From cd78b40930a2aa6086e37b863fbd9d5d0cd7ee23 Mon Sep 17 00:00:00 2001
From: Martin Goik <goik@hdm-stuttgart.de>
Date: Sun, 16 Jul 2023 22:33:48 +0200
Subject: [PATCH] Awarding points for calculation polynomial values
---
.../mi/sd1/task2/SquarePolynom.java | 45 ++-
.../mi/sd1/ShowReachedPoints.java | 4 +-
.../mi/sd1/task2/TestSquarePolynom.java | 302 ++++++++++++++++++
.../mi/sd1/task2/SquarePolynom.java | 183 +----------
.../mi/sd1/task2/TestSquarePolynom.java | 107 +++++--
5 files changed, 441 insertions(+), 200 deletions(-)
create mode 100644 Klausuren/Sd1/2021winter/Exam/src/test/java/de/hdm_stuttgart/mi/sd1/task2/TestSquarePolynom.java
diff --git a/Klausuren/Sd1/2021winter/Exam/src/main/java/de/hdm_stuttgart/mi/sd1/task2/SquarePolynom.java b/Klausuren/Sd1/2021winter/Exam/src/main/java/de/hdm_stuttgart/mi/sd1/task2/SquarePolynom.java
index 07a7379d9..0368a93d3 100644
--- a/Klausuren/Sd1/2021winter/Exam/src/main/java/de/hdm_stuttgart/mi/sd1/task2/SquarePolynom.java
+++ b/Klausuren/Sd1/2021winter/Exam/src/main/java/de/hdm_stuttgart/mi/sd1/task2/SquarePolynom.java
@@ -7,19 +7,47 @@ package de.hdm_stuttgart.mi.sd1.task2;
* \(a\), \(b\) and \(c\). We assume all three to be of type <code>int</code>.</p>
*
*
- * <h2>Providing zeroes (German: "Nullstellen") of square polynomials,
- * case \( \mathbf{a \neq 0}\), true square polynomial</h2>
+ * <h2>Calculating polynomial values.</h2>
+ *
+ * <table class="goikTableDefaults">
+ * <caption>Sample code calculating polynomial values</caption>
+ * <tbody>
+ * <tr>
+ * <th>Code</th>
+ * <th>Result</th>
+ * </tr>
+ * <tr>
+ * <td>
+ * <pre><code class="language-java"> final SquarePolynom poly = // Representing
+ * new SquarePolynom(-1, 2, 1); // p(x) = -x² + 2x + 1
+ *
+ * double y = poly.get(3.0); // -1 * 3.0 * 3.0 + 2 * 3.0 + 1
+ *
+ * System.out.println(y);</code></pre>
+ * </td>
+ * <td>
+ * <pre><code class="nohighlight">-2</code></pre>
+ * </td>
+ * </tr>
+ * </tbody>
+ * </table>
+ *
+ * <h2>Providing zeroes (German: "Nullstellen") of square polynomials.</h2>
*
* <p>Zeroes are being calculated using:</p>
*
- * <p>\[ x_{1,2} = {{-b \pm \sqrt{b^2 - 4 ac}} \over {2a}} \]</p>
+ * \[ x_{1,2} = {{-b \pm \sqrt{b^2 - 4 ac}} \over {2a}} \]
*
- * <p>There are thus three cases:</p>
+ * <p>There are two main cases \( \mathbf{a \neq 0}\) and \( \mathbf{a = 0}\):</p>
+ *
+ * <h3>Case \( \mathbf{a \neq 0}\), true square polynomial</h3>
+ *
+ * <p>There are three sub cases:</p>
*
* <dl>
* <dt>\(\mathbf{ 0 < b^2 - 4 ac}\):</dt>
* <dd>
- * <p>Two zeroes \(x_1\) and \(x_2\) according to above formular:</p>
+ * <p>Two zeroes \(x_1\) and \(x_2\) according to the above formular:</p>
*
* <table class="goikTableDefaults">
* <caption>Sample code illustrating zero values calculation</caption>
@@ -49,7 +77,8 @@ package de.hdm_stuttgart.mi.sd1.task2;
* </tbody>
* </table>
*
- * <p>Note the two values in the <code>double[] zeroes</code> array being ordered by value.</p>
+ * <p>Note the two values in the array being ordered by value like <code>double[] zeroes = {-1.25, 2.0}</code>
+ * rather than <code>... {2.0, -1.25}</code></p>
* </dd>
*
* <dt>\(\mathbf{ 0 = b^2 - 4 ac}\):</dt>
@@ -121,9 +150,9 @@ package de.hdm_stuttgart.mi.sd1.task2;
* </dd>
* </dl>
*
- * <h2>Case \( \mathbf{a = 0}\), linear polynomial</h2>
+ * <h3>Case \( \mathbf{a = 0}\), linear polynomial</h3>
*
- * <p>This leaves us with just a linear polynomial \(bx + c\) also resulting in three different cases:</p>
+ * <p>This leaves us with just a linear polynomial \(bx + c\) also resulting in three different sub cases:</p>
*
*
* <dl>
diff --git a/Klausuren/Sd1/2021winter/Exam/src/test/java/de/hdm_stuttgart/mi/sd1/ShowReachedPoints.java b/Klausuren/Sd1/2021winter/Exam/src/test/java/de/hdm_stuttgart/mi/sd1/ShowReachedPoints.java
index b86901bc1..e17743839 100644
--- a/Klausuren/Sd1/2021winter/Exam/src/test/java/de/hdm_stuttgart/mi/sd1/ShowReachedPoints.java
+++ b/Klausuren/Sd1/2021winter/Exam/src/test/java/de/hdm_stuttgart/mi/sd1/ShowReachedPoints.java
@@ -3,7 +3,7 @@ package de.hdm_stuttgart.mi.sd1;
import de.hdm_stuttgart.mi.exam.unitmarking.RunTests;
import de.hdm_stuttgart.mi.sd1.task1.*;
-import de.hdm_stuttgart.mi.sd1.task2.Test_SquarePolynom;
+import de.hdm_stuttgart.mi.sd1.task2.TestSquarePolynom;
public class ShowReachedPoints {
@@ -17,6 +17,6 @@ public class ShowReachedPoints {
"Task 1"
, A_TrafficLightTest.class, B_StringHelperTest.class, C_ArrayHelperTest.class, D_TextFrameTest.class
);
- RunTests.exec("Task 2", Test_SquarePolynom.class);
+ RunTests.exec("Task 2", TestSquarePolynom.class);
}
}
\ No newline at end of file
diff --git a/Klausuren/Sd1/2021winter/Exam/src/test/java/de/hdm_stuttgart/mi/sd1/task2/TestSquarePolynom.java b/Klausuren/Sd1/2021winter/Exam/src/test/java/de/hdm_stuttgart/mi/sd1/task2/TestSquarePolynom.java
new file mode 100644
index 000000000..2909bfeb5
--- /dev/null
+++ b/Klausuren/Sd1/2021winter/Exam/src/test/java/de/hdm_stuttgart/mi/sd1/task2/TestSquarePolynom.java
@@ -0,0 +1,302 @@
+package de.hdm_stuttgart.mi.sd1.task2;
+
+import de.hdm_stuttgart.mi.exam.unitmarking.ExaminationTestDefaults;
+import de.hdm_stuttgart.mi.exam.unitmarking.Marking;
+import de.hdm_stuttgart.mi.sd1.ignore_me.ObjectWrapper;
+import org.junit.Assert;
+import org.junit.FixMethodOrder;
+import org.junit.Test;
+import org.junit.runners.MethodSorters;
+@FixMethodOrder(MethodSorters.NAME_ASCENDING)
+
+public class TestSquarePolynom extends ExaminationTestDefaults {
+
+ @Test
+ @Marking(points = 5)
+ public void test_100_constructor_getValue() {
+
+ assertPolynomValue(0, 0, 3, 20.5);
+ assertPolynomValue(0, 0, 3, -10.);
+ assertPolynomValue(0, 0, 3, 75.);
+
+ assertPolynomValue(-1, 3, 5, 2.);
+ assertPolynomValue(4, -4, 10, -3);
+
+ assertPolynomValue(-1, 2, 1, 1);
+ }
+
+ @Test
+ @Marking(points = 5)
+ public void test_200_set_getValue() {
+
+ assertPolynomValue(0, 0, -8, -10);
+ assertPolynomValue(0, 0, -8, 100.);
+ assertPolynomValue(0, 0, -8, -103.3);
+ {
+ final ObjectWrapper<SquarePolynom> poly = new ObjectWrapper<>(SquarePolynom.class, 0, 0, -8);
+ poly.invoke(void.class, "setA", 7);
+ poly.invoke(void.class, "setB", -1);
+ final double expected = 2.5 * (7 * 2.5 - 1) - 8;
+ final String msg = composeDescription(7, -1, -8).append(" should return " + expected).toString();
+ Assert.assertEquals(msg, expected, poly.invoke(double.class, "get", 2.5), delta);
+ }
+ }
+
+ @Test
+ @Marking(points = 4)
+ public void test_400_NoZero() {
+ final ObjectWrapper<SquarePolynom> poly = new ObjectWrapper<>(SquarePolynom.class,1, 1, 1);
+ assertNoZero(poly, composeDescription(1,2,1).toString());
+
+ final ObjectWrapper<SquarePolynom> poly2 = new ObjectWrapper<>(SquarePolynom.class,1, 2, 3);
+ assertNoZero(1, 6, 20, poly2);
+ assertNoZero(2, 13, 41, poly2);
