From 948243676cd25a464dc25369c18b0226ceeca000 Mon Sep 17 00:00:00 2001 From: Antonio Jimenez Pastor Date: Tue, 28 Aug 2018 19:14:05 +0200 Subject: [PATCH] Added algorithm for DiffAlgOver(k) --> DiffAlgOver(k-1) --- ajpastor/dd_functions/ddFunction.py | 26 +- ajpastor/dd_functions/toDiffAlgebraic.py | 649 ++++++++++++--------- ajpastor/misc/matrix.py | 4 +- releases/diff_defined_functions__0.5.zip | Bin 109179 -> 110419 bytes ...f_defined_functions__0.5__18.08.28_19:14:05.zip | Bin 0 -> 110419 bytes 5 files changed, 407 insertions(+), 272 deletions(-) create mode 100644 releases/old/diff_defined_functions__0.5__18.08.28_19:14:05.zip diff --git a/ajpastor/dd_functions/ddFunction.py b/ajpastor/dd_functions/ddFunction.py index 470446b..d268678 100644 --- a/ajpastor/dd_functions/ddFunction.py +++ b/ajpastor/dd_functions/ddFunction.py @@ -130,7 +130,10 @@ class DDRing (Ring_w_Sequence, IntegralDomain): from sage.categories.pushout import FractionField as fraction; current = parent; - const = parent.construction(); + try: + const = parent.construction(); + except AttributeError: + raise RuntimeError("Impossible to get construction of %s" %parent); gens = [el for el in parent.gens()]; res = {'algebraic' : [], 'polynomial': [], 'other' : []}; @@ -157,15 +160,18 @@ class DDRing (Ring_w_Sequence, IntegralDomain): ## Cleaning "1" from the result ## Put everything as tuples - if(1 in res['algebraic']): - raise TypeError("1 is a generator of an algebraic extension"); - res['algebraic'] = tuple(res['algebraic']); - while(1 in res['polynomial']): - res['polynomial'].remove(1 ); - res['polynomial'] = tuple(set(res['polynomial'])); - while(1 in res['other']): - res['other'].remove(1 ); - res['other'] = tuple(set(res['other'])); + try: + if(1 in res['algebraic']): + raise TypeError("1 is a generator of an algebraic extension"); + res['algebraic'] = tuple(res['algebraic']); + while(1 in res['polynomial']): + res['polynomial'].remove(1 ); + res['polynomial'] = tuple(set(res['polynomial'])); + while(1 in res['other']): + res['other'].remove(1 ); + res['other'] = tuple(set(res['other'])); + except TypeError: + raise RuntimeError("Non hashable object found"); return res, current; diff --git a/ajpastor/dd_functions/toDiffAlgebraic.py b/ajpastor/dd_functions/toDiffAlgebraic.py index bb76b27..7767bce 100644 --- a/ajpastor/dd_functions/toDiffAlgebraic.py +++ b/ajpastor/dd_functions/toDiffAlgebraic.py @@ -1,6 +1,14 @@ 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 ajpastor.dd_functions.ddFunction import *; +from sage.rings.polynomial.infinite_polynomial_ring import InfinitePolynomialRing; + +from ajpastor.misc.matrix import matrix_of_dMovement; + ################################################################################ ### ### Second approach: use an infinite polynomial field @@ -28,289 +36,408 @@ def get_InfinitePolynomialRingVaribale(parent, gen, number): def infinite_derivative(element, times=1): if(times in ZZ and times > 1): return infinite_derivative(infinite_derivative(element, times-1)) - if(not is_InfinitePolynomialRing(element.parent())): + try: + parent = element.parent(); + except AttributeError: + return 0; + + if(not is_InfinitePolynomialRing(parent)): try: return element.derivative(); except AttributeError: - return element.parent().zero(); + return parent.zero(); if(element.is_monomial()): if(len(element.variables()) == 1): - parent = element.parent() return parent(repr(parent.gen()).replace("*", str(int(str(element).split("_")[-1])+1))); else: degrees = element.degrees(); - variables = element.variables(); - part = prod(variables[i]^(degrees[i]-1) for i in range(len(degrees))); + variables = [parent("y_%d" %i) for i in range(len(degrees))]; variables.reverse(); + print degrees; + print variables; + part = prod(variables[i]**(degrees[i]-1) for i in range(len(degrees))); return sum([degrees[i]*infinite_derivative(variables[i])*prod(variables[j] for j in range(len(variables)) if i != j) for i in range(len(variables))]); else: coefficients = element.coefficients(); monomials = element.monomials(); - return sum([coefficients[i].derivative()*monomials[i] + coefficients[i]*infinite_derivative(monomials[i]) for i in range(len(monomials))]); - -################################################################################ -### -### 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); + return sum([coefficients[i].derivative()*monomials[i] + coefficients[i]*infinite_derivative(parent(monomials[i])) for i in range(len(monomials))]); -## 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(); +def fromInfinityPolynomial_toFinitePolynomial(poly): + if(not is_InfinitePolynomialRing(poly.parent())): + return poly; - return sum(y[i]*final_ring(func.equation[i]) for i in range(order+1)); + gens = poly.variables(); + base = poly.parent().base(); -## 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"); + parent = PolynomialRing(base, gens); + return parent(str(poly)); - 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:]; +def toDifferentiallyAlgebraic_Below(poly): + ''' + Method that receives a polynomial with variables y_0,...,y_m with coefficients in some ring DD(R) and reduce it