@Override
public IExpr evaluate(final IAST ast) {
if ((ast.size() == 2) && ast.get(1).isList()) {
final AST lst = (AST) ast.get(1);
final int len0 = lst.size() - 1;
final IAST resultList = List();
final int[] indexArray = new int[2];
indexArray[0] = len0;
indexArray[1] = len0;
final IIndexFunction<IExpr> function =
new IIndexFunction<IExpr>() {
public IExpr evaluate(int[] index) {
return Power(lst.get(index[0] + 1), IntegerSym.valueOf(index[1]));
}
};
final IndexTableGenerator<IExpr, IAST> generator =
new IndexTableGenerator<IExpr, IAST>(indexArray, resultList, function, AST.COPY);
final IAST matrix = (IAST) generator.table();
if (matrix != null) {
matrix.addEvalFlags(IAST.IS_MATRIX);
}
return matrix;
}
return null;
}
@Override
public IExpr evaluate(final IAST functionList) {
if (functionList.size() != 2) {
throw new WrongNumberOfArguments(functionList, 1, functionList.size() - 1);
}
return F.bool(functionList.get(1).isVector() != (-1));
}
/**
* This method is used by <code>evaluate(double[], int, int)</code> methods to
* verify that the input parameters designate a subarray of positive length.
* <p>
* <ul>
* <li>returns <code>true</code> iff the parameters designate a subarray of
* non-negative length</li>
* <li>throws <code>IllegalArgumentException</code> if the array is null or or
* the indices are invalid</li>
* <li>returns <code>false</li> if the array is non-null, but
* <code>length</code> is 0 unless <code>allowEmpty</code> is
* <code>true</code>
* </ul>
* </p>
*
* @param values
* the input array
* @param begin
* index of the first array element to include
* @param length
* the number of elements to include
* @param allowEmpty
* if <code>true</code> then zero length arrays are allowed
* @return true if the parameters are valid
* @throws IllegalArgumentException
* if the indices are invalid or the array is null
* @since 3.0
*/
protected boolean test(
final IAST values, final int begin, final int length, final boolean allowEmpty) {
if (values == null) {
throw new NullArgumentException(LocalizedFormats.INPUT_ARRAY);
}
if (begin < 0) {
throw new NotPositiveException(LocalizedFormats.START_POSITION, begin);
}
if (length < 0) {
throw new NotPositiveException(LocalizedFormats.LENGTH, length);
}
if (begin + length > values.size()) {
throw new NumberIsTooLargeException(
LocalizedFormats.SUBARRAY_ENDS_AFTER_ARRAY_END, begin + length, values.size(), true);
}
if (length == 0 && !allowEmpty) {
return false;
}
return true;
}
public boolean apply(IExpr expr) {
if (expr.isRational()) {
return true;
}
if (expr.isSymbol()) {
return true;
}
if (expr.isTimes() || expr.isPlus()) {
IAST ast = (IAST) expr;
for (int i = 1; i < ast.size(); i++) {
if (!apply(ast.get(i))) {
return false;
}
}
return true;
}
if (expr.isPower() && ((IAST) expr).get(1).isSymbol() && ((IAST) expr).get(2).isInteger()) {
try {
int in = ((IInteger) ((IAST) expr).get(2)).toInt();
if (in > 0) {
return true;
}
} catch (ArithmeticException ae) {
}
return false;
}
return false;
}
@Override
public IExpr evaluate(final IAST ast) {
Validate.checkSize(ast, 2);
if (ast.get(1).isAST()) {
return ast.get(1).replaceRepeated(REPLACE_RULES);
}
return ast.get(1);
}
/**
* Converts a given function into the corresponding TeX output
*
* @param buf StringBuffer for MathML output
* @param f The math function which should be converted to MathML
*/
public boolean convert(final StringBuffer buf, final IAST f, final int precedence) {
if (f.size() != 2) {
return false;
}
buf.append(" \\neg ");
fFactory.convert(buf, f.get(1), 0);
return true;
}
@Override
public IExpr numericEval(final IAST functionList) {
Validate.checkSize(functionList, 2);
if (functionList.get(1) instanceof Num) {
