From 2d0538761cfe44894cbc84eb36d45153cdddf8df Mon Sep 17 00:00:00 2001 From: Antonio Jimenez Pastor Date: Wed, 5 Sep 2018 11:25:01 +0200 Subject: [PATCH] Updated the algorithm diff_to_diffalg to allow parameters in the DDRings. --- ajpastor/dd_functions/ddFunction.py | 7 +- ajpastor/dd_functions/toDiffAlgebraic.py | 274 +-------------------- releases/diff_defined_functions__0.5.zip | Bin 112344 -> 109802 bytes ...f_defined_functions__0.5__18.09.05_11:25:00.zip | Bin 0 -> 109802 bytes 4 files changed, 9 insertions(+), 272 deletions(-) create mode 100644 releases/old/diff_defined_functions__0.5__18.09.05_11:25:00.zip diff --git a/ajpastor/dd_functions/ddFunction.py b/ajpastor/dd_functions/ddFunction.py index f3e5dbb..c712ec8 100644 --- a/ajpastor/dd_functions/ddFunction.py +++ b/ajpastor/dd_functions/ddFunction.py @@ -937,7 +937,7 @@ class DDFunction (IntegralDomainElement): try: self.equation = self.__buildOperator(equation); except Exception as e: - print e; + #print "here -- ", e; raise TypeError("The input for this operator is not valid"); ### Managing the inhomogeneous term @@ -1992,7 +1992,7 @@ class DDFunction (IntegralDomainElement): ''' Hash method for DDFunctions. ''' - return sum(self.getInitialValueList(20)); + return sum(hash(el) for el in self.getInitialValueList(20)); #return int("%d%d%d" %(self.getOrder(),self.equation.get_jp_fo(),self.size())); #return sum([hash(coeff) for coeff in self.getOperator().getCoefficients()]); @@ -2489,7 +2489,6 @@ def _get_initial_poly(poly, dic, m): ''' ## Constant case if(poly.is_constant()): - #print "Calling (%s +++ %s +++ %d)" %(poly, dic, m); if(m > 0): return 0; return poly.parent().base()(poly); @@ -2505,12 +2504,10 @@ def _get_initial_poly(poly, dic, m): if(el[0] == dic): found = True; if(m in el[1]): - #print "Calling (%s +++ %s +++ %d) -- CACHED" %(poly, dic, m); return el[1][m]; break; if(not found): __CACHED_INIT_POLY[poly] += [(dic, {})]; - #print "Calling (%s +++ %s +++ %d)" %(poly, dic, m); result = None; ## General case (poly is not a monomial) diff --git a/ajpastor/dd_functions/toDiffAlgebraic.py b/ajpastor/dd_functions/toDiffAlgebraic.py index ab62169..e901bda 100644 --- a/ajpastor/dd_functions/toDiffAlgebraic.py +++ b/ajpastor/dd_functions/toDiffAlgebraic.py @@ -33,7 +33,7 @@ def get_InfinitePolynomialRingGen(parent, var, with_number = False): def get_InfinitePolynomialRingVaribale(parent, gen, number): return parent(repr(gen).replace("*", str(number))); -def infinite_derivative(element, times=1): +def infinite_derivative(element, times=1, var=x): if(times in ZZ and times > 1): return infinite_derivative(infinite_derivative(element, times-1)) try: @@ -43,7 +43,10 @@ def infinite_derivative(element, times=1): if(not is_InfinitePolynomialRing(parent)): try: - return element.derivative(); + try: + return element.derivative(var); + except Exception: + return element.derivative(); except AttributeError: return parent.zero(); if(element.is_monomial()): @@ -135,7 +138,7 @@ def toDifferentiallyAlgebraic_Below(poly): for el in dict_to_derivatives: try: index = dict_to_derivatives[el].index(coeff); - dict_to_derivatives[el][index] += monomial; + dict_to_vectors[el][index] += monomial; used = True; break; except ValueError: @@ -171,7 +174,7 @@ def diff_to_diffalg(func): if(isinstance(parent, DDRing)): R = InfinitePolynomialRing(parent.base(), "y"); - p = sum(func[i]*R("y_%d" %i) for i in range(func.getOrder()+1)); + p = sum([R("y_%d" %i)*func[i] for i in range(func.getOrder()+1)], R.zero()); for i in range(parent.depth()-1): p = toDifferentiallyAlgebraic_Below(p); return p; @@ -180,269 +183,6 @@ def diff_to_diffalg(func): return R.gens()[0] - func; -################################################################################ -### -### Special cases for diff_to_diffalg -### -################################################################################ -## Polynomial in x case -#def diff_to_diffalg_poly(func): -# base, is_x = __get_base_field(func.parent()); -# final_ring = PolynomialRing(base, ["x", "y0"], order='deglex'); -# x = final_ring.gens()[0]; -# y = final_ring.gens()[1]; -# return y - final_ring(func); -# -## D-finite case -#def diff_to_diffalg_dfinite(func): -# if(not (isinstance(func.parent(), DDRing) and func.parent().depth()==1)): -# raise TypeError("diff_to_diffalg_dfinite called with a non-dfinite function"); -# if(func.is_constant): -# return