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WIP #1001
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@axkr
axkr committed Jun 11, 2024
1 parent 34666cf commit 6ce9120
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Showing 3 changed files with 94 additions and 1 deletion.
49 changes: 48 additions & 1 deletion ..._library/matheclipse-core/src/main/java/org/matheclipse/core/builtin/SeriesFunctions.java
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Original file line number Diff line number Diff line change
Expand Up @@ -315,7 +315,7 @@ private static IExpr evalLimit(final IExpr expr, LimitData data, EvalEngine engi
return limitValue;
}

if (limitValue.isNumericFunction(true)) {
if (limitValue.isNumericFunction(true) && expression.isFree(x -> x == S.Piecewise, true)) {
IExpr temp = evalReplaceAll(expression, data, engine);
if (temp.isPresent()) {
return temp;
Expand Down Expand Up @@ -354,6 +354,8 @@ private static IExpr evalLimit(final IExpr expr, LimitData data, EvalEngine engi
return timesLimit(ast, data, engine);
} else if (ast.isPower() && !ast.base().isPositive() && !ast.exponent().isPositive()) {
return powerLimit(ast, data, engine);
} else if (ast.isAST(S.Piecewise)) {
return piecewiseLimit(ast, data, engine);
} else if (ast.argSize() > 0 && ast.topHead().isNumericFunctionAttribute()) {
IASTMutable copy = ast.copy();
IExpr temp = F.NIL;
Expand Down Expand Up @@ -603,6 +605,7 @@ private static IExpr lHospitalesRule(IExpr numerator, IExpr denominator, LimitDa
expr = engine.evalQuiet(F.Simplify(expr));
}
if (expr.isFree(v -> v.equals(S.D) || v.equals(S.Derivative), true)) {
engine.incRecursionCounter();
return evalLimit(expr, data, engine);
}
} catch (RecursionLimitExceeded rle) {
Expand Down Expand Up @@ -782,6 +785,43 @@ private static IExpr numeratorDenominatorLimit(IExpr numerator, IExpr denominato
// return F.Times(data.limit(numerator), F.Power(data.limit(denominator), F.CN1));
}

private static IExpr piecewiseLimit(final IAST piecwiseAST, LimitData data, EvalEngine engine) {
IExpr limit = data.limitValue();
IExpr variable = data.variable();
if (limit.isReal()) {
int[] piecewiseDimension = piecwiseAST.isPiecewise();
if (piecewiseDimension != null && piecewiseDimension[0] > 0) {
IAST matrixNx2 = (IAST) piecwiseAST.first();
for (int i = 0; i < piecewiseDimension[0]; i++) {
IAST row2 = matrixNx2.getAST(i + 1);
IExpr result = row2.first();
IExpr comparison = row2.second();

if (data.direction == Direction.FROM_BELOW) {
if (comparison.isAST(S.Less, 3) && comparison.first().equals(variable)
&& comparison.second().equals(limit)) {
comparison = ((IAST) comparison).setAtCopy(0, S.LessEqual);
}
} else if (data.direction == Direction.FROM_ABOVE) {
if (comparison.isAST(S.Greater, 3) && comparison.first().equals(variable)
&& comparison.second().equals(limit)) {
comparison = ((IAST) comparison).setAtCopy(0, S.GreaterEqual);
}
}
IExpr temp = engine.evaluate(F.subs(comparison, variable, limit));
if (temp.isTrue()) {
return engine.evaluate(F.subs(result, variable, limit));
} else if (!temp.isFalse()) {
return F.NIL;
}

}
return piecwiseAST.second();
}
}
return F.NIL;
}

private static IExpr plusLimit(final IAST plusAST, LimitData data, EvalEngine engine) {
// Limit[a_+b_+c_,sym->lim] ->
// Limit[a,sym->lim]+Limit[b,sym->lim]+Limit[c,sym->lim]
Expand Down Expand Up @@ -1226,6 +1266,7 @@ public void setUp(final ISymbol newSymbol) {
}
}


/**
*
*
Expand Down Expand Up @@ -1405,6 +1446,7 @@ public int[] expectedArgSize(IAST ast) {
}
}


/**
*
*
Expand Down Expand Up @@ -1459,6 +1501,7 @@ public IExpr evaluate(final IAST ast, EvalEngine engine) {
}
}


/**
*
*
Expand Down Expand Up @@ -1495,6 +1538,7 @@ public IExpr evaluate(final IAST ast, EvalEngine engine) {
}
}


/**
*
*
Expand Down Expand Up @@ -1549,6 +1593,7 @@ public IExpr evaluate(final IAST ast, EvalEngine engine) {

}


/**
*
*
Expand Down Expand Up @@ -1815,6 +1860,7 @@ public static IExpr polynomialSeriesCoefficient(IExpr univariatePolynomial, IExp
}
}


