package org.geogebra.cas;
import static org.geogebra.test.util.IsEqualPolynomialEquation.equalToPolynomialEquation;
import static org.geogebra.test.util.IsEqualStringIgnoreWhitespaces.equalToIgnoreWhitespaces;
import static org.junit.Assert.assertThat;
import java.util.HashSet;
import java.util.Locale;
import org.geogebra.cas.logging.CASTestLogger;
import org.geogebra.common.cas.CASparser;
import org.geogebra.common.cas.view.CASCellProcessor;
import org.geogebra.common.kernel.GeoGebraCasInterface;
import org.geogebra.common.kernel.Kernel;
import org.geogebra.common.kernel.KernelCAS;
import org.geogebra.common.kernel.StringTemplate;
import org.geogebra.common.kernel.arithmetic.Command;
import org.geogebra.common.kernel.arithmetic.ExpressionNodeConstants;
import org.geogebra.common.kernel.arithmetic.ExpressionValue;
import org.geogebra.common.kernel.arithmetic.MyArbitraryConstant;
import org.geogebra.common.kernel.arithmetic.Traversing.CommandCollector;
import org.geogebra.common.kernel.arithmetic.ValidExpression;
import org.geogebra.common.kernel.geos.GeoCasCell;
import org.geogebra.common.kernel.geos.GeoElement;
import org.geogebra.common.plugin.GeoClass;
import org.geogebra.common.util.debug.Log;
import org.geogebra.common.util.lang.Unicode;
import org.geogebra.desktop.main.AppDNoGui;
import org.geogebra.desktop.main.LocalizationD;
import org.junit.AfterClass;
import org.junit.Assert;
import org.junit.Before;
import org.junit.BeforeClass;
import org.junit.Rule;
import org.junit.Test;
import org.junit.rules.Timeout;
@SuppressWarnings("javadoc")
public class GeoGebraCasIntegrationTest {
private static final String GermanSolve = "L\u00f6se";
static public boolean silent = false;
static GeoGebraCasInterface cas;
static Kernel kernel;
static AppDNoGui app;
/**
* Logs all tests which don't give the expected but a valid result.
*/
static CASTestLogger logger;
static private MyArbitraryConstant arbconst;
@BeforeClass
public static void setupCas () {
app = new AppDNoGui(new LocalizationD(3), false);
if (silent) {
Log.setLogger(null);
}
// Set language to something else than English to test automatic translation.
app.setLanguage(Locale.GERMANY);
// app.fillCasCommandDict();
kernel = app.getKernel();
arbconst = new MyArbitraryConstant(new GeoCasCell(kernel.getConstruction()));
cas = kernel.getGeoGebraCAS();
logger = new CASTestLogger();
// Setting the general timeout to 9 seconds. Feel free to change this.
kernel.getApplication().getSettings().getCasSettings().setTimeoutMilliseconds(9000);
}
/**
* Handles the logs about test warnings.
*/
@AfterClass
public static void handleLogs () {
if (!silent) {
logger.handleLogs();
}
}
/**
* Before every test: Clear the construction list to make sure there is nothing already defined.
*/
@Before
public void beforeTest () {
kernel.clearConstruction(true);
}
/**
* Executes the given expression in the CAS.
*
* @param input
* The expression to be evaluated, in geogebra's CAS syntax.
* @return The string returned by GeogebraCAS.
*/
private static String executeInCAS (String input) throws Throwable {
CASparser parser = (CASparser) cas.getCASparser();
ValidExpression inputVe = parser.parseGeoGebraCASInputAndResolveDummyVars(input, kernel, null);
String result = cas.evaluateGeoGebraCAS(inputVe, arbconst, StringTemplate.numericDefault,null, kernel);
if (result == null || result.length() <= 0) {
return "";
}
// Parse input into valid expression.
ExpressionValue outputVe = parser.parseGeoGebraCASInput(result, null);
// Resolve Variable objects in ValidExpression as GeoDummy objects.
parser.resolveVariablesForCAS(outputVe, kernel);
boolean includesNumericCommand = false;
HashSet<Command> commands = new HashSet<Command>();
inputVe.traverse(CommandCollector.getCollector(commands));
if (!commands.isEmpty()) {
for (Command cmd : commands) {
String cmdName = cmd.getName();
// Numeric used
includesNumericCommand = includesNumericCommand || ("Numeric".equals(cmdName) && cmd.getArgumentNumber() > 1);
}
}
return outputVe.toString(includesNumericCommand ? StringTemplate.testNumeric : StringTemplate.testTemplate);
}
private static void tk (String input, String expectedResult, String ... validResults) {
ta(true, input, expectedResult, validResults);
}
private static void t (String input, String expectedResult, String ... validResults) {
ta(false, input, expectedResult, validResults);
}
private static void ta(boolean keepInput, String input,
String expectedResult, String... validResults) {
GeoCasCell f = new GeoCasCell(kernel.getConstruction());
ta(f, keepInput, input, expectedResult, validResults);
}
/**
* ta contains the code shared by {@link #t} and {@link #tk}. In explicit: If tkiontki is false, it behaves exactly like t used to. If tkiontki is
* true, it switches to Keepinput mode, simulating evaluation with Keepinput.
*
* <p>
* Note: Direct calls to ta are "Not Recommended". Use t or tk instead.
* </p>
*
* @param keepInput
* To Keepinput or not to Keepinput.
* @param input
* The input.
* @param expectedResult
* The expected result.
* @param validResults
* Valid, but undesired results.
*/
private static void ta(GeoCasCell f, boolean keepInput, String input,
String expectedResult, String... validResults) {
String result;
try {
f.setInput(input);
if (keepInput) {
f.setEvalCommand("Keepinput");
}
if (!f.hasVariablesOrCommands()) {
kernel.getConstruction().addToConstructionList(f, false);
f.computeOutput();
f.setLabelOfTwinGeo();
} else {
kernel.getConstruction().removeFromConstructionList(f);
KernelCAS.dependentCasCell(f);
}
boolean includesNumericCommand = false;
HashSet<Command> commands = new HashSet<Command>();
f.getInputVE().traverse(CommandCollector.getCollector(commands));
if (!commands.isEmpty()) {
for (Command cmd : commands) {
String cmdName = cmd.getName();
// Numeric used
includesNumericCommand = includesNumericCommand
|| ("Numeric".equals(cmdName) && cmd
.getArgumentNumber() > 1);
}
}
result = f.getOutputValidExpression() != null ? f
.getOutputValidExpression().toString(
includesNumericCommand ? StringTemplate.testNumeric
: StringTemplate.testTemplate) : f
.getOutput(StringTemplate.testTemplate);
if (f.getOutputValidExpression() != null
&& f.getOutputValidExpression().unwrap() instanceof GeoElement) {
result = ((GeoElement) f.getOutputValidExpression().unwrap())
.toValueString(StringTemplate.testTemplate);
}
} catch (Throwable t) {
String sts = "";
StackTraceElement[] st = t.getStackTrace();
for (int i = 0; i < 10 && i < st.length; i++) {
StackTraceElement stElement = st[i];
sts += stElement.getClassName() + ":"
+ stElement.getMethodName() + stElement.getLineNumber()
+ "\n";
}
result = t.getClass().getName() + ":" + t.getMessage() + sts;
}
assertThat(
result,
equalToIgnoreWhitespaces(logger, input, expectedResult,
validResults));
}
/**
* For comparing polynomial equations<br/>
* Tests if the given input is equal to the expected result ignoring the ordering of the terms on each side
*
* @param input
* The polynomial equation in GeogebraCAS syntax
* @param expectedResult
* The regular expression that the output should match
*/
@SuppressWarnings("unused")
private static void pe (String input, String expectedResult) {
try {
String result = executeInCAS(input);
assertThat(result, equalToPolynomialEquation(expectedResult));
} catch (Throwable t) {
propagate(t);
}
}
/**
* Tests if the given input produces a result that matches a given regular expression.
*
* @param input
* The input expression in GeogebraCAS syntax.
* @param expectedPattern
* The regular expression that the output should match.
* @param readablePattern
* The pattern that is used as "expected" value when the input doesn't match the output. If null, expectedPattern will be used.
*/
private static String checkRegex (String input, String expectedPattern, String readablePattern) {
try {
String result = executeInCAS(input);
if (result.matches(expectedPattern)) {
return null;
}
if (readablePattern != null) {
return "\nExpected: " + readablePattern + "\ngot: " + result;
}
return "\nExpected: " + expectedPattern + "\ngot: ";
} catch (Throwable t) {
return t.getClass().getName() + ":" + t.getMessage();
}
}
private static void r (String input, String expectedPattern, String readablePattern) {
String error = checkRegex(input, expectedPattern, readablePattern);
if (error != null) {
Assert.fail(error);
}
}
/**
* Tests that the given input produces a result that matches a given output.
*
* The pattern for the output is basically a normal regular expression, except that many RE special characters will be taken literally, e.g. braces,
* parenthesis etc. Additionally, all whitespace will be optional and character- class boxes (e.g. [a-z]) do not work!
*
* @param input
* The input expression in GeogebraCAS syntax.
* @param expectedPattern
* The simplified regular expression that the output should match.
*/
private static void s (String input, String expectedPattern) {
String originalPattern = expectedPattern;
String newPattern = expectedPattern;
newPattern = newPattern.replace("{", "\\{");
newPattern = newPattern.replace("}", "\\}");
newPattern = newPattern.replace("(", "\\(");
newPattern = newPattern.replace(")", "\\)");
// + and * can have both arithmetic meaning (addition/multiplication),
// as well as be part of a multiplier in a regex (e.g. in \d+ ).
// Likewise, brackets [] can be part of a character class box or of a
// function call in Geogebra. We escape these signs so they'll retain
// their
// function call meaning, not their character-class box meaning!
newPattern = newPattern.replaceAll("([^\\\\].|^.)\\+", "$1\\\\+");
newPattern = newPattern.replaceAll("([^\\\\].|^.)\\*", "$1\\\\*");
newPattern = newPattern.replaceAll("([^\\\\].|^.)\\^", "$1\\\\^");
newPattern = newPattern.replaceAll("INDEX", "\\\\{?\\\\d+\\\\}?");
newPattern = newPattern.replace(" ", "\\s*"); // make whitespace
// optional
Log.debug(newPattern);
r(input, newPattern, originalPattern);
}
// 100 seconds max per method tested
@SuppressWarnings("deprecation")
@Rule
public Timeout globalTimeout = new Timeout(50000);
// Self Test Section
/* Forgetting before tests */
@Test
public void Selftest_Forget_0 () {
t("f(x) := x^2 + p * x + q", "x^(2) + p * x + q", "p * x + q + x^(2)", "x^(2) + x * p + q");
}
@Test
public void Selftest_Forget_1 () {
t("f(x)", "f(x)");
}
/* Remembering during tests */
@Test
public void Selftest_Remember_0 () {
t("f(x) := x^2 + p * x + q", "x^(2) + p * x + q", "p * x + q + x^(2)", "x^(2) + x * p + q");
t("f(x)", "x^(2) + p * x + q", "p * x + q + x^(2)", "x^(2) + x * p + q");
}
// Test Section
/* Assignment */
/**
* Checks if the assignment of variables by using the ':=' operator is working
*/
@Test
public void Assignment_0 () {
t("testvar", "testvar");
t("testvar := 1", "1");
t("testvar", "1");
// Tidy up
try {
t("Delete[testvar]", "true");
} catch (Throwable t) {
propagate(t);
}
}
/* Simplification of Terms */
/* One variable */
@Test
public void SimplificationOfTerms_ConstantsOnly () {
t("((15 + 9) * 3.5 - 2 * 0.5) / 4", "83 / 4");
}
@Test
public void SimplificationOfTerms_OneVariable () {
t("x + x", "2 * x");
}
/* Two variables */
@Test
public void SimplificationOfTerms_TwoVariables () {
t("6a * 3b - (5a b + b * 2a)", "11 * a * b");
}
/* Power of one Variable */
@Test
public void SimplificationOfTerms_PowerOfOneVariable () {
t("x*x", "x^(2)");
}
/* Power of two Variables */
@Test
public void SimplificationOfTerms_PowerOfTwoVariables_0 () {
t("x^2 y^2 (x y)^2", "x^(4) * y^(4)");
}
@Test
public void SimplificationOfTerms_PowerOfTwoVariables_1 () {
t("((a + b)^2) / c^2", "(a + b)^(2) / c^(2)");
}
@Test
public void SimplificationOfTerms_PowerOfTwoVariables_2 () {
t("((a + b) / (c + d))^2", "((a + b) / (c + d))^(2)");
}
/* Ordering of Powers */
@Test
public void SimplificationOfTerms_OrderingOfPowers_0 () {
t("(a^2 - 3 b) * (-3 a + 5 b^2)",
"(a^(2) - 3 * b) * (5 * b^(2) - 3 * a)");
}
@Test
public void SimplificationOfTerms_OrderingOfPowers_1 () {
t("f(x) := a * x^3 + b * x^2 + c * x + d", "a * x^(3) + b * x^(2) + c * x + d");
}
@Test
public void SimplificationOfTerms_OrderingOfPowers_2 () {
t("x^3 + c * x^2 + a*x + b","x^(3) + c * x^(2) + a * x + b");
}
@Test
public void SimplificationOfTerms_OrderingOfPowers_3 () {
t("x^2 + a * x","x^(2) + a * x");
}
/* Polynomial Division */
@Test
public void SimplificationOfTerms_PolynomialDivision_0 () {
t("x^2 / x", "x");
}
@Test
public void SimplificationOfTerms_PolynomialDivision_1 () {
t("(7x^3-14 x^2)/(6x-12)", "7 / 6 * x^(2)", "(7 / 6 * x^(2))");
}
@Test
public void SimplificationOfTerms_PolynomialDivision_2 () {
t("(x^2 - y^2) / (x - y)", "x + y");
}
/* Simplification of Equations */
/* Constants only */
@Test
public void SimplificationOfEquations_ConstantsOnly_0 () {
t("3 + 4 = 9 - 2", "7 = 7");
}
@Test
public void SimplificationOfEquations_ConstantsOnly_1 () {
t("3 + 4 = 10 - 2", "7 = 8");
}
@Test
public void SimplificationOfEquations_ConstantsOnly_2 () {
t("(39 / 9 = 4 + 1 / 3) 3", "13 = 13");
}
@Test
public void SimplificationOfEquations_ConstantsOnly_3 () {
t("(2 + 3 = 4 + 1 / 3) 3 ", "15 = 13");
}
/* One Variable */
@Test
public void SimplificationOfEquations_OneVariable_0 () {
t("x + x = 3 x - x", "2 * x = 2 * x");
}
@Test
public void SimplificationOfEquations_OneVariable_1 () {
t("x + x = 4 x - x", "2 * x = 3 * x");
}
@Test
public void SimplificationOfEquations_OneVariable_2 () {
t("(2 x + 3 = 4 + 1 / 3) 3", "6 * x + 9 = 13");
}
@Test
public void SimplificationOfEquations_OneVariable_3 () {
t("(3 - 5 / x = 7) x", "3 * x - 5 = 7 * x");
}
@Test
public void SimplificationOfEquations_OneVariable_4 () {
t("(3 - 5 / (x + 1) = 7) (x + 1)", "3 * x - 2 = 7 * x + 7");
}
/* Several Variables */
@Test
public void SimplificationOfEquations_SeveralVariables_0 () {
t("(a - 7 x)^2 = b - 56 x y + c",
"(a - 7 * x)^(2) = -56 * x * y + b + c");
}
@Test
public void SimplificationOfEquations_SeveralVariables_1 () {
t("(a x^2 + b x + c = 0) / a", "(a * x^(2) + b * x + c) / a = 0");
}
/* Parametrics */
/* Parametric Term */
@Test
public void Parametric_Term_0 () {
t("(3, 2) + t * (5, 1)", "(5 * t + 3, t + 2)");
}
@Test
public void Parametric_Term_1 () {
t("(3, 2) + t * (0, 0)", "(3, 2)");
}
@Test
public void Parametric_Term_2 () {
t("(0, 0) + t * (5, 1)", "(5 * t, t)");
}
@Test
public void Parametric_Term_3 () {
t("(3, sqrt(2)) + t * (sqrt(5), 1)", "(t * sqrt(5) + 3, t + sqrt(2))",
"(sqrt(5) * t + 3, t + sqrt(2))");
}
@Test
public void Parametric_Term_4 () {
t("Numeric[(3, sqrt(2)) + t * (sqrt(5), 1)]", "(2.2360679775 * t + 3, t + 1.414213562373)");
}
@Test
public void Parametric_Term_5 () {
tk("(3, sqrt(2)) + t * (sqrt(5), 1)", "(3, sqrt(2)) + t * (sqrt(5), 1)");
}
/* Parametric Function */
@Test
public void Parametric_Function_0 () {
t("f(t) := (3, 2) + t * (5, 1)", "(5 * t + 3, t + 2)");
}
@Test
public void Parametric_Function_1 () {
t("f(t) := (3, 2) + t * (0, 0)", "(3, 2)");
}
@Test
public void Parametric_Function_2 () {
t("f(t) := (0, 0) + t * (5, 1)", "(5 * t, t)");
}
@Test
public void Parametric_Function_3 () {
t("f(t) := (3, sqrt(2)) + t * (sqrt(5), 1)",
"(t * sqrt(5) + 3, t + sqrt(2))",
"(sqrt(5) * t + 3, t + sqrt(2))");
}
@Test
public void Parametric_Function_4 () {
t("f(t) := Numeric[(3, sqrt(2)) + t * (sqrt(5), 1), 10]", "(2.236067977 * t + 3, t + 1.414213562)");
}
@Test
public void Parametric_Function_5 () {
tk("f(t) := (3, sqrt(2)) + t * (sqrt(5), 1)", "(3, sqrt(2)) + t * (sqrt(5), 1)");
}
/* Parametric Equation Elaborate */
@Test
public void Parametric_EquationE_0 () {
t("(x, y) = (3, 2) + t * (5, 1)", "(x, y) = (5 * t + 3, t + 2)");
}
@Test
public void Parametric_EquationE_1 () {
t("(x, y) = (3, 2) + t * (0, 0)", "(x, y) = (3, 2)");
}
@Test
public void Parametric_EquationE_2 () {
t("(x, y) = (0, 0) + t * (5, 1)", "(x, y) = (5 * t, t)");
}
@Test
public void Parametric_EquationE_3 () {
t("(x, y) = (3, sqrt(2)) + t * (sqrt(5), 1)",
"(x, y) = (t * sqrt(5) + 3, t + sqrt(2))",
"(x, y) = (sqrt(5) * t + 3, t + sqrt(2))");
}
@Test
public void Parametric_EquationE_4 () {
t("Numeric[(x, y) = (3, sqrt(2)) + t * (sqrt(5), 1)]", "(x, y) = (2.2360679775 * t + 3, t + 1.414213562373)");
}
@Test
public void Parametric_EquationE_5 () {
tk("(x, y) = (3, sqrt(2)) + t * (sqrt(5), 1)", "(x, y) = (3, sqrt(2)) + t * (sqrt(5), 1)");
}
/* Parametric Equation Abbreviation */
@Test
public void Parametric_EquationA_0 () {
t("X = (3, 2) + t * (5, 1)", "X = (5 * t + 3, t + 2)");