+ }
+
+ @Test
+ @Marking(points = 1)
+ public void test_500_OneZeroLinearOneZero() {
+ final ObjectWrapper<SquarePolynom> poly = new ObjectWrapper<>(SquarePolynom.class,0, 1, 1);
+ assertOneZero(poly, -1, composeDescription(0,1,1).toString());
+ }
+
+ @Test
+ @Marking(points = 1)
+ public void test_600_OneZeroLinearNoZero() {
+ final ObjectWrapper<SquarePolynom> poly = new ObjectWrapper<>(SquarePolynom.class,0, 0, 1);
+ assertNoZero(poly, composeDescription(0,0,1).toString());
+ }
+
+ @Test
+ @Marking(points = 1)
+ public void test_610_OneZero() {
+ final ObjectWrapper<SquarePolynom> poly = new ObjectWrapper<>(SquarePolynom.class,1, 2, 1);
+ assertOneZero(poly, -1, composeDescription(1,2,1).toString());
+
+ final ObjectWrapper<SquarePolynom> poly2 = new ObjectWrapper<>(SquarePolynom.class,1, 2, 3);
+ assertOneZero(6, -84, 294, poly2, 7);
+ assertOneZero(21, 126, 189, poly2, -3);
+ }
+
+ @Test
+ @Marking(points = 1)
+ public void test_700_twoZeroes() {
+
+ final ObjectWrapper<SquarePolynom> poly = new ObjectWrapper<>(SquarePolynom.class,1, 3, 2);
+ assertTwoZeroes(poly, -2, -1, "x² + 3x + 2");
+
+ assertTwoZeroes(3, 7, 4, poly, -4./3, -1);
+
+ assertTwoZeroes(-2, 1, 3, poly, -1, 1.5);
+
+ assertTwoZeroes(-1, 5, 6, poly, -1, 6);
+
+ assertTwoZeroes(7, 11, 4, poly, -1, -4./7);
+
+ assertTwoZeroes(4, -3, -10, poly, -1.25, 2);
+
+ assertTwoZeroes(5, 6, 1, poly, -1, -0.2);
+
+ }
+
+ @Test
+ @Marking(points = 1)
+ public void test_800_Exception() {
+ final ObjectWrapper<SquarePolynom> poly = new ObjectWrapper<>(SquarePolynom.class,0, 0, 0);
+
+ final Class<ArithmeticException> expectedArithmeticException = ArithmeticException.class;
+
+ // Either of a, b or c must be non-zero
+ poly.invoke(double[].class, "getZeroes", expectedArithmeticException);
+ }
+
+ @Test
+ @Marking(points = 1)
+ public void test_900_TwoZeroExzess() {
+ final ObjectWrapper<SquarePolynom> poly = new ObjectWrapper<>(SquarePolynom.class,
+ 46010, 598130,-1960026000);
+ assertTwoZeroes(poly,-213,200,
+ composeDescription(46010, 598130,-1960026000).toString());
+ }
+
+ // End of tests -------------------------------------------------------------------------------------------------
+ // Test helper methods
+ //
+ static private final double delta = 1.E-12;
+ private static void assertPolynomValue(int a, int b, int c, double x) {
+ final ObjectWrapper<SquarePolynom> poly = new ObjectWrapper<>(SquarePolynom.class, a, b, c);
+ final double expected = x * (a * x + b) + c;
+ final String msg = composeDescription(a,b,c) + " for x == " + x + " should return " + expected;
+ Assert.assertEquals(msg, expected, poly.invoke(double.class, "get", x), delta);
+ }
+
+ static private StringBuffer composeDescription(final int a, final int b, final int c) {
+
+ final StringBuffer ret = new StringBuffer("p(x)=");
+
+ boolean initialized = false;
+
+ if (a != 0) {
+ if (-1 == a) {
+ ret.append("-");
+ } else if (1 != a) {
+ ret.append(a);
+ }
+ ret.append("x²");
+ initialized = true;
+ }
+
+ if (0 != b) {
+ if (initialized) {
+ if (0 < b) {
+ ret.append("+");
+ }
+ } else {
+ initialized = true;
+ }
+ if (-1 == b) {
+ ret.append("-");
+ } else if (1 != b) {
+ ret.append(b);
+ }
+ ret.append("x");
+ }
+
+ if (0 != c) {
+ if (initialized) {
+ if (0 < c) {
+ ret.append("+");
+ }
+ }
+ ret.append(c);
+ }
+ return ret;
+ }
+
+ /**
+ * Testing given polynomial for no real zero value.
