# 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 ;
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);
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];
projects / ajpastor / diff_defined_functions.git / commitdiff