}
@Test
public void Parametric_EquationA_1 () {
t("X = (3, 2) + t * (0, 0)", "X = (3, 2)");
}
@Test
public void Parametric_EquationA_2 () {
t("X = (0, 0) + t * (5, 1)", "X = (5 * t, t)");
}
@Test
public void Parametric_EquationA_3 () {
t("X = (3, sqrt(2)) + t * (sqrt(5), 1)",
"X = (t * sqrt(5) + 3, t + sqrt(2))",
"X = (sqrt(5) * t + 3, t + sqrt(2))");
}
@Test
public void Parametric_EquationA_4 () {
t("Numeric[X = (3, sqrt(2)) + t * (sqrt(5), 1)]", "X = (2.2360679775 * t + 3, t + 1.414213562373)");
}
@Test
public void Parametric_EquationA_5 () {
tk("X = (3, sqrt(2)) + t * (sqrt(5), 1)", "X = (3, sqrt(2)) + t * (sqrt(5), 1)");
}
/* Labeled Parametric Equation */
@Test
public void Parametric_EquationL_0 () {
t("f: (x, y) = (3, 2) + t * (5, 1)", "(x, y) = (5 * t + 3, t + 2)");
}
@Test
public void Parametric_EquationL_1 () {
t("f: X = (3, 2) + t * (5, 1)", "X = (5 * t + 3, t + 2)");
}
@Test
public void Parametric_EquationL_2 () {
t("f: (x, y) = (3, sqrt(2)) + t * (sqrt(5), 1)",
"(x, y) = (t * sqrt(5) + 3, t + sqrt(2))",
"(x, y) = (sqrt(5) * t + 3, t + sqrt(2))");
}
@Test
public void Parametric_EquationL_3 () {
t("f: X = (3, sqrt(2)) + t * (sqrt(5), 1)",
"X = (t * sqrt(5) + 3, t + sqrt(2))",
"X = (sqrt(5) * t + 3, t + sqrt(2))");
}
@Test
public void Parametric_EquationL_4 () {
t("f: Numeric[(x, y) = (3, sqrt(2)) + t * (sqrt(5), 1)]", "(x, y) = (2.2360679775 * t + 3, t + 1.414213562373)");
}
@Test
public void Parametric_EquationL_5 () {
t("f: Numeric[X = (3, sqrt(2)) + t * (sqrt(5), 1)]", "X = (2.2360679775 * t + 3, t + 1.414213562373)");
}
@Test
public void Parametric_EquationL_6 () {
tk("f: (x, y) = (3, sqrt(2)) + t * (sqrt(5), 1)", "(x, y) = (3, sqrt(2)) + t * (sqrt(5), 1)");
}
@Test
public void Parametric_EquationL_7 () {
tk("f: X = (3, sqrt(2)) + t * (sqrt(5), 1)", "X = (3, sqrt(2)) + t * (sqrt(5), 1)");
}
/* Parametric Term Multiple Parameters */
@Test
public void Parametric_TermM_0 () {
t("(3, 2) + t * (5, 1) + s * (-1, 7)",
"(-s + 5 * t + 3, 7 * s + t + 2)",
"(3, 2) + s * (-1, 7) + t * (5, 1)");
}
@Test
public void Parametric_TermM_1 () {
t("(3, 2) + t * (0, 0) + s * (-1, 7)", "(-s + 3, 7 * s + 2)",
"(3, 2) + s * (-1, 7)");
}
@Test
public void Parametric_TermM_2 () {
t("(3, 2) + t * (0, 0) + s * (0, 0)", "(3, 2)");
}
@Test
public void Parametric_TermM_3 () {
t("(0, 0) + t * (5, 1) + s * (-1, 7)", "(-s + 5 * t, 7 * s + t)",
"s * (-1, 7) + t * (5, 1)");
}
/* Parametric Function Multiple Parameters */
@Test
public void Parametric_FunctionM_0 () {
t("f(t, s) := (3, 2) + t * (5, 1) + s * (-1, 7)", "(-s + 5 * t + 3, 7 * s + t + 2)");
}
@Test
public void Parametric_FunctionM_1 () {
t("f(t, s) := (3, 2) + t * (0, 0) + s * (-1, 7)", "(-s + 3, 7 * s + 2)");
}
@Test
public void Parametric_FunctionM_2 () {
t("f(t, s) := (3, 2) + t * (0, 0) + s * (0, 0)", "(3, 2)");
}
@Test
public void Parametric_FunctionM_3 () {
t("f(t, s) := (0, 0) + t * (5, 1) + s * (-1, 7)", "(-s + 5 * t, 7 * s + t)");
}
/* Parametric Equation Elaborate Multiple Parameters */
@Test
public void Parametric_EquationEM_0 () {
t("(x, y) = (3, 2) + t * (5, 1) + s * (-1, 7)", "(x, y) = (-s + 5 * t + 3, 7 * s + t + 2)");
}
@Test
public void Parametric_EquationEM_1 () {
t("(x, y) = (3, 2) + t * (0, 0) + s * (-1, 7)", "(x, y) = (-s + 3, 7 * s + 2)");
}
@Test
public void Parametric_EquationEM_2 () {
t("(x, y) = (3, 2) + t * (0, 0) + s * (0, 0)", "(x, y) = (3, 2)");
}
@Test
public void Parametric_EquationEM_3 () {
t("(x, y) = (0, 0) + t * (5, 1) + s * (-1, 7)", "(x, y) = (-s + 5 * t, 7 * s + t)");
}
/* Parametric Equation Abbreviation Multiple Parameters */
@Test
public void Parametric_EquationAM_0 () {
t("X = (3, 2) + t * (5, 1) + s * (-1, 7)", "X = (-s + 5 * t + 3, 7 * s + t + 2)");
}
@Test
public void Parametric_EquationAM_1 () {
t("X = (3, 2) + t * (0, 0) + s * (-1, 7)", "X = (-s + 3, 7 * s + 2)");
}
@Test
public void Parametric_EquationAM_2 () {
t("X = (3, 2) + t * (0, 0) + s * (0, 0)", "X = (3, 2)");
}
@Test
public void Parametric_EquationAM_3 () {
t("X = (0, 0) + t * (5, 1) + s * (-1, 7)", "X = (-s + 5 * t, 7 * s + t)");
}
/* Labeled Parametric Equation Multiple Parameters */
@Test
public void Parametric_EquationLM_0 () {
t("f: (x, y) = (3, 2) + t * (5, 1) + s * (-1, 7)", "(x, y) = (-s + 5 * t + 3, 7 * s + t + 2)");
}
@Test
public void Parametric_EquationLM_1 () {
t("f: X = (3, 2) + t * (5, 1) + s * (-1, 7)", "X = (-s + 5 * t + 3, 7 * s + t + 2)");
}
@Test
public void Parametric_EquationLM_2 () {
t("f: (x, y) = (3, sqrt(2)) + t * (sqrt(5), 1) + s * (-1, sqrt(7))",
"(x, y) = (-s + t * sqrt(5) + 3, s * sqrt(7) + t + sqrt(2))",
"(x, y) = (-s + sqrt(5) * t + 3, sqrt(7) * s + t + sqrt(2))");
}
@Test
public void Parametric_EquationLM_3 () {
t("f: X = (3, sqrt(2)) + t * (sqrt(5), 1) + s * (-1, sqrt(7))",
"X = (-s + t * sqrt(5) + 3, s * sqrt(7) + t + sqrt(2))",
"X = (-s + sqrt(5) * t + 3, sqrt(7) * s + t + sqrt(2))");
}
@Test
public void Parametric_EquationLM_4 () {
t("f: Numeric[(x, y) = (3, sqrt(2)) + t * (sqrt(5), 1) + s * (-1, sqrt(7))]",
"(x, y) = (-s + 2.2360679775 * t + 3, 2.645751311065 * s + t + 1.414213562373)");
}
@Test
public void Parametric_EquationLM_5 () {
t("f: Numeric[X = (3, sqrt(2)) + t * (sqrt(5), 1) + s * (-1, sqrt(7))]",
"X = (-s + 2.2360679775 * t + 3, 2.645751311065 * s + t + 1.414213562373)");
}
@Test
public void Parametric_EquationLM_6 () {
tk("f: (x, y) = (3, sqrt(2)) + t * (sqrt(5), 1) + s * (-1, sqrt(7))", "(x, y) = (3, sqrt(2)) + t * (sqrt(5), 1) + s * (-1, sqrt(7))");
}
@Test
public void Parametric_EquationLM_7 () {
tk("f: X = (3, sqrt(2)) + t * (sqrt(5), 1) + s * (-1, sqrt(7))", "X = (3, sqrt(2)) + t * (sqrt(5), 1) + s * (-1, sqrt(7))");
}
/* Absolute Value */
/* Absolute Value of Constants */
@Test
public void AbsoluteValues_ConstantsOnly_0 () {
t("Abs(17)", "17");
}
@Test
public void AbsoluteValues_ConstantsOnly_1 () {
t("Abs(0)", "0");
}
@Test
public void AbsoluteValues_ConstantsOnly_2 () {
t("Abs(-5)", "5");
}
/* Absolute Value of Variables */
@Test
public void AbsoluteValues_Variables_0 () {
t("Abs(x)", "abs(x)");
}
@Test
public void AbsoluteValues_Variables_1 () {
t("Abs(-x)", "abs(x)");
}
/* Binomial Coefficient (alias Binomial) */
@Test
public void BinomialCoefficient_0 () {
t("BinomialCoefficient[4, 5]", "0");
}
@Test
public void BinomialCoefficient_1 () {
t("BinomialCoefficient[5, 3]", "10");
}
@Test
public void BinomialCoefficient_2 () {
t("BinomialCoefficient[n, 0]", "1");
}
@Test
public void BinomialCoefficient_3 () {
t("BinomialCoefficient[n, 1]", "n");
}
@Test
public void BinomialCoefficient_4 () {
t("BinomialCoefficient[n, 3]", "(n^(3) - 3 * n^(2) + 2 * n) / 6");
}
@Test
public void BinomialCoefficient_5 () {
t("BinomialCoefficient[n, n - 3]", "(n^(3) - 3 * n^(2) + 2 * n) / 6");
}
@Test
public void BinomialCoefficient_6 () {
t("BinomialCoefficient[n, n - 1]", "n");
}
@Test
public void BinomialCoefficient_7 () {
t("BinomialCoefficient[n, n]", "1");
}
@Test
public void BinomialCoefficient_8 () {
t("BinomialCoefficient[n, 3]", "(n^(3) - 3 * n^(2) + 2 * n) / 6");
}
@Test
public void BinomialCoefficient_9 () {
t("BinomialCoefficient[154, 53]", "766790648099833656282026107194109056868560");
}
/* BinomialDist */
/* Non-Cumulative */
@Test
public void BinomialDist_NonCumulative_0 () {
t("BinomialDist[3, 0.9, 0, false]", "1 / 1000");
}
@Test
public void BinomialDist_NonCumulative_1 () {
t("BinomialDist[3, 0.9, 1, false]", "27 / 1000");
}
@Test
public void BinomialDist_NonCumulative_2 () {
t("BinomialDist[3, 0.9, 2, false]", "243 / 1000");
}
@Test
public void BinomialDist_NonCumulative_3 () {
t("BinomialDist[3, 0.9, 3, false]", "729 / 1000");
}
@Test
public void BinomialDist_NonCumulative_4 () {
t("BinomialDist[3, 0.9, 4, false]", "0");
}
/* Cumulative */
@Test
public void BinomialDist_Cumulative_0 () {
t("BinomialDist[3, 0.9, 0, true]", "1 / 1000");
}
@Test
public void BinomialDist_Cumulative_1 () {
t("BinomialDist[3, 0.9, 1, true]", "7 / 250");
}
@Test
public void BinomialDist_Cumulative_2 () {
t("BinomialDist[3, 0.9, 2, true]", "271 / 1000");
}
@Test
public void BinomialDist_Cumulative_3 () {
t("BinomialDist[3, 0.9, 3, true]", "1");
}
@Test
public void BinomialDist_Cumulative_4 () {
t("BinomialDist[3, 0.9, 4, true]", "1");
}
/* Complex Numbers */
// # TODO Extend
@Test
public void ComplexNumbers () {
t("(5 + 3 \u03af) + Conjugate(5 + 3 \u03af)", "10");
}
/* Cauchy */
@Test
public void Cauchy_0 () {
t("Cauchy[1, 2, 3]", "3 / 4");
}
/* CFactor */
@Test
public void CFactor_0 () {
t("CFactor[x^2 + 4]", "(x + 2 * \u03af) * (x - 2 * \u03af)",
"(x - 2 * \u03af) * (x + 2 * \u03af)");
}
@Test
public void CFactor_1 () {
t("CFactor[a^2 + x^2, a]", "(a + \u03af * x) * (a - \u03af * x)",
"(a - x * \u03af) * (a + x * \u03af)",
"(\u03af * x + a) * (- \u03af * x + a)");
}
@Test
public void CFactor_2 () {
t("CFactor[a^2 + x^2, x]", "(x + \u03af * a) * (x - \u03af * a)",
"(x + a * \u03af) * (x - a * \u03af)");
}
/* ChiSquared */
/* Exact Evaluation */
@Test
public void ChiSquared_Exact_0 () {
t("ChiSquared[4, 3]", "gammaRegularized(2, 3 / 2)");
}
/* Numeric Evaluation */
@Test
public void ChiSquared_Numeric_0 () {
t("Numeric[ChiSquared[4, 3], 3]", "0.442");
}
/* Coefficients */
@Test
public void Coefficients_0 () {
t("Coefficients[x^3 - 3 x^2 + 3 x]", "{1, -3, 3, 0}");
}
@Test
public void Coefficients_1 () {
t("Coefficients[x^3 - 3 x^2 + 3 x, a]", "{x^(3) - 3 * x^(2) + 3 * x}");
}
@Test
public void Coefficients_2 () {
t("Coefficients[a^3 - 3 a^2 + 3 a, a]", "{1, -3, 3, 0}");
}
@Test
public void Coefficients_3 () {
t("Coefficients[a^3 - 3 a^2 + 3 a, x]", "{a^(3) - 3 * a^(2) + 3 * a}");
}
/* CompleteSquare */
@Test
public void CompleteSquare_0 () {
t("CompleteSquare[3 x^4 + x^2]", "3 * (x^(2) + 1 / 6)^(2) - 1 / 12");
}
@Test
public void CompleteSquare_1() {
t("CompleteSquare[x^4+x^2+1]", "(x^(2) + 1 / 2)^(2) + 3 / 4");
}
@Test
public void CompleteSquare_2() {
t("CompleteSquare[x^6+x^3]", "(x^(3) + 1 / 2)^(2) - 1 / 4");
}
@Test
public void CompleteSquare_3() {
t("CompleteSquare[x^6+x^3+1]", "(x^(3) + 1 / 2)^(2) + 3 / 4");
}
@Test
public void CompleteSquare_4() {
t("CompleteSquare[-9x^12-8x^6-9]", "-9 * (x^(6) + 4 / 9)^(2) - 65 / 9");
}
@Test
public void CompleteSquare_5() {
t("CompleteSquare[(-6 x^18 - 9x^9 + 2)]",
"-6 * (x^(9) + 3 / 4)^(2) + 43 / 8");
}
@Test
public void CompleteSquare_6() {
t("CompleteSquare[(-6 x^2 - 9x + 2)]", "-6 * (x + 3 / 4)^(2) + 43 / 8");
}
@Test
public void CompleteSquare_7() {
t("CompleteSquare[-10x^7+3]", "?");
}
@Test
public void CompleteSquare_8() {
t("CompleteSquare[((-9) * x^(10)) + 4]", "-9 * x^(10) + 4");
}
@Test
public void CompleteSquare_9() {
t("CompleteSquare[-3x^2+5x+8]", "-3 * (x - 5 / 6)^(2) + 121 / 12");
}
@Test
public void CompleteSquare_10() {
t("CompleteSquare[3x^2+5x+8]", "3 * (x + 5 / 6)^(2) + 71 / 12");
}
/* CommonDenomiator */
@Test
public void CommonDenomiator_0 () {
t("CommonDenominator[(5 x + 3 x) / 5 x, 2 / (5 x - 5)]", "5 * x - 5");
}
@Test
public void CommonDenomiator_1 () {
t("CommonDenominator[5 / 3, 1.35]", "60");
}
@Test
public void CommonDenomiator_2 () {
t("CommonDenominator[3 / (2 x + 1), 3 / (4 x^2 + 4 x + 1)]", "4 * x^(2) + 4 * x + 1");
}
/* Covariance */
@Test
public void Covariance_0 () {
t("Covariance[{1, 2, 3}, {1, 3, 7}]", "2");
}
@Test
public void Covariance_1 () {
t("Covariance[{(1, 1), (2, 3), (3, 7)}]", "2");
}
/* Cross */
@Test
public void Cross_0 () {
t("Cross[{1, 3, 2}, {0, 3, -2}]", "{-12, 2, 3}");
}
@Test
public void Cross_1() {
try {
t("Delete[f]", "true");
} catch (Throwable t) {
Log.warn(t.getMessage());
}
t("Cross[{a, b, c}, {d, e, f}]",
"{b * f - c * e, c * d - a * f, a * e - b * d}",
"{b * f - c * e, -a * f + c * d, a * e - b * d}");
}
@Test
public void Cross_2 () {
t("Cross[(a, b), (d, e)]", "a * e - b * d");
}
@Test
public void Cross_3 () {
t("(a, b, c)\u2297 (d, e, f)",
"(b * f - c * e, c * d - a * f, a * e - b * d)",
"(b * f - c * e, -a * f + c * d, a * e - b * d)");
}
@Test
public void Cross_4 () {
t("(1,2)\u2297 (3,4)", "-2");
}
/* CSolutions */
/* One Equation and one Variable */
@Test
public void CSolutions_OneVariable_0 () {
t("CSolutions[x^2 = -1]", "{\u03af, -\u03af}", "{-\u03af, \u03af}");
}
@Test
public void CSolutions_OneVariable_1 () {
t("CSolutions[x^2 + 1 = 0]", "{\u03af, -\u03af}", "{-\u03af, \u03af}");
}
@Test
public void CSolutions_OneVariable_2 () {
t("CSolutions[a^2 = -1, a]", "{\u03af, -\u03af}", "{-\u03af, \u03af}");
}
/* Several Equations and Variables */
@Test
public void CSolutions_Several_0 () {
t("CSolutions[{y^2 = x - 1, x = 2 * y - 1}, {x, y}]", "{{1 - 2 * \u03af, 1 - \u03af}, {1 + 2 * \u03af, 1 + \u03af}}",
"{{1 + 2 * \u03af, 1 + \u03af}, {1 - 2 * \u03af, 1 - \u03af}}");
}
/* CSolve */
/* One Equation and one Variable */
@Test
public void CSolve_OneVariable_0 () {
t("CSolve[x^2 = -1]", "{x = \u03af, x = -\u03af}",
"{x = -\u03af, x = \u03af}");
}
@Test
public void CSolve_OneVariable_1 () {
t("CSolve[x^2 + 1 = 0, x]", "{x = \u03af, x = -\u03af}",
"{x = -\u03af, x = \u03af}");
}
@Test
public void CSolve_OneVariable_2 () {
t("CSolve[a^2 = -1, a]", "{a = \u03af, a = -\u03af}",
"{a = -\u03af, a = \u03af}");
}
/* Several Equations and Variables */
@Test
public void CSolve_Several_0 () {
t("CSolve[{y^2 = x - 1, x = 2 * y - 1}, {x, y}]", "{{x = 1 - 2 * \u03af, y = 1 - \u03af}, {x = 1 + 2 * \u03af, y = 1 + \u03af}}",
"{{x = 1 + 2 * \u03af, y = 1 + \u03af}, {x = 1 - 2 *- \u03af, y = 1 - \u03af}}");
}
/* Degree */
@Test
public void Degree_0 () {
t("Degree[x^4 + 2 x^2]", "4");
}
@Test
public void Degree_1 () {
t("Degree[a x^4 + 2 x^2, x]", "4");
}
@Test
public void Degree_2 () {
t("Degree[a x^4 + 2 x^2, a]", "1");
}
@Test
public void Degree_3 () {
t("Degree[x^4 y^3 + 2 x^2 y^3, x]", "4");
}
@Test
public void Degree_4 () {
t("Degree[x^4 y^3 + 2 x^2 y^3, y]", "3");
}
@Test
public void Degree_Total () {
t("Degree[7 x^5 + x y + 3 y + 2 x ]", "5");
t("Degree[pi]", "0");
t("Degree[i]", "1");
t("Degree[e]", "1");
t("Degree[" + Unicode.IMAGINARY + "]", "0");
t("Degree[exp(1)]", "0");
}
/* Delete */
@Test
public void Delete_0 () {
t("a := 4", "4");
t("a", "4");
t("Delete[a]", "true");
t("a", "a");
}
/* Denominator */
@Test
public void Denominator_0 () {
t("Denominator[2 / 3 + 1 / 15]", "15");
}
@Test
public void Denominator_1 () {
t("Denominator[5 / (x^2 + 2)]", "x^(2) + 2");
}
/* Derivative */
@Test
public void Derivative_0 () {
t("Derivative[x^2]", "2 * x");
}
@Test
public void Derivative_1 () {
try {
executeInCAS("Delete[a]");
} catch (Throwable t) {
propagate(t);
}
t("Derivative[a x^3]", "3 * a * x^(2)", "3 * x^(2) * a");
}
@Test
public void Derivative_2 () {
t("Derivative[a x^3, a]", "x^(3)");
}
@Test
public void Derivative_3 () {
t("Derivative[a x^3, x, 2]", "6 * a * x", "6 * x * a");
}
/* Determinant */
@Test
public void Determinant_0 () {
t("Determinant[{{1, 2}, {3, 4}}]", "-2");
}
@Test
public void Determinant_1 () {
t("Determinant[{{1, a}, {b, 4}}]", "-a * b + 4");
}
/* Dimension */
@Test
public void Dimension_0 () {
t("Dimension[{1, 2, 0, -4, 3}]", "5");
}
@Test
public void Dimension_1 () {
t("Dimension[{{1, 2}, {0, -4}, {3, a}}]", "{3, 2}");
}
@Test
public void Dimension_2 () {
t("Dimension[{{a, b}, {c, d}, {e, f}}]", "{3, 2}");
}
/* Div */
@Test
public void Div_0 () {
t("Div[16, 3]", "5");
}
@Test
public void Div_1 () {
t("Div[x^2 + 3 x + 1, x - 1]", "x + 4");
}
/* Division */
@Test
public void Division_0 () {
t("Division[16, 3]", "{5, 1}");
}
@Test
public void Division_1 () {
t("Division[x^2 + 3 x + 1, x - 1]", "{x + 4, 5}");
}
/* Divisors */
@Test
public void Divisiors_0 () {
t("Divisors[15]", "4");
}
/* DivisorsList */
@Test
public void DivisorsList_0 () {
t("DivisorsList[15]", "{1, 3, 5, 15}");
}
/* DivisorsSum */
@Test
public void DivisorsSum_0 () {
t("DivisorsSum[15]", "24");
}
/* Dot */
@Test
public void Dot_0 () {
t("Dot[{1, 3, 2}, {0, 3, -2}]", "5");
}
@Test
public void Dot_1 () {
t("(1,2) * (a,b)", "a+2*b");
}
/* Element */
/* Singledimensional List */
@Test
public void Element_ListSD_0 () {
t("Element[{1, 3, 2}, 2]", "3");
}
@Test
public void Element_ListSD_1 () {
t("Element[{a, b, c}, 2]", "b");
}
/* Matrix */
@Test
public void Element_Matrix_0 () {
t("Element[{{1, 3, 2}, {0, 3, -2}}, 2, 3]", "-2");
}
@Test
public void Element_Matrix_1 () {
t("Element[{{a, b, c}, {d, e, f}}, 2, 3]", "f");
}
/*
* Note:
*
* Although Geogebra itself supports the element command for multidimensional lists, Geogebra CAS does not.