return numericEvalD1((Num) functionList.get(1));
}
if (functionList.get(1) instanceof ComplexNum) {
return numericEvalDC1((ComplexNum) functionList.get(1));
}
return numericEvalArg1(functionList.get(1));
}
/**
* Converts a given function into the corresponding MathML output
*
* @param buf StringBuffer for MathML output
* @param f The math function which should be converted to MathML
*/
public boolean convert(final StringBuffer buf, final IAST f, final int precedence) {
if (f.size() != 2) {
return false;
}
fFactory.tagStart(buf, "mrow");
// ⌊ &x0230A;
fFactory.tag(buf, "mo", "⌊");
fFactory.convert(buf, f.get(1), 0);
// ⌋ æB;
fFactory.tag(buf, "mo", "æB;");
fFactory.tagEnd(buf, "mrow");
return true;
}
@Override
public IExpr evaluate(final IAST ast) {
Validate.checkRange(ast, 2, 3);
IExpr arg = F.evalExpandAll(ast.get(1));
try {
if (arg.isTimes() || arg.isPower()) {
IExpr[] parts = Apart.getFractionalParts(arg);
if (parts != null) {
if (parts[0].isPlus() && parts[1].isPlus()) {
IAST[] numParts = ((IAST) parts[0]).split(new PolynomialPredicate());
IAST[] denParts = ((IAST) parts[1]).split(new PolynomialPredicate());
IExpr denParts0 = F.eval(denParts[0]);
if (!denParts0.equals(F.C1)) {
IExpr[] result = Cancel.cancelGCD(numParts[0], denParts0);
if (result != null) {
return F.Times(
result[0], numParts[1], F.Power(F.Times(result[1], denParts[1]), F.CN1));
}
}
}
}
}
} catch (JASConversionException jce) {
if (Config.DEBUG) {
jce.printStackTrace();
}
}
return arg;
}
/**
* This default implementation just calls {@link #increment} in a loop over the specified portion
* of the input array.
*
* <p>Throws IllegalArgumentException if the input values array is null.
*
* @param values array holding values to add
* @param begin index of the first array element to add
* @param length number of array elements to add
* @throws IllegalArgumentException if values is null
* @see
* org.apache.commons.math3.stat.descriptive.StorelessUnivariateStatistic#incrementAll(double[],
* int, int)
*/
public void incrementAll(IAST values, int begin, int length) {
if (test(values, begin, length)) {
int k = begin + length;
for (int i = begin; i < k; i++) {
increment(values.get(i));
}
}
}
/**
* This method is used by <code>evaluate(double[], double[], int, int)</code>
* methods to verify that the begin and length parameters designate a subarray
* of positive length and the weights are all non-negative, non-NaN, finite,
* and not all zero.
* <p>
* <ul>
* <li>returns <code>true</code> iff the parameters designate a subarray of
* non-negative length and the weights array contains legitimate values.</li>
* <li>throws <code>IllegalArgumentException</code> if any of the following
* are true:
* <ul>
* <li>the values array is null</li>
* <li>the weights array is null</li>
* <li>the weights array does not have the same length as the values array</li>
* <li>the weights array contains one or more infinite values</li>
* <li>the weights array contains one or more NaN values</li>
* <li>the weights array contains negative values</li>
* <li>the start and length arguments do not determine a valid array</li>
* </ul>
* </li>
* <li>returns <code>false</li> if the array is non-null, but
* <code>length</code> is 0 unless <code>allowEmpty</code> is
* <code>true</code>.
* </ul>
* </p>
*
* @param values
* the input array.
* @param weights
* the weights array.
* @param begin
* index of the first array element to include.
* @param length
* the number of elements to include.
* @param allowEmpty
* if {@code true} than allow zero length arrays to pass.
* @return {@code true} if the parameters are valid.
* @throws IllegalArgumentException
* if the indices are invalid or the array is {@code null}.
* @since 3.0
*/
protected boolean test(
final IAST values,
final IAST weights,
final int begin,
final int length,
final boolean allowEmpty) {
if (weights == null) {
throw new NullArgumentException(LocalizedFormats.INPUT_ARRAY);
}
if (weights.size() != values.size()) {
throw new DimensionMismatchException(weights.size(), values.size());
}
boolean containsPositiveWeight = false;
for (int i = begin; i < begin + length; i++) {
// TODO implement exceptions
// if (Double.isNaN(weights[i])) {
// throw new
// MathIllegalArgumentException(LocalizedFormats.NAN_ELEMENT_AT_INDEX, i);
// }
// if (Double.isInfinite(weights[i])) {
// throw new
// MathIllegalArgumentException(LocalizedFormats.INFINITE_ARRAY_ELEMENT,
// weights[i], i);
// }
// if ( weights.get(i) < 0) {
// throw new
// MathIllegalArgumentException(LocalizedFormats.NEGATIVE_ELEMENT_AT_INDEX,
// i, weights[i]);
// }
// if (!containsPositiveWeight && weights[i] > 0.0) {
// containsPositiveWeight = true;
// }
}
if (!containsPositiveWeight) {
throw new MathIllegalArgumentException(LocalizedFormats.WEIGHT_AT_LEAST_ONE_NON_ZERO);
}
return test(values, begin, length, allowEmpty);
}
/**
* Returns <code>True</code> if the given expression is a polynoomial object; <code>False</code>
* otherwise
*/
@Override
public IExpr evaluate(final IAST ast) {
if (ast.size() != 3) {
throw new WrongNumberOfArguments(ast, 2, ast.size() - 1);
}
IAST list;
if (ast.get(2).isList()) {
list = (IAST) ast.get(2);
} else {
list = List(ast.get(2));
}
return F.bool(polynomialQ(ast.get(1), list));
}
/** @see org.matheclipse.core.expression.AST#hashCode() */
public int visit(IAST list) {
try {
++currentDepth;
if (currentDepth <= fMaxDepth) {
int hash = 0;
if (list.size() > 1) {
hash = (31 * list.get(0).hashCode() + list.get(1).accept(this) + list.size());
} else {
if (list.size() == 1) {
hash = (17 * list.get(0).hashCode());
} else {
// this case shouldn't happen
hash = 41;
}
}
return hash;
} else {
return (31 * list.head().hashCode() + list.size());
}
} finally {
--currentDepth;
}
}
@Override
public IExpr evaluate(final IAST ast) {
if (ast.size() != 2) {
return null;
}
IExpr temp = roots(ast, true);
if (temp == null || !temp.isList()) {
return null;
}
IAST list = (IAST) temp;
IAST result = F.List();
for (int i = 1; i < list.size(); i++) {
result.add(F.evaln(list.get(i)));
}
return result;
}
/**
* Check if the expression is canonical negative.
*
* @return <code>true</code> if the first argument is canonical negative
*/
public static boolean isNegativeExpression(final IExpr expr) {
if (expr.isNumber()) {
if (((INumber) expr).complexSign() < 0) {
return true;
}
} else if (expr.isTimes()) {
IAST times = (IAST) expr;
if (times.get(1).isNumber()) {
if (((INumber) times.get(1)).complexSign() < 0) {
return true;
}
}
} else if (expr.isPlus()) {
IAST plus = (IAST) expr;
if (plus.get(1).isNumber()) {
if (((INumber) plus.get(1)).complexSign() < 0) {
return true;
}
}
}
return false;
}
@Override
public IExpr evaluate(final IAST lst) {
if (lst.size() >= 3) {
try {
if (lst.get(1).isVector() < 0) {
return null;
}
if (lst.get(2).isVector() < 0) {
return null;
}
if (lst.size() == 3) {
IAST vars = (IAST) lst.get(2);
if (vars.size() <= 1) {
return null;
}
List<ISymbol> varList = new ArrayList<ISymbol>(vars.size() - 1);
String[] pvars = new String[vars.size() - 1];
for (int i = 1; i < vars.size(); i++) {
if (!vars.get(i).isSymbol()) {
return null;
}
varList.add((ISymbol) vars.get(i));
pvars[i - 1] = ((ISymbol) vars.get(i)).toString();
}
GroebnerBasePartial<BigRational> gbp = new GroebnerBasePartial<BigRational>();
IAST polys = (IAST) lst.get(1);
List<GenPolynomial<BigRational>> polyList =
new ArrayList<GenPolynomial<BigRational>>(polys.size() - 1);
JASConvert<BigRational> jas = new JASConvert<BigRational>(varList, BigRational.ZERO);
for (int i = 1; i < polys.size(); i++) {
IExpr expr = F.evalExpandAll(polys.get(i));
GenPolynomial<BigRational> poly = jas.expr2JAS(expr);
polyList.add(poly);
}
OptimizedPolynomialList<BigRational> opl = gbp.partialGB(polyList, pvars);
// System.out.println(opl);
