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improve implemen. of FindSequenceFunction for simple int sequences
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@axkr
axkr committed Nov 1, 2024
1 parent 9e354b1 commit 8b513d2
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Showing 2 changed files with 56 additions and 26 deletions.
78 changes: 52 additions & 26 deletions ...lipse-core/src/main/java/org/matheclipse/core/reflection/system/FindSequenceFunction.java
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Original file line number Diff line number Diff line change
Expand Up @@ -79,6 +79,7 @@ public IExpr evaluate(final IAST ast, EvalEngine engine) {
if (result.isPresent()) {
return result;
}

result = findIntegerFunction(sequence, F.C2, variable, engine);
if (result.isPresent()) {
return result;
Expand All @@ -88,7 +89,7 @@ public IExpr evaluate(final IAST ast, EvalEngine engine) {
return F.NIL;
}

protected IExpr findIntegerFunction(IInteger[] sequence, IInteger startValue, IExpr variable,
private static IExpr findIntegerFunction(IInteger[] sequence, IInteger startValue, IExpr variable,
EvalEngine engine) {
IInteger factor = F.C1;
IInteger addend = F.C0;
Expand All @@ -97,16 +98,18 @@ protected IExpr findIntegerFunction(IInteger[] sequence, IInteger startValue, IE
IInteger[] newSequence = null;
if (!startValue.isZero() && sequence[0].mod(startValue).equals(F.C0)) {
factor = sequence[0].divideBy(startValue).numerator();
hasFactor = true;
newSequence = new IInteger[sequence.length];
for (int i = 0; i < sequence.length; i++) {
IRational divideBy = sequence[i].divideBy(factor);
if (!divideBy.denominator().isOne()) {
hasFactor = false;
factor = F.C1;
break;
if (!factor.isZero()) {
hasFactor = true;
newSequence = new IInteger[sequence.length];
for (int i = 0; i < sequence.length; i++) {
IRational divideBy = sequence[i].divideBy(factor);
if (!divideBy.denominator().isOne()) {
hasFactor = false;
factor = F.C1;
break;
}
newSequence[i] = divideBy.numerator();
}
newSequence[i] = divideBy.numerator();
}
}
if (!hasFactor) {
Expand All @@ -131,18 +134,23 @@ protected IExpr findIntegerFunction(IInteger[] sequence, IInteger startValue, IE
return F.NIL;
}

protected IExpr findIntegerFunction0(IInteger[] sequence, IExpr variable, IInteger factor,
private static IExpr findIntegerFunction0(IInteger[] sequence, IExpr variable, IInteger factor,
IInteger addend, EvalEngine engine) {
IExpr result =
compareSequence(F.PrimePi(F.Slot1), PRIMEPI100, sequence, factor, addend, variable, engine);
if (result.isPresent()) {
return result;
}

result = compareSequence(F.Subfactorial(F.Slot1), SUBFACTORIAL12, sequence, factor, addend,
variable, engine);
if (result.isPresent()) {
return result;
}
return F.NIL;
}

protected IExpr findIntegerFunction1(IInteger[] sequence, IExpr variable, IInteger factor,
private static IExpr findIntegerFunction1(IInteger[] sequence, IExpr variable, IInteger factor,
IInteger addend, EvalEngine engine) {
IExpr result = compareSequence(F.Factorial(F.Slot1), FACTORIAL12, sequence, factor, addend,
variable, engine);
Expand Down Expand Up @@ -207,10 +215,15 @@ protected IExpr findIntegerFunction1(IInteger[] sequence, IExpr variable, IInteg
return result;
}

result = compareSequence(F.Hyperfactorial(F.Slot1), HYPERFACTORIAL5, sequence, factor, addend,
variable, engine);
if (result.isPresent()) {
return result;
}
return F.NIL;
}

protected IExpr findIntegerFunction2(IInteger[] sequence, IExpr variable, IInteger factor,
private static IExpr findIntegerFunction2(IInteger[] sequence, IExpr variable, IInteger factor,
IInteger addend, EvalEngine engine) {
IExpr result =
compareSequence(F.Prime(F.Slot1), PRIME40, sequence, factor, addend, variable, engine);
Expand Down Expand Up @@ -250,6 +263,12 @@ protected IExpr findIntegerFunction2(IInteger[] sequence, IExpr variable, IInteg
{1, 2, 3, 8, 15, 48, 105, 384, 945, 3840, 10395, 46080, 135135, 645120, 2027025, 10321920,
34459425, 185794560, 654729075};

private final static int[] HYPERFACTORIAL5 = //
{1, 4, 108, 27648, 86400000};

private final static int[] SUBFACTORIAL12 = //
{0, 1, 2, 9, 44, 265, 1854, 14833, 133496, 1334961, 14684570, 176214841};

private final static int[] FIBONACCI40 = //
{1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, 6765, 10946,
17711, 28657, 46368, 75025, 121393, 196418, 317811, 514229, 832040, 1346269, 2178309,
Expand Down Expand Up @@ -284,26 +303,33 @@ protected IExpr findIntegerFunction2(IInteger[] sequence, IExpr variable, IInteg
21, 21, 21, 21, 22, 22, 22, 22, 23, 23, 23, 23, 23, 23, 24, 24, 24, 24, 24, 24, 24, 24,
25, 25, 25, 25};

private static IExpr compareSequence(IExpr intFunction, int[] intSequence, IInteger[] sequence,
private static IExpr compareSequence(IExpr intFunction, int[] startSequence, IInteger[] inputSequence,
IInteger factor, IInteger addend, IExpr variable, EvalEngine engine) {
if (sequence.length <= intSequence.length) {
for (int i = 0; i < sequence.length; i++) {
if (!sequence[i].equalsInt(intSequence[i])) {
if (inputSequence.length <= startSequence.length) {
for (int i = 0; i < inputSequence.length; i++) {
if (!inputSequence[i].equalsInt(startSequence[i])) {
return F.NIL;
}
}

if (!addend.isZero()) {
IExpr plus = F.Plus(addend, intFunction);
IAST function = F.Function(plus);
return createFunction(function, variable, engine);
}
if (inputSequence.length > startSequence.length) {
for (int i = startSequence.length; i < inputSequence.length; i++) {
IAST function = F.unaryAST1(F.Function(intFunction), F.ZZ(i));
IExpr bigValue = engine.evaluate(function);
if (!inputSequence[i - 1].equals(bigValue)) {
return F.NIL;
}
}
IExpr times = factor.isOne() ? intFunction : F.Times(factor, intFunction);
IAST function = F.Function(times);
return createFunction(function, variable, engine);
}

return F.NIL;
if (!addend.isZero()) {
IExpr plus = F.Plus(addend, intFunction);
IAST function = F.Function(plus);
return createFunction(function, variable, engine);
}
IExpr times = factor.isOne() ? intFunction : F.Times(factor, intFunction);
IAST function = F.Function(times);
return createFunction(function, variable, engine);
}

private static IExpr createFunction(IAST function, IExpr variable, EvalEngine engine) {
Expand Down
4 changes: 4 additions & 0 deletions ...library/matheclipse-core/src/test/java/org/matheclipse/core/system/LowercaseTestCase.java
View file
Original file line number Diff line number Diff line change
Expand Up @@ -8349,6 +8349,10 @@ public void testFindRoot() {

@Test
public void testFindSequenceFunction() {
check(
"FindSequenceFunction({0,1,2,9,44,265,1854,14833,133496,1334961,14684570,176214841,2290792932,32071101049,481066515734,7697064251745,130850092279664},n)", //
"Subfactorial(n)");

check("FindSequenceFunction({1, 1, 2, 2, 4, 2, 6, 4},n)", //
"EulerPhi(n)");
check("FindSequenceFunction({1, 1, 2, 2, 4, 2, 6, 2},n)", //
Expand Down

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