*/
/* Expand */
@Test
public void Expand_0 () {
t("Expand[((a + b) / c)^2]", "(a^(2) + 2 * a * b + b^(2)) / c^(2)");
}
@Test
public void Expand_1 () {
t("Expand[((a + b) / (c + d))^2]", "(a^(2) + 2 * a * b + b^(2)) / (c^(2) + 2 * c * d + d^(2))");
}
@Test
public void Expand_2 () {
t("Expand[Factor[a x^2 + b x^2]]", "a * x^(2) + b * x^(2)", "x^(2) * a + x^(2) * b");
}
@Test
public void Expand_4 () {
t("Expand[(x^6 + 6 x^5 + 30 x^4 + 120 x^3 + 360 x^2 + 720 x + 720) / 720]",
"1/ 720 * x^(6) + 1 / 120 * x^(5) + 1 / 24 * x^(4) + 1 / 6 *x^(3) + 1 / 2 * x^(2) + x + 1");
}
@Test
public void Expand_5 () {
t("Expand[(2 x - 1)^2 + 2 x + 3]", "4 * x^(2) - 2 * x + 4");
}
@Test
public void Expand_6 () {
t("Expand[(a + b)^2] / (a + b)", "a + b");
}
/* Exponential */
@Test
public void Exponential_0 () {
// TODO not sure if second is acceptable
t("Exponential[2, 1]", "1 - 1 / " + Unicode.EULER_STRING + "^(2)",
"(" + Unicode.EULER_STRING + "^(2) - 1) / "
+ Unicode.EULER_STRING + "^(2)");
}
/* FDistribution */
@Test
public void FDistribution_0 () {
t("Fdistribution[5, 7, 3]", "betaRegularized(5/2, 7/2, 15/22)");
}
@Test
public void FDistribution_1 () {
// Giac only supports 13dp
t("Numeric[Fdistribution[5, 7, 3], 14]", "0.9077534389794",
"0.90775343897945");
}
/* Factor */
/* Factor with Constants */
@Test
public void Factor_ConstantsOnly_0 () {
t("Factor[-15]", "-(3 * 5)");
}
@Test
public void Factor_ConstantsOnly_1 () {
t("Factor[15]", "3 * 5");
}
@Test
public void Factor_ConstantsOnly_2 () {
t("Factor[1024]", "2^(10)");
}
@Test
public void Factor_ConstantsOnly_3 () {
t("Factor[42]", "2 * 3 * 7");
}
/* Factor with Variables */
@Test
public void Factor_Variables_0 () {
t("Factor[x^2 + x - 6]", "(x - 2) * (x + 3)", "(x + 3) * (x - 2)");
}
@Test
public void Factor_Variables_1 () {
t("Factor[x^2 - y^2]", "(x - y) * (x + y)", "(x + y) * (x - y)");
}
@Test
public void Factor_Variables_2 () {
// t("Factor[9 a^2 - 3 a b]", "3 * (3 * a - b) * a");
// Giac
t("Factor[9 a^2 - 3 a b]", "-3 * a * (b - 3 * a)");
}
@Test
public void Factor_Variables_3 () {
t("Factor[9 a^2 - 3 a^2 b]", "-3 * a^(2) * (b - 3)",
"-3 * (b - 3) * a^(2)");
}
@Test
public void Factor_Variables_4 () {
// t("Factor[9 a^2 b^3 - 3 a b^2 c]", "3 * a * b^(2) * (3 * a * b - c) ", "3 * (3 * a * b - c) * a * b^(2)");
// Giac
t("Factor[9 a^2 b^3 - 3 a b^2 c]", "-3 * b^(2) * a * (c - 3 * b * a)");
}
@Test
public void Factor_Variables_5 () {
t("Factor[9x^2 - 25 y^2]", "(3 * x - 5 * y) * (3 * x + 5 * y)",
"(3 * x + 5 * y) * (3 * x - 5 * y)");
}
@Test
public void Factor_Variables_6 () {
// t("Factor[5 a x+5 b x-2 b y-2 a y]", "(a + b) * (5 * x - 2 * y)");
// Giac
t("Factor[5 a x+5 b x-2 b y-2 a y]", "(b + a) * (5 * x - 2 * y)",
"(-b - a) * (-5 * x + 2 * y)");
}
@Test
public void Factor_Variables_7 () {
t("Factor[36 r^2 + 24 r t + 4 t^2]", "4 * (3 * r + t)^(2)");
}
@Test
public void Factor_Variables_8 () {
t("Factor[15 + 3 b^2 - 10 a - 2 a b^2]", "(-b^(2) - 5) * (2 * a - 3)",
"(-2 * a + 3) * (b^(2) + 5)");
}
@Test
public void Factor_Variables_9 () {
t("Factor[((a + b) / (c + d))^2]", "(a + b)^(2) / (c + d)^(2)");
}
@Test
public void Factor_Variables_10 () {
t("Factor[(a^2 - 2 * a * b + b^2)^2]", "(a - b)^(4)");
}
@Test
public void Factor_Variables_11 () {
t("Factor[x^2 - y^2, x]", "(x - y) * (x + y)", "(x + y) * (x - y)");
}
@Test
public void Factor_Variables_12 () {
t("Factor[x^2 - y^2, y]", "-(y - x) * (y + x)", "(-x - y) * (-x + y)");
}
/* Factors */
/* Factors with Constants */
@Test
public void Factors_ConstantsOnly_0 () {
// t("Factors[-15]", "{{-3, 1}, {5, 1}}");
// Giac
t("Factors[-15]", "{{-1,1}, {3, 1}, {5, 1}}");
}
@Test
public void Factors_ConstantsOnly_1 () {
t("Factors[15]", "{{3, 1}, {5, 1}}");
}
@Test
public void Factors_ConstantsOnly_2 () {
t("Factors[1024]", "{{2, 10}}");
}
@Test
public void Factors_ConstantsOnly_3 () {
t("Factors[42]", "{{2, 1}, {3, 1}, {7, 1}}");
}
/* Factors of Polynomials */
@Test
public void Factors_Variables_0 () {
t("Factors[x^8 - 1]",
"{{x - 1, 1}, {x + 1, 1}, {x^(2) + 1, 1}, {x^(4) + 1, 1}}",
"{{x^(4) + 1, 1}, {x^(2) + 1, 1}, {x + 1, 1}, {x - 1, 1}}");
}
/* First */
/* Constants Only */
@Test
public void First_ConstantsOnly_0 () {
t("First[{1, 4, 3}]", "{1}");
}
@Test
public void First_ConstantsOnly_1 () {
t("First[{1, 4, 3}, 2]", "{1, 4}");
}
/* Variables */
@Test
public void First_Variables_0 () {
t("First[{a, b, c, d}]", "{a}");
}
@Test
public void First_Variables_1 () {
t("First[{a, b, c, d}, 2]", "{a, b}");
}
/* Fit Exp */
@Test
public void FitExp_0 () {
// Giac only supports 13dp
t("Numeric[FitExp[{(0, 1), (2, 4)}], 15]",
Unicode.EULER_STRING + "^(0.6931471805599 * x)",
Unicode.EULER_STRING + "^(0.693147180559945 * x)");
}
/* Fit Log */
@Test
public void FitLog_0 () {
t("FitLog[{(" + Unicode.EULER_STRING + ",1), (" + Unicode.EULER_STRING
+ "^2, 4)}]", "3 * log(x) - 2");
}
/* Fit Poly */
@Test
public void FitPoly_0 () {
t("FitPoly[{(-1, -1), (0, 1), (1, 1), (2, 5)}, 3]", "x^(3) - x^(2) + 1");
}
/* Fit Pow */
@Test
public void FitPow_0 () {
// Giac only supports 13dp
t("FitPow[{(1, 1), (3, 2), (7, 4)}]",
"0.9744885773743 * x^(0.708475312856)",
"0.974488577374291 * x^(0.7084753128560123)");
}
/* Fit Sin */
// TODO Check whether we can have this at all.
// @Test
// public void FitSin_0() {
// t("FitSin[{(1, 1), (2, 2), (3, 1), (4, 0), (5, 1), (6, 2)}]", "1 + sin((pi / 2) * x + pi / 2)");
// }
// TODO Abstract, as well?
/* FractionalPart */
@Test
public void FractionalPart_0 () {
t("FractionalPart[6/5]", "1 / 5");
}
@Test
public void FractionalPart_1 () {
t("FractionalPart[1/5 + 3/2 + 2]", "7 / 10");
}
@Test
public void FractionalPart_2 () {
t("FractionalPart[-14/5]", "(-4) / 5");
}
/* GCD */
/* Constants only */
@Test
public void GCD_ConstantsOnly_0 () {
t("GCD[12, 15]", "3");
}
@Test
public void GCD_ConstantsOnly_1 () {
t("GCD[{12, 30, 18}]", "6");
}
/* Variables */
@Test
public void GCD_Variables_0 () {
t("GCD[x^2 + 4 x + 4, x^2 - x - 6]", "x + 2");
}
@Test
public void GCD_Variables_1 () {
t("GCD[{x^2 + 4 * x + 4, x^2 - x - 6, x^3 - 4 * x^2 - 3 * x + 18}]", "x + 2");
}
/* HyperGeometric */
/* Non-Cumulative */
@Test
public void HyperGeometric_NonCumulative_0 () {
t("HyperGeometric[10, 2, 2, 0, false]", "28 / 45");
}
@Test
public void HyperGeometric_NonCumulative_1 () {
t("HyperGeometric[10, 2, 2, 1, false]", "16 / 45");
}
@Test
public void HyperGeometric_NonCumulative_2 () {
t("HyperGeometric[10, 2, 2, 2, false]", "1 / 45");
}
@Test
public void HyperGeometric_NonCumulative_3 () {
t("HyperGeometric[10, 2, 2, 3, false]", "0");
}
/* Cumulative */
@Test
public void HyperGeometric_Cumulative_0 () {
t("HyperGeometric[10, 2, 2, 0, true]", "28 / 45");
}
@Test
public void HyperGeometric_Cumulative_1 () {
t("HyperGeometric[10, 2, 2, 1, true]", "44 / 45");
}
@Test
public void HyperGeometric_Cumulative_2 () {
t("HyperGeometric[10, 2, 2, 2, true]", "1");
}
@Test
public void HyperGeometric_Cumulative_3 () {
t("HyperGeometric[10, 2, 2, 3, true]", "1");
}
/* Identity */
@Test
public void Identity_0 () {
t("Identity[3]", "{{1, 0, 0}, {0, 1, 0}, {0, 0, 1}}");
}
@Test
public void Identity_1 () {
t("dim := 3", "3");
t("Identity[dim]", "{{1, 0, 0}, {0, 1, 0}, {0, 0, 1}}");
t("Delete[dim]", "true");
t("dim := 4", "4");
t("Identity[dim]", "{{1, 0, 0, 0}, {0, 1, 0, 0}, {0, 0, 1, 0}, {0, 0, 0, 1}}");
t("Delete[dim]", "true");
}
@Test
public void Identity_2 () {
t("A := {{2, 17, -3}, {b, c, 0}, {f, 0, 1}}", "{{2, 17, -3}, {b, c, 0}, {f, 0, 1}}");
t("A^0", "{{1, 0, 0}, {0, 1, 0}, {0, 0, 1}}");
// Tidy up
try {
executeInCAS("Delete[A]");
} catch (Throwable t) {
propagate(t);
}
}
/* Imaginary */
@Test
public void Imaginary_0 () {
t("Imaginary[17 + 3 \u03af]", "3");
}
/* ImplicitDerivative */
@Test
public void ImplicitDerivative_0 () {
t("ImplicitDerivative[x + y + 5, y, x]", "-1");
}
@Test
public void ImplicitDerivative_1 () {
t("ImplicitDerivative[x^2 + y^2, y, x]", "(-x) / y");
}
/* Integral */
/* Indefinite Integral */
@Test
public void Integral_Indefinite_0 () {
s("Integral[cos(x)]", "sin(x) + c_INDEX");
}
@Test
public void Integral_Indefinite_1 () {
// s("Integral[cos(a * t), t]", "sin (a * t) / a + c_INDEX");
s("Integral[cos(a * t), t]", "sin (a * t) / a + c_INDEX");
}
@Test
public void Integral_Indefinite_2 () {
s("Integral[-x^3 + x^2]", "(-1) / 4 * x^(4) + 1 / 3 * x^(3) + c_INDEX");
}
/* Definite Integral */
@Test
public void Integral_Definite_0 () {
t("Integral[cos(x), x, a, b]", "-sin(a) + sin(b)");
}
@Test
public void Integral_Definite_1 () {
t("Integral[cos(t), t, a, b]", "-sin(a) + sin(b)");
}
/* IntegralBetween */
@Test
public void IntegralBetween_0 () {
t("IntegralBetween[sin(x), cos(x), pi / 4, pi * 5 / 4]", "sqrt(2) * 2",
"4 / sqrt(2)",
"2 * sqrt(2)");
}
@Test
public void IntegralBetween_1 () {
t("IntegralBetween[a * sin(t), a * cos(t), t, pi / 4, pi * 5 / 4]",
"2 * a * sqrt(2)", "2 * sqrt(2) * a");
}
@Test
public void Intersect () {
t("Intersect[m_1 x + b_1 , m_2 x +b_2 ]", "{((-b_1 + b_2) / (m_1 - m_2), (-b_1 * m_2 + b_2 * m_1) / (m_1 - m_2))}");
}
/* Invert */
/* Constants Only */
@Test
public void Invert_ConstantsOnly_0 () {
t("Invert[{{1, 2}, {3, 4}}]", "{{-2, 1}, {3 / 2, (-1) / 2}}");
}
/* Variables */
@Test
public void Invert_Variables_0 () {
t("Invert[{{a, b}, {c, d}}]", "{{d / (a * d - b * c), (-b) / (a * d - b * c)}, {(-c) / (a * d - b * c), a / (a * d - b * c)}}");
}
/* IsPrime */
@Test
public void IsPrime_0 () {
t("IsPrime[-11]", "false");
}
@Test
public void IsPrime_1 () {
t("IsPrime[-10]", "false");
}
@Test
public void IsPrime_2 () {
t("IsPrime[-2]", "false");
}
@Test
public void IsPrime_3 () {
t("IsPrime[-1]", "false");
}
@Test
public void IsPrime_4 () {
t("IsPrime[0]", "false");
}
@Test
public void IsPrime_5 () {
t("IsPrime[1]", "false");
}
@Test
public void IsPrime_6 () {
t("IsPrime[2]", "true");
}
@Test
public void IsPrime_7 () {
t("IsPrime[10]", "false");
}
@Test
public void IsPrime_8 () {
t("IsPrime[11]", "true");
}
/* Last */
/* Constants Only */
@Test
public void Last_ConstantsOnly_0 () {
t("Last[{1, 4, 3}]", "{3}");
}
@Test
public void Last_ConstantsOnly_1 () {
t("Last[{1, 4, 3}, 2]", "{4, 3}");
}
/* Variables */
@Test
public void Last_Variables_0 () {
t("Last[{a, b, c, d}]", "{d}");
}
@Test
public void Last_Variables_1 () {
t("Last[{a, b, c, d}, 2]", "{c, d}");
}
/* LeftSide */
@Test
public void LeftSide_0 () {
in("lsa:x+y+z=1");
t("LeftSide[lsa]", "x + y + z");
t("RightSide[lsa]", "1");
in("lsb:xx+yy+zz=1");
t("LeftSide[lsb]", "x^(2) + y^(2) + z^(2)");
t("RightSide[lsb]", "1");
in("lsc:x+y+0z=1");
t("LeftSide[lsc]", "x + y");
t("RightSide[lsc]", "1");
in("lsd:x+y=1");
t("LeftSide[lsd]", "x + y");
t("RightSide[lsd]", "1");
}
private static void in(String string) {
app.getKernel().getAlgebraProcessor()
.processAlgebraCommand(string, false);
}
@Test
public void LeftSide_1 () {
t("LeftSide[x + 2 = 3x + 1]", "x + 2");
t("LeftSide[{a^2 + b^2 = c^2, x + 2 = 3 x + 1}]",
"{a^(2) + b^(2), x + 2}");
}
@Test
public void LeftSide_2 () {
t("LeftSide[{a^2 + b^2 = c^2, x + 2 = 3 x + 1}, 1]", "a^(2) + b^(2)");
}
/* Length */
@Test
public void Length_0 () {
t("Length[2 x, 0, 1]", "sqrt(5)");
}
@Test
public void Length_1 () {
t("Length[2 a, a, 0, 1]", "sqrt(5)");
}
/* Limits */
/* Limit */
@Test
public void Limits_Limit_0 () {
t("Limit[a sin(x)/x, 0]", "a");
}
@Test
public void Limits_Limit_1 () {
t("Limit[a sin(v)/v, v, 0]", "a");
}
@Test
public void Limits_Limit_2 () {
t("Limit[3^n, Infinity]", "Infinity");
}
@Test
public void Limits_Limit_3 () {
t("Limit[pi^n, Infinity]", "Infinity");
}
@Test
public void Limits_Limit_4 () {
t("Limit[pi^n / sqrt(2), Infinity]", "Infinity");
}
@Test
public void Limits_Limit_5 () {
t("Limit[pi^n * sqrt(2), Infinity]", "Infinity");
}
@Test
public void Limits_Limit_6 () {
t("Limit[sqrt(2) * pi^n / exp(1), Infinity]", "Infinity");
}
@Test
public void Limits_Limit_7 () {
t("Limit[3^n, -Infinity]", "0");
}
@Test
public void Limits_Limit_8 () {
t("Limit[pi^n, -Infinity]", "0");
}
@Test
public void Limits_Limit_9 () {
t("Limit[pi^n / sqrt(2), -Infinity]", "0");
}
@Test
public void Limits_Limit_10 () {
t("Limit[pi^n * sqrt(2), -Infinity]", "0");
}
@Test
public void Limits_Limit_11 () {
t("Limit[sqrt(2) * pi^n / exp(1), -Infinity]", "0");
}
@Test
public void Limits_Limit_12 () {
t("Limit[1 - 0.4^n,n, Infinity]", "1");
}
/* LimitAbove */
@Test
public void Limits_LimitAbove_0 () {
t("LimitAbove[1 / x, 0]", "Infinity");