IAST resultList = F.List();
for (GenPolynomial<BigRational> p : opl.list) {
// System.out.println(p);
resultList.add(jas.poly2Expr(p, null));
}
return resultList;
}
} catch (JASConversionException e) {
if (Config.SHOW_STACKTRACE) {
e.printStackTrace();
}
}
}
return null;
}
public IExpr evaluate(final IAST ast) {
IAST list = ast;
if (list.size() > 1) {
IAST resultList = list.copyHead();
if (AST.COPY.flatten(F.List, list, resultList, 1)) {
list = resultList;
}
// IExpr max = F.Times(F.CN1, ExprFactory.Infinity);
IExpr max1;
IExpr max2;
max1 = list.get(1);
IAST f = list.copyHead();
COMPARE_RESULT comp;
for (int i = 2; i < list.size(); i++) {
max2 = list.get(i);
comp = Less.CONST.prepareCompare(max1, max2);
if (comp == COMPARE_RESULT.TRUE) {
max1 = max2;
} else {
if (comp == COMPARE_RESULT.UNDEFINED) {
// undetermined
if (max1.isNumber()) {
f.add(max2);
} else {
f.add(max1);
max1 = max2;
}
}
}
}
if (f.size() > 1) {
f.add(1, max1);
if (f.equals(list)) {
return null;
}
return f;
} else {
return max1;
}
}
return null;
}
public IExpr evaluate(final IAST ast) {
if (ast.size() != 2) {
return null;
}
return F.stringx(new StringBuffer(ast.get(1).fullFormString()));
}
/**
* This default implementation calls {@link #clear}, then invokes {@link #increment} in a loop
* over the the input array, and then uses {@link #getResult} to compute the return value.
*
* <p>Note that this implementation changes the internal state of the statistic. Its side effects
* are the same as invoking {@link #clear} and then {@link #incrementAll(double[])}.
*
* <p>Implementations may override this method with a more efficient and possibly more accurate
* implementation that works directly with the input array.
*
* <p>If the array is null, an IllegalArgumentException is thrown.
*
* @param values input array
* @return the value of the statistic applied to the input array
* @see org.apache.commons.math3.stat.descriptive.UnivariateStatistic#evaluate(double[])
*/
public IExpr evaluate(final IAST values) {
if (values == null) {
throw new NullArgumentException(LocalizedFormats.INPUT_ARRAY);
}
return evaluate(values, 1, values.size() - 1);
}
@Override
public IExpr evaluate(final IAST ast) {
Validate.checkRange(ast, 3);
if (ast.size() == 3 && ast.get(2).isList() && ((IAST) ast.get(2)).size() == 4) {
IAST list = (IAST) ast.get(2);
if (ast.get(1).isPlus()) {
return ((IAST) ast.get(1)).map(Functors.replace1st(F.Sum(F.Null, ast.get(2))));
}
if (list.get(1).isSymbol() && list.get(2).isInteger() && list.get(3).isSymbol()) {
final ISymbol var = (ISymbol) list.get(1);
final IInteger from = (IInteger) list.get(2);
final ISymbol to = (ISymbol) list.get(3);
if (ast.get(1).isFree(var, true) && ast.get(1).isFree(to, true)) {
if (from.equals(F.C1)) {
return F.Times(to, ast.get(1));
}
if (from.equals(F.C0)) {
return F.Times(Plus(to, C1), ast.get(1));
}
} else {
if (ast.get(1).isTimes()) {
// Sum[ Times[a,b,c,...], {var, from, to} ]
IAST filterCollector = F.Times();
IAST restCollector = F.Times();
((IAST) ast.get(1))
.filter(
filterCollector,
restCollector,
new Predicate<IExpr>() {
@Override
public boolean apply(IExpr input) {
return input.isFree(var, true) && input.isFree(to, true);
}
});
if (filterCollector.size() > 1) {
if (restCollector.size() == 2) {
filterCollector.add(F.Sum(restCollector.get(1), ast.get(2)));
} else {
filterCollector.add(F.Sum(restCollector, ast.get(2)));
}
return filterCollector;
}
}
if (from.equals(F.C0)) {
IExpr repl =
ast.get(1).replaceAll(F.List(F.Rule(var, F.Slot(F.C1)), F.Rule(to, F.Slot(F.C2))));
if (repl != null) {
IExpr temp = MAP_0_N.get(repl);
if (temp != null) {
return temp.replaceAll(F.Rule(F.Slot(F.C1), to));
}
}
}
}
if (from.isPositive()) {
return F.Subtract(
F.Sum(ast.get(1), F.List(var, C0, to)),
F.Sum(ast.get(1), F.List(var, C0, from.minus(F.C1))));
}
}
}
IAST resultList = Plus();
IExpr temp = evaluateTable(ast, resultList, C0);
if (temp.equals(resultList)) {
return null;
}
return temp;
}
/**
* This default implementation just calls {@link #increment} in a loop over the input array.
