
The second argument is a lambda expression that calls the abstract method from the Executable functional interface.
assertThrows returns a Throwable object of type T. In this case, a reasonable Throwable object to use is ArithmeticException. You can assert the Exception message.

@Test
void setDenominatorZero() {
    // Act and Assert
    assertThrows(ArithmeticException.class, () -> f1.setDenominator(0));
    
    ArithmeticException e = assertThrows(ArithmeticException.class, () -> f1.setDenominator(0));
	assertEquals("Denominator cannot be zero", e.getMessage());
}

ended here

Mon-Wed class

Write Code to Pass Tests

After writing the unit tests, go back to the regular class and implement the code that will get the test to pass.

public void setDenominator(int denominator) {
    if(denominator == 0){
        throw new ArithmeticException("Denominator cannot be zero");
    }
    if(denominator < 0 && numerator > 0 || denominator < 0 && numerator < 0) {
        numerator *= -1;
        denominator *= -1;
    }
    this.denominator = denominator;
}

Update Parameterized Constructor

Update the parameterized constructor to call the setter methods to validate the input, rather than potentially assigning invalid values to the attributes.

public Fraction(int numerator, int denominator) {
    setNumerator(numerator);
    setDenominator(denominator);
}

Test Static Methods

In the gcd test method, call the static gcd method from the Fraction class.
The following assertions seem logical, but they don't fully test it.

To correctly test the greatest common denominator of two integers, we must test for positive and negative values.
Call assertTrue by passing a single boolean expression.

@Test
void gcd() {
	assertEquals(15, Fraction.gcd(75, 45));
    assertEquals(2, Fraction.gcd(2, 4));
    assertEquals(1, Fraction.gcd(5, 7));
    int result1 = Fraction.gcd(5, 7);
    int result2 = Fraction.gcd(-5, 7);
    int result3 = Fraction.gcd(5, -7);
    int result4 = Fraction.gcd(-5, -7);
    assertTrue(result1 == result2 && result2 == result3 && result3 == result4);
}

@Test
void gcd() {
    assertEquals(15, Fraction.gcd(75, 45));
    assertEquals(2, Fraction.gcd(2, 4));
    assertEquals(1, Fraction.gcd(5, 7));
}

Write Code to Pass Tests

The greatest common divisor of two numbers is the largest positive integer number that divides both the numbers without leaving any remainder. For example, the greatest common divisor of 30 and 45 is 15
We will use this solution.
If you run the unit test now, it will fail.
Update the Fraction class gcd method to return Math.abs(a).

public static int gcd(int a, int b) {
    if (b == 0) {
        return Math.abs(a);
    }
    return gcd(b,a % b);
}

Test toMixedNumber Method

Inside this method, call the simplify method.
If the simplified fraction's denominator is 1, return the simplified fraction's numerator, converted to a String.
- For example, if the Fraction is 2/1, return "2".
Otherwise, return the simplified fraction as a String by calling the toString() method.

public String toMixedNumber() {
    simplify();
    if(denominator == 1) {
        return numerator + "";
    } else {
        return toString();
    }
}

Test toMixedNumber Method

If the simplified fraction's numerator is 0, return "0".
- For example, if the Fraction is 0/1, return "0"
If the simplified fraction's numerator is greater than the denominator, return the fraction as a mixed number.
1. For example, 13/5 is 2 3/5.
  1. 13 / 5 is 2 (the whole number)
  2. 13 % 5 is 3 (the remainder)
The ternary operator is used If the simplified fraction's numerator is less than 0, return the fraction as a negative mixed number.

public String toMixedNumber() {
    simplify();
    if(denominator == 1) {
        return numerator + "";
    } else if(Math.abs(numerator) > denominator) {
        int wholeNumber = Math.abs(numerator) / denominator;
        int remainder = Math.abs(numerator) % denominator;
        return (numerator < 0 ? "-" : "") + wholeNumber + " " + remainder + "/" + denominator;
    } else if(numerator == 0) {
        return "0";
    } else {
        return toString();
    }
}

GitHub Update

Go to the Commit tab.
Check all of the boxes under "Changes" and "Unversioned Files".
Type a commit message like "Created FractionTest class".
Press the "Commit and Push" button.
Review the files committed, then press "Push".
View the files on GitHub.

Java 2 - Week 2

By Marc Hauschildt

Java 2 - Week 2

Marc Hauschildt

Web Technologies and Computer Software Development Instructor at Kirkwood Community College in Cedar Rapids, IA.

kirkwood.edu/businessit

Java 2

4. Development (Coding)

IntelliJ Project Setup

pom.xml

Main.java

Fraction.java

Fraction.java

Fraction.java

Fraction.java

Static vs Non-Static Methods

Static vs Non-Static Methods

Javadoc Comments

Javadoc Comments

GitHub Setup

Fraction Class Diagram

GitHub Setup

6. Deployment

GitHub Setup

GitHub Setup

Mac Users Only

GitHub Setup

GitHub Setup

5. Testing

BeforeEach Methods

Run the tests to fail

Test the Getters and toString

Test the Setters

Test Exceptions

ended here

Mon-Wed class

Write Code to Pass Tests

Update Parameterized Constructor

Test Static Methods

Write Code to Pass Tests

Test toMixedNumber Method

Test toMixedNumber Method

GitHub Update

Java 2 - Week 2

Java 2 - Week 2

Marc Hauschildt

More from Marc Hauschildt