}
@Test
public void Limits_LimitAbove_1 () {
t("LimitAbove[1 / a, a, 0]", "Infinity");
}
/* LimitBelow */
@Test
public void Limits_LimitBelow_0 () {
t("LimitBelow[1 / x, 0]", "-Infinity");
}
@Test
public void Limits_LimitBelow_1 () {
t("LimitBelow[1 / a, a, 0]", "-Infinity");
}
/* MatrixRank */
@Test
public void MatrixRank_0 () {
t("MatrixRank[{{0, 0}, {0, 0}}]", "0");
}
@Test
public void MatrixRank_1 () {
t("MatrixRank[{{2, 2}, {1, 1}}]", "1");
}
@Test
public void MatrixRank_2 () {
t("MatrixRank[{{1, 2}, {3, 4}}]", "2");
}
/* Max */
@Test
public void Max_0 () {
t("Max[12, 15]", "15");
}
@Test
public void Max_1 () {
t("Max[{-2, 12, -23, 17, 15}]", "17");
}
/* Mean */
@Test
public void Mean_0 () {
t("Mean[{1, 2, 3, 5, 44}]", "11");
}
@Test
public void Mean_1 () {
t("Mean[{1, 8}]", "9 / 2");
}
/* Median */
@Test
public void Median_0 () {
t("Median[{1, 2, 3}]", "2");
}
@Test
public void Median_1 () {
// t("Median[{1, 1, 8, 8}]", "9 / 2");
// Giac
t("Median[{1, 1, 8, 8}]", "4.5");
}
/* Min */
@Test
public void Min_0 () {
t("Min[12, 15]", "12");
}
@Test
public void Min_1 () {
t("Min[{-2, 12, -23, 17, 15}]", "-23");
}
/* MixedNumber */
@Test
public void MixedNumber_0 () {
t("MixedNumber[-3.5]", "-3 + (-1) / 2");
}
@Test
public void MixedNumber_1 () {
t("MixedNumber[3.5]", "3 + 1 / 2");
}
@Test
public void MixedNumber_2 () {
t("MixedNumber[12 / 3]", "4");
}
@Test
public void MixedNumber_3 () {
t("MixedNumber[12 / 14]", "0 + 6 / 7");
}
/* Mod */
@Test
public void Mod_0 () {
t("Mod[9, 4]", "1");
}
@Test
public void Mod_1 () {
t("Mod[x^3 + x^2 + x + 6, x^2 - 3]", "4 * x + 9");
}
/* NIntegral */
@Test
public void NIntegral_0 () {
// Giac only supports 13dp
t("NIntegral[" + Unicode.EULER_STRING + "^(-x^2), 0, 1]",
"0.7468241328124");
}
@Test
public void NIntegral_1 () {
// Giac only supports 13dp
t("NIntegral[" + Unicode.EULER_STRING + "^(-a^2), a, 0, 1]",
"0.7468241328124");
}
/* NRoot */
@Test
public void NRoot_0 () {
t("NRoot[16, 4]", "2");
}
@Test
public void NRoot_1 () {
t("NRoot[x^8, 2]", "x^(4)");
}
/* NextPrime */
@Test
public void NextPrime_0 () {
t("NextPrime[-10]", "2");
}
@Test
public void NextPrime_1 () {
t("NextPrime[10000]", "10007");
}
/* Normal */
@Test
public void Normal_0 () {
t("Normal[2, 0.5, 1]", "(erf(-sqrt(2)) + 1) / 2",
"(-erf(2 / sqrt(2)) + 1) / 2");
}
@Test
public void Normal_1 () {
t("NSolve[Normal[0, 1, eps]-Normal[0, 1, -eps]=0.5]", "{eps = 0.6744897501961}");
}
/* Numerator */
@Test
public void Numerator_0 () {
t("Numerator[(3x"+Unicode.Superscript_2+" + 1) / (2x - 1)]", "3 * x^(2) + 1");
}
@Test
public void Numerator_1 () {
t("Numerator[2/3 + 1/15]", "11");
}
/* Numeric Evaluation */
/* Constants only */
@Test
public void NumericEvaluation_ConstantsOnly_0 () {
t("Numeric[3 / 2]", "1.5");
}
@Test
public void NumericEvaluation_ConstantsOnly_1 () {
t("Numeric[((15 + 9) * 3.5 - 2 * 0.5) / 4]", "20.75");
}
@Test
public void NumericEvaluation_ConstantsOnly_2 () {
t("Numeric[pi,15]", "3.14159265358979");
}
@Test
public void NumericEvaluation_ConstantsOnly_3 () {
t("Numeric[sin(1), 20 ]", "0.84147098480789650665");
}
@Test
public void NumericEvaluation_ConstantsOnly_4 () {
t("a := Numeric[sin(1), 20 ]", "0.84147098480789650665");
}
/* One Variable */
@Test
public void NumericEvaluation_OneVariable_0 () {
t("Numeric[x + x / 2]", "1.5 * x");
}
@Test
public void NumericEvaluation_OneVariable_1 () {
t("Numeric[x + 0.2 x]", "1.2 * x");
}
@Test
public void NumericEvaluation_OneVariable_2 () {
t("f(x) := Numeric[x + 0.2 x + 1 / 3, 10]", "1.2 * x + 0.3333333333");
}
/* Two Variables */
@Test
public void NumericEvaluation_TwoVariables_0 () {
t("Numeric[6 a * 3 b - (5 a b + b * 2a) / 2]", "14.5 * a * b");
}
@Test
public void NumericEvaluation_NumericEvaluation_TwoVariables_1 () {
t("Numeric[0.2 * (a^2 - 3 b) * (-3 a + 5 b^2)]",
"-0.6 * a^(3) + 1 * a^(2) * b^(2) + 1.8 * a * b - 3 * b^(3)",
"a^(2) * b^(2) - 0.6 * a^(3) - 3 * b^(3) + 1.8 * a * b",
"-0.6 * a^(3) + a^(2) * b^(2) + 1.8 * a * b - 3 * b^(3)");
}
/* Precision */
@Test
public void NumericEvaluation_Precision_0 () {
t("Numeric[10 + 22/7, 6]", "13.1429");
}
@Test
public void NumericEvaluation_Precision_1 () {
t("Numeric[2 a - a/3, 2]", "1.7 * a");
}
@Test
public void NumericEvaluation_Precision_2 () {
t("Numeric[2 a - a/3, 3]", "1.67 * a");
}
/* PartialFractions */
@Test
public void PartialFractions_0 () {
t("PartialFractions[x^2 / (x^2 - 2x + 1)]", "1 + 1 / (x - 1)^(2) + 2 / (x - 1)");
}
@Test
public void PartialFractions_1 () {
t("PartialFractions[a^2 / (a^2 - 2a + 1), a]", "1 + 1 / (a - 1)^(2) + 2 / (a - 1)");
}
/* PerpendicularVector */
@Test
public void PerpendicularVector_0 () {
t("PerpendicularVector[(3, 2)]", "(-2, 3)");
}
@Test
public void PerpendicularVector_1 () {
try {
executeInCAS("Delete[a]");
executeInCAS("Delete[b]");
} catch (Throwable t) {
propagate(t);
}
t("PerpendicularVector[(a, b)]", "(-b, a)");
}
/* PreviousPrime */
@Test
public void PreviousPrime_0 () {
t("PreviousPrime[-10]", "?");
}
@Test
public void PreviousPrime_1 () {
t("PreviousPrime[-1]", "?");
}
@Test
public void PreviousPrime_2 () {
t("PreviousPrime[0]", "?");
}
@Test
public void PreviousPrime_3 () {
t("PreviousPrime[1]", "?");
}
@Test
public void PreviousPrime_4 () {
t("PreviousPrime[2]", "?");
}
@Test
public void PreviousPrime_5 () {
t("PreviousPrime[3]", "2");
}
@Test
public void PreviousPrime_6 () {
t("PreviousPrime[10]", "7");
}
@Test
public void PreviousPrime_7 () {
t("PreviousPrime[10000]", "9973");
}
/* Product */
@Test
public void Product_0 () {
t("Product[{1, 2, x}]", "2 * x");
}
@Test
public void Product_1 () {
t("Product[x + 1, x, 2, 3]", "12");
}
/* Root */
@Test
public void Root_0 () {
t("Root[x^3 - 3 * x^2 - 4 * x + 12]", "{x = -2, x = 2, x = 3}");
}
/* RandomBinomial */
@Test
public void RandomBinomial_0 () {
r("RandomBinomial[3, 0.1]", "[0123]", "Any one of {0, 1, 2, 3}.");
}
/* RandomElement */
@Test
public void RandomElement_0 () {
r("RandomElement[{3, 2, -4, 7}]", "([237]|-4)", "Any one of {-4, 2, 3, 7}.");
}
/* RandomNormal */
@Test
public void RandomNormal_0 () {
// TODO Currently extremely weak test.
s("RandomNormal[3, 0.1]", "\\d+\\.\\d+");
}
/* RandomPoisson */
@Test
public void RandomPoisson_0 () {
// TODO Currently weak test.
s("RandomPoisson[3]", "\\d+");
}
/* RandomPolynomial */
@Test
public void RandomPolynomial_0 () {
/* Beware: This test is random based. */
for (int i = 0; i < 100; i++) {
s("RandomPolynomial[0, 1, 2]", "[12]");
}
}
@Test
public void RandomPolynomial_1 () {
/* Beware: This test is random based. */
for (int i = 0; i < 100; i++) {
r("RandomPolynomial[2, 1, 2]", "(2\\s\\*\\s)?x\\^\\(2\\)\\s\\+\\s(2\\s\\*\\s)?x\\s\\+\\s[12]",
" A polynomial in x of degree 2 with all coefficients from {1, 2}.");
}
}
@Test
public void RandomPolynomial_2 () {
/* Beware: This test is random based. */
for (int i = 0; i < 100; i++) {
s("RandomPolynomial[a, 0, 1, 2]", "[12]");
}
}
@Test
public void RandomPolynomial_3 () {
/* Beware: This test is random based. */
for (int i = 0; i < 100; i++) {
r("RandomPolynomial[a, 2, 1, 2]", "(2\\s\\*\\s)?a\\^\\(2\\)\\s\\+\\s(2\\s\\*\\s)?a\\s\\+\\s[12]",
" A polynomial in a of degree 2 with all coefficients from {1, 2}.");
}
}
/* Rationalize */
@Test
public void Rationalize_0 () {
t("Rationalize[-3.5]", "(-7) / 2");
}
@Test
public void Rationalize_1 () {
t("Rationalize[0]", "0");
}
@Test
public void Rationalize_2 () {
t("Rationalize[1]", "1");
}
@Test
public void Rationalize_3 () {
t("Rationalize[3.5]", "7 / 2");
}
/* Real */
@Test
public void Real_0 () {
t("Real[17 + 3 \u03af]", "17");
}
/* ReducedRowEchelonForm */
@Test
public void ReducedRowEchelonForm_0 () {
t("ReducedRowEchelonForm[{{0, 0}, {0, 0}}]", "{{0, 0}, {0, 0}}");
}
@Test
public void ReducedRowEchelonForm_1 () {
t("ReducedRowEchelonForm[{{2, 2}, {1, 1}}]", "{{1, 1}, {0, 0}}");
}
@Test
public void ReducedRowEchelonForm_2 () {
t("ReducedRowEchelonForm[{{1, 2}, {3, 4}}]", "{{1, 0}, {0, 1}}");
}
@Test
public void ReducedRowEchelonForm_3 () {
t("ReducedRowEchelonForm[{{1, 6, 4}, {2, 8, 9}, {4, 5, 6}}]", "{{1, 0, 0}, {0, 1, 0}, {0, 0, 1}}");
}
/* RightSide */
@Test
public void RightSide_0 () {
t("RightSide[x + 2 = 3x + 1]", "3 * x + 1");
}
@Test
public void RightSide_1 () {
t("RightSide[{a^2 + b^2 = c^2, x + 2 = 3x + 1}]", "{c^(2), 3 * x + 1}");
}
/* Rounding */
/* Round */
@Test
public void Rounding_Round_0 () {
t("Round(-5.5)", "-5");
}
@Test
public void Rounding_Round_1 () {
t("Round(-5.4)", "-5");
}
@Test
public void Rounding_Round_2 () {
t("Round(-4.5)", "-4");
}
@Test
public void Rounding_Round_3 () {
t("Round(-4.4)", "-4");
}
@Test
public void Rounding_Round_4 () {
t("Round(4.4)", "4");
}
@Test
public void Rounding_Round_5 () {
t("Round(4.5)", "5");
}
@Test
public void Rounding_Round_6 () {
t("Round(5.4)", "5");
}
@Test
public void Rounding_Round_7 () {
t("Round(5.5)", "6");
}
/* Floor */
@Test
public void Rounding_Floor_0 () {
t("Floor(-5.5)", "-6");
}
@Test
public void Rounding_Floor_1 () {
t("Floor(-5.4)", "-6");
}
@Test
public void Rounding_Floor_2 () {
t("Floor(-4.5)", "-5");
}
@Test
public void Rounding_Floor_3 () {
t("Floor(-4.4)", "-5");
}
@Test
public void Rounding_Floor_4 () {
t("Floor(4.4)", "4");
}
@Test
public void Rounding_Floor_5 () {
t("Floor(4.5)", "4");
}
@Test
public void Rounding_Floor_6 () {
t("Floor(5.4)", "5");
}
@Test
public void Rounding_Floor_7 () {
t("Floor(5.5)", "5");
}
/* Ceil */
@Test
public void Rounding_Ceil_0 () {
t("Ceil(-5.5)", "-5");
}
@Test
public void Rounding_Ceil_1 () {
t("Ceil(-5.4)", "-5");
}
@Test
public void Rounding_Ceil_2 () {
t("Ceil(-4.5) ", "-4");
}
@Test
public void Rounding_Ceil_3 () {
t("Ceil(-4.4)", "-4");
}
@Test
public void Rounding_Ceil_4 () {
t("Ceil(4.4)", "5");
}
@Test
public void Rounding_Ceil_5 () {
t("Ceil(4.5)", "5");
}
@Test
public void Rounding_Ceil_6 () {
t("Ceil(5.4)", "6");
}
@Test
public void Rounding_Ceil_7 () {
t("Ceil(5.5)", "6");
}
/* SD */
@Test
public void SD_0 () {
t("SD[{1, 2, 3, 4, 5}]", "sqrt(2)");
}
/* Sample */
@Test
public void Sample_0 () {
/* Beware: This test is random based. */
for (int i = 0; i < 100; i++) {
s("Sample[{1, 2, 3, 4, 5}, 5]", "{[12345], [12345], [12345], [12345], [12345]}");
}
}
@Test
public void Sample_1 () {
/* Beware: This test is random based. */
for (int i = 0; i < 100; i++) {
r("Sample[{-5, 2, a, 7, c}, 3]", "\\{(([ac27]|-5),\\s){2}([ac27]|-5)\\}",
"A list containing three elements out of {a, c, -5, 2, 7}, where elements may be contained several times.");
}
}
@Test
public void Sample_2 () {
/* Beware: This test is random based. */
for (int i = 0; i < 100; i++) {
r("Sample[{1, 2, 3, 4, 5}, 5, true]", "\\{([1-5],\\s){4}[1-5]\\}",
"A list containing five elements out of {1, 2, 3, 4, 5}, where elements may be contained several times.");
}
}
@Test
public void Sample_3 () {
/* Beware: This test is random based. */
// TODO Check for multiple elements.
for (int i = 0; i < 100; i++) {
r("Sample[{{1, 2, 3}, 4, 5, 6, 7, 8}, 3, false]", "\\{(([4-8]|\\{1,\\s2,\\s3\\}),\\s){2}([4-8]|\\{1,\\s2,\\s3\\})\\}",
"A list containing three elements out of {{1, 2, 3}, 4, 5, 6, 7, 8}, where each element may be contained only once.");
}
}
/* SampleSD */
@Test
public void SampleSD_0 () {
// TODO Result unchecked.
t("SampleSD[{1, 2, 3}]", "1");
}
@Test
public void SampleSD_1 () {
// TODO Result unchecked.
t("SampleSD[{1, 2, a}]", "sqrt(a^(2) - 3 * a + 3) / sqrt(3)");
}
/* SampleVariance */
@Test
public void SampleVariance_0 () {
// TODO Result unchecked.
t("SampleVariance[{x, y, z}]",
"1 / 3 * x^(2) - 1 / 3 * x * y - 1 / 3 * x * z + 1 / 3 * y^(2) - 1 / 3 * y * z + 1 / 3 * z^(2)",
"(x^(2) - x * y - x * z + y^(2) - y * z + z^(2)) / 3");
}
/* Sequence */
@Test
public void Sequence_0 () {
t("Sequence[5]", "{1, 2, 3, 4, 5}");
}
@Test
public void Sequence_1 () {
t("Sequence[x^i, i, 1, 10]", "{x, x^(2), x^(3), x^(4), x^(5), x^(6), x^(7), x^(8), x^(9), x^(10)}");
}
@Test
public void Sequence_2 () {
t("Sequence[x^i, i, 1, 10, 2]", "{x, x^(3), x^(5), x^(7), x^(9)}");
}
/* Shuffle */
@Test
public void Shuffle_0 () {
/* Beware: This test is random based. */
// TODO Check for missing / multiple elements.
r("Shuffle[{3, 5, 1, 7, 3}]", "\\{([1357],\\s){4}[1357]\\}", "An arbitrary permutation of the list {1, 3, 3, 5, 7}.");
}
/* Simplify */
@Test
public void Simplify_0 () {
t("Simplify[3 * x + 4 * x + a * x]", "a * x + 7 * x", "x * a + 7 * x");
}
/* Solutions */
// TODO Extend.