+ *
+ * @param poly Polynomial to be tested
+ * @param description E.g. "-2x² + 4x -3"
+ */
+ static private void assertNoZero(final ObjectWrapper<SquarePolynom> poly, final String description) {
+
+ Assert.assertEquals("No zero expected for polynom »" + description + "«",
+ 0, poly.invoke(double[].class, "getZeroes").length);
+ }
+
+ /**
+ * Testing for no real valued zero solution.
+ *
+ * @param a Square coefficient
+ * @param b Linear coefficient
+ * @param c Constant coefficient
+ * @param poly Square polynomial
+ */
+ static private void assertNoZero(final int a,
+ final int b,
+ final int c,
+ final ObjectWrapper<SquarePolynom> poly) {
+ poly.invoke(void.class, "setA", a);
+ poly.invoke(void.class, "setB", b);
+ poly.invoke(void.class, "setC", c);
+ Assert.assertEquals("One zero expected for polynom »" + composeDescription(a, b, c) + "«",
+ 0, poly.invoke(double[].class, "getZeroes").length);
+
+
+ }
+
+ /**
+ * Testing given polynomial for one zeroes to be returned
+ *
+ * @param poly Polynomial to be tested
+ * @param expected zero value
+ * @param description E.g. "-2x² + 4x -3"
+ */
+ static private void assertOneZero(final ObjectWrapper<SquarePolynom> poly,
+ double expected,
+ final String description) {
+ final double[] result = poly.invoke(double[].class, "getZeroes");
+
+ Assert.assertEquals("One zero expected for polynom »" + description + "«",
+ 1, result.length);
+ Assert.assertEquals("Expected zero of »" + description +"« to be " + expected, expected, result[0], delta);
+ }
+
+ /**
+ * Like {@link #assertOneZero(ObjectWrapper, double, String)} but re-setting coefficients beforehand,
+ * @param a Square coefficient
+ * @param b Linear coefficient
+ * @param c Constant coefficient
+ * @param poly Square polynomial
+ */
+ static private void assertOneZero(final int a,
+ final int b,
+ final int c,
+ final ObjectWrapper<SquarePolynom> poly,
+ double expected) {
+ poly.invoke(void.class, "setA", a);
+ poly.invoke(void.class, "setB", b);
+ poly.invoke(void.class, "setC", c);
+ final double[] result = poly.invoke(double[].class, "getZeroes");
+
+ final StringBuffer polynomDescription = composeDescription(a, b, c);
+
+ Assert.assertEquals(2 + " zeroes expected for polynom »" + polynomDescription + "«",
+ 1, result.length);
+ Assert.assertEquals("Expected zero of »" + polynomDescription +"« to be " + expected,
+ expected, result[0], delta);
+ }
+
+ /**
+ * Testing given polynomial for two zeroes to be returned
+ *
+ * @param poly Polynomial to be tested
+ * @param expectedLower Lower zero value
+ * @param expectedUpper Upper zero value
+ * @param description E.g. "-2x² + 4x -3"
+ */
+ static private void assertTwoZeroes(final ObjectWrapper<SquarePolynom> poly,
+ double expectedLower,
+ double expectedUpper,
+ final String description) {
+ final double[] result = poly.invoke(double[].class, "getZeroes");
+
+ Assert.assertEquals(2 + " zeroes expected for polynom »" + description + "«",
+ 2, result.length);
+ Assert.assertEquals("Expected lower zero of »" + description +"« to be " + expectedLower,
+ expectedLower, result[0], delta);
+ Assert.assertEquals("Expected upper zero of »" + description +"« to be " + expectedUpper,
+ expectedUpper, result[1], delta);
+ }
+
+ /**
+ * Like {@link #assertTwoZeroes(ObjectWrapper, double, double, String)} but re-setting coeficients beforehand,
+ * @param a Square coefficient
+ * @param b Linear coefficient
+ * @param c Constant coefficient
+ * @param poly Square polynomial
+ * @param expectedLower Expected lower zero value
+ * @param expectedUpper Expected upper zero value
+ */
+ static private void assertTwoZeroes(final int a,
+ final int b,
+ final int c,
+ final ObjectWrapper<SquarePolynom> poly,
+ double expectedLower,
+ double expectedUpper) {
+ poly.invoke(void.class, "setA", a);
+ poly.invoke(void.class, "setB", b);
+ poly.invoke(void.class, "setC", c);
+ final double[] result = poly.invoke(double[].class, "getZeroes");
+
+ final StringBuffer polynomDescription = composeDescription(a, b, c);
+
+ Assert.assertEquals(2 + " zeroes expected for polynom »" + polynomDescription + "«",
+ 2, result.length);
+ Assert.assertEquals("Expected lower zero of »" + polynomDescription +"« to be " + expectedLower,
+ expectedLower, result[0], delta);
+ Assert.assertEquals("Expected upper zero of »" + polynomDescription +"« to be " + expectedUpper,
+ expectedUpper, result[1], delta);
+ }
+}
diff --git a/Klausuren/Sd1/2021winter/Solve/src/main/java/de/hdm_stuttgart/mi/sd1/task2/SquarePolynom.java b/Klausuren/Sd1/2021winter/Solve/src/main/java/de/hdm_stuttgart/mi/sd1/task2/SquarePolynom.java
index ec0c8b829..519f934e3 100644
--- a/Klausuren/Sd1/2021winter/Solve/src/main/java/de/hdm_stuttgart/mi/sd1/task2/SquarePolynom.java
+++ b/Klausuren/Sd1/2021winter/Solve/src/main/java/de/hdm_stuttgart/mi/sd1/task2/SquarePolynom.java
@@ -3,7 +3,7 @@ package de.hdm_stuttgart.mi.sd1.task2;
/**
* <p>Representing square polynomials having coefficients of type <code>int</code>.</p>
*
- * <p>A square polynomial \( p(x) = a x² + b x + c \) is being defined by its three coefficients
+ * <p>A square polynomial \( p(x) = a x^2 + b x + c \) is being defined by its three coefficients
* \(a\), \(b\) and \(c\). We assume all three to be of type <code>int</code>.</p>
*
*/
@@ -11,7 +11,7 @@ public class SquarePolynom {
private int a, b, c;
/**
- * <p>Defining a polynomial \( p(x) = a x² + b x + c \).</p>
+ * <p>Defining a polynomial \( p(x) = a x^2 + b x + c \).</p>
*
* @param a Square coefficient.
* @param b Linear coefficient.
@@ -23,6 +23,16 @@ public class SquarePolynom {
setC(c);
}
+ /**
+ * <p>The polynomial's value for a given argument of x.</p>
+ *
+ * @param x The argument i.e. x = 3.0
+ * @return Returning e.g. \( a \cdot 3.0^2 + b \cdot 3.0 + c\) for \( x = 3.0 \).
+ */
+ public double get(double x) {
+ return x * (a * x + b) + c; // Horner's scheme
+ }
+
/**
* <p>Re- setting the square coefficient in \( a x² \).</p>
*
@@ -51,174 +61,11 @@ public class SquarePolynom {
}
/**
- * <p>Providing zeroes (German: "Nullstellen") of the given square polynomial.</p>
- *
- * <p>There are two different cases \( \mathbf{a \neq 0}\) and \( \mathbf{a = 0}\):</p>
- *
- * <h2>Case \( \mathbf{a \neq 0}\), true square polynomial</h2>
- *
- * <p>Zeroes are being calculated using:</p>
- *
- * <p>\[ x_{1,2} = {{-b \pm \sqrt{b^2 - 4 ac}} \over {2a}} \]</p>
- *
- * <p>There are thus three cases:</p>
- *
- * <dl>
- * <dt>\(\mathbf{ 0 < b^2 - 4 ac}\):</dt>
- * <dd>
- * <p>Two zeroes \(x_1\) and \(x_2\) according to above formular:</p>
- *
- * <table class="goikTableDefaults">
- * <caption>Sample code illustrating zero values calculation</caption>
- * <tbody>
- * <tr>
- * <th>Code</th>
- * <th>Result</th>
- * </tr>
- * <tr>
- * <td>
- * <pre><code class="language-java"> final SquarePolynom poly = // Representing
- * new SquarePolynom(4, -3, -10); // p(x) = 4x² - 3x - 10
- *
- * double[] zeroes = poly.getZeroes();
- *
- * System.out.println("Found " + zeroes.length + " zeroes:");
- *
- * System.out.println("x_1 = " + zeroes[0]);
- * System.out.println("x_2 = " + zeroes[1]);</code></pre>
- * </td>
- * <td>
- * <pre><code class="nohighlight"> Found 2 zeroes:
- * x_1 = -1.25
- * x_2 = 2.0</code></pre>
- * </td>
- * </tr>
- * </tbody>
- * </table>
- *
- * <p>Note the two values in the <code>double[] zeroes</code> array being ordered by value.</p>
- * </dd>
- *
- * <dt>\(\mathbf{ 0 = b^2 - 4 ac}\):</dt>
- *
- * <dd>
- * <p>One zero \(x = {-b\over 2a}\).</p>
- *
- * <p>We allow for changing a polynomial's coefficients. Continuing from the above example we have:</p>
- *
- * <table class="goikTableDefaults">
- * <caption>Changing coefficients</caption>
- * <tbody>
- * <tr>
- * <th>Code</th>
- * <th>Result</th>
- * </tr>
- * <tr>
- * <td>
- * <pre><code class="java"> ...
- * poly.setA(1); // Representing
- * poly.setB(-8); // p(x) = x² -8x + 16
- * poly.setC(16);
- *
- * zeroes = poly.getZeroes();
- * System.out.println("Found " + zeroes.length + " zero:");
- *
- * System.out.println("x_1 = " + zeroes[0]);</code></pre>
- * </td>
- * <td>
- * <pre><code class="nohighlight"> ...
- * Found 1 zero:
- * x_1 = 4.0</code></pre>
- * </td>
- * </tr>
- * </tbody>
- * </table>
- * <p> </p>
- * </dd>
- *
- * <dt>\(\mathbf{ b^2 - 4 ac < 0 }\):</dt>
- *
- * <dd>
- * <p>Square root of negative thus no real valued solution:</p>
- *
- * <table class="goikTableDefaults">
- * <caption>Changing coefficients again</caption>
- * <tbody>
- * <tr>
- * <th>Code</th>
- * <th>Result</th>
- * </tr>
- * <tr>
- * <td>
- * <pre><code class="java"> ...
- * poly.setA(1); // Representing
- * poly.setB(0); // p(x) = x² + 1
- * poly.setC(1); // (No real valued zero)
- *
- * zeroes = poly.getZeroes();
- * System.out.println("Found " + zeroes.length + " zero");</code></pre>
- * </td>
- * <td>
- * <pre><code class="nohighlight"> ...
- * Found 0 zero</code></pre>
- * </td>
- * </tr>
- * </tbody>
- * </table>
- * </dd>
- * </dl>
- *
- * <h2>Case \( \mathbf{a = 0}\), linear polynomial</h2>
- *
- * <p>This leaves us with just a linear polynomial \(bx + c\) also resulting in three different cases:</p>
- *
- *
- * <dl>
- * <dt>\( \mathbf{b \neq 0} :\)</dt>
- *
- * <dd>
- * <p>Exactly one zero</p>
- * </dd>
- *
- * <dt>\( \mathbf{b = 0 \ \text{and} \ c \neq 0 :}\)</dt>
- * <dd>
- * <p>No zero at all</p>
- * </dd>
- *
- * <dt>\(\mathbf{b = 0 \ \text{and} \ c = 0} \):</dt>
- * <dd>
- * <p>An infinite number of zeroes. Since this cannot be represented by a finite <code>double[]</code> array
- * an {@link ArithmeticException} is being thrown like in the subsequent code sample:</p>
- *
- * <table class="goikTableDefaults">
- * <caption>Dealing with \( \mathbf{a = b = c = 0} \)</caption>
- * <tbody>
- * <tr>
- * <th>Code</th>
- * <th>Result</th>
- * </tr>
- * <tr>
- * <td>
- * <pre><code class="java"> ...
