From 040edf704153d86f79f9e15d8915678eb86c44ff Mon Sep 17 00:00:00 2001 From: Antonio Jimenez Pastor Date: Thu, 20 Sep 2018 17:21:47 +0200 Subject: [PATCH] Modified the _element_constructor_ method of DDFunction to allow elements in the FractionField of the base domain. Added combinatorial examples: Fibonacci (with option to two parameters) and Catalan numbers --- ajpastor/dd_functions/ddExamples.py | 39 +++++++++++++++++++++ ajpastor/dd_functions/ddFunction.py | 19 +++++++--- releases/diff_defined_functions__0.5.zip | Bin 117537 -> 117890 bytes ...f_defined_functions__0.5__18.09.20_17:21:47.zip | Bin 0 -> 117890 bytes 4 files changed, 54 insertions(+), 4 deletions(-) create mode 100644 releases/old/diff_defined_functions__0.5__18.09.20_17:21:47.zip diff --git a/ajpastor/dd_functions/ddExamples.py b/ajpastor/dd_functions/ddExamples.py index 69079ee..990c203 100644 --- a/ajpastor/dd_functions/ddExamples.py +++ b/ajpastor/dd_functions/ddExamples.py @@ -67,6 +67,10 @@ def ddExamples(functions = False, names=False): - HeunD ** COULOMB WAVE FUNCTION (see chapter 33 in https://dlmf.nist.gov) - CoulombF + + ** COMBINATORIAL FUNCTIONS + - Catalan + - Fibonacci ''' if(not functions): print ddExamples.__doc__; @@ -1367,6 +1371,41 @@ def CoulombF(m='m', l='l'): return destiny_ring.element([x**2-2*rm*x-rl*(rl+1), 0, x**2], init=init, name=DinamicString("CoulombF(_1;_2)(_3)", [repr(rm), repr(rl), "x"])); +################################################################################## +################################################################################## +### +### Combinatorial functions +### +################################################################################## +################################################################################## +@cached_function +def Catalan(): + return DFinite.element([2, 10*x-2, 4*x**2-x], [1,1]); + +@cached_function +def Fibonacci(init=(1,1)): + parent, rinit = __check_list([el for el in init], [str(el) for el in DFinite.variables()]); + params = [str(v) for v in parent.gens()]; + pos = ord('a'); + if(len(init) < 2): + if(len(init) < 1): + while(chr(pos) in params): + pos += 1; + rinit = [chr(pos)]; + if(len(init) == 1): + while(chr(pos) in params): + pos += 1; + rinit += [chr(pos)]; + return Fibonacci(tuple(rinit)); + + if(parent is QQ): + destiny_ring = DFinite; + else: + destiny_ring = ParametrizedDDRing(DFinite, params); + + x = destiny_ring.variables()[0]; + + return destiny_ring(((rinit[1]-rinit[0])*x + rinit[0])/(1-x-x**2)); ################################################################################## ################################################################################## diff --git a/ajpastor/dd_functions/ddFunction.py b/ajpastor/dd_functions/ddFunction.py index d90ecf1..aa3dbc6 100644 --- a/ajpastor/dd_functions/ddFunction.py +++ b/ajpastor/dd_functions/ddFunction.py @@ -481,13 +481,24 @@ class DDRing (Ring_w_Sequence, IntegralDomain): else: try: try: - X = self.base()(X); + num = self.base()(X); den = self.base().one(); except TypeError as e: try: - X = self.base()(str(X)); + num = self.base()(str(X)); den = self.base().one(); except: - raise e; - el = self.element([-self.base_derivation(X), X]); + ## Trying the fraction field + try: + X = self.base().fraction_field()(X); + num = self.base()(X.numerator()); den = self.base()(X.denominator()); + except: + try: + X = self.base().fraction_field()(str(X)); + num = self.base()(X.numerator()); den = self.base()(X.denominator()); + except: + raise e; + + dnum = self.base_derivation(num); dden = self.base_derivation(den); + el = self.element([dden*num - dnum*den, num*den]); name = str(X); try: name = X._DDFunction__name; diff --git a/releases/diff_defined_functions__0.5.zip b/releases/diff_defined_functions__0.5.zip index 914736f37becaaaa1412250f0b593b5f76a00520..221e173e648f21191c70514c2dc71536830201ba 100644 GIT binary patch delta 37756 zcmZ6S1x%mK(zp5J4#nLm?(Xgdin}|--EZ98t);lTySuvXvfNcIFIVi<(>e4T$*!VGPK9s$Ie@;`)^kjjhOPkz$bw_vj2CxV>ZISu;TLs z_b<$cro#UVHVK*7{{mbo5Bh)LpOZ0@v^zro$FfNboe2Lr;OnISKaYSnm>T;Z+ z0jm^g3y6lLuXmo^3)VvTRF2Zh?xO2i12WC23ofQ|jb z)p}$7U8$r7fvBJ?YGhxo?;kE#zp^ij6@}#& z5BwJVagrItQZzo?7{F1o+Sgz|UTbf^{m_pQ88%lQf-{oLDcIj;Q^?1Od(`>pnK*oh 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