From 4c76036d340b59ec474271349a6886ac31fc8967 Mon Sep 17 00:00:00 2001 From: Antonio Jimenez Pastor Date: Tue, 2 Oct 2018 13:23:30 +0200 Subject: [PATCH] Finished the implementation of __pow__ for DDFunctions. Now it allows to compute the power of DDFunctions to any other DDFunction (if some conditions with the initial values hold). See documentation of __pow__ in DDFunction class for more information. --- ajpastor/dd_functions/ddFunction.py | 104 +++++++++++++++------ releases/diff_defined_functions__0.6.zip | Bin 120513 -> 121261 bytes ...f_defined_functions__0.6__18.10.02_13:23:30.zip | Bin 0 -> 121261 bytes 3 files changed, 73 insertions(+), 31 deletions(-) create mode 100644 releases/old/diff_defined_functions__0.6__18.10.02_13:23:30.zip diff --git a/ajpastor/dd_functions/ddFunction.py b/ajpastor/dd_functions/ddFunction.py index 340f954..bc66494 100644 --- a/ajpastor/dd_functions/ddFunction.py +++ b/ajpastor/dd_functions/ddFunction.py @@ -1958,13 +1958,32 @@ class DDFunction (IntegralDomainElement): # Integer powering def __pow__(self, other): - try: - return self.__pows[other]; - except KeyError: - f = self; - if(f.is_null): ## Trivial case when order is 0 + ''' + Method to compute the power of a DDFunction to other object. The current implementation allow the user to compute the power to: + - Integers + - Rational numbers (to be done) + - Elements in self.parent().base_field (to be done) + - Other DDFunctions (with some conditions) + + The method works as follows: + 1 - Tries to compute integer or rational power. + 2 - If 'other' is neither in ZZ nor QQ, then try to cast 'other' to a DDFunction. + 3 - Check if self(0) != 0. If self(0) != 1, check log(self(0)) in self.parent().base_field and set f2 = self/self(0). + 4 - If other(0) != 0, compute g2 = other - other(0) and return self**other(0) * self**g2 + 5 - If other(0) == 0, compute ((log(self(0)) + log(f2))other)', and return the function with initial value 1. + + + The only case that is not included is when self(0) = 0 or self**other(0) is not implemented. + ''' + if(other not in self.__pows): + f = self; g = other; f0 = f(x=0); + if(f.is_null or other == 0): + raise ValueError("Value 0**0 not well defined"); + if(f.is_null): # Trivial case when f == 0, then f**g = 0. self.__pows[other] = f; - elif(other in ZZ): ## Trying integer power + elif(g == 0): # Second trivial case when f != 0 and g == 0. Then f**g = 1 + self.__pows[other] = f.parent().one(); + elif(other in ZZ): # Integer case: can always be computed other = int(other); if(other >= 0 ): a = other >> 1 ; @@ -1981,10 +2000,31 @@ class DDFunction (IntegralDomainElement): except Exception: raise ZeroDivisionError("Impossible to compute the inverse"); return inverse.__pow__(-other); - else: ## Trying a generic power - if(is_DDFunction(other) or other in self.parent()): - if(self(x=0) != 1): - raise ValueError("The base of exponentiation must have initial value 1"); + elif(g in f.parent().base_field): # Constant case: need extra condition (f(0) != 0 and f(0)**g is a valid element + g = f.parent().base_field(g); + if(f0 == 0): + raise NotImplementedError("The powers for elements with f(0) == 0 is not implemented"); + try: + h0 = f0**g; + if(not h0 in f.parent().base_field): + raise ValueError("The initial value is not in the base field"); + except Exception as e: + raise ValueError("The power %s^%s could not be computed, hence the initial values can not be properly computed.