- * poly.setA(0);
- * poly.setB(0);
- * poly.setC(0);
- * zeroes = poly.getZeroes();</code></pre>
- * </td>
- * <td>
- * <pre><code class="nohighlight"> ...
- * Exception in thread "main" java.lang.ArithmeticException:
- * <b style="color:red;">Polynomial is identical to zero function</b></code></pre>
- * </td>
- * </tr>
- * </tbody>
- * </table>
+ * <p>Providing zeroes (German: "Nullstellen") of a given square polynomial.</p>
*
- * </dd>
- * </dl>
+ * @return The ordered finite set of zeroes. In case of an infinite number of zeroes an {@link ArithmeticException}
+ * is being thrown.
*
- * @return The finite set of zeroes. In case of an infinite number of zeroes an {@link ArithmeticException} is being
- * thrown.
* @throws ArithmeticException In case of \(a = b = c = 0 \) an infinite number of zeroes exists which cannot be
* represented by a finite array of double values.
*/
diff --git a/Klausuren/Sd1/2021winter/Solve/src/test/java/de/hdm_stuttgart/mi/sd1/task2/TestSquarePolynom.java b/Klausuren/Sd1/2021winter/Solve/src/test/java/de/hdm_stuttgart/mi/sd1/task2/TestSquarePolynom.java
index 5f6de7b47..8c35e0519 100644
--- a/Klausuren/Sd1/2021winter/Solve/src/test/java/de/hdm_stuttgart/mi/sd1/task2/TestSquarePolynom.java
+++ b/Klausuren/Sd1/2021winter/Solve/src/test/java/de/hdm_stuttgart/mi/sd1/task2/TestSquarePolynom.java
@@ -13,7 +13,38 @@ public class TestSquarePolynom extends ExaminationTestDefaults {
@Test
@Marking(points = 5)
- public void test_100_NoZero() {
+ public void test_100_constructor_getValue() {
+
+ assertPolynomValue(0, 0, 3, 20.5);
+ assertPolynomValue(0, 0, 3, -10.);
+ assertPolynomValue(0, 0, 3, 75.);
+
+ assertPolynomValue(-1, 3, 5, 2.);
+ assertPolynomValue(4, -4, 10, -3);
+
+ assertPolynomValue(-1, 2, 1, 1);
+ }
+
+ @Test
+ @Marking(points = 5)
+ public void test_200_set_getValue() {
+
+ assertPolynomValue(0, 0, -8, -10);
+ assertPolynomValue(0, 0, -8, 100.);
+ assertPolynomValue(0, 0, -8, -103.3);
+ {
+ final ObjectWrapper<SquarePolynom> poly = new ObjectWrapper<>(SquarePolynom.class, 0, 0, -8);
+ poly.invoke(void.class, "setA", 7);
+ poly.invoke(void.class, "setB", -1);
+ final double expected = 2.5 * (7 * 2.5 - 1) - 8;
+ final String msg = composeDescription(7, -1, -8).append(" should return " + expected).toString();
+ Assert.assertEquals(msg, expected, poly.invoke(double.class, "get", 2.5), delta);
+ }
+ }
+
+ @Test
+ @Marking(points = 4)
+ public void test_400_NoZero() {
final ObjectWrapper<SquarePolynom> poly = new ObjectWrapper<>(SquarePolynom.class,1, 1, 1);
assertNoZero(poly, composeDescription(1,2,1).toString());
@@ -24,21 +55,21 @@ public class TestSquarePolynom extends ExaminationTestDefaults {
@Test
@Marking(points = 1)
- public void test_200_OneZeroLinearOneZero() {
+ public void test_500_OneZeroLinearOneZero() {
final ObjectWrapper<SquarePolynom> poly = new ObjectWrapper<>(SquarePolynom.class,0, 1, 1);
assertOneZero(poly, -1, composeDescription(0,1,1).toString());
}
@Test
@Marking(points = 1)
- public void test_200_OneZeroLinearNoZero() {
+ public void test_600_OneZeroLinearNoZero() {
final ObjectWrapper<SquarePolynom> poly = new ObjectWrapper<>(SquarePolynom.class,0, 0, 1);