diff_to_diffalg(func(0)); -# order = func.getOrder(); -# base, is_x = __get_base_field(func.parent().base()); -# -# name_vars = []; -# if(is_x): -# name_vars += ["x"]; -# name_vars += ["y%d" %i for i in range(order+1)]; -# final_ring = PolynomialRing(base, name_vars, order='deglex'); -# if(is_x): -# x = final_ring.gens()[0]; -# y = final_ring.gens()[1:]; -# else: -# y = final_ring.gens(); -# -# return sum(y[i]*final_ring(func.equation[i]) for i in range(order+1)); -# -## DD-finite case -#def diff_to_diffalg_ddfinite(func): -# if(not (isinstance(func.parent(), DDRing) and func.parent().depth()==2)): -# raise TypeError("diff_to_diffalg_ddfinite called with a non-ddfinite function"); -# -# base, is_x = __get_base_field(func.parent().base().base()); -# -# polys = [diff_to_diffalg(coeff) for coeff in func.equation.getCoefficients()]; -# orders = [coeff.getOrder() for coeff in func.equation.getCoefficients()]; -# S = sum(orders); -# name_vars = ["y%d" %i for i in range(S+func.getOrder())]; -# if(is_x): -# name_vars = ["x"] + name_vars; -# final_ring = PolynomialRing(base, name_vars, order='deglex'); -# x = None; -# if(is_x): -# x = final_ring.gens()[0]; -# y = final_ring.gens()[1:]; -# else: -# y = final_ring.gens(); -# first_row = []; -# for i in range(len(orders)): -# if(func.equation[i].getOrder() > 1 or polys[i].degree() > 1): -# first_row += [[final_ring.one()] + [final_ring.zero() for j in range(1,orders[i])]]; -# first_row += [final_ring.zero()]; -# rows = [first_row]; -# -# -# for i in range(S): -# # Each element is r[-1][a]'+r[-1][a-1]+r[-1][-1]*eq -# # Part: r[-1][a]' -# new_row = [[__get_derivative(el, [],[],y,x) for el in list] for list in rows[-1][:-1]] + [__get_derivative(rows[-1][-1], [],[],y,x)]; -# -# # Part: r[-1][a-1] -# for i in range(len(rows[:-1])): -# for j in range(1, len(rows[-1][:-1][i])): -# new_row[i][j] += rows[-1][i][j-1]; -# -# # Part: r[-1][-1]*eq -# for i in range(len(new_row)-1): -# for j in range(len(new_row[i])): -# coeff = polys[i].coefficient({y[-1]:1}); -# new_row[i][j] -= polys[i].coefficient({y[j]:1})/coeff; -# new_row[-1] -= polys[i].coefficients()[-1]/coeff; -# -# dens = sum([[el.denominator() for el in list] for list in new_row[:-1]],[]); -# dens += [new_row[-1].denominator()]; -# new_lcm = lcm(dens); -# fin_new_row = [[new_lcm*el for el in list] for list in new_row[:-1]]; -# fin_new_row += [new_lcm*new_row[-1]]; -# rows += [fin_new_row]; -# -# mat = [sum(rows[i][:-1], []) + [rows[i][-1]] for i in range(len(rows))]; -# M = Matrix(mat); -# return M.determinant(); -# -#@cached_function -#def diff_to_diffalg(func): -# ## Particular imports for this method -# from sage.categories.pushout import pushout; -# -# ## Dificult case: diff. definable function -# if(isinstance(func, DDRing.Element)): -# order = func.getOrder(); -# base = func.parent().base(); -# -# ######################################################################## -# ## Recursive-case -# if(func.parent().depth() > 2): -# # Main recursive step -# coeff_poly = [diff_to_diffalg(coeff) for coeff in func.equation.getCoefficients()]; -# -# # Building some data for getting the final polynomial ring -# base = reduce(pushout, [poly.parent().base() for poly in coeff_poly]); -# coeff_order = []; -# is_x = False; -# for i in range(order+1): -# try: -# ## Case x in poly.parent() -# coeff_poly[i].parent()('x'); -# coeff_order += [coeff_poly[i].parent().ngens()-2]; -# is_x = True; -# except: -# coeff_order += [coeff_poly[i].parent().ngens()-1]; -# -# # Getting the variables needed for the middle step -# name_vars = ["z%d_%d" %(i,j) for i in range(order+1) for j in range(coeff_order[i],-1,-1)]; -# if(is_x): -# name_vars += ["x"]; -# -# exe = 0; -# eqs = []; -# while(True): -# max_order = 1+exe;#max(coeff_order)+exe; -# -# # Building the middle polynomial ring -# mon_order = [TermOrder('deglex', coeff_order[i]+1) for i in range(order+1)]; -# if(is_x): -# mon_order += [TermOrder('deglex', 1)]; -# mon_order += [TermOrder('lex', order+max_order+1)]; -# mon_order = reduce(lambda p,q : p + q, mon_order); -# middle_ring = PolynomialRing(base, name_vars_f, order=mon_order); -# -# # Recovering the variables of the polynomial ring -# gens = middle_ring.gens(); -# z = []; -# j = 0; -# for i in range(order+1): -# z += [list(gens[j:j+coeff_order[i]+1])] -# z[-1].reverse(); -# j += coeff_order[i]+1; -# if(is_x): -# x = gens[j]; -# j += 1; -# else: -# x = None; -# y = list(gens[j:]); y.reverse(); -# -# # Computing all the required polynomials for the reduction -# # We start with the equations from the coefficients -# eqs = [middle_ring(el) for el in eqs]; -# for i in range(len(eqs),order+1): -# args = {"y%d" %j : z[i][j] for j in range(coeff_order[i]+1)}; -# eqs += [coeff_poly[i](**args)]; -# -# # We keep computing the derivatives from the equation of func -# if(len(eqs) < order+2): -# eqs += [sum(y[i]*z[i][0] for i in range(order+1))]; -# for i in range(len(eqs), order+2+max_order): -# eqs += [__get_derivative(eqs[-1], eqs[:order+1], z,y,x)]; -# -# # Now we compute a Groebner-basis to eliminate all possible variables -# # It is important to remark that the order of the variables were chosen -# # so all possible variables are eliminated and the smallest possible -# # polynomial equation remains. -# gb = ideal(eqs).groebner_basis(); -# -# # We get the final ring for the equation -# final_vars = [str(y[i]) for i in range(len(y))]; -# if(is_x): -# final_vars = ["x"] + final_vars; -# final_ring = PolynomialRing(base, final_vars, order='deglex'); -# try: -# return final_ring(str(gb[-1])); -# except TypeError: -# print "The polynomial obtained has too many variables:\n\t- Expected: %s\n\t- Got: %s" %(final_ring.gens(), gb[-1]); -# -# exe += 1; -# -# ######################################################################## -# ## Basic cases -# elif(func.parent().depth() == 2): -# return diff_to_diffalg_ddfinite(func); -# else: -# return diff_to_diffalg_dfinite(func); -# -# ############################################################################ -# ## Base case: polynomial or non-diff_definable functions -# return diff_to_diffalg_poly(func); -# -#def __get_base_field(base): -# ## Particular imports for this method -# from sage.rings.polynomial.polynomial_ring import is_PolynomialRing; -# from sage.misc.functional import is_field; -# -# ## Checking the case is R(x) -# if(is_field(base) and not (base.base() == base)): -# return __get_base_field(base.base()); -# -# ## Checking the case is R[x] -# is_x = False; -# if(is_PolynomialRing(base) and str(base.gens()[0]) == 'x'): -# base = base.base(); -# is_x = True; -# -# if(not base.is_field()): -# base = base.fraction_field(); -# -# return base, is_x; -# -#__CACHE_OF_DICS = {}; -# -#def __get_derivative(poly, equations, z,y,x): -# if(poly.is_constant()): -# return 0; -# global __CACHE_OF_DICS; -# key = tuple([tuple(equations), tuple([tuple(row) for row in z]), tuple(y)]); -# dic_of_derivatives = __CACHE_OF_DICS.get(key, {}); -# -# coeffs = poly.coefficients(); monomials = poly.monomials(); -# gens = poly.parent().gens(); -# der_mon = []; -# for mon in monomials: -# degrees = mon.degrees(); -# basic = prod(gens[i]**max(0,degrees[i]-1) for i in range(len(gens))); -# extra = poly.parent().zero(); -# for i in range(len(gens)): -# if(degrees[i] > 0): -# extra += degrees[i]*__get_variable_derivative(dic_of_derivatives, gens[i], equations, z, y ,x)*prod(gens[j] for j in range(len(gens)) if (j != i and degrees[j] > 0)); -# der_mon += [basic*extra]; -# -# __CACHE_OF_DICS[key] = dic_of_derivatives; -# -# element = sum(coeffs[i]*der_mon[i] for i in range(len(coeffs))); -# if(hasattr(element, "numerator")): -# element = element.numerator(); -# -# return element; -# -#def __get_variable_derivative(cache, var, equations, z,y,x): -# if(var not in cache): -# if(var == x): -# cache[var] = 1; -# if(var in y): -# cache[var] = y[y.index(var)+1]; -# else: -# for i in range(len(z)): -# if(var in z[i]): -# j = z[i].index(var); -# if(j < len(z[i])-1): -# cache[var] = z[i][j+1]; -# else: -# # Computing derivative of z[i][-1] -# d = equations[i].degree(z[i][j]); -# alpha = [equations[i].coefficient({z[i][j]: k}) for k in range(d+1)]; -# cache[var] = -sum(__get_derivative(alpha[i], equations,z,y,x)*z[i][-1]^i for i in range(d+1))/sum(alpha[i]*i*z[i][-1]^(i-1) for i in range(1,d+1)); -# return cache[var]; -# #################################################################################################### #### PACKAGE ENVIRONMENT VARIABLES #################################################################################################### diff --git a/releases/diff_defined_functions__0.5.zip b/releases/diff_defined_functions__0.5.zip index 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