From 36534ca0114b2cf123c6e6e077e4155397bfea44 Mon Sep 17 00:00:00 2001 From: axexlck Date: Sat, 29 Jul 2023 18:16:28 +0200 Subject: [PATCH] Improve HypergeometricPFQ --- .../matheclipse/core/reflection/system/D.java | 114 ++++++++++++------ .../system/rules/FunctionExpandRules.java | 3 + .../system/rules/HypergeometricPFQRules.java | 11 +- .../core/system/LowercaseTestCase.java | 9 ++ symja_android_library/rules/DRules.m | 2 +- .../rules/FunctionExpandRules.m | 1 + .../rules/HypergeometricPFQRules.m | 7 +- 7 files changed, 105 insertions(+), 42 deletions(-) diff --git a/symja_android_library/matheclipse-core/src/main/java/org/matheclipse/core/reflection/system/D.java b/symja_android_library/matheclipse-core/src/main/java/org/matheclipse/core/reflection/system/D.java index ce8790aa0a..89b5e40e9a 100644 --- a/symja_android_library/matheclipse-core/src/main/java/org/matheclipse/core/reflection/system/D.java +++ b/symja_android_library/matheclipse-core/src/main/java/org/matheclipse/core/reflection/system/D.java @@ -471,52 +471,20 @@ private static IExpr binaryD(final IExpr functionOfX, IExpr x, final IAST ast, } else if (function.isTimes()) { return function.map(F.PlusAlloc(16), new BinaryBindIth1st(function, F.D(S.Null, x))); } else if (function.isPower()) { - // f ^ g - final IExpr f = function.base(); - final IExpr g = function.exponent(); - if (g.isFree(x)) { - // g*D(f,y)*f^(g-1) - return F.Times(g, F.D(f, x), F.Power(f, g.dec())); - } - if (f.isFree(x)) { - if (f.isE()) { - return F.Times(F.D(g, x), F.Exp(g)); - } - // D(g,y)*Log(f)*f^g - return F.Times(F.D(g, x), F.Log(f), F.Power(f, g)); - } - - // D[f_^g_,y_]:= f^g*(((g*D[f,y])/f)+Log[f]*D[g,y]) - final IASTAppendable resultList = F.TimesAlloc(2); - resultList.append(F.Power(f, g)); - resultList - .append(F.Plus(F.Times(g, F.D(f, x), F.Power(f, F.CN1)), F.Times(F.Log(f), F.D(g, x)))); - return resultList; + return power(function, x); } else if (function.isAST(S.Surd, 3)) { // Surd[f,g] - final IExpr f = function.base(); - - if (function.exponent().isInteger()) { - final IInteger g = (IInteger) function.exponent(); - if (g.isMinusOne()) { - return F.Times(F.CN1, F.D(f, x), F.Power(f, F.CN2)); - } - final IRational gInverse = g.inverse(); - if (g.isNegative()) { - if (g.isEven()) { - return F.Times(gInverse, F.D(f, x), F.Power(F.Surd(f, g.negate()), g.dec())); - } - return F.Times(gInverse, F.D(f, x), F.Power(f, F.CN1), - F.Power(F.Surd(f, g.negate()), F.CN1)); - } - return F.Times(gInverse, F.D(f, x), F.Power(F.Surd(f, g), g.dec().negate())); - } + return surd(function, x); } else if ((header == S.Log) && (function.isAST2())) { if (function.isFreeAt(1, x)) { // D[Log[i_FreeQ(x), x_], z_]:= (x*Log[a])^(-1)*D[x,z]; return F.Times(F.Power(F.Times(function.arg2(), F.Log(function.arg1())), F.CN1), F.D(function.arg2(), x)); } + } else if (function.isAST(S.HypergeometricPFQ, 4)// + && function.first().isList()// + && function.second().isList()) { + return hypergeometricPFQ(function, x); // } else if (header == F.LaplaceTransform && (listArg1.size() // == 4)) { // if (listArg1.arg3().equals(x) && listArg1.arg1().isFree(x, @@ -566,6 +534,76 @@ private static IExpr binaryD(final IExpr functionOfX, IExpr x, final IAST ast, return F.NIL; } + private static IExpr power(final IAST function, IExpr x) { + // f ^ g + final IExpr f = function.base(); + final IExpr g = function.exponent(); + if (g.isFree(x)) { + // g*D(f,y)*f^(g-1) + return F.Times(g, F.D(f, x), F.Power(f, g.dec())); + } + if (f.isFree(x)) { + if (f.isE()) { + return F.Times(F.D(g, x), F.Exp(g)); + } + // D(g,y)*Log(f)*f^g + return F.Times(F.D(g, x), F.Log(f), F.Power(f, g)); + } + + // D[f_^g_,y_]:= f^g*(((g*D[f,y])/f)+Log[f]*D[g,y]) + final IASTAppendable resultList = F.TimesAlloc(2); + resultList.append(F.Power(f, g)); + resultList + .append(F.Plus(F.Times(g, F.D(f, x), F.Power(f, F.CN1)), F.Times(F.Log(f), F.D(g, x)))); + return resultList; + } + + private static IExpr surd(final IAST function, IExpr x) { + final IExpr f = function.base(); + if (function.exponent().isInteger()) { + final IInteger g = (IInteger) function.exponent(); + if (g.isMinusOne()) { + return F.Times(F.CN1, F.D(f, x), F.Power(f, F.CN2)); + } + final IRational gInverse = g.inverse(); + if (g.isNegative()) { + if (g.isEven()) { + return F.Times(gInverse, F.D(f, x), F.Power(F.Surd(f, g.negate()), g.dec())); + } + return F.Times(gInverse, F.D(f, x), F.Power(f, F.CN1), + F.Power(F.Surd(f, g.negate()), F.CN1)); + } + return F.Times(gInverse, F.D(f, x), F.Power(F.Surd(f, g), g.dec().negate())); + } + return F.NIL; + } + + private static IExpr hypergeometricPFQ(final IAST function, IExpr x) { + IAST list1 = (IAST) function.first(); + IAST list2 = (IAST) function.second(); + if (list1.isFree(x)&&list2.isFree(x)) { + IExpr arg3 = function.arg3(); + if (list1.isEmpty() && list2.isEmpty()) { + return F.Times(F.Exp(arg3), F.D(arg3, x)); + } + IExpr timesNumerator = list1.argSize() == 0 ? F.C1 : list1.apply(S.Times, 1); + IExpr timesDenominator = list2.argSize() == 0 ? F.C1 : list2.apply(S.Times, 1); + IASTAppendable newList1 = F.ListAlloc(list1.argSize()); + + for (int i = 1; i < list1.size(); i++) { + newList1.append(F.Plus(F.C1, list1.get(i))); + } + IASTAppendable newList2 = F.ListAlloc(list2.argSize()); + for (int i = 1; i < list2.size(); i++) { + newList2.append(F.Plus(F.C1, list2.get(i))); + } + return F.Times(timesNumerator, F.Power(timesDenominator, F.CN1), // + F.HypergeometricPFQ(newList1, newList2, arg3), // + F.D(arg3, x)); + } + return F.NIL; + } + private static IExpr dPiecewise(int[] dim, final IAST piecewiseFunction, final IAST ast, EvalEngine engine) { diff --git