From 93822d8b2dadceda004bc5bbf623a9b0df711203 Mon Sep 17 00:00:00 2001 From: Antonio Jimenez Pastor Date: Wed, 17 Oct 2018 08:43:35 +0200 Subject: [PATCH] Finiched the first version of the guess function for DC-finite functions --- ajpastor/dd_functions/toDiffAlgebraic.py | 87 +++++++++++++++++---- releases/diff_defined_functions__0.6.zip | Bin 123196 -> 123671 bytes ...f_defined_functions__0.6__18.10.17_08:43:35.zip | Bin 0 -> 123671 bytes 3 files changed, 73 insertions(+), 14 deletions(-) create mode 100644 releases/old/diff_defined_functions__0.6__18.10.17_08:43:35.zip diff --git a/ajