From 0fdacfaf0fe7d0117524f5e9465bee35796316f2 Mon Sep 17 00:00:00 2001 From: Antonio Jimenez Pastor Date: Tue, 2 Oct 2018 16:30:51 +0200 Subject: [PATCH] Changed the basic examples to compute the differential equation directly instead that a composition Fixed a small bug that threw errors in the LazyRing with DD-finite functions and over. Added a method (not completed) to_simpler that reduces the basic ring. The part for order 1 D-finite functions works properly. --- ajpastor/dd_functions/ddExamples.py | 35 ++++++++++----------- ajpastor/dd_functions/ddFunction.py | 34 ++++++++++++++++++-- ajpastor/lazy/lazyRing.py | 2 +- releases/diff_defined_functions__0.6.zip | Bin 121261 -> 121508 bytes ...f_defined_functions__0.6__18.10.02_16:30:51.zip | Bin 0 -> 121508 bytes 5 files changed, 49 insertions(+), 22 deletions(-) create mode 100644 releases/old/diff_defined_functions__0.6__18.10.02_16:30:51.zip diff --git a/ajpastor/dd_functions/ddExamples.py b/ajpastor/dd_functions/ddExamples.py index 14b6b86..9fe0262 100644 --- a/ajpastor/dd_functions/ddExamples.py +++ b/ajpastor/dd_functions/ddExamples.py @@ -104,9 +104,8 @@ def Sin(input, ddR = None): This function can be converted into symbolic expressions. ''' - - if(is_DDFunction(input)): - return Sin(x)(input); + #if(is_DDFunction(input)): + # return Sin(x)(input); f,dR = __decide_parent(input, ddR); evaluate = lambda p : dR.getSequenceElement(p,_sage_const_0 ); @@ -138,8 +137,8 @@ def Cos(input, ddR = None): This function can be converted into symbolic expressions. ''' - if(is_DDFunction(input)): - return Cos(x)(input); + #if(is_DDFunction(input)): + # return Cos(x)(input); f,dR = __decide_parent(input, ddR); evaluate = lambda p : dR.getSequenceElement(p,_sage_const_0 ); @@ -171,8 +170,8 @@ def Tan(input, ddR = None): This function can be converted into symbolic expressions. ''' - if(is_DDFunction(input)): - return Tan(x)(input); + #if(is_DDFunction(input)): + # return Tan(x)(input); if(input == x): return DDFinite.element([-_sage_const_2,0,Cos(x)**2],[0,1]); g, dR = __decide_parent(input, ddR,_sage_const_2 ); @@ -221,8 +220,8 @@ def Sinh(input, ddR = None): This function can be converted into symbolic expressions. ''' - if(is_DDFunction(input)): - return Sinh(x)(input); + #if(is_DDFunction(input)): + # return Sinh(x)(input); f,dR = __decide_parent(input, ddR); evaluate = lambda p : dR.getSequenceElement(p,_sage_const_0 ); @@ -254,8 +253,8 @@ def Cosh(input, ddR = None): This function can be converted into symbolic expressions. ''' - if(is_DDFunction(input)): - return Cosh(x)(input); + #if(is_DDFunction(input)): + # return Cosh(x)(input); f,dR = __decide_parent(input, ddR); evaluate = lambda p : dR.getSequenceElement(p,_sage_const_0 ); @@ -294,8 +293,8 @@ def Log(input, ddR = None): This function can be converted into symbolic expressions. ''' - if(is_DDFunction(input)): - return Log(x+_sage_const_1 )(input-1); + #if(is_DDFunction(input)): + # return Log(x+_sage_const_1 )(input-1); f,dR = __decide_parent(input, ddR); evaluate = lambda p : dR.getSequenceElement(p,_sage_const_0 ); @@ -327,8 +326,8 @@ def Log1(input, ddR = None): This function can be converted into symbolic expressions. ''' - if(is_DDFunction(input)): - return Log1(x)(input); + #if(is_DDFunction(input)): + # return Log1(x)(input); f,dR = __decide_parent(input, ddR); evaluate = lambda p : dR.getSequenceElement(p,_sage_const_0 ); @@ -362,8 +361,8 @@ def Exp(input, ddR = None): This function can be converted into symbolic expressions. ''' - if(is_DDFunction(input)): - return Exp(x)(input); + #if(is_DDFunction(input)): + # return Exp(x)(input); f,dR = __decide_parent(input, ddR); evaluate = lambda p : dR.getSequenceElement(p,_sage_const_0 ); @@ -958,7 +957,7 @@ def HillD(a='a',q='q',init=()): - init: a TUPLE with the initial values for the function. Each element can be a string to create a variable, any rational number or any polynomial expression which variables will be considered as parameters (so 'x' is not allowed). ''' if(is_DDFunction(q)): - destiny_ring = DDRing(q.parent()); + destiny_ring = q.parent().to_depth(q.parent().depth()); parent, new_all = __check_list([a] + list(init), [str(el) for el in DFinite.variables()]); if(not (parent is QQ)): diff --git a/ajpastor/dd_functions/ddFunction.py b/ajpastor/dd_functions/ddFunction.py index bc66494..75054c7 100644 --- a/ajpastor/dd_functions/ddFunction.py +++ b/ajpastor/dd_functions/ddFunction.py @@ -674,7 +674,7 @@ class DDRing (Ring_w_Sequence, IntegralDomain): elif(len(input) == 0 ): return element; - raise NotImplementedError("Not implemented evaluation of an element of this ring (%s) with the parameters %s and %s" %(self,rx,input)); + raise NotImplementedError("Not implemented evaluation of an element of this ring (%s) with the parameters %s and %s" %(self,repr(rx),input)); def get_recurrence(self, *args, **kwds): if(self.__get_recurrence is None): @@ -1531,13 +1531,24 @@ class DDFunction (IntegralDomainElement): ##################################### ### Differential methods ##################################### - def derivative(self, *args): + def derivative(self, *args, **kwds): ''' Method to get a DDFunction `g` that satisfies `D(self) = g`. INPUT: - ``args``: ignored input - ''' + - ''kwds'': if times is included, we compute the times-th derivative + ''' + if('times' in kwds): + if(kwds['times'] in ZZ): + times = kwds['times']; + if(times < 0): + raise ValueError("Negative derivatives can not be computed"); + elif(times == 0): + return self; + elif(times > 1): + return self.derivative(times=times-1).derivative(); + if(self.__derivative is None): if(self.is_constant): ### Special case: is a constant @@ -1838,12 +1849,29 @@ class DDFunction (IntegralDomainElement): to_mult *= value; return float(res),float(abs(to_sum)); + @cached_method def to_symbolic(self): evaluation = sage_eval(str(self.__name).replace("'", ".derivative()").replace("^", "**"), locals=globals()); if(isinstance(evaluation, sage.symbolic.expression.Expression)): evaluation = evaluation.simplify_full(); return evaluation; + + @cached_method + def to_simpler(self): + try: + R = self.parent().base(); + if(is_DDRing(R)): + return R(self).to_simpler(); + elif(is_PolynomialRing(R)): + if(self.getOrder() == 1): + degree = abs(self[0].lc()); + if(self.derivative(times=degree+1).is_null): + x = self.parent().variables()[0]; + return sum(self.getSequenceElement(i)*x**i for i in range(degree+1)); + except: + pass; + return self; def quick_equals(self,other): ### TO REVIEW ''' diff --git a/ajpastor/lazy/lazyRing.py b/ajpastor/lazy/lazyRing.py index d1e162d..6f2e32d 100644 --- a/ajpastor/lazy/lazyRing.py +++ b/ajpastor/lazy/lazyRing.py @@ -210,7 +210,7 @@ class _LazyElement(IntegralDomainElement): def is_zero(self): result = (self.poly() == _sage_const_0 ); - if((not result) and (self(**{str(self.parent().base().variables()[_sage_const_0 ]):_sage_const_0 }) == _sage_const_0 )): + if((not result) and (self(**{repr(self.parent().base().variables()[_sage_const_0 ]):_sage_const_0 }) == _sage_const_0 )): if(not (self.__raw is None)): result = self.raw() == _sage_const_0 ; else: diff --git a/releases/diff_defined_functions__0.6.zip 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