@Test
public void Solutions_0 () {
t("Solutions[x^2 = 4 * x]", "{0, 4}");
}
@Test
public void Solutions_1 () {
t("Solutions[x * a^2 = 4 * a, a]", "{4 / x, 0}", "{0, 4 / x}");
}
@Test
public void Solutions_2 () {
t("Solutions[{x = 4 * x + y , y + x = 2}, {x, y}]", "{{-1, 3}}");
}
@Test
public void Solutions_3 () {
t("Solutions[{2 * a^2 + 5 * a + 3 = b, a + b = 3}, {a, b}]",
"{{0, 3}, {-3, 6}}", "{{-3, 6}, {0, 3}}");
}
/* Solve */
/* Constants only */
@Test
public void Solve_ConstantsOnly_0 () {
s("Solve[1 = 1]", "{x = x}");
}
@Test
public void Solve_ConstantsOnly_1 () {
t("Solve[1 = 2]", "{}");
}
@Test
public void Solve_ConstantsOnly_2 () {
s("Solve[1 = 1, x]", "{x = x}");
}
@Test
public void Solve_ConstantsOnly_3 () {
t("Solve[1 = 2, x]", "{}");
}
@Test
public void Solve_ConstantsOnly_4 () {
s("Solve[{1 = 1, 2 = 2}, {x, y}]", "{{x = x, y = y}}");
}
@Test
public void Solve_ConstantsOnly_5 () {
t("Solve[{1 = 2, 2 = 3}, {x, y}]", "{}");
}
/* One Variable */
@Test
public void Solve_OneVariable_0 () {
t("Solve[x = 1]", "{x = 1}");
t("Solve[x^5 = -1]", "{x = -1}");
}
@Test
public void Solve_OneVariable_1 () {
t("Solve[x = 1, x]", "{x = 1}");
}
@Test
public void Solve_OneVariable_2 () {
t("Solve[2 x + 3 = 4 + 1 / 3, x]", "{x = 2 / 3}");
}
@Test
public void Solve_OneVariable_3 () {
t("Solve[3 - 5 / x = 7, x]", "{x = (-5) / 4}");
t("Solve[{sin(x)=1,x>0,x<pi}]", "{x = 1 / 2 * " + Unicode.PI_STRING
+ "}");
}
@Test
public void Solve_OneVariable_4 () {
t("Solve[(x + 7) / 3 - (4 - x) / 4 - 3 = 3 x / 8, x]", "{x = 8}");
}
@Test
public void Solve_OneVariable_5 () {
t("Solve[x^2 - 5 x + 6 = 0, x]", "{x = 2, x = 3}");
}
@Test
public void Solve_OneVariable_6 () {
t("Solve[x^2 - 4 = 0, x]", "{x = -2, x = 2}");
}
@Test
public void Solve_OneVariable_7 () {
t("Solve[x^2 - 4 x - 1 = 0, x]", "{x = -sqrt(5) + 2, x = sqrt(5) + 2}");
}
@Test
public void Solve_OneVariable_8 () {
t("Solve[x^2 - 4 x + 4 = 0, x]", "{x = 2}");
}
@Test
public void Solve_OneVariable_9 () {
t("Solve[x^2 + 1 = 0, x]", "{}");
}
/* One Variable, variable Coefficients */
@Test
public void Solve_OneVariableVC_0 () {
t("Solve[a x^2 + b x + c, x]", "{x = (sqrt(-4 * a * c + b^(2)) - b) / (2 * a), x = (-sqrt(-4 * a * c + b^(2)) - b) / (2 * a)}");
}
@Test
public void Solve_OneVariableVC_1 () {
t("Solve[1 / p - (a - k^2) / a = k^2 / (p a), a]", "{a = k^(2)}");
}
@Test
public void Solve_OneVariableVC_2 () {
t("Solve[1 / p - (a - k^2) / a = k^2 / (p a), k]", "{k = sqrt(a), k = -sqrt(a)}");
}
@Test
public void Solve_OneVariableVC_3 () {
t("Solve[1 / p - (a - k^2) / a = k^2 / (p a), p]", "{p = 1}");
}
@Test
public void Solve_OneVariableVC_4 () {
t("Solve[-(10 c + 3) / (2 (4 c^2 - 9)) = -1 / (2 (2 c - 3)), c]", "{c = 0}");
}
@Test
public void Solve_OneVariableVC_5 () {
t("Solve[a = b^c, a]", "{a = b^(c)}");
}
@Test
public void Solve_OneVariableVC_6 () {
t("Solve[a = b^c, b]", "{b = a^(1 / c)}");
}
@Test
public void Solve_OneVariableVC_7 () {
t("Solve[a = b^c, c]", "{c = log(a) / log(b)}");
}
@Test
public void Solve_OneVariableVC_8 () {
// in Giac, {} is correct
t("Solve[0 = b^c, b]", "{}");
}
@Test
public void Solve_OneVariableVC_9 () {
t("Solve[-1 = b^c, b]", "{}");
}
@Test
public void Solve_OneVariableVC_10 () {
t("Solve[0.5 N0 = N0 exp(-0.3 t), t]", "{t = 10 / 3 * log(2)}", "{t = (10 * log(2)) / 3}");
}
@Test
public void Solve_OneVariableVC_11 () {
t("Solve[x^2 = a]", "{x = sqrt(a), x = -sqrt(a)}",
"{x = -sqrt(a), x = sqrt(a)}");
}
@Test
public void Solve_OneVariableVC_12 () {
t("Solve[x^2 - 2 a x + (a^2 - 1)]", "{x = a - 1, x = a + 1}", "{x = a + 1, x = a - 1}");
}
/* Trigonometric Problems */
@Test
public void Solve_Trig_0 () {
// "{x = (4 * k_INDEX * pi - pi) / 4}"
s("Solve[3 * tan(x) + 3 = 0]", "{x = k_INDEX * " + Unicode.PI_STRING
+ " - 1 / 4 * " + Unicode.PI_STRING + "}");
s("Solve[e^(-x/4)*(sin(x)+4*cos(x))]", "{x = k_INDEX * "
+ Unicode.PI_STRING + " - arctan(4)}");
}
@Test
public void Solve_Trig_1 () {
// s("Solve[2*cos(x)^2+sqrt(2)*cos(x)-2,x]","{x = (8 * k_INDEX * pi + pi) / 4, x = (8 * k_INDEX * pi - pi) / 4}");
s("Solve[2 * cos(x)^2 + sqrt(2) * cos(x) - 2, x]", "{x = 2 * k_INDEX * " + Unicode.PI_STRING + " - 1 / 4 * " + Unicode.PI_STRING + ", x = 2 * k_INDEX * " + Unicode.PI_STRING + " + 1 / 4 * " + Unicode.PI_STRING + "}");
}
/* Several Equations and Variables */
@Test
public void Solve_Several_0 () {
t("Solve[{x = 4 x + y , y + x = 2}, {x, y}]", "{{x = -1, y = 3}}");
}
@Test
public void Solve_Several_1 () {
t("Solve[{2a^2 + 5a + 3 = b, a + b = 3}, {a, b}]",
"{{a = 0, b = 3}, {a = -3, b = 6}}",
"{{a = -3, b = 6}, {a = 0, b = 3}}");
}
@Test
public void Solve_Several_2 () {
t("Solve[{2a^2 + 5a + 3 = b, a + b = 3, a = b}, {a, b}]", "{}");
}
@Test
public void Solve_Several_3 () {
t("Solve[13 = 3 + 5 t + 10 s, {t, s}]", "{{t = - 2 * s + 2, s = s}}");
}
@Test
public void Solve_Several_4 () {
t("Solve[{13 = 3 + 5 t + 10 s}, {t, s}]", "{{t = - 2 * s + 2, s = s}}");
}
@Test
public void Solve_Several_5 () {
t("Solve[{a + b = 0, c = 0}]", "{{a = -b, b = b}}");
}
@Test
public void Solve_Several_6 () {
t("Solve[{a + b = 0, c = 0}, {a, b}]", "{{a = -b, b = b}}");
}
@Test
public void Solve_Several_7 () {
t("Solve[{a + b = 0, c = 0}, {a, c}]", "{{a = -b, c = 0}}");
}
@Test
public void Solve_Several_8 () {
t("Solve[{a + b = 0, c = 0}, {c, b}]", "{{c = 0, b = -a}}");
}
@Test
public void Solve_Several_9 () {
t("Solve[{a + b = 0, c = 0}, {a, b, c}]", "{{a = -b, b = b, c = 0}}");
}
@Test
public void Solve_Several_10 () {
t("Solve[{a + b = 0, b = b, c = 0}]", "{{a = -b, b = b, c = 0}}");
}
@Test
public void Solve_Several_11 () {
t("Solve[{a + b = 0, b = b, c = 0}, {a, b, c}]", "{{a = -b, b = b, c = 0}}");
}
@Test
public void Solve_Several_12 () {
t("Solve[{c = 0, a + b = 0, b = b}]", "{{a = -b, b = b, c = 0}}");
}
@Test
public void Solve_Several_13 () {
t("Solve[a + b = 0]", "{a = -b}");
}
@Test
public void Solve_Several_14 () {
t("Solve[{a + b = 0}]", "{a = -b}");
}
@Test
public void Solve_Several_15 () {
t("Solve[{a + b = 0}, {a, b}]", "{{a = -b, b = b}}");
}
// solves wrt {a,b}
@Test
public void Solve_Several_16 () {
t("Solve[{c = 0, a + b = 0}]", "{{a = -b, b = b}}");
}
@Test
public void Solve_Several_17 () {
t("Solve[{a + b = 0, c^2 - 1 = 0}]", "{{a = -b, b = b}}");
}
@Test
public void Solve_Several_18 () {
t("Solve[{c^2 - 1 = 0, a + b = 0}]", "{{a = -b, b = b}}");
}
@Test
public void Solve_Several_19 () {
t("Solve[{c^2 - 1 = 0, a + b = 0}, c]", "{c = -1, c = 1}");
}
@Test
public void Solve_Several_20 () {
t("Solve[{c^2 - 1 = 0, a + b = 0}, {c}]", "{c = -1, c = 1}");
}
@Test
public void Solve_Several_21 () {
t("Solve[{c^2 - 1 = 0, a + b = 0}, {c, b}]", "{{c = 1, b = -a}, {c = -1, b = -a}}");
}
@Test
public void Solve_Several_22 () {
t("Solve[8 = 3 + 5 t^2 + 10 s, {t, s}]", "{{t = t, s = (-1) / 2 * t^(2) + 1 / 2}}");
}
@Test
public void Solve_Several_23 () {
t("Solve[{x = 3 + 5 t, y = 2 + t, x = 8 + 10 s, y = 3 + 2 s}, {x, y, t, s}]", "{{x = 10 * s + 8, y = 2 * s + 3, t = 2 * s + 1, s = s}}");
}
@Test
public void Solve_Poly_Deg5 () {
t("Solve[(22a^5+135a^3)/125=1.75*1784/125,a]", "{a = 2.31205450048}",
"{a = 2.312054500480007}");
}
/* Parametric Equations One Parameter */
@Test
public void Solve_ParametricEOP_0 () {
t("Solve[(3, 2) = (3, 2) + t * (5, 1), t]", "{t = 0}");
t("Solve[(3t+5,2t-3)=(20,7),t]", "{t = 5}");
}
@Test
public void Solve_ParametricEOP_1 () {
t("Solve[(3, 2) = (3, 2) + t * (5, 1)]", "{t = 0}");
}
@Test
public void Solve_ParametricEOP_2 () {
t("Solve[(3, 2) + t * (5, 1) = (3, 2)]", "{t = 0}");
}
@Test
public void Solve_ParametricEOP_3 () {
t("Solve[(-2, 1) = (3, 2) + t * (5, 1)]", "{t = -1}");
}
@Test
public void Solve_ParametricEOP_4 () {
t("Solve[(5.5, 2.5) = (3, 2) + t * (5, 1)]", "{t = 1 / 2}");
}
@Test
public void Solve_ParametricEOP_5 () {
t("Numeric[Solve[(5.5, 2.5) = (3, 2) + t * (5, 1)]]", "{t = 0.5}");
}
@Test
public void Solve_ParametricEOP_6 () {
// Please note that the language is German. "L\u00f6se" is "Solve" in
// German.
tk("Solve[(5.5, 2.5) = (3, 2) + t * (5, 1)]", GermanSolve + "[(5.5, 2.5) = (3, 2) + t * (5, 1)]");
}
/* Parametric Function One Parameter */
@Test
public void Solve_ParametricFOP_0 () {
t("f(t) := (3, 2) + t * (5, 1)", "(5 * t + 3, t + 2)");
t("Solve[f(t) = (8, 3)]", "{t = 1}");
}
@Test
public void Solve_ParametricFOP_1 () {
t("f(t) := (3, 2) + t * (5, 1)", "(5 * t + 3, t + 2)");
t("Solve[(8, 3) = f(t)]", "{t = 1}");
}
@Test
public void Solve_ParametricFOP_2 () {
t("f(t) := (3, 2) + t * (5, 1)", "(5 * t + 3, t + 2)");
t("Solve[f(t) = (5.5, 2.5)]", "{t = 1 / 2}");
}
@Test
public void Solve_ParametricFOP_3 () {
t("f(t) := (3, 2) + t * (5, 1)", "(5 * t + 3, t + 2)");
t("Numeric[Solve[f(t) = (5.5, 2.5)]]", "{t = 0.5}");
}
@Test
public void Solve_ParametricFOP_4 () {
t("f(t) := (3, 2) + t * (5, 1)", "(5 * t + 3, t + 2)");
// Please note that the language is German. "L\u00f6se" is "Solve" in
// German.
tk("Solve[f(t) = (5.5, 2.5)]", GermanSolve + "[f(t) = (5.5, 2.5)]");
}
/* Parametric Equation Multiple Parameters */
@Test
public void Solve_ParametricEMP_0 () {
t("Solve[(3, 2) = (3, 2) + t * (5, 1) + s * (-1, 7), {s, t}]", "{{s = 0, t = 0}}");
}
@Test
public void Solve_ParametricEMP_1 () {
t("Solve[(-3, 8) = (3, 2) + t * (5, 1) + s * (-1, 7), {s, t}]", "{{s = 1, t = -1}}");
}
@Test
public void Solve_ParametricEMP_2 () {
t("Solve[(-3, 8) = (3, 2) + t * (5, 1) + s * (-1, 7), {t, s}]", "{{t = -1, s = 1}}");
t("Solve[{X=(t,t),X=(2s-1,3s+3)}]", "{{s = -4, t = -9}}");
}
@Test
public void Solve_ParametricEMP_3 () {
t("Solve[(13, 4) = (3, 2) + t * (5, 1) + s * (10, 2), {s, t}]", "{{s = (-1) / 2 * t + 1, t = t}}");
}
@Test
public void Solve_ParametricEMP_4 () {
t("Solve[(13, 4) = (3, 2) + t * (5, 1) + s * (10, 2), {t, s}]", "{{t = -2 * s + 2, s = s}}");
}
@Test
public void Solve_ParametricEMP_5 () {
t("Solve[(13, 4) = (3, 2) + t * (5, 1) + s * (10, 2), s]", "{s = (-1) / 2 * t + 1}");
}
@Test
public void Solve_ParametricEMP_6 () {
t("Solve[(13, 4) = (3, 2) + t * (5, 1) + s * (10, 2), t]", "{t = -2 * s + 2}");
}
@Test
public void Solve_ParametricEMP_7 () {
t("Solve[(13, 5) = (3, 2) + t * (5, 1) + s * (10, 2), {s, t}]", "{}");
}
/* Parametric Function Multiple Parameters */
@Test
public void Solve_ParametricFMP_0 () {
t("f(t, s) := (3, 2) + t * (5, 1) + s * (-1, 7)", "(-s + 5 * t + 3, 7 * s + t + 2)");
t("Solve[f(t, s) = (3, 2), {s, t}]", "{{s = 0, t = 0}}");
}
@Test
public void Solve_ParametricFMP_1 () {
t("f(t, s) := (3, 2) + t * (5, 1) + s * (-1, 7)", "(-s + 5 * t + 3, 7 * s + t + 2)");
t("Solve[f(t, s) = (-3, 8), {s, t}]", "{{s = 1, t = -1}}");
}
@Test
public void Solve_ParametricFMP_2 () {
t("f(t, s) := (3, 2) + t * (5, 1) + s * (-1, 7)", "(-s + 5 * t + 3, 7 * s + t + 2)");
t("Solve[f(t, s) = (-3, 8), {t, s}]", "{{t = -1, s = 1}}");
}
@Test
public void Solve_ParametricFMP_3 () {
t("f(t, s) := (3, 2) + t * (5, 1) + s * (-1, 7)", "(-s + 5 * t + 3, 7 * s + t + 2)");
t("Solve[f(s, t) = (-3, 8), {s, t}]", "{{s = -1, t = 1}}");
}
@Test
public void Solve_ParametricFMP_4 () {
t("f(t, s) := (3, 2) + t * (5, 1) + s * (10, 2)", "(10 * s + 5 * t + 3, 2 * s + t + 2)");
t("Solve[f(t, s) = (13, 4), {s, t}]", "{{s = (-1) / 2 * t + 1, t = t}}");
}
@Test
public void Solve_ParametricFMP_5 () {
t("f(t, s) := (3, 2) + t * (5, 1) + s * (10, 2)", "(10 * s + 5 * t + 3, 2 * s + t + 2)");
t("Solve[f(t, s) = (13, 4), {t, s}]", "{{t = -2 * s + 2, s = s}}",
"{{t = 2 - 2 * s, s = s}}");
}
@Test
public void Solve_ParametricFMP_6 () {
t("f(t, s) := (3, 2) + t * (5, 1) + s * (10, 2)", "(10 * s + 5 * t + 3, 2 * s + t + 2)");
t("Solve[f(t, s) = (13, 4), s]", "{s = (-1) / 2 * t + 1}");
}
@Test
public void Solve_ParametricFMP_7 () {
t("f(t, s) := (3, 2) + t * (5, 1) + s * (10, 2)", "(10 * s + 5 * t + 3, 2 * s + t + 2)");
t("Solve[f(t, s) = (13, 4), t]", "{t = -2 * s + 2}", "{t = 2 - 2 * s}");
}
@Test
public void Solve_ParametricFMP_8 () {
t("f(t, s) := (3, 2) + t * (5, 1) + s * (10, 2)", "(10 * s + 5 * t + 3, 2 * s + t + 2)");
t("Solve[f(t, s) = (13, 5), {s, t}]", "{}");
}
@Test
public void Solve_ParametricFMP_9 () {
t("f(t, s) := (3, 2) + t * (5, 1) + s * (-1, 7)", "(-s + 5 * t + 3, 7 * s + t + 2)");
t("Solve[f(t, s) = (7, -8), {t, s}]", "{{t = 1 / 2, s = (-3) / 2}}");
}
@Test
public void Solve_ParametricFMP_10 () {
t("f(t, s) := (3, 2) + t * (5, 1) + s * (-1, 7)", "(-s + 5 * t + 3, 7 * s + t + 2)");
t("Numeric[Solve[f(t, s) = (7, -8), {t, s}]]", "{{t = 0.5, s = -1.5}}");
}
@Test
public void Solve_ParametricFMP_11 () {
t("f(t, s) := (3, 2) + t * (5, 1) + s * (-1, 7)", "(-s + 5 * t + 3, 7 * s + t + 2)");
// Please note that the language is German. "L\u00f6se" is "Solve" in
// German.
tk("Solve[f(t, s) = (7, -8), {t, s}]", GermanSolve + "[f(t, s) = (7, -8), {t, s}]");
}
/* Parametric Equations Twosided */
@Test
public void Solve_ParametricET_0 () {
t("Solve[(3, 2) + t (5, 1) = (4, 1) + s (1, -1), {t, s}]", "{{t = 0, s = -1}}");
}
@Test
public void Solve_ParametricET_1 () {
t("Solve[(3, 2) + t (5, 1) = (8, 3) + s (10, 2), {t, s}]", "{{t = 2 * s + 1, s = s}}");
}
@Test
public void Solve_ParametricET_2 () {
t("Solve[(3, 2) + t (5, 1) = (4, 1) + s (10, 2), {t, s}]", "{}");
}
@Test
public void Solve_ParametricET_3 () {
t("Solve[(3, 2) + t (5, 1) = (4, 1) + s (2, -2), {t, s}]", "{{t = 0, s = (-1) / 2}}");
}
@Test
public void Solve_ParametricET_4 () {
t("Numeric[Solve[(3, 2) + t (5, 1) = (4, 1) + s (2, -2), {t, s}]]", "{{t = 0, s = -0.5}}");
}
@Test
public void Solve_ParametricET_5 () {
// Please note that the language is German. "L\u00f6se" is "Solve" in
// German.
tk("Solve[(3, 2) + t (5, 1) = (4, 1) + s (2, -2), {t, s}]", GermanSolve + "[(3, 2) + t * (5, 1) = (4, 1) + s * (2, -2), {t, s}]");
}
/* Multiple Parametric Equations Eloquent */
@Test
public void Solve_ParametricMEE_0 () {
t("Solve[{(x, y) = (3, 2) + t (5, 1), (x, y) = (4, 1) + s (1, -1)}, {x, y, t, s}]", "{{x = 3, y = 2, t = 0, s = -1}}");
}
@Test
public void Solve_ParametricMEE_1 () {
t("Solve[{(x, y) = (3, 2) + t (5, 1), (x, y) = (8, 3) + s (10, 2)}, {x, y, t, s}]", "{{x = 10 * s + 8, y = 2 * s + 3, t = 2 * s + 1, s = s}}");
}
@Test
public void Solve_ParametricMEE_2 () {
t("Solve[{(x, y) = (3, 2) + t (5, 1), (x, y) = (4, 1) + s (10, 2)}, {x, y, t, s}]", "{}");
}
@Test
public void Solve_ParametricMEE_3 () {
t("Solve[{(x, y) = (3, 2) + t (5, 1), (x, y) = (4, 1) + s (2, -2)}, {x, y, t, s}]", "{{x = 3, y = 2, t = 0, s = (-1) / 2}}");
}
@Test
public void Solve_ParametricMEE_4 () {
t("Numeric[Solve[{(x, y) = (3, 2) + t (5, 1), (x, y) = (4, 1) + s (2, -2)}, {x, y, t, s}]]", "{{x = 3, y = 2, t = 0, s = -0.5}}");
}
@Test
public void Solve_ParametricMEE_5 () {
// Please note that the language is German. "L\u00f6se" is "Solve" in
// German.
tk("Solve[{(x, y) = (3, 2) + t (5, 1), (x, y) = (4, 1) + s (2, -2)}, {x, y, t, s}]",
GermanSolve + "[{(x, y) = (3, 2) + t * (5, 1), (x, y) = (4, 1) + s * (2, -2)}, {x, y, t, s}]");
}
/* Multiple Parametric Equations Abbreviation */
@Test
public void Solve_ParametricMEA_0 () {
t("Solve[{X = (3, 2) + t (5, 1), X = (4, 1) + s (1, -1)}, {t, s}]", "{{t = 0, s = -1}}");
}
@Test
public void Solve_ParametricMEA_1 () {
t("Solve[{X = (3, 2) + t (5, 1), X = (8, 3) + s (10, 2)}, {t, s}]", "{{t = 2 * s + 1, s = s}}");
}
@Test
public void Solve_ParametricMEA_2 () {
t("Solve[{X = (3, 2) + t (5, 1), X = (4, 1) + s (10, 2)}, {t, s}]", "{}");
}
@Test
public void Solve_ParametricMEA_3 () {
t("Solve[{X = (3, 2) + t (5, 1), X = (4, 1) + s (2, -2)}, {t, s}]",
"{{t = 0, s = (-1) / 2}}", "{{t = 0, s = -1 / 2}}");
}
@Test
public void Solve_ParametricMEA_4 () {
t("Numeric[Solve[{X = (3, 2) + t (5, 1), X = (4, 1) + s (2, -2)}, {t, s}]]", "{{t = 0, s = -0.5}}");
}
@Test
public void Solve_ParametricMEA_5 () {
// Please note that the language is German. "L\u00f6se" is "Solve" in
// German.
tk("Solve[{X = (3, 2) + t (5, 1), X = (4, 1) + s (2, -2)}, {t, s}]", GermanSolve + "[{X = (3, 2) + t * (5, 1), X = (4, 1) + s * (2, -2)}, {t, s}]");
}
/* Multiple Parametric Equations Labeled */
@Test
public void Solve_ParametricMEL_0 () {
t("f: (x, y) = (3, 2) + t (5, 1)", "(x, y) = (5 * t + 3, t + 2)");
t("g: (x, y) = (4, 1) + s (2, -2)", "(x, y) = (2 * s + 4, -2 * s + 1)");
t("Solve[{f, g}, {t, s, x, y}]", "{{t = 0, s = (-1) / 2, x = 3, y = 2}}");
}
@Test
public void Solve_ParametricMEL_1 () {
t("f: X = (3, 2) + t (5, 1)", "X = (5 * t + 3, t + 2)");
t("g: X = (4, 1) + s (2, -2)", "X = (2 * s + 4, -2 * s + 1)");
t("Solve[{f, g}, {t, s}]", "{{t = 0, s = (-1) / 2}}");
}
@Test
public void Solve_ParametricMEL_2 () {
t("f: (x, y) = (3, 2) + t (5, 1)", "(x, y) = (5 * t + 3, t + 2)");
t("g: (x, y) = (4, 1) + s (2, -2)", "(x, y) = (2 * s + 4, -2 * s + 1)");
t("Numeric[Solve[{f, g}, {t, s, x, y}]]", "{{t = 0, s = -0.5, x = 3, y = 2}}");
}
@Test
public void Solve_ParametricMEL_3 () {
t("f: X = (3, 2) + t (5, 1)", "X = (5 * t + 3, t + 2)");
t("g: X = (4, 1) + s (2, -2)", "X = (2 * s + 4, -2 * s + 1)");
t("Numeric[Solve[{f, g}, {t, s}]]", "{{t = 0, s = -0.5}}");
}
@Test
public void Solve_ParametricMEL_4 () {
t("f: (x, y) = (3, 2) + t (5, 1)", "(x, y) = (5 * t + 3, t + 2)");
t("g: (x, y) = (4, 1) + s (2, -2)", "(x, y) = (2 * s + 4, -2 * s + 1)");
// Please note that the language is German. "L\u00f6se" is "Solve" in
// German.