*
* <p>Throws IllegalArgumentException if the input values array is null.
*
* @param values values to add
* @throws IllegalArgumentException if values is null
* @see
* org.apache.commons.math3.stat.descriptive.StorelessUnivariateStatistic#incrementAll(double[])
*/
public void incrementAll(IAST values) {
if (values == null) {
throw new NullArgumentException(LocalizedFormats.INPUT_ARRAY);
}
incrementAll(values, 1, values.size() - 1);
}
@Override
public IExpr evaluate(final IAST ast) {
final EvalEngine engine = EvalEngine.get();
if ((ast.size() == 3) && (ast.get(1)).isList()) {
final IAST lst = (IAST) ast.get(1);
final List<IExpr> variables = new ArrayList<IExpr>();
IExpr result;
try {
// remember which local variables we use:
for (int i = 1; i < lst.size(); i++) {
if (lst.get(i).isSymbol()) {
variables.add(lst.get(i));
((Symbol) lst.get(i)).pushLocalVariable();
} else {
if (lst.get(i).isAST(F.Set, 3)) {
// lhs = rhs
final IAST setFun = (IAST) lst.get(i);
if (setFun.get(1).isSymbol()) {
variables.add(setFun.get(1));
((Symbol) setFun.get(1)).pushLocalVariable(engine.evaluate(setFun.get(2)));
}
}
}
}
result = engine.evaluate(ast.get(2));
} finally {
// pop all local variables from local variable stack
for (int i = 0; i < variables.size(); i++) {
((Symbol) variables.get(i)).popLocalVariable();
}
}
return result;
}
return null;
}
public IExpr evaluate(final IAST ast) {
Validate.checkSize(ast, 3);
if (ast.get(1).isSymbol()) {
if (ast.get(2).isAST("Blank")) {
IAST blank = (IAST) ast.get(2);
if (blank.size() == 1) {
return F.$p((ISymbol) ast.get(1));
}
if (blank.size() == 2) {
return F.$p((ISymbol) ast.get(1), blank.get(1));
}
}
if (ast.get(2).isPattern()) {
IPattern blank = (IPattern) ast.get(2);
if (blank.isBlank()) {
return F.$p((ISymbol) ast.get(1), blank.getCondition());
}
}
}
return null;
}
@Override
public IExpr e2ObjArg(final IExpr o0, final IExpr o1) {
if (o0.isList() && o1.isList()) {
final IAST v0 = (IAST) o0;
final IAST v1 = (IAST) o1;
if ((v0.size() == 4) || (v1.size() == 4)) {
return List(
Plus(Times(v0.get(2), v1.get(3)), Times(F.CN1, v0.get(3), v1.get(2))),
Plus(Times(v0.get(3), v1.get(1)), Times(F.CN1, v0.get(1), v1.get(3))),
Plus(Times(v0.get(1), v1.get(2)), Times(F.CN1, v0.get(2), v1.get(1))));
}
}
return null;
}
@Override
public IExpr evaluate(final IAST ast) {
Validate.checkSize(ast, 2);
return evaluateArg1(ast.get(1));
}