From 12119620782941fbfa1f28d3b828d52eb7a73f43 Mon Sep 17 00:00:00 2001 From: Antonio Jimenez Pastor <antonio@ebook.dk-compmath.jku.at> Date: Thu, 30 Aug 2018 15:39:48 +0200 Subject: [PATCH] Added more examples of D-finite functions. Added Airy functions and ParabolicCylindric Functions --- ajpastor/dd_functions/ddExamples.py | 70 +++++++++++++++++++++ releases/diff_defined_functions__0.5.zip | Bin 110567 -> 111226 bytes ...f_defined_functions__0.5__18.08.30_15:39:48.zip | Bin 0 -> 111226 bytes 3 files changed, 70 insertions(+) create mode 100644 releases/old/diff_defined_functions__0.5__18.08.30_15:39:48.zip diff --git a/ajpastor/dd_functions/ddExamples.py b/ajpastor/dd_functions/ddExamples.py index 69d6cdc..4137183 100644 --- a/ajpastor/dd_functions/ddExamples.py +++ b/ajpastor/dd_functions/ddExamples.py @@ -460,6 +460,76 @@ def MathieuSin(a=None,q=None): @cached_function def MathieuCos(a=None,q=None): return MathieuD(a,q,(_sage_const_1 ,_sage_const_0 )); + +### Airy's functions +@cached_function +def AiryD(init=()): + name = None; + if(len(init) >= 2): ## Complete Airy function, we can build the name + ## Rejecting the zero case + if(init[0] == init[1] and init[0] == 0): + return DFinite.zero(); + + ## Simplifying the name if there is zero coefficients + if(init[0] != 0): + name_a1 = "(3**(2/3)*gamma(2/3))*%s" %init[0]; + name_b1 = "(3**(1/3)*gamma(2/3))*%s" %init[0]; + else: + name_a1 = ""; + name_b1 = ""; + if(init[1] != 0): + name_a2 = "-(3**(1/3)*gamma(1/3))*%s" %init[1]; + name_b2 = "+(gamma(1/3))*%s" %init[1]; + else: + name_a2 = ""; + name_b2 = ""; + + ## Building the final name + name = DinamicString("((%s%s)/2)*airy_ai(_1) + ((%s%s)/(2*3**(1/6)))*airy_bi(_1)" %(name_a1, name_a2, name_b1, name_b2), ["x"]); + return DFinite.element([-x,0,1], init, name=name); + +### Struve's functions +@cached_function +def StruveD(mu,kind=1): + raise NotImplementedError("Struve functions not yet implemented"); + if(kind != 1): + raise TypeError("Only struve_H functions are implemented"); + elif((mu < 0) or (mu not in ZZ)): + raise TypeError("Parameter must be greater or equal to -1 to have a power series (got %d)" %mu); + + name=DinamicString("(%s)*struve_H(%s,_1)" %((1/(struve_H(mu,x).derivative(mu+1)(x=0))),mu), ["x"]); + init = [0 for i in range(mu+1)] + [1]; + return DFinite.element([x**2*(1-mu)-mu**2,x*(x**2-mu**2-mu),-(mu-2)*x**2,x**3], init, name=name); + +### Parabolic Cylinder Functions +@cached_function +def ParabolicCylinderD(a=None,b=None,c=None, init=()): + params =[]; + if(a is None): + params += ['a']; + if(b is None): + params += ['b']; + if(c is None): + params += ['c']; + + destiny_ring = DFinite; ra = a; rb = b; rc = c; + if(len(params) > _sage_const_0 ): + destiny_ring = ParametrizedDDRing(DFinite, params); + if(len(params) == 3 ): + ra,rb,rc = destiny_ring.parameters(); + elif(len(params) == 2 and 'a' not in params): + rb,rc = destiny_ring.parameters(); + elif(len(params) == 2 and 'b' not in params): + ra,rc = destiny_ring.parameters(); + elif(len(params) == 2 and 'c' not in params): + ra,rb = destiny_ring.parameters(); + elif('a' in params): + ra = destiny_ring.parameters()[0]; + elif('b' in params): + rb = destiny_ring.parameters()[0]; + elif('c' in params): + rc = destiny_ring.parameters()[0]; + return destiny_ring.element([(rc+rb*x+ra*x**2),0,1], init, name=DinamicString("ParabolicCylinder(_1,_2,_3;_4)", [repr(ra), repr(rb), repr(rc), "x"])); ################################################################################## ################################################################################## diff --git a/releases/diff_defined_functions__0.5.zip b/releases/diff_defined_functions__0.5.zip index 44dd984fa541f39ac03fb4ff4ceabb6744b87446..fe3cab331aa34e7c6df0ce97bb38791ee26991e0 100644 GIT binary patch delta 11268 zcma)Cby!r}*FJ~t?vj-5ltx0NTaYdRrMq<K7K8zYE<uoP1VvIn38hpNq*SC!6p;94 z;6C?v`4n|{&R?wku6M=WXU)8OVH$1!BO0!jDl!TdfcWeN(k0?vU@qK_G)6pLzSsbW z@&y?HP;B7;{hyta=18Iz3ybLuR%4v9-`Kh845}q&@G>Wl(i=~Og#R9JRe<?7fFy7N z7yuj)Di6w&{t~b*6a0pPj4<J5mpR8Im|Y0<#AFIb_8b!dTwSyilVmjMb4(V{T238B z5ufL1l2{$<1f_~m>Kqi1iT%`3A@(^Y&~MluPe8cnB+dZ|q~k!r{I`10#dhZ3mG3l* 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