tk("Solve[{f, g}, {t, s, x, y}]", GermanSolve + "[{f, g}, {t, s, x, y}]");
}
@Test
public void Solve_ParametricMEL_5 () {
t("f: X = (3, 2) + t (5, 1)", "X = (5 * t + 3, t + 2)");
t("g: X = (4, 1) + s (2, -2)", "X = (2 * s + 4, -2 * s + 1)");
// Please note that the language is German. "L\u00f6se" is "Solve" in
// German.
tk("Solve[{f, g}, {t, s}]", GermanSolve + "[{f, g}, {t, s}]");
}
/* Multiple Parametric Functions */
@Test
public void Solve_ParametricMF_0 () {
t("f(t) := (3, 2) + t (5, 1)", "(5 * t + 3, t + 2)");
t("g(s) := (4, 1) + s (1, -1)", "(s + 4, -s + 1)");
t("Solve[f(u) = g(v), {u, v}]", "{{u = 0, v = -1}}");
}
@Test
public void Solve_ParametricMF_1 () {
t("f(t) := (3, 2) + t (5, 1)", "(5 * t + 3, t + 2)");
t("g(s) := (8, 3) + s (10, 2)", "(10 * s + 8, 2 * s + 3)");
t("Solve[f(u) = g(v), {u, v}]", "{{u = 2 * v + 1, v = v}}");
}
@Test
public void Solve_ParametricMF_2 () {
t("f(t) := (3, 2) + t (5, 1)", "(5 * t + 3, t + 2)");
t("g(s) := (8, 3) + s (10, 2)", "(10 * s + 8, 2 * s + 3)");
t("Solve[f(u) = g(v), {t, s}]", "{}");
}
@Test
public void Solve_ParametricMF_3 () {
t("f(t) := (3, 2) + t (5, 1)", "(5 * t + 3, t + 2)");
t("g(s) := (4, 1) + s (2, -2)", "(2 * s + 4, -2 * s + 1)");
t("Solve[f(u) = g(v), {u, v}]", "{{u = 0, v = (-1) / 2}}");
}
@Test
public void Solve_ParametricMF_4 () {
t("f(t) := (3, 2) + t (5, 1)", "(5 * t + 3, t + 2)");
t("g(s) := (4, 1) + s (2, -2)", "(2 * s + 4, -2 * s + 1)");
t("Numeric[Solve[f(u) = g(v), {u, v}]]", "{{u = 0, v = -0.5}}");
}
@Test
public void Solve_ParametricMF_5 () {
t("f(t) := (3, 2) + t (5, 1)", "(5 * t + 3, t + 2)");
t("g(s) := (4, 1) + s (2, -2)", "(2 * s + 4, -2 * s + 1)");
// Please note that the language is German. "L\u00f6se" is "Solve" in
// German.
tk("Solve[f(u) = g(v), {u, v}]", GermanSolve + "[f(u) = g(v), {u, v}]");
}
@Test
public void Solve_ParametricMF_6 () {
t("f(t) := (1, 2) + t * (2, 8)", "(2 * t + 1, 8 * t + 2)");
t("g(t) := (1, 1) + t * (2, 1)", "(2 * t + 1, t + 1)");
t("Solve[f(t) = g(s), {t, s}]", "{{t = (-1) / 7, s = (-1) / 7}}");
}
/* Parametrics Three Dimensions */
@Test
public void Solve_ParametricTD_0 () {
t("Solve[(2, 3, -1) = (3, 1, 2) + t (-2, 4, -6), t]", "{t = 1 / 2}");
}
@Test
public void Solve_ParametricTD_1 () {
t("Numeric[Solve[(2, 3, -1) = (3, 1, 2) + t (-2, 4, -6), t]]", "{t = 0.5}");
}
@Test
public void Solve_ParametricTD_2 () {
// Please note that the language is German. "L\u00f6se" is "Solve" in
// German.
tk("Solve[(2, 3, -1) = (3, 1, 2) + t (-2, 4, -6), t]", GermanSolve + "[(2, 3, -1) = (3, 1, 2) + t * (-2, 4, -6), t]");
}
@Test
public void Solve_ParametricTD_3 () {
t("f(t) := (3, 1, 2) + t (-2, 4, -6)",
"(3 - 2 * t, 1 + 4 * t, 2 - 6 * t)",
"(-2 * t + 3, 4 * t + 1, -6 * t + 2)");
t("Solve[f(t) = (2, 3, -1), t]", "{t = 1 / 2}");
}
@Test
public void Solve_ParametricTD_4 () {
t("f(t) := (3, 1, 2) + t (-2, 4, -6)",
"(3 - 2 * t, 1 + 4 * t, 2 - 6 * t)",
"(-2 * t + 3, 4 * t + 1, -6 * t + 2)");
t("Numeric[Solve[f(t) = (2, 3, -1), t]]", "{t = 0.5}");
}
@Test
public void Solve_ParametricTD_5 () {
t("f(t) := (3, 1, 2) + t (-2, 4, -6)",
"(3 - 2 * t, 1 + 4 * t, 2 - 6 * t)",
"(-2 * t + 3, 4 * t + 1, -6 * t + 2)");
// Please note that the language is German. "L\u00f6se" is "Solve" in
// German.
tk("Solve[f(t) = (2, 3, -1), t]", GermanSolve + "[f(t) = (2, 3, -1), t]");
}
@Test
public void Solve_ParametricTD_6 () {
t("Solve[{(x, y, z) = (3, 1, 2) + t (-2, 4, -6), (x, y, z) = (3, 7, -4) + s (1, 4, -3)}, {x, y, z, t, s}]",
"{{x = 2, y = 3, z = -1, t = 1 / 2, s = -1}}");
}
@Test
public void Solve_ParametricTD_7 () {
t("Numeric[Solve[{(x, y, z) = (3, 1, 2) + t (-2, 4, -6), (x, y, z) = (3, 7, -4) + s (1, 4, -3)}, {x, y, z, t, s}]]",
"{{x = 2, y = 3, z = -1, t = 0.5, s = -1}}");
}
@Test
public void Solve_ParametricTD_8 () {
// Please note that the language is German. "L\u00f6se" is "Solve" in
// German.
tk("Solve[{(x, y, z) = (3, 1, 2) + t (-2, 4, -6), (x, y, z) = (3, 7, -4) + s (1, 4, -3)}, {x, y, z, t, s}]",
GermanSolve + "[{(x, y, z) = (3, 1, 2) + t * (-2, 4, -6), (x, y, z) = (3, 7, -4) + s * (1, 4, -3)}, {x, y, z, t, s}]");
}
@Test
public void Solve_ParametricTD_9 () {
t("Solve[{X = (3, 1, 2) + t (-2, 4, -6), X = (3, 7, -4) + s (1, 4, -3)}, {t, s}]", "{{t = 1 / 2, s = -1}}");
}
@Test
public void Solve_ParametricTD_10 () {
t("Numeric[Solve[{X = (3, 1, 2) + t (-2, 4, -6), X = (3, 7, -4) + s (1, 4, -3)}, {t, s}]]", "{{t = 0.5, s = -1}}");
}
@Test
public void Solve_ParametricTD_11 () {
// Please note that the language is German. "L\u00f6se" is "Solve" in
// German.
tk("Solve[{X = (3, 1, 2) + t (-2, 4, -6), X = (3, 7, -4) + s (1, 4, -3)}, {t, s}]",
GermanSolve + "[{X = (3, 1, 2) + t * (-2, 4, -6), X = (3, 7, -4) + s * (1, 4, -3)}, {t, s}]");
}
@Test
public void Solve_ParametricTD_12 () {
t("f(t) := (3, 1, 2) + t (-2, 4, -6)",
// "(-2 * t + 3, 4 * t + 1, -6 * t + 2)",
"(3 - 2 * t, 1 + 4 * t, 2 - 6 * t)");
t("g(t) := (3, 7, -4) + t (1, 4, -3)", "(t + 3, 4 * t + 7, -3 * t - 4)");
t("Solve[f(u) = g(v), {u, v}]", "{{u = 1 / 2, v = -1}}");
}
@Test
public void Solve_ParametricTD_13 () {
t("f(t) := (3, 1, 2) + t (-2, 4, -6)",
"(3 - 2 * t, 1 + 4 * t, 2 - 6 * t)",
"(-2 * t + 3, 4 * t + 1, -6 * t + 2)");
t("g(t) := (3, 7, -4) + t (1, 4, -3)", "(t + 3, 4 * t + 7, -3 * t - 4)");
t("Numeric[Solve[f(u) = g(v), {u, v}]]", "{{u = 0.5, v = -1}}");
}
@Test
public void Solve_ParametricTD_14 () {
t("f(t) := (3, 1, 2) + t (-2, 4, -6)",
"(3 - 2 * t, 1 + 4 * t, 2 - 6 * t)",
"(-2 * t + 3, 4 * t + 1, -6 * t + 2)");
t("g(t) := (3, 7, -4) + t (1, 4, -3)", "(t + 3, 4 * t + 7, -3 * t - 4)");
// Please note that the language is German. "L\u00f6se" is "Solve" in
// German.
tk("Solve[f(u) = g(v), {u, v}]", GermanSolve + "[f(u) = g(v), {u, v}]");
}
@Test
public void Solve_ParametricTD_15 () {
t("f(t, s) := (3, 1, 2) + t (-2, 4, -6) + s *(1, 0, 0)",
"(3 - 2 * t + s, 1 + 4 * t, 2 - 6 * t)",
"(s - 2 * t + 3, 4 * t + 1, -6 * t + 2)");
t("g(t) := (4, 7, -4) + t (1, 4, -3)", "(t + 4, 4 * t + 7, -3 * t - 4)");
t("Solve[f(u, v) = g(w), {u, v, w}]", "{{u = 1 / 2, v = 1, w = -1}}");
}
@Test
public void Solve_ParametricTD_16 () {
t("f(t, s) := (3, 1, 2) + t (-2, 4, -6) + s *(1, 0, 0)",
"(3 - 2 * t + s, 1 + 4 * t, 2 - 6 * t)",
"(s - 2 * t + 3, 4 * t + 1, -6 * t + 2)");
t("g(t) := (4, 7, -4) + t (1, 4, -3)", "(t + 4, 4 * t + 7, -3 * t - 4)");
t("Numeric[Solve[f(u, v) = g(w), {u, v, w}]]", "{{u = 0.5, v = 1, w = -1}}");
}
@Test
public void Solve_ParametricTD_17 () {
t("f(t, s) := (3, 1, 2) + t (-2, 4, -6) + s *(1, 0, 0)",
"(3 - 2 * t + s, 1 + 4 * t, 2 - 6 * t)",
"(s - 2 * t + 3, 4 * t + 1, -6 * t + 2)");
t("g(t) := (4, 7, -4) + t (1, 4, -3)", "(t + 4, 4 * t + 7, -3 * t - 4)");
// Please note that the language is German. "L\u00f6se" is "Solve" in
// German.
tk("Solve[f(u, v) = g(w), {u, v, w}]", GermanSolve + "[f(u, v) = g(w), {u, v, w}]");
}
/* SolveODE */
@Test
public void SolveODE_0 () {
s("SolveODE[y / x]", "y = c_INDEX * x");
}
@Test
public void SolveODE_1 () {
// s("SolveODE[y / x, y, x]", "y = x * c_INDEX");
s("SolveODE[y / x, y, x]", "y = c_INDEX * x");
}
/* Substitute */
@Test
public void Substitute_0 () {
t("Substitute[3 m - 3, 3 m - 3, a]", "a");
}
@Test
public void Substitute_1 () {
t("Substitute[(3 m - 3)^2, 3 m - 3, a]", "a^(2)");
}
@Test
public void Substitute_2 () {
t("Substitute[(3 m - 3)^2 - (n + 3)^2, 3 m - 3, a]", "a^(2) - (n + 3)^(2)", "a^(2) - n^(2) - 6 * n - 9");
}
@Test
public void Substitute_3 () {
t("Substitute[(3 m - 3)^2 - (m + 3)^2, m, a]", "8 * a^(2) - 24 * a", "(3 * a - 3)^(2) - (a + 3)^(2)");
}
@Test
public void Substitute_4 () {
try {
executeInCAS("Delete[a]");
executeInCAS("Delete[b]");
executeInCAS("Delete[c]");
executeInCAS("Delete[x]");
executeInCAS("Delete[y]");
executeInCAS("Delete[z]");
} catch (Throwable t) {
propagate(t);
}
t("Substitute[2x + 3y - z, {x=a, y=2, z=b}]", "2 * a - b + 6","2 * a + 6 - b");
}
@Test
public void Substitute_5 () {
// Substitute with Keep Input should substitute without evaluation.
tk("Substitute[1 + 2 + x + 3, {x=7}]", "1 + 2 + 7 + 3");
}
/* Sum */
@Test
public void Sum_0 () {
t("Substitute[3 m - 3, 3 m - 3, a]", "a");
}
@Test
public void Sum_1 () {
t("Sum[i^2, i, 1, 3]", "14");
}
@Test
public void Sum_2 () {
t("Sum[r^i, i, 0, n]", "r^(n + 1) / (r - 1) - 1 / (r - 1)");
}
@Test
public void Sum_3 () {
t("Sum[(1/3)^i, i, 0, Infinity]", "3 / 2");
}
/* Take */
@Test
public void Take_0 () {
t("Take[{1, 2, a, 4, 5}, 2, 4]", "{2, a, 4}");
}
/* Tangent */
/* Point on the Conic */
@Test
public void Tangent_PointOnConic_0 () {
t("c := Ellipse[(1, 1), (3, 2), (2, 3)]",
"8 * sqrt(10) * x^(2) - 32 * sqrt(10) * x + 8 * sqrt(10) * y^(2) - 24 * sqrt(10) * y + 32 * sqrt(10) + 12 * x^(2) - 16 * x * y - 24 * x + 24 * y^(2) - 40 * y = 0",
"8 * x^(2) * sqrt(10) + 12 * x^(2) - 32 * x * sqrt(10) - 16 * x * y - 24 * x + 8 * sqrt(10) * y^(2) - 24 * sqrt(10) * y + 32 * sqrt(10) + 24 * y^(2) - 40 * y = 0");
t("P := (2, 0)", "(2, 0)");
t("Tangent[P, c]", "{y = -2 * sqrt(10) + 6 + (sqrt(10) - 3) * x}",
"{y = (sqrt(10) - 3) x - 2 * sqrt(10) + 6}");
}
@Test
public void Tangent_PointOnConic_1 () {
t("c := Ellipse[(1, 1), (3, 2), (2, 3)]",
"8 * sqrt(10) * x^(2) - 32 * sqrt(10) * x + 8 * sqrt(10) * y^(2) - 24 * sqrt(10) * y + 32 * sqrt(10) + 12 * x^(2) - 16 * x * y - 24 * x + 24 * y^(2) - 40 * y = 0",
"8 * x^(2) * sqrt(10) + 12 * x^(2) - 32 * x * sqrt(10) - 16 * x * y - 24 * x + 8 * sqrt(10) * y^(2) - 24 * sqrt(10) * y + 32 * sqrt(10) + 24 * y^(2) - 40 * y = 0");
t("P := (2, 3)", "(2, 3)");
t("Tangent[P, c]", "{y = -2 * sqrt(10) + 9 + (sqrt(10) - 3) * x}",
"{y = (sqrt(10) - 3) x - 2 * sqrt(10) + 9}");
}
@Test
public void Tangent_PointOnConic_2 () {
// Tangent through the very same point (same object) we used to create the ellipse.
t("A := (1, 1)", "(1, 1)");
t("B := (3, 2)", "(3, 2)");
t("C := (2, 3)", "(2, 3)");
t("c := Ellipse[A, B, C]",
"8 * sqrt(10) * x^(2) - 32 * sqrt(10) * x + 8 * sqrt(10) * y^(2) - 24 * sqrt(10) * y + 32 * sqrt(10) + 12 * x^(2) - 16 * x * y - 24 * x + 24 * y^(2) - 40 * y = 0",
"8 * x^(2) * sqrt(10) + 12 * x^(2) - 32 * x * sqrt(10) - 16 * x * y - 24 * x + 8 * sqrt(10) * y^(2) - 24 * sqrt(10) * y + 32 * sqrt(10) + 24 * y^(2) - 40 * y = 0");
t("Tangent[C, c]", "{y = -2 * sqrt(10) + 9 + (sqrt(10) - 3) * x}",
"{y = (sqrt(10) - 3) x - 2 * sqrt(10) + 9}");
}
// TODO Add tests for other conics.
/* Point not on the Conic */
@Test
public void Tangent_PointOffConic_0 () {
t("c := Ellipse[(1, 1), (3, 2), (2, 3)]",
"8 * sqrt(10) * x^(2) - 32 * sqrt(10) * x + 8 * sqrt(10) * y^(2) - 24 * sqrt(10) * y + 32 * sqrt(10) + 12 * x^(2) - 16 * x * y - 24 * x + 24 * y^(2) - 40 * y = 0",
"8 * x^(2) * sqrt(10) + 12 * x^(2) - 32 * x * sqrt(10) - 16 * x * y - 24 * x + 8 * sqrt(10) * y^(2) - 24 * sqrt(10) * y + 32 * sqrt(10) + 24 * y^(2) - 40 * y = 0");
t("P := (0, (-3 * sqrt(10) * sqrt(224 * sqrt(10) + 687) * sqrt(31) + 672 * sqrt(10) - 11 * sqrt(224 * sqrt(10) + 687) * sqrt(31) + 2061) / (448 * sqrt(10) + 1374))",
"(0, (-sqrt(2 * sqrt(10) + 3) + 3) / 2)");
t("Tangent[P, c]",
"{y = (-sqrt(2 * sqrt(10) + 3) + 3) / 2, y = 5.558213948645 * x - 0.02680674287352}",
"{y = (-sqrt(2 * sqrt(10) + 3) + 3) / 2, y = 5.558213948644 * x - 0.02680674287311}",
"{y = (-sqrt(2 * sqrt(10) + 3) + 3) / 2, y = 5.558213948645 * x - 0.02680674287353}",
"{y = (-sqrt(2 * sqrt(10) + 3) + 3) / 2, y = 5.558213948644 * x - 0.02680674287309}");
}
// TODO Add tests for other conics.
// TODO Add tests for the other syntax variants:
//
// Tangent[Line, Conic],
// Tangent[Segment, Conic],
// Tangent[Number a, Function],
// Tangent[Point A, Function],
// Tangent[Point, Curve] and
// Tangent[Circle, Circle].
// TODO Add tests for TangentThroughPoint.
// TODO Put these in the right place.
