def to_simpler(self):
try:
R = self.parent().base();
- if(is_DDRing(R)):
- return R(self).to_simpler();
+ if(self.is_constant):
+ return self.parent().base_field(self.getInitialValue(0));
+ elif(is_DDRing(R)):
+ coeffs = [el.to_simpler() for el in self.equation.getCoefficients()];
+ parents = [el.parent() for el in coeffs];
+ final_base = reduce(lambda p,q : pushout(p,q), parents, parents[0]);
+
+ dR = None;
+ if(is_DDRing(final_base)):
+ dR = final_base.to_depth(final_base.depth()+1);
+
+ elif(not is_DDRing(final_base)):
+ params = [str(g) for g in final_base.gens()];
+ var = repr(self.parent().variables()[0]);
+
+ if(var in params):
+ params.remove(var);
+ hyper_base = DDRing(PolynomialRing(QQ,[var]));
+ if(len(params) > 0):
+ dR = ParametrizedDDRing(hyper_base, params);
+ else:
+ dR = hyper_base;
+ else:
+ raise TypeError("1:No optimization found in the simplifacion");
+
+ return dR.element([dR.base()(el) for el in coeffs], self.getInitialValueList(self.equation.jp_value+1), name=self.__name).to_simpler();
+
elif(is_PolynomialRing(R)):
degs = [self[i].degree() - i for i in range(self.getOrder()+1)];
m = max(degs);
maxs = [i for i in range(len(degs)) if degs[i] == m];
if(len(maxs) <= 1):
- raise ValueError("1:Function %s is not a polynomial" %repr(self));
+ raise ValueError("2:Function %s is not a polynomial" %repr(self));
x = R.gens()[0];
pol = sum(falling_factorial(x,i)*self[i].lc() for i in maxs);
if(pol == self):
return pol;
- raise ValueError("2:Function %s is not a polynomial" %repr(self));
+ raise ValueError("3:Function %s is not a polynomial" %repr(self));
except Exception as e:
- print e;
+ pass;
return self;
def quick_equals(self,other): ### TO REVIEW
from ajpastor.dd_functions.ddExamples import Log;
lf = Log(self);
- R = sage.categories.pushout.pushout(other.parent(), lf.parent());
+ R = pushout(other.parent(), lf.parent());
g = R(other); lf = R(lf);
R = R.to_depth(R.depth()+1);
from sage.rings.polynomial.polynomial_ring import is_PolynomialRing;
from sage.rings.polynomial.multi_polynomial_ring import is_MPolynomialRing;
+from sage.rings.fraction_field import is_FractionField;
from ajpastor.dd_functions.ddFunction import *;
from sage.rings.polynomial.infinite_polynomial_ring import InfinitePolynomialRing;
rows += [row for row in matrix_of_dMovement(C, vector(goal_ring, dict_to_vectors[el]), infinite_derivative, S)];
M = Matrix(rows);
+ print M;
return M.determinant().numerator();
def diff_to_diffalg(func):
else:
R = PolynomialRing(PolynomialRing(QQ,x).fraction_field, "y_0");
return R.gens()[0] - func;
+
+def inverse_DA(poly, vars=None):
+ '''
+ Method that computes the DA equation for the multiplicative inverse
+ of the solutions of a DA equation.
+
+ We assume that the variables given by vars are the variables representing
+ the solution, namely vars[i+1] = vars[i].derivative().
+ If vars is not provided, we take all the variables from the polynomial
+ that is given.
+ '''
+ ## Checking that poly is a polynomial
+
+ parent = poly.parent();
+ if(is_FractionField(parent)):
+ parent = parent.base();
+ if(is_InfinitePolynomialRing(parent)):
+ poly = fromInfinityPolynomial_toFinitePolynomial(poly);
+ return inverse_DA(poly, vars);
+ if(not (is_PolynomialRing(parent) or is_MPolynomialRing(parent))):
+ raise TypeError("No polynomial is given");
+ poly = parent(poly);
+
+ ## Getting the list of variables
+ if(vars is None):
+ g = poly.parent().gens();
+ else:
+ if(any(v not in poly.parent().gens())):
+ raise TypeError("The variables given are not in the polynomial ring");
+ g = vars;
+
+ ## Computing the derivative of the inverse using Faa di Bruno's formula
+ derivatives = [1/g[0]] + [sum((falling_factorial(-1, k)/g[0]**(k+1))*bell_polynomial(n,k)(*g[1:n-k+2]) for k in range(1,n+1)) for n in range(1,len(g
+))];
+
+ ## Computing the final equation
+ return poly(**{str(g[i]): derivatives[i] for i in range(len(g))}).numerator();
####################################################################################################
#### PACKAGE ENVIRONMENT VARIABLES
####################################################################################################
-__all__ = ["is_InfinitePolynomialRing", "get_InfinitePolynomialRingGen", "get_InfinitePolynomialRingVaribale", "infinite_derivative", "toDifferentiallyAlgebraic_Below", "diff_to_diffalg"];
+__all__ = ["is_InfinitePolynomialRing", "get_InfinitePolynomialRingGen", "get_InfinitePolynomialRingVaribale", "infinite_derivative", "toDifferentiallyAlgebraic_Below", "diff_to_diffalg", "inverse_DA"];
projects / ajpastor / diff_defined_functions.git / commitdiff