a/symja_android_library/matheclipse-core/src/main/java/org/matheclipse/core/reflection/system/rules/FunctionExpandRules.java b/symja_android_library/matheclipse-core/src/main/java/org/matheclipse/core/reflection/system/rules/FunctionExpandRules.java index b22fb5a09e..658327f0f8 100644 --- a/symja_android_library/matheclipse-core/src/main/java/org/matheclipse/core/reflection/system/rules/FunctionExpandRules.java +++ b/symja_android_library/matheclipse-core/src/main/java/org/matheclipse/core/reflection/system/rules/FunctionExpandRules.java @@ -164,6 +164,9 @@ public interface FunctionExpandRules { // HypergeometricPFQ({a_},{b_},z_):=Hypergeometric1F1(a,b,z) SetDelayed(HypergeometricPFQ(list(a_),list(b_),z_), Hypergeometric1F1(a,b,z)), + // HypergeometricPFQ({a_,b_},{c_},z_):=Hypergeometric2F1(a,b,c,z) + SetDelayed(HypergeometricPFQ(list(a_,b_),list(c_),z_), + Hypergeometric2F1(a,b,c,z)), // Hypergeometric2F1(2,b_,c_,-1/2):=1/3*(3-b)/;5/2-b/2==Expand(c) SetDelayed(Hypergeometric2F1(C2,b_,c_,CN1D2), Condition(Times(C1D3,Subtract(C3,b)),Equal(Plus(QQ(5L,2L),Times(CN1D2,b)),Expand(c)))), diff --git a/symja_android_library/matheclipse-core/src/main/java/org/matheclipse/core/reflection/system/rules/HypergeometricPFQRules.java b/symja_android_library/matheclipse-core/src/main/java/org/matheclipse/core/reflection/system/rules/HypergeometricPFQRules.java index 28b30694a0..7a936a42e3 100644 --- a/symja_android_library/matheclipse-core/src/main/java/org/matheclipse/core/reflection/system/rules/HypergeometricPFQRules.java +++ b/symja_android_library/matheclipse-core/src/main/java/org/matheclipse/core/reflection/system/rules/HypergeometricPFQRules.java @@ -15,10 +15,19 @@ public interface HypergeometricPFQRules { *
  • index 0 - number of equal rules in RULES
    • * */ - final public static int[] SIZES = { 0, 2 }; + final public static int[] SIZES = { 0, 5 }; final public static IAST RULES = List( IInit(HypergeometricPFQ, SIZES), + // HypergeometricPFQ({},{},z_):=E^z + ISetDelayed(HypergeometricPFQ(List(),List(),z_), + Exp(z)), + // HypergeometricPFQ({a_},{},z_):=(1-z)^(-a) + ISetDelayed(HypergeometricPFQ(list(a_),List(),z_), + Power(Subtract(C1,z),Negate(a))), + // HypergeometricPFQ({},{b_},z_):=z^(1/2-b/2)*BesselI(-1+b,2*Sqrt(z))*Gamma(b) + ISetDelayed(HypergeometricPFQ(List(),list(b_),z_), + Times(Power(z,Plus(C1D2,Times(CN1D2,b))),BesselI(Plus(CN1,b),Times(C2,Sqrt(z))),Gamma(b))), // HypergeometricPFQ({a_,b_},{c_,b_},z_):=HypergeometricPFQ({a},{c},z) ISetDelayed(HypergeometricPFQ(list(a_,b_),list(c_,b_),z_), HypergeometricPFQ(list(a),list(c),z)), diff --git a/symja_android_library/matheclipse-core/src/test/java/org/matheclipse/core/system/LowercaseTestCase.java b/symja_android_library/matheclipse-core/src/test/java/org/matheclipse/core/system/LowercaseTestCase.java index 1690e9ecde..f1dcdc5804 100644 --- a/symja_android_library/matheclipse-core/src/test/java/org/matheclipse/core/system/LowercaseTestCase.java +++ b/symja_android_library/matheclipse-core/src/test/java/org/matheclipse/core/system/LowercaseTestCase.java @@ -4658,6 +4658,15 @@ public void testCyclotomic() { } public void testD() { + check("D(HypergeometricPFQ({}, {}, x), x)", // + "E^x"); + check("D(HypergeometricPFQ({a}, {}, x), x)", // + "a/(1-x)^(1+a)"); + check("D(HypergeometricPFQ({a,b}, {u,v,w}, x), x)", // + "(a*b*HypergeometricPFQ({1+a,1+b},{1+u,1+v,1+w},x))/(u*v*w)"); + check("D(HypergeometricPFQ({a, b,c,d,e,f}, {u,v,w,y,z}, x), x)", // + "(a*b*c*d*e*f*HypergeometricPFQ({1+a,1+b,1+c,1+d,1+e,1+f},{1+u,1+v,1+w,1+y,1+z},x))/(u*v*w*y*z)"); + check("D(HarmonicNumber(Sin(Cos(x)), y), x)", // "y*Cos(Cos(x))*Sin(x)*(HarmonicNumber(Sin(Cos(x)),1+y)-Zeta(1+y))"); check("D(Sin(f(x)),{x,3})", // diff --git a/symja_android_library/rules/DRules.m b/symja_android_library/rules/DRules.m index 85c8bba236..ca1c25d499 100644 --- a/symja_android_library/rules/DRules.m +++ b/symja_android_library/rules/DRules.m @@ -47,7 +47,7 @@ /; FreeQ({f},x), D(Zeta(f_,g_),x_?NotListQ):=(-f)*Zeta(1+f, g)*D(g,x) /; FreeQ({f},x), - + D(Hypergeometric2F1(a_, b_, c_, f_), x_?NotListQ) := (a*b*Hypergeometric2F1(1 + a, 1 + b, 1 + c, f)*D(f,x))/c /; FreeQ({a,b,c},x), D(Hypergeometric2F1(a_, b_, c_, x_), {x_,n_}) := Hypergeometric2F1(a + n, b + n, c + n, x)*(Pochhammer(a, n)*Pochhammer(b, n))/Pochhammer(c, n) diff --git a/symja_android_library/rules/FunctionExpandRules.m b/symja_android_library/rules/FunctionExpandRules.m index 0a872b4258..f6ca033cbb 100644 --- a/symja_android_library/rules/FunctionExpandRules.m +++ b/symja_android_library/rules/FunctionExpandRules.m @@ -73,6 +73,7 @@ HypergeometricPFQ({1/2}, {1, 1}, z_) := BesselI(0, Sqrt(z))^2, HypergeometricPFQ({a_}, {b_}, z_) := Hypergeometric1F1(a,b,z), + HypergeometricPFQ({a_,b_}, {c_}, z_) := Hypergeometric2F1(a,b,c,z), Hypergeometric2F1(2, b_, c_, -1/2) := (3-b)/3 /; (5/2 - 1/2*b)==Expand(c), Hypergeometric2F1(a_, a_ + 1/2, c_, z_) := (2^(-1+2*a)*(1+Sqrt(1-z))^(1-2*a))/Sqrt(1-z) diff --git a/symja_android_library/rules/HypergeometricPFQRules.m b/symja_android_library/rules/HypergeometricPFQRules.m index d1864d259a..ba32d1918f 100644 --- a/symja_android_library/rules/HypergeometricPFQRules.m +++ b/symja_android_library/rules/HypergeometricPFQRules.m @@ -1,5 +1,8 @@ -{ - HypergeometricPFQ({a_,b_},{c _,b_},z_) := HypergeometricPFQ({a},{c},z), +{ + HypergeometricPFQ[{},{},z_] := E^(z), + HypergeometricPFQ[{a_},{},z_] := (1-z)^(-a), + HypergeometricPFQ[{},{b_},z_] := z^(1/2-b/2)*BesselI(-1+b,2*Sqrt(z))*Gamma(b), + HypergeometricPFQ({a_,b_},{c_,b_},z_) := HypergeometricPFQ({a},{c},z), HypergeometricPFQ({1/2, b_}, {3/2, c_}, z_) := (b/(2*b - 1))*(Sqrt(Pi/z)*Erfi(Sqrt(z)) - (Gamma(b) - Gamma(b,-z))/(-z)^b) /; PossibleZeroQ(b+1-c) } \ No newline at end of file