@Test
public void Mike_1254 () {
t("Tangent[(0.2, 10), sqrt(1 - x^2)]",
"y = (-sqrt(6)) / 12 * x + 5 * sqrt(6) / 12",
"y = (-1) / 5 * sqrt(24 / 25)^(-1) * (x - 1 / 5) + sqrt(24 / 25)",
"y = (((-sqrt(6))) / 12 * x) + (5 * sqrt(6) / 12)");
}
@Test
public void Mike_1255 () {
t("Tangent[0.2, sqrt(1 - x^2)]",
"y = (-sqrt(6)) / 12 * x + 5 * sqrt(6) / 12",
"y = (-1) / 5 * sqrt(24 / 25)^(-1) * (x - 1 / 5) + sqrt(24 / 25)",
"y = (((-sqrt(6))) / 12 * x) + (5 * sqrt(6) / 12)");
}
@Test
public void Mike_1256 () {
t("Tangent[a, sqrt(1 - x^2)]",
"y = (a * sqrt(-a^(2) + 1) * x - sqrt(-a^(2) + 1)) / (a^(2) - 1)",
"y = -a * sqrt(1 - a^(2))^(-1) * (x - a) + sqrt(1 - a^(2))",
"y = (((a * sqrt((-a^(2)) + 1)) * x) - sqrt((-a^(2)) + 1)) / (a^(2) - 1)");
}
@Test
public void Mike_1257 () {
t("Tangent[(1 / sqrt(2), 1 / sqrt(2)), x^2 + y^2 = 1]",
"{y = -x + sqrt(2)}");
}
@Test
public void Mike_1258 () {
t("Tangent[(1, 0), x^2 + y^2 = 1]", "{x = 1}");
}
@Test
public void Mike_1259 () {
t("Tangent[(1, 0), x^3 + y^3 = 1]", "{x = 1}");
}
@Test
public void Mike_1260 () {
t("Tangent[(1, 1), x^3 + y^3 = 1]", "{x = 1, y = 1}", "{y = 1, x = 1}");
}
@Test
public void Mike_1261 () {
t("Tangent[(a, sqrt(1 - a^2)), x^2 + y^2 = 1]",
"{y = a * sqrt(-a^(2) + 1) / (a^(2) - 1) * x - sqrt(-a^(2) + 1) / (a^(2) - 1)}");
}
@Test
public void Mike_1262 () {
t("Tangent[(a, cbrt(1 - a^3)), x^3 + y^3 = 1]",
"{y = a^(2) * cbrt(-a^(3) + 1) / (a^(3) - 1) * x + (-a^(3) + 1) * cbrt(-a^(3) + 1) / (a^(6) - 2 * a^(3) + 1)}",
"{y = (a^(2) * (-a^(3) + 1)^(1/3) / (a^(3) - 1) * x + (-a^(3) + 1) * (-a^(3) + 1)^(1/3) / (a^(6) - 2 * a^(3) + 1))}");
}
@Test
public void Mike_1263 () {
t("Tangent[(0, 0) ,x^2 - y^3 + 2y^2 - y = 0]", "{y = 0}");
}
@Test
public void Mike_1264 () {
// singular point (two tangents) so ? is correct
t("Tangent[(0, 1), x^2 - y^3 + 2y^2 - y = 0]", "?");
}
/* TaylorPolynomial (alias TaylorSeries) */
/* Variable not specified */
@Test
public void TaylorPolynomial_VariableNotSpecified_0 () {
try {
executeInCAS("Delete[a]");
executeInCAS("Delete[x]");
} catch (Throwable t) {
propagate(t);
}
t("TaylorPolynomial[x^2, 3, 1]", "9 +6 * (x - 3)");
}
@Test
public void TaylorPolynomial_VariableNotSpecified_1 () {
try {
executeInCAS("Delete[a]");
executeInCAS("Delete[x]");
} catch (Throwable t) {
propagate(t);
}
t("TaylorPolynomial[x^2, a, 1]", "a^(2) + 2 * a*(x-a)");
}
private static void propagate(Throwable t) {
throw new RuntimeException(t);
}
/* Variable specified */
@Test
public void TaylorPolynomial_VariableSpecified_0 () {
t("TaylorPolynomial[x^3, x, 1, 1]", "1 + 3*(x - 1)");
}
@Test
public void TaylorPolynomial_VariableSpecified_1 () {
t("TaylorPolynomial[x^3, x, 1, 2]", "1 + 3*(x-1)+3*(x-1)^(2)");
}
@Test
public void TaylorPolynomial_VariableSpecified_2 () {
t("TaylorPolynomial[x^3, x, 0, 3]", "x^(3)");
}
@Test
public void TaylorPolynomial_VariableSpecified_3 () {
t("TaylorPolynomial[x^3, x, 1, 3]", "1 + 3 * (x - 1) + 3 * (x - 1)^(2) + (x - 1)^(3)");
}
@Test
public void TaylorPolynomial_VariableSpecified_4 () {
t("TaylorPolynomial[x^3 sin(y), x, 3, 2]", "27*sin(y)+27*sin(y)*(x-3)+9*sin(y)*(x-3)^(2)");
}
@Test
public void TaylorPolynomial_VariableSpecified_5 () {
t("TaylorPolynomial[x^3 sin(y), y, 3, 1]",
"x^(3) * sin(3) + x^(3) * cos(3) * (y-3)",
"sin(3) * x^(3) + cos(3) * x^(3) * (y-3)");
}
@Test
public void TaylorPolynomial_VariableSpecified_6 () {
t("TaylorPolynomial[x^3 sin(y), y, 3, 2]",
"x^(3) * sin(3) + x^(3) * cos(3) * (y - 3) - x^(3) * sin(3) / 2 * (y - 3)^(2)",
"sin(3) * x^(3) + cos(3) * x^(3) * (y - 3) - (sin(3) * x^(3)) / 2 * (y - 3)^(2)");
}
/* ToComplex */
@Test
public void ToComplex_0 () {
t("ToComplex[(3, 2)]", "3 + 2 * \u03af", "2 * \u03af + 3");
}
/* ToExponential */
@Test
public void ToExponential_0 () {
t("ToExponential[1 + \u03af]", "sqrt(2) * "+ Unicode.EULER_STRING +"^(\u03af * " + Unicode.PI_STRING + " / 4)");
}
/* ToPoint */
@Test
public void ToPoint_0 () {
t("ToPoint[3 + 2 \u03af]", "(3, 2)");
}
/* ToPolar */
@Test
public void ToPolar_0 () {
t("ToPolar[(1, sqrt(3))]", "(2; " + Unicode.PI_STRING + " / 3)");
}
@Test
public void ToPolar_1 () {
t("ToPolar[1 + sqrt(3) * \u03af]", "(2; " + Unicode.PI_STRING + " / 3)");
}
/* Transpose */
@Test
public void Transpose_0 () {
t("Transpose[{{1, 2, 3}, {4, 5, 6}, {7, 8, 9}}]", "{{1, 4, 7}, {2, 5, 8}, {3, 6, 9}}");
}
@Test
public void Transpose_1 () {
t("Transpose[{{a, b}, {c, d}}]", "{{a, c}, {b, d}}");
}
/* Unique */
@Test
public void Unique_0 () {
t("Unique[{1, 2, 4, 1, 4}]", "{1, 2, 4}");
}
@Test
public void Unique_1 () {
t("Unique[{1, x, x, 1, a}]", "{1, x, a}");
}
/* UnitPerpendicularVector (alias UnitOrthogonalVector) */
@Test
public void UnitPerpendicularVector_0 () {
t("UnitPerpendicularVector[(3, 4)]", "((-4) / 5, 3 / 5)");
}
@Test
public void UnitPerpendicularVector_1 () {
t("UnitPerpendicularVector[(a, b)]",
"((-b) / sqrt(a^(2) + b^(2)), a / sqrt(a^(2) + b^(2)))");
}
/* UnitVector */
@Test
public void UnitVector_0 () {
t("UnitVector[(3, 4)]", "(3 / 5, 4 / 5)");
}
@Test
public void UnitVector_1 () {
t("UnitVector[(a, b)]",
"(a / sqrt(a * a + b * b), b / sqrt(a * a + b * b))",
"(a / sqrt(a^(2) + b^(2)), b / sqrt(a^(2) + b^(2)))");
}
@Test
public void UnitVector_2 () {
t("UnitVector[(2, 4, 4)]", "(1 / 3, 2 / 3, 2 / 3)");
}
/* Variance */
@Test
public void Variance_0 () {
t("Variance[{1, 2, 3}]", "2 / 3");
}
@Test
public void Variance_1 () {
t("Variance[{1, 2, a}]", "2 / 9 * a^(2) - 2 / 3 * a + 2 / 3",
"(2 * a^(2) - 6 * a + 6) / 9");
}
/* Vector Operations */
/* Adding Vectors */
@Test
public void Vectors_AddingVectors_0 () {
t("(1, 2) + (3, 4)", "(4, 6)");
}
@Test
public void Vectors_AddingVectors_1 () {
t("(1, 2) + {3, 3}", "(4, 5)");
}
@Test
public void Vectors_AddingVectors_2 () {
t("{a, b} + (3, 2)", "(a + 3, b + 2)");
}
/* Subtracting Vectors */
@Test
public void Vectors_SubtractingVectors_0 () {
t("(1, 2) - (3, 4)", "(-2, -2)");
}
@Test
public void Vectors_SubtractingVectors_1 () {
t("(1, 2) - {3, 3}", "(-2, -1)");
}
@Test
public void Vectors_SubtractingVectors_2 () {
t("{a, b} - (3, 2)", "(a - 3, b - 2)");
}
/* Multiplying Vectors: Scalar Product */
@Test
public void Vectors_ScalarProduct_0 () {
t("(1, 2) * (3, 4)", "11");
}
@Test
public void Vectors_ScalarProduct_1 () {
t("{1, 2} * (3, 4)", "11");
}
@Test
public void Vectors_ScalarProduct_2 () {
t("(1, 2) * {3, 4}", "11");
}
@Test
public void Vectors_ScalarProduct_3 () {
t("(x, 2)*{3,4}", "3*x+8");
}
/* Multiplying Vectors: Matrices */
@Test
public void Vectors_MatrixTimesVector_0 () {
t("{{a, b}, {c, d}} * (x, y)", "(a * x + b * y, c * x + d * y)");
}
@Test
public void Vectors_MatrixTimesVector_1 () {
t("{{1, 2}, {2, 1}} * (3, 4)", "(11, 10)");
}
@Test
public void Vectors_MatrixTimesVector_2 () {
t("(a, b) * {{1, 2}, {3, 4}}", "(a + 3 * b, 2 * a + 4 * b)");
}
/* Ticket */
/* Ticket 697: Solve[ {x -1 = 1, y+x = 3}, {x, y}] puts answer in () not {} */
// TODO Add test! Forget about the existing one.
@Test
public void Ticket_Ticket697_0 () {
tk("f(x) := x^2", "x^(2)");
t("f'(x)", "2 * x");
}
/* Ticket 801: Numeric factorization */
@Test
public void Ticket_Ticket801_0 () {
t("Factor(x^2 - 2)", "x^(2) - 2");
}
@Test
public void Ticket_Ticket801_1 () {
t("IFactor(x^2 - 2)", "(x - sqrt(2)) * (x + sqrt(2))");
}
@Test
public void Ticket_Ticket801_2 () {
t("CIFactor(x^2 - 2)", "(x - sqrt(2)) * (x + sqrt(2))");
}
/* Ticket 1274: Derivative of exp(2x) wrong */
@Test
public void Ticket_Ticket1274_0 () {
// TODO the third option is a bit ugly, maybe remove
t("Derivative[" + Unicode.EULER_STRING + "^(2 * x)]",
"2 * " + Unicode.EULER_STRING + "^(2 * x)",
"2 * (" + Unicode.EULER_STRING + "^(x))^(2)",
Unicode.EULER_STRING + "^(2 * x) * 2");
}
/* Ticket 1336: Support for brackets with built-in functions */
@Test
public void Ticket_Ticket1336_0 () {
t("Abs[17]", "17");
}
@Test
public void Ticket_Ticket1336_1 () {
t("Round[4.4]", "4");
}
@Test
public void Ticket_Ticket1336_2 () {
t("Ceil[4.4]", "5");
}
@Test
public void Ticket_Ticket1336_3 () {
t("Floor[4.4]", "4");
}
@Test
public void Ticket_Ticket1336_4 () {
t("(5 + 3 \u03af) + Conjugate[5 + 3 \u03af]", "10");
}
/* Ticket 1477: e becomes E in CAS */
@Test
public void Ticket_Ticket1477_0 () {
t("e", "e");
}
/* Ticket 1899: Solve[2^x = 8] yields unwanted result */
@Test
public void Ticket_Ticket1899_0 () {
t("Solve[2^x = 8]", "{x = 3}", "{x = log(8) / log(2)}");
}
/* Ticket 2481: NSolves gives wrong solution */
@Test
public void Ticket_Ticket2481_0 () {
t("Numeric[NSolve[13^(x+1)-2*13^x=1/5*5^x,x], 11]", "{x = -4.1939143755}");
/*
* Autotest and offline evaluation results differ in this test case.
*
* Since minor differences are to be expected with numeric algorithms, this is not considered an error. Therefore the number of significant
* figures of this test has been decreased artificially.
*
* The original test was t("[NSolve[13^(x+1)-2*13^x=1/5*5^x,x]", "{x = -4.193914375465535}");. The result from autotest was {x =
* -4.193914375476052}. The exact result is {x = (-ln(55)) / (ln(13) - ln(5))}.
*/
}
/* Ticket 2651: Function not Evaluated */
@Test
public void Ticket_Ticket2651_0 () {
t("f(x) := FitPoly[{(-1, -1), (0, 1), (1, 1), (2, 5)}, 3]", "x^(3) - x^(2) + 1");
t("f(-1)", "-1");
}
/* Ticket 3370: Integral symbol for integrals in CAS */
@Test
public void Ticket_Ticket3370_0 () {
GeoCasCell f = new GeoCasCell(kernel.getConstruction());
kernel.getConstruction().addToConstructionList(f, false);
f.setInput("Integral[x^2, x, 1, 2]");
f.setEvalCommand("Keepinput");
f.computeOutput();
Assert.assertEquals("\\mathbf{\\int\\limits_{1}^{2}x^{2}\\,\\mathrm{d}x}", f.getLaTeXOutput());
}
@Test
public void Ticket_Ticket3370_1 () {
GeoCasCell f = new GeoCasCell(kernel.getConstruction());
kernel.getConstruction().addToConstructionList(f, false);
f.setInput("Integral[f(y), y, somevar, g(h)]");
f.setEvalCommand("Keepinput");
f.computeOutput();
Assert.assertEquals("\\mathbf{\\int\\limits_{somevar}^{g \\left(h \\right)}f \\left(y \\right)\\,\\mathrm{d}y}", f.getLaTeXOutput());
}
@Test
public void Ticket_Ticket3370_2 () {
GeoCasCell f = new GeoCasCell(kernel.getConstruction());
kernel.getConstruction().addToConstructionList(f, false);
f.setInput("Sum[x^2, x, 1, 2]");
f.setEvalCommand("Keepinput");
f.computeOutput();
Assert.assertEquals("\\mathbf{\\sum_{x=1}^{2}x^{2}}", f.getLaTeXOutput());
}
@Test
public void Ticket_Ticket3370_3 () {
GeoCasCell f = new GeoCasCell(kernel.getConstruction());
kernel.getConstruction().addToConstructionList(f, false);
f.setInput("Sum[f(y), y, somevar, g(h)]");
f.setEvalCommand("Keepinput");
f.computeOutput();
Assert.assertEquals("\\mathbf{\\sum_{y=somevar}^{g \\left(h \\right)}f \\left(y \\right)}", f.getLaTeXOutput());
}
/* Ticket 3377: Expand Improvements */
@Test
public void Ticket_Ticket3377_0 () {
t("Expand[sqrt(3) * sqrt(3 + x - 1)]", "sqrt(3) * sqrt(x + 2)");
}
@Test
public void Ticket_Ticket3377_1 () {
t("Expand[a / c + b / d]", "(a * d + b * c) / (c * d)");
}
@Test
public void Ticket_Ticket3377_2 () {
t("Factor[a / c + b / d]", "(a * d + c * b) / (d * c)",
"(a * d + b * c) / (c * d)");
}
/* Ticket 3381: Problem with Solve and exponential function */
@Test
public void Ticket_Ticket3381_0 () {
t("Solve[{a = 2, 12 * sqrt(3) * a * b^2 * exp(-3 * b) - 6 * sqrt(3) * a * b *exp(-3 * b) = 0}, {a, b}]",
"{{a = 2, b = 0}, {a = 2, b = 1 / 2}}");
}
/* Ticket 3385: Intersection and Union in CAS */
@Test
public void Ticket_Ticket3385_0 () {
t("Union[{a, b, c}, {a, b}]", "{a, b, c}");
}
@Test
public void Ticket_Ticket3385_1 () {
t("Intersection[{a, b, c}, {c, d}]", "{c}");
}
@Test
public void Ticket_Ticket3385_2 () {
t("Union[{a, b, c}, {b, c, d}]", "{a, b, c, d}");
}
@Test
public void Ticket_Ticket3385_3 () {
t("a "+ExpressionNodeConstants.strIS_ELEMENT_OF+"{a, b, c}", "true");
}
@Test
public void Ticket_Ticket3385_4 () {
t("d "+ExpressionNodeConstants.strIS_ELEMENT_OF+" {a, b, c}", "false");
}
@Test
public void Ticket_Ticket3385_5 () {
t("{} "+ExpressionNodeConstants.strIS_SUBSET_OF+" {}", "true");
}
@Test
public void Ticket_Ticket3385_6 () {
t("{a, b} "+ExpressionNodeConstants.strIS_SUBSET_OF+"{a, b, c}", "true");
}
@Test
public void Ticket_Ticket3385_7 () {
t("{a, b, c} "+ExpressionNodeConstants.strIS_SUBSET_OF+" {a, b, c}", "true");
}
@Test
public void Ticket_Ticket3385_8 () {
t("{a, b, c} "+ExpressionNodeConstants.strIS_SUBSET_OF+" {a, b}", "false");
}
@Test
public void Ticket_Ticket3385_9 () {
t("{} "+ExpressionNodeConstants.strIS_SUBSET_OF_STRICT+" {}", "false");
}
@Test
public void Ticket_Ticket3385_10 () {
t("{a, b} "+ExpressionNodeConstants.strIS_SUBSET_OF_STRICT+" {a, b, c}", "true");
}
@Test
public void Ticket_Ticket3385_11 () {
t("{a, b, c} "+ExpressionNodeConstants.strIS_SUBSET_OF_STRICT+" {a, b, c}", "false");
}
/* Ticket 3524: Solve fails for large numbers and definition as function */
// TODO What is the correct result for f'(x) = 0 and g(x) = 0 (should be identical)?
@Test
public void Ticket_Ticket3524_0 () {
t("c := Ellipse[(1, 1), (3, 2), (2, 3)]",
"8 * sqrt(10) * x^(2) - 32 * sqrt(10) * x + 8 * sqrt(10) * y^(2) - 24 * sqrt(10) * y + 32 * sqrt(10) + 12 * x^(2) - 16 * x * y - 24 * x + 24 * y^(2) - 40 * y = 0",
"8 * x^(2) * sqrt(10) + 12 * x^(2) - 32 * x * sqrt(10) - 16 * x * y - 24 * x + 8 * sqrt(10) * y^(2) - 24 * sqrt(10) * y + 32 * sqrt(10) + 24 * y^(2) - 40 * y = 0");
t("f(x) := Element[Solve[c, y], 2]",
"(2 * x + 3 * sqrt(10) - 3 * sqrt(x^(2) * (-2 * sqrt(10) - 6) + x * (8 * sqrt(10) + 24) - 2 * sqrt(10) - 5) + 5) / (2 * sqrt(10) + 6)",
"(x * (-4 * sqrt(10) + 6) - sqrt(10) + 3 * sqrt(x^(2) * (-sqrt(10) * 26 - 54) + x * (sqrt(10) * 104 + 216) - sqrt(10) * 38 - 5) - 45) / (-6 * sqrt(10) - 22)");
t("Solve[f'(x) = 0, x]",
"{x = (-sqrt(2 * sqrt(10) - 3) * sqrt(31) + 62) / 31}");
t("g(x) := f'(x)",
"(x^(2) * (-2 * sqrt(10) - 6) + (x * (3 * sqrt(10) + 9) - 6 * sqrt(10) - 18) * sqrt(x^(2) * (-2 * sqrt(10) - 6) + x * (8 * sqrt(10) + 24) - 2 * sqrt(10) - 5) + x * (8 * sqrt(10) + 24) - 2 * sqrt(10) - 5) / (x^(2) * (-sqrt(10) * 12 - 38) + x * (sqrt(10) * 48 + 152) - sqrt(10) * 11 - 35)",
"(x^(2) * (sqrt(10) * 30 + 358) + (x * (-sqrt(10) * 39 - 81) + sqrt(10) * 78 + 162) * sqrt(x^(2) * (-sqrt(10) * 26 - 54) + x * (sqrt(10) * 104 + 216) - sqrt(10) * 38 - 5) + x * (-sqrt(10) * 120 - 1432) - sqrt(10) * 104 + 745) / (x^(2) * (sqrt(10) * 448 + 1374) + x * (-sqrt(10) * 1792 - 5496) + sqrt(10) * 433 + 1195)");
// Solve[((x^2 (sqrt(10) 30 + 358) + (x (-sqrt(10) 39 - 81) + sqrt(10)
// 78
// + 162) sqrt(x^2 (-sqrt(10) 26 - 54) + x (sqrt(10) 104 + 216) -
// sqrt(10) 38 - 5) + x (-sqrt(10) 120 - 1432) - sqrt(10) 104 + 745) /
// (x^2 (sqrt(10) 448 + 1374) + x (-sqrt(10) 1792 - 5496) + sqrt(10) 433
// + 1195)),x]
// just one correct answer not 3
t("Solve[g(x) = 0, x]",
"{x = (-sqrt(2 * sqrt(10) - 3) * sqrt(31) + 62) / 31}");
}
/* Ticket 3525: Simplification improvements in Giac */
/*
@Test
public void Ticket_Ticket3525_0 () {
t("c := Ellipse[(1, 1), (3, 2), (2, 3)]",
"(8 * sqrt(10) + 12) * x^(2) - 16 * x * y - (32 * sqrt(10) + 24) * x + (8 * sqrt(10) + 24) * y^(2) - (24 * sqrt(10) + 40) * y + 32 * sqrt(10) = 0",
"8 * x^(2) * sqrt(10) + 12 * x^(2) - 32 * x * sqrt(10) - 16 * x * y - 24 * x + 8 * sqrt(10) * y^(2) - 24 * sqrt(10) * y + 32 * sqrt(10) + 24 * y^(2) - 40 * y = 0");
t("f(x) := Element[Solve[c, y], 1]",
"((-4 * sqrt(10) + 6) * x - sqrt(10) - 45 - 3 * sqrt(-(26 * sqrt(10) + 54) * x^(2) + (104 * sqrt(10) + 216) * x - 38 * sqrt(10) - 5)) / (-6 * sqrt(10) - 22)",
"(x * (-4 * sqrt(10) + 6) - sqrt(10) - 3 * sqrt(x^(2) * (-sqrt(10) * 26 - 54) + x * (sqrt(10) * 104 + 216) - sqrt(10) * 38 - 5) - 45) / (-6 * sqrt(10) - 22)");
t("f(RightSide[Element[Solve[f'(x) = 0, x], 1]])",
// y-coord of top of ellipse (2.33, 3.03) ie approx 3.03
"(sqrt(10) * 93 * sqrt(31 * (sqrt(10) * 224 + 687)) + 341 * sqrt(31 * (sqrt(10) * 224 + 687)) + sqrt(10) * 20832 + 63891) / (sqrt(10) * 13888 + 42594)");
}
/* Ticket 3554: f '(x) doesn't work in Keep Input mode */
@Test
public void Ticket_Ticket3554_0 () {
tk("f(x) := x^2", "x^(2)");
t("f'(x)", "2 * x");
}
@Test
public void Ticket_Ticket3554_1 () {
tk("f(x) := x^2", "x^(2)");
t("Numeric[f'(x)]", "2 * x");
}
@Test
public void Ticket_Ticket3554_2 () {
tk("f(x) := x^2", "x^(2)");
tk("f'(x)", "f'(x)");
}
/* Ticket 3557: Substitute and Simplification */
@Test
public void Ticket_Ticket3557_0 () {
// TODO Add Test.