/**
*
*
Expand Down Expand Up @@ -1875,6 +1921,7 @@ public IExpr evaluate(final IAST ast, EvalEngine engine) {
}
return F.NIL;
}

}


Expand Down
14 changes: 14 additions & 0 deletions ...ibrary/matheclipse-core/src/main/java/org/matheclipse/core/builtin/SimplifyFunctions.java
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Original file line number Diff line number Diff line change
Expand Up @@ -29,6 +29,7 @@
import org.matheclipse.core.interfaces.IInteger;
import org.matheclipse.core.interfaces.INum;
import org.matheclipse.core.interfaces.INumber;
import org.matheclipse.core.interfaces.IRational;
import org.matheclipse.core.interfaces.ISymbol;
import org.matheclipse.core.patternmatching.hash.HashedOrderlessMatcher;
import org.matheclipse.core.patternmatching.hash.HashedOrderlessMatcherPlus;
Expand Down Expand Up @@ -654,6 +655,19 @@ private IExpr visitTimes(IASTMutable timesAST, SimplifiedResult sResult) {
final IExpr denominator = eval(F.Denominator(timesAST));
if (!denominator.isNumber()) {
final IExpr numerator = eval(F.Numerator(timesAST));
if (numerator.isAST(S.RealAbs, 2) && numerator.first().equals(denominator)
&& denominator.isPlus() && denominator.first().isRational()) {
IRational n = (IRational) denominator.first();
IExpr rest = denominator.rest().oneIdentity0();
// Piecewise({{-1,rest<(-n)}},1)
return F.Piecewise(F.list(F.list(F.CN1, F.Less(rest, n.negate()))), F.C1);
} else if (denominator.isAST(S.RealAbs, 2) && denominator.first().equals(numerator)
&& numerator.isPlus() && numerator.first().isRational()) {
IRational n = (IRational) numerator.first();
IExpr rest = numerator.rest().oneIdentity0();
// Piecewise({{-1,rest<(-n)}},1)
return F.Piecewise(F.list(F.list(F.CN1, F.Less(rest, n.negate()))), F.C1);
}
if (fFullSimplify || numerator.isTimes() || denominator.isTimes()) {
IExpr numer = F.evalExpandAll(numerator);
IExpr denom = F.evalExpandAll(denominator);
Expand Down
32 changes: 32 additions & 0 deletions ...library/matheclipse-core/src/test/java/org/matheclipse/core/system/LowercaseTestCase.java
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Original file line number Diff line number Diff line change
Expand Up @@ -12762,6 +12762,23 @@ public void testLimit() {
"0");
}

@Test
public void testLimitIssue1001() {
// github issue #1001
check("Simplify(RealAbs(x + 2)/(x+2))", //
"Piecewise({{-1,x<-2}},1)");
check("Simplify(RealAbs(x - 2)/(x-2))", //
"Piecewise({{-1,x<2}},1)");
check("Limit(RealAbs(x + 2), x -> -2, Direction -> -1)", //
"0");
check("Limit(x + 2, x -> -2, Direction -> -1)", //
"0");
check("Limit(RealAbs(x + 2)/(x+2), x -> -2, Direction -> -1)", //
"1");
check("Limit(RealAbs(x + 2)/(x+2), x -> -2, Direction -> 1)", //
"-1");
}

@Test
public void testLimitIssue536() {
// avoid endless recursion:
Expand Down Expand Up @@ -24161,6 +24178,20 @@ public void testToString() {

@Test
public void testTotal() {
// TODO only add up elements inside List, Association, SparseArray,...
// check("t = Array(Subscript(a, ##) &, {2, 3, 4})", //
// "{{{Subscript(a,1,1,1),Subscript(a,1,1,2),Subscript(a,1,1,3),Subscript(a,1,1,4)},{Subscript(a,\n"
// //
// + "1,2,1),Subscript(a,1,2,2),Subscript(a,1,2,3),Subscript(a,1,2,4)},{Subscript(a,1,\n" //
// + "3,1),Subscript(a,1,3,2),Subscript(a,1,3,3),Subscript(a,1,3,4)}},{{Subscript(a,2,\n" //
// + "1,1),Subscript(a,2,1,2),Subscript(a,2,1,3),Subscript(a,2,1,4)},{Subscript(a,2,2,\n" //
// +
// "1),Subscript(a,2,2,2),Subscript(a,2,2,3),Subscript(a,2,2,4)},{Subscript(a,2,3,1),Subscript(a,\n"
// //
// + "2,3,2),Subscript(a,2,3,3),Subscript(a,2,3,4)}}}");
// check("Total(t, {-1})", //
// "");

check("Total({x^2, 3*x^3, 1})", //
"1+x^2+3*x^3");

Expand Down Expand Up @@ -24198,6 +24229,7 @@ public void testTotal() {
"{6,15,24}");
check("Total({{1,2,3},{4,5,6},{7,8,9}},2)", //
"45");

}

@Test
Expand Down

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