to a polynomial + with coefficients in R. + ''' + ### Preprocessing the input + parent = poly.parent(); + if(not is_InfinitePolynomialRing(parent)): + if(not is_MPolynomialRing(parent)): + if(not is_PolynomialRing(parent)): + raise TypeError("The input is not a valid polynomial. Obtained something in %s" %parent); + if(not str(parent.gens()[0]).startswith("y_")): + raise TypeError("The input is not a valid polynomial. Obtained %s but wanted something with variables y_*" %poly); + parent = InfinitePolynomialRing(parent.base(), "y"); + else: + gens = list(parent.gens()); + to_delete = []; + for gen in gens: + if(str(gen).startswith("y_")): + to_delete += [gen]; + if(len(to_delete) == 0): + raise TypeError("The input is not a valid polynomial. Obtained %s but wanted something with variables y_*" %poly); + for gen in to_delete: + gens.remove(gen); + parent = InfinitePolynomialRing(PolynomialRing(parent.base(), gens), "y"); 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]; + if(parent.ngens() > 1 or repr(parent.gen()) != "y_*"): + raise TypeError("The input is not a valid polynomial. Obtained %s but wanted something with variables y_*" %poly); + poly = parent(poly); - 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); + ### Now poly is in a InfinitePolynomialRing with one generator "y_*" and some base ring. + if(not isinstance(parent.base(), DDRing)): + print "The base ring is not a DDRing. Returning the original polynomial (reached the bottom)"; + return fromInfinityPolynomial_toFinitePolynomial(poly); -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; + up_ddring = parent.base() + dw_ddring = up_ddring.base(); + goal_ring = InfinitePolynomialRing(dw_ddring, "y"); - ## 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; + coefficients = poly.coefficients(); + monomials = poly.monomials(); -__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, {}); + ## Arraging the coefficients and organize the vector-space notation + dict_to_derivatives = {}; + dict_to_vectors = {}; + S = 0; + for i in range(len(coefficients)): + coeff = coefficients[i]; monomial = goal_ring(monomials[i]); + if(coeff in dw_ddring): + if(1 not in dict_to_vectors): + S += 1; + dict_to_vectors[1] = goal_ring.zero(); + dict_to_vectors[1] += dw_ddring(coeff)*monomial; + else: + used = False; + for el in dict_to_derivatives: + try: + index = dict_to_derivatives[el].index(coeff); + dict_to_derivatives[el][index] += monomial; + used = True; + break; + except ValueError: + pass; + if(not used): + list_of_derivatives = [coeff]; + for j in range(coeff.getOrder()-1): + list_of_derivatives += [list_of_derivatives[-1].derivative()]; + dict_to_derivatives[coeff] = list_of_derivatives; + dict_to_vectors[coeff] = [monomial] + [0 for j in range(coeff.getOrder()-1)]; + S += coeff.getOrder(); - 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(); + rows = []; + for el in dict_to_vectors: + if(el == 1): + row = [dict_to_vectors[el]]; + for i in range(S-1): + row += [infinite_derivative(row[-1])]; + rows += [row]; + else: + rows += [row for row in matrix_of_dMovement(el.equation.companion(), vector(goal_ring, dict_to_vectors[el]), infinite_derivative, S)]; - return element; + M = Matrix(goal_ring, rows); + print M; -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]; + return M.determinant(); + +def diff_to_diffalg(func): + try: + parent = func.parent(); + except AttributeError: + return PolynomialRing(QQ,"y_0")("y_0 + %s" %func); -################################################################################################### -### PACKAGE ENVIRONMENT VARIABLES -################################################################################################### -__all__ = ["is_InfinitePolynomialRing", "get_InfinitePolynomialRingGen", "get_InfinitePolynomialRingVaribale", "infinite_derivative"]; + if(isinstance(parent, DDRing)): + R = InfinitePolynomialRing(parent.base(), "y"); + p = sum(func[i]*R("y_%d" %i) for i in range(func.getOrder()+1)); + for i in range(parent.depth()-1): + p = toDifferentiallyAlgebraic_Below(p); + else: + R = PolynomialRing(PolynomialRing(QQ,x).fraction_field, "y_0"); + 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 +#################################################################################################### +__all__ = ["is_InfinitePolynomialRing", "get_InfinitePolynomialRingGen", "get_InfinitePolynomialRingVaribale", "infinite_derivative", "toDifferentiallyAlgebraic_Below", "diff_to_diffalg"]; diff --git a/ajpastor/misc/matrix.py b/ajpastor/misc/matrix.py index 5822b73..93ac2c8 100644 --- a/ajpastor/misc/matrix.py +++ b/ajpastor/misc/matrix.py @@ -378,9 +378,11 @@ def __dm(M,v,D): return differential_movement(M,v,D); def matrix_of_dMovement(M,v,D, cols): + from sage.categories.pushout import pushout; + parent = pushout(M.parent().base(), v.parent().base()); res = [v]; for j in range(1 ,cols): res += [__dm(M,res[-1 ],D)]; - return Matrix(M.parent().base(), res).transpose(); + return Matrix(parent, res).transpose(); diff --git a/releases/diff_defined_functions__0.5.zip b/releases/diff_defined_functions__0.5.zip index 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