assertNoZero(poly, composeDescription(0,0,1).toString());
}
@Test
- @Marking(points = 3)
- public void test_210_OneZero() {
+ @Marking(points = 1)
+ public void test_610_OneZero() {
final ObjectWrapper<SquarePolynom> poly = new ObjectWrapper<>(SquarePolynom.class,1, 2, 1);
assertOneZero(poly, -1, composeDescription(1,2,1).toString());
@@ -48,8 +79,8 @@ public class TestSquarePolynom extends ExaminationTestDefaults {
}
@Test
- @Marking(points = 5)
- public void test_300_twoZeroes() {
+ @Marking(points = 1)
+ public void test_700_twoZeroes() {
final ObjectWrapper<SquarePolynom> poly = new ObjectWrapper<>(SquarePolynom.class,1, 3, 2);
assertTwoZeroes(poly, -2, -1, "x² + 3x + 2");
@@ -69,8 +100,8 @@ public class TestSquarePolynom extends ExaminationTestDefaults {
}
@Test
- @Marking(points = 2)
- public void test_400_Exception() {
+ @Marking(points = 1)
+ public void test_800_Exception() {
final ObjectWrapper<SquarePolynom> poly = new ObjectWrapper<>(SquarePolynom.class,0, 0, 0);
final Class<ArithmeticException> expectedArithmeticException = ArithmeticException.class;
@@ -80,8 +111,8 @@ public class TestSquarePolynom extends ExaminationTestDefaults {
}
@Test
- @Marking(points = 3)
- public void test_500_TwoZeroExzess() {
+ @Marking(points = 1)
+ public void test_900_TwoZeroExzess() {
final ObjectWrapper<SquarePolynom> poly = new ObjectWrapper<>(SquarePolynom.class,
46010, 598130,-1960026000);
assertTwoZeroes(poly,-213,200,
@@ -92,20 +123,52 @@ public class TestSquarePolynom extends ExaminationTestDefaults {
// Test helper methods
//
static private final double delta = 1.E-12;
+ private static void assertPolynomValue(int a, int b, int c, double x) {
+ final ObjectWrapper<SquarePolynom> poly = new ObjectWrapper<>(SquarePolynom.class, a, b, c);
+ final double expected = x * (a * x + b) + c;
+ final String msg = composeDescription(a,b,c) + " for x == " + x + " should return " + expected;
+ Assert.assertEquals(msg, expected, poly.invoke(double.class, "get", x), delta);
+ }
static private StringBuffer composeDescription(final int a, final int b, final int c) {
- final StringBuffer ret = new StringBuffer();
- ret.append(a).append("x²");
- if (0 < b) {
- ret.append(" + ").append(b).append("x");
- } else if (b < 0) {
- ret.append(" ").append(b).append("x");
+
+ final StringBuffer ret = new StringBuffer("p(x)=");
+
+ boolean initialized = false;
+
+ if (a != 0) {
+ if (-1 == a) {
+ ret.append("-");
+ } else if (1 != a) {
+ ret.append(a);
+ }
+ ret.append("x²");
+ initialized = true;
}
- // Slight code duplication avoiding a method definition. Yepp: I'm lazy sometimes!
- if (0 < c) {
- ret.append(" + ").append(c);
- } else if (c < 0) {
- ret.append(" ").append(c);
+
+ if (0 != b) {
+ if (initialized) {
+ if (0 < b) {
+ ret.append("+");
+ }
+ } else {
+ initialized = true;
+ }
+ if (-1 == b) {
+ ret.append("-");
+ } else if (1 != b) {
+ ret.append(b);
+ }
+ ret.append("x");
+ }
+
+ if (0 != c) {
+ if (initialized) {
+ if (0 < c) {
+ ret.append("+");
+ }
+ }
+ ret.append(c);
}
return ret;
}
--
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