}
/* Ticket 3558: Curve always on X - Axis */
// TODO This actually is a bug in its own right. But a different one.
@Test
public void Ticket_Ticket3558_0 () {
t("Curve[t, 5 t, t, 0, 10]", "y - 5 * x = 0");
}
/* Ticket 3563: Solve Yields Empty Set for under-defined Systems */
@Test
public void Ticket_Ticket3563_0 () {
t("Solve[13 = 3 + 5 t + 10 s, {t, s}]", "{{t = -2 * s + 2, s = s}}");
}
@Test
public void Ticket_Ticket3563_1 () {
t("Solve[{b + a = 0, c^2 - 1 = 0}]", "{{a = -b, b = b}}");
}
@Test
public void Ticket_Ticket3563_2 () {
t("Solve[{c^2 - 1 = 0, b + a = 0}]", "{{a = -b, b = b}}");
}
@Test
public void Ticket_Ticket3563_3 () {
t("Solve[{c^2 - 1 = 0, b + a = 0, x = 0}]", "{{x = 0, a = -b, b = b}}");
}
@Test
public void Ticket_Ticket3563_4 () {
t("Solve[{c^2 - 1 = 0, b + a = 0, x = 0}, b]", "{b = -a}");
}
@Test
public void Ticket_Ticket3563_5 () {
t("Solve[{c^2 - 1 = 0, b + a = 0, x = 0}, c]", "{c = -1, c = 1}");
}
/* Ticket 3579: Keepinput Being Kept */
/**
* Test is ignored. Keepinput is no user command anymore, internal use seems to meet our expectations.
*
* Therefore we don't want to mess with this anytime soon, except somebody complains.
*/
@Test
public void Ticket_Ticket3579_0 () {
tk("f(x) := x * x", "x * x");
}
/* Ticket 3594: Problem with Solve[{$1, $2}] and Solve tool */
@Test
public void Ticket_Ticket3594_0 () {
// Test case for dynamic row references.
t("x + 2 y = 3", "x + 2 * y = 3");
t("4 x + 5 y = 6", "4 * x + 5 * y = 6");
t("Solve[{$1, $2}]", "{{x = -1, y = 2}}");
// Please note that static row references cannot be tested here
// for we are bypassing the CASInputHandler,
// which is employed to resolve them.
}
/* Test cases for tickets that never were created */
/* "f(x):=" not being shown in the output when changing a cell into a definition via the marble */
@Test
public void Ticket_NoTicket_0 () {
GeoCasCell f = new GeoCasCell(kernel.getConstruction());
kernel.getConstruction().addToConstructionList(f, false);
f.setInput("f(x) := a * x^3 + b * x^2 + c * x + d");
f.computeOutput();
Assert.assertEquals("f(x):=a x"+Unicode.Superscript_3+" + b x"+Unicode.Superscript_2+" + c x + d", f.getOutput(StringTemplate.defaultTemplate));
}
/* Test for GGB-1636 */
@Test
public void Ticket_Ticket1636_0() {
t("Sequence[Vector[(i, i)],i,1,3]", "{(1, 1), (2, 2), (3, 3)}");
t("Element[$1,1]", "(1, 1)");
GeoCasCell gv = (GeoCasCell) app.getKernel().lookupLabel("$2");
gv.plot();
Assert.assertTrue(gv.getTwinGeo().isGeoVector());
}
/*
* Examples from the article "GeoGebraCAS - Vom symbolischen Notizblock zur dynamischen CAS Ansicht" published in "CAS Rundbrief".
*/
/* Figure 2: "Gleichungsumformungen" (Manipulation of Equations) */
@Test
public void CASRundbrief_Figure2_0 () {
tk("x - 1/2 = 2 x + 3", "x - 1 / 2 = 2 * x + 3");
}
@Test
public void CASRundbrief_Figure2_1 () {
tk("(x - 1 / 2 = 2x + 3) + 1/2", "(x - 1 / 2 = 2 * x + 3) + 1/2");
}
@Test
public void CASRundbrief_Figure2_2 () {
t("(x - 1 / 2 = 2x + 3) + 1 / 2", "x = 2 * x + 7 / 2",
"x = (4 * x + 7) / 2", "x = 7 / 2 + 2 * x");
}
@Test
public void CASRundbrief_Figure2_3 () {
t("Numeric[(x - 1 / 2 = 2x + 3) + 1/2]", "x = 2 * x + 3.5");
}
/* Figure 3: "Einfache Exponentialgleichungen" (Simple Exponential Equations) */
@Test
public void CASRundbrief_Figure3_0 () {
t("f(t) := 100 * 1.5^t", "100 * (3 / 2) ^ (t)");
}
@Test
public void CASRundbrief_Figure3_1 () {
// Depends on CASRundbrief_Figure3_0.
t("f(t) := 100 * 1.5^t", "100 * (3 / 2) ^ (t)");
t("f(2)", "225");
}
@Test
public void CASRundbrief_Figure3_2 () {
// Depends on CASRundbrief_Figure3_0.
t("f(t) := 100 * 1.5^t", "100 * (3 / 2) ^ (t)");
t("Numeric[Solve[f(t) = 225, t]]", "{t = 2}");
}
@Test
public void CASRundbrief_Figure3_3 () {
// Depends on CASRundbrief_Figure3_0.
t("f(t) := 100 * 1.5^t", "100 * (3 / 2) ^ (t)");
// Do the same using symbolic evaluation.
t("Solve[f(t) = 225, t]", "{t = 2}");
// TODO Remove lines below.
// Old test:
// t("Solve[f(t) = 225, t]", "{t = 2}", "{t = log(9 / 4) / log(3 / 2)}");
}
@Test
public void CASRundbrief_Figure3_4 () {
t("Solve[225 = c * 1.5^2, c]", "{c = 100}");
}
@Test
public void CASRundbrief_Figure3_5 () {
t("Solve[225 = 100 * a^2, a]", "{a = (-3) / 2 , a = 3 / 2}");
}
/*
* Figure 4: "L\u00f6sung mit unbelegten Variablen" (Solution with undefined
* variables)
*/
@Test
public void CASRundbrief_Figure4_0 () {
t("f(t) := c * a^t", "a^(t) * c");
}
@Test
public void CASRundbrief_Figure4_1 () {
// Depends on CASRundbrief_Figure4_0.
t("f(t) := c * a^t", "a^(t) * c");
t("Solve[f(2) = 225, a]",
"{a = -15 * sqrt(c) / c, a = 15 * sqrt(c) / c}",
"{a = 15 * sqrt(c) / c, a = -15 * sqrt(c) / c}");
}
/* Figure 5: "Computeralgebra und Geometrie" (Computer Algebra and Geometrics) */
@Test
public void CASRundbrief_Figure5_0 () {
t("f(x) := (2x^2 - 3x + 4) / 2", "x^(2) - 3 / 2 * x + 2");
}
@Test
public void CASRundbrief_Figure5_1 () {
// Suppress output using semicolon.
// Warning: This does not affect the output here!
// Therefore this test does not test suppression of the output,
// but just semicolon at the end of the input not breaking anything here.
t("f(x) := (2x^2 - 3x + 4) / 2;", "x^(2) - 3 / 2 * x + 2");
}
@Test
public void CASRundbrief_Figure5_2 () {
t("g(x) := (x + 4) / 2", "1 / 2 * x + 2");
}
@Test
public void CASRundbrief_Figure5_3 () {
// Depends on CASRundbrief_Figure5_1.
t("f(x) := (2x^2 - 3x + 4) / 2;", "x^(2) - 3 / 2 * x + 2");
// Depends on CASRundbrief_Figure5_2.
t("g(x) := (x + 4) / 2", "1 / 2 * x + 2");
t("h(x) := f(x) - g(x)", "x^(2) - 2 * x");
}
@Test
public void CASRundbrief_Figure5_4 () {
// Depends on CASRundbrief_Figure5_1.
t("f(x) := (2x^2 - 3x + 4) / 2;", "x^(2) - 3 / 2 * x + 2");
// Depends on CASRundbrief_Figure5_2.
t("g(x) := (x + 4) / 2", "1 / 2 * x + 2");
// Depends on CASRundbrief_Figure5_3.
t("h(x) := f(x) - g(x)", "x^(2) - 2 * x");
t("Factor[h(x)]", "x * (x - 2)", "(x - 2) * x");
}
@Test
public void CASRundbrief_Figure5_5 () {
// Depends on CASRundbrief_Figure5_1.
t("f(x) := (2x^2 - 3x + 4) / 2;", "x^(2) - 3 / 2 * x + 2");
// Depends on CASRundbrief_Figure5_2.
t("g(x) := (x + 4) / 2", "1 / 2 * x + 2");
// Depends on CASRundbrief_Figure5_3.
t("h(x) := f(x) - g(x)", "x^(2) - 2 * x");
t("Solve[h(x) = 0, x]", "{x = 0, x = 2}");
}
@Test
public void CASRundbrief_Figure5_6 () {
// Depends on CASRundbrief_Figure5_1.
t("f(x) := (2x^2 - 3x + 4) / 2;", "x^(2) - 3 / 2 * x + 2");
// Depends on CASRundbrief_Figure5_2.
t("g(x) := (x + 4) / 2", "1 / 2 * x + 2");
t("Intersect[f(x), g(x)]", "{(0, 2), (2, 3)}", "{(2, 3), (0, 2)}");
}
/* Figure 6: "Umgekehrte Kurvendiskussion" (Backward Curve Sketching) */
@Test
public void CASRundbrief_Figure6_0 () {
t("f(x) := a x^3 + b x^2 + c x + d", "a * x^(3) + b * x^(2) + c * x + d");
}
@Test
public void CASRundbrief_Figure6_1 () {
// Depends on CASRundbrief_Figure6_0.
t("f(x) := a x^3 + b x^2 + c x + d", "a * x^(3) + b * x^(2) + c * x + d");
// Suppress output using semicolon.
// Warning: This does not affect the output here!
// Therefore this test does not test suppression of the output,
// but just semicolon at the end of the input not breaking anything here.
t("g_1: f(1) = 1;", "a + b + c + d = 1");
}
@Test
public void CASRundbrief_Figure6_2 () {
// Depends on CASRundbrief_Figure6_0.
t("f(x) := a x^3 + b x^2 + c x + d", "a * x^(3) + b * x^(2) + c * x + d");
// Suppress output using semicolon.
// Warning: This does not affect the output here!
// Therefore this test does not test suppression of the output,
// but just semicolon at the end of the input not breaking anything here.
t("g_2: f(2) = 2;", "8 * a + 4 * b + 2 * c + d = 2");
}
@Test
public void CASRundbrief_Figure6_3 () {
// Depends on CASRundbrief_Figure6_0.
t("f(x) := a x^3 + b x^2 + c x + d", "a * x^(3) + b * x^(2) + c * x + d");
// Suppress output using semicolon.
// Warning: This does not affect the output here!
// Therefore this test does not test suppression of the output,
// but just semicolon at the end of the input not breaking anything here.
t("g_3: f'(1) = 0;", "3 * a + 2 * b + c = 0");
}
@Test
public void CASRundbrief_Figure6_4 () {
// Depends on CASRundbrief_Figure6_0.
t("f(x) := a x^3 + b x^2 + c x + d", "a * x^(3) + b * x^(2) + c * x + d");
// Suppress output using semicolon.
// Warning: This does not affect the output here!
// Therefore this test does not test suppression of the output,
// but just semicolon at the end of the input not breaking anything here.
t("g_4: f''(1) = 0;", "6 * a + 2 * b = 0");
}
@Test
public void CASRundbrief_Figure6_5 () {
// Depends on CASRundbrief_Figure6_0.
t("f(x) := a x^3 + b x^2 + c x + d", "a * x^(3) + b * x^(2) + c * x + d");
// Depends on CASRundbrief_Figure6_1.
t("g_1: f(1) = 1;", "a + b + c + d = 1");
// Depends on CASRundbrief_Figure6_2.
t("g_2: f(2) = 2;", "8 * a + 4 * b + 2 * c + d = 2");
// Depends on CASRundbrief_Figure6_3.
t("g_3: f'(1) = 0;", "3 * a + 2 * b + c = 0");
// Depends on CASRundbrief_Figure6_4.
t("g_4: f''(1) = 0;", "6 * a + 2 * b = 0");
t("Solve[{g_1, g_2, g_3, g_4}, {a, b, c, d}]", "{{a = 1, b = -3, c = 3, d = 0}}");
}
/* Figure 7: "Matrix in der CAS Ansicht" (Matrix in the CAS View) */
@Test
public void CASRundbrief_Figure7_0 () {
t("A := {{2, 3, 2}, {1, 1, 1}, {0, -1, 3}}", "{{2, 3, 2}, {1, 1, 1}, {0, -1, 3}}");
}
/* Figure 8: "Gleichungssystem mittels Matrizen" (System of Equations via Matrices) */
@Test
public void CASRundbrief_Figure8_0 () {
// Suppress output using semicolon.
// Warning: This does not affect the output here!
// Therefore this test does not test suppression of the output,
// but just semicolon at the end of the input not breaking anything here.
t("A := {{2, 3, 2}, {1, 1, 1}, {0, -1, 3}};", "{{2, 3, 2}, {1, 1, 1}, {0, -1, 3}}");
}
@Test
public void CASRundbrief_Figure8_1 () {
// Suppress output using semicolon.
// Warning: This does not affect the output here!
// Therefore this test does not test suppression of the output,
// but just semicolon at the end of the input not breaking anything here.
t("B := {{3}, {2}, {7}};", "{{3}, {2}, {7}}");
}
@Test
public void CASRundbrief_Figure8_2 () {
// Suppress output using semicolon.
// Warning: This does not affect the output here!
// Therefore this test does not test suppression of the output,
// but just semicolon at the end of the input not breaking anything here.
t("X := {{x}, {y}, {z}};", "{{x}, {y}, {z}}");
}
@Test
public void CASRundbrief_Figure8_3 () {
// Depends on CASRundbrief_Figure8_0.
t("A := {{2, 3, 2}, {1, 1, 1}, {0, -1, 3}};", "{{2, 3, 2}, {1, 1, 1}, {0, -1, 3}}");
// Depends on CASRundbrief_Figure8_1.
t("B := {{3}, {2}, {7}};", "{{3}, {2}, {7}}");
// Depends on CASRundbrief_Figure8_2.
t("X := {{x}, {y}, {z}};", "{{x}, {y}, {z}}");
t("A * X = B", "{{2 * x + 3 * y + 2 * z}, {x + y + z}, {-y + 3 * z}} = {{3}, {2}, {7}}");
}
/*
* Figure 9: "L\u00f6sung des Gleichungssystemes" (Solution of the System of
* Equations)
*/
@Test
public void CASRundbrief_Figure9_0 () {
// Depends on CASRundbrief_Figure8_0.
t("A := {{2, 3, 2}, {1, 1, 1}, {0, -1, 3}};", "{{2, 3, 2}, {1, 1, 1}, {0, -1, 3}}");
// Depends on CASRundbrief_Figure8_1.
t("B := {{3}, {2}, {7}};", "{{3}, {2}, {7}}");
t("Invert[A] * B", "{{1}, {-1}, {2}}");
}
@Test
public void QuickStart () {
t("f(x) := x^2 - 3/2 * x + 2", "x^(2) - 3 / 2 * x + 2",
"(2* x^(2) - 3 * x + 4) / 2");
t("g(x) := 1/2 * x + 2", "1 / 2 * x + 2", "(x + 4) / 2");
t("h(x):=f(x)-g(x)", "x^(2) - 2 * x");
t("Factor[h(x)]", "x * (x - 2)", "(x - 2) * x");
t("Solve[h(x) = 0, x]", "{x = 0, x = 2}", "{x = 2, x = 0}");
t("S:=Intersect[f(x),g(x)]", "{(0, 2), (2, 3)}", "{(2, 3), (0, 2)}");
t("Delete[f]", "true");
t("Delete[g]", "true");
t("Delete[h]", "true");
}
@Test
public void SolveArbconst(){
t("a(t):=2t+3","2 * t + 3");
t("v(t):=Integral[a(t),t]","t^(2) + 3 * t + c_1");
t("Solve[v(0)=0,c_1]","{c_1 = 0}");
}
@Test
public void assignSolve(){
t("f(x):=a*x^2+3x-5","a * x^(2) + 3 * x -5");
t("Solve[f(x)=0]","{x = (sqrt(20 * a + 9) - 3) / (2 * a), x = (-sqrt(20 * a + 9) - 3) / (2 * a)}");
t("Solve[20a + 9 = 0]","{a = (-9) / 20}");
}
@Test
public void ExponentialEqs() {
t("Solve[7^(2 x - 5) 5^x = 9^(x + 1), x]",
"{x = (5 * log(7) + log(9)) / (log(5) + 2 * log(7) - log(9))}");
t("Solve[13^(x+1)-2*13^x=(1/5)*5^x,x]",
"{x = (-log(11) - log(5)) / (log(13) - log(5))}");
// These take too long (more than 1 minute)
// t("Solve[{6.7 * 10^9 = c * a^2007, 3 * 10^8 = c * a^950}, {c, a}]",
// "{{c = 300000000 / ((67 / 3)^(1 / 1057))^(950), a = 67 / (3 * ((67 /
// 3)^(1 / 1057))^(1056))}}");
// t("Solve[{6.7 * 10^9 = c * a^2007, 3 * 10^8 = c * a^950}, {a, c}]",
// "{{c = 300000000 / ((67 / 3)^(1 / 1057))^(950), a = 67 / (3 * ((67 /
// 3)^(1 / 1057))^(1056))}}");
}
@Test
public void FDashedTest() {
t("f(x):=g(x)/x", "g(x) / x");
t("f'(x)", "(-g(x) + x * g'(x)) / x^(2)");
t("f'(x+1)", "(-g(x + 1) + g'(x + 1) * (x + 1)) / (x + 1)^(2)");
}
@Test
/** GGB-1663 */
public void ENotationTest() {
t("a:=1/1E8", "1 / 100000000");
t("b:=1/1E-8", "100000000");
}
@Test
public void vectorPointTest(){
t("v:=(1,1)","(1,1)");
t("V:=v+v", "(2,2)");
Assert.assertEquals(GeoClass.VECTOR,
app.getKernel().lookupLabel("V").getGeoClassType());
t("w:=(1,1,1)", "(1,1,1)");
t("W:=w+w", "(2,2,2)");
Assert.assertEquals(GeoClass.VECTOR3D,
app.getKernel().lookupLabel("W").getGeoClassType());
}
@Test
public void orthogonalVectorFallbackTest() {
t("E:=Plane[(1,-2,3), (-2, 0,1),(0,3,2)]", "8x - y - 13z = -29");
t("PerpendicularVector[E]", "(8, -1, -13)");
}
@Test
public void quadricReloadTest() {
t("a:=2", "2");
t("K:=x^2+y^2+z^2=a", "x^(2) + y^(2) + z^(2) = 2");
Assert.assertEquals("Sphere",
app.getKernel().lookupCasCellLabel("K").getTwinGeo()
.getTypeString());
String xml = app.getXML();
app.getKernel().clearConstruction(true);
app.setXML(xml, true);
Assert.assertEquals("Sphere", app.getKernel().lookupCasCellLabel("K")
.getTwinGeo().getTypeString());
}
@Test
public void renameCellShouldNotReplaceInput() {
t("a(x) := x^2 * x", "x^(3)");
t("b(x) := -a(x)", "-x^(3)");
GeoCasCell a = app.getKernel().lookupCasCellLabel("a");
String input = "c(x) := x^2 * x";
ta(a, false, input, "x^(3)");
new CASCellProcessor(app.getLocalization()).fixInput(a, input, false);
Assert.assertEquals("c(x) := x^2 * x",
a.getInput(StringTemplate.defaultTemplate));
Assert.assertFalse(a.isError());
}
}