\n\tReason: %s" %(f0,g,e)); + R = f.parent().to_depth(f.parent().depth()+1); + name = None; + if(f.has_name()): + name = DinamicString("(_1)^(%s)" %g, [repr(f)]); + self.__pows[other] = R.element([-other*f.derivative(), f], [h0]); + else: # Generic case: need extra condition (f(0) != 0, log(f(0)) and f(0)**g(0) are valid elements) + if(f0 == 0): + raise NotImplementedError("The powers for elements with f(0) == 0 is not implemented"); + lf0 = log(f0); + if(log(f0) not in f.parent().base_field): + raise ValueError("Invalid value for log(f(0)). Need to be an element of %s, but got %s" %(f.parent().base_field, log(f0))); + lf0 = f.parent().base_field(lf0); + f = f/f0; + + if(is_DDFunction(g) or g in self.parent()): from ajpastor.dd_functions.ddExamples import Log; lf = Log(self); @@ -1992,28 +2032,30 @@ class DDFunction (IntegralDomainElement): g = R(other); lf = R(lf); R = R.to_depth(R.depth()+1); - if((g(x=0) != 0)): - raise ValueError("The exponent must have initial value 0"); - - newName = None; - if((not is_DDFunction(g)) or (g._DDFunction__name is not None)): - newName = DinamicString("(_1)^(_2)", [self.__name, repr(other)]); - - self.__pows[other] = R.element([-(lf*other).derivative(),1],[1],name=newName); - else: - try: - newDDRing = DDRing(self.parent()); - other = self.parent().base_ring()(other); - self.__pows[other] = newDDRing.element([(-other)*f.derivative(),f], [el**other for el in f.getInitialValueList(1 )], check_init=False); + g0 = g(x=0); + if(g0 != 0): + self.__pows[other] = self**g0 * self**(g-g0); + else: + name = None; + if(g.has_name() and f.has_name()): + nname = DinamicString("(_1)^(_2)", [f.__name, g.__name]); - newName = None; - if(not(self.__name is None)): - newName = DinamicString("(_1)^%s" %(other), self.__name); - self.__pows[other].__name = newName; - except TypeError: - raise TypeError("Impossible to compute (%s)^(%s) within the basic field %s" %(f.getInitialValue(0 ), other, f.parent().base_ring())); - except ValueError: - raise NotImplementedError("Powering to an element of %s not implemented" %(other.parent())); + self.__pows[other] = R.element([-((lf + lf0)*g).derivative(),1],[1],name=name); + else: + raise NotImplementedError("No path found for this __pow__ computation:\n\t- base: %s\n\t- expo: %s" %(repr(self),repr(other))); + # try: + # newDDRing = DDRing(self.parent()); + # other = self.parent().base_ring()(other); + # self.__pows[other] = newDDRing.element([(-other)*f.derivative(),f], [el**other for el in f.getInitialValueList(1 )], check_init=False); + # + # newName = None; + # if(not(self.__name is None)): + # newName = DinamicString("(_1)^%s" %(other), self.__name); + # self.__pows[other].__name = newName; + # except TypeError: + # raise TypeError("Impossible to compute (%s)^(%s) within the basic field %s" %(f.getInitialValue(0 ), other, f.parent().base_ring())); + # except ValueError: + # raise NotImplementedError("Powering to an element of %s not implemented" %(other.parent())); return self.__pows[other]; diff --git a/releases/diff_defined_functions__0.6.zip b/releases/diff_defined_functions__0.6.zip index c4cca1b1c77189f8cd352003c38a3d3fdfa7385a..e156066a4144650311af1ecd26905ab8ef18d71d 100644 GIT binary patch delta 31285 zcma%>bC4&?+vVG~r)}G|?VdKKZBDztZJX1!ZQHhO+unQcZfwN6dw=_GMP$?;b>j1! zI!{JcL}m6?LRQv8!Yj&vg24d&eO+4$$H5bjF{{;U|2NQT`d@T% zaZ05Bz0h8HQZ_D)fi!WRP+R1q;{QpEyJTkme^f^M%K;Qnu@ASLfwQoPE;ta7+YcZh zx&$R)f`k|d40P$3^8dR;eH(-YIOtz45<2Mx(EoO^>-&GWs7GdC1xKio;gNf3fPLu% 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