From a49148a78e634cd98b5d620cb83cb2cde7ee7f11 Mon Sep 17 00:00:00 2001 From: Antonio Jimenez Pastor Date: Fri, 12 Oct 2018 10:59:18 +0200 Subject: [PATCH] Added function to compute the equation for the multiplicative inverse of DA-algebraic functions. --- ajpastor/dd_functions/ddFunction.py | 37 ++++++++++++++++--- ajpastor/dd_functions/toDiffAlgebraic.py | 41 ++++++++++++++++++++- releases/diff_defined_functions__0.6.zip | Bin 121686 -> 122415 bytes ...f_defined_functions__0.6__18.10.12_10:59:18.zip | Bin 0 -> 122415 bytes 4 files changed, 71 insertions(+), 7 deletions(-) create mode 100644 releases/old/diff_defined_functions__0.6__18.10.12_10:59:18.zip diff --git a/ajpastor/dd_functions/ddFunction.py b/ajpastor/dd_functions/ddFunction.py index 82468ab..45b6bb5 100644 --- a/ajpastor/dd_functions/ddFunction.py +++ b/ajpastor/dd_functions/ddFunction.py @@ -1861,15 +1861,40 @@ class DDFunction (IntegralDomainElement): 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); @@ -1879,9 +1904,9 @@ class DDFunction (IntegralDomainElement): 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 @@ -2067,7 +2092,7 @@ class DDFunction (IntegralDomainElement): 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); diff --git a/ajpastor/dd_functions/toDiffAlgebraic.py b/ajpastor/dd_functions/toDiffAlgebraic.py index e061b46..9b9f885 100644 --- a/ajpastor/dd_functions/toDiffAlgebraic.py +++ b/ajpastor/dd_functions/toDiffAlgebraic.py @@ -3,6 +3,7 @@ from sage.all_cmdline import * # import sage library 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; @@ -203,6 +204,7 @@ def toDifferentiallyAlgebraic_Below(poly): 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): @@ -220,9 +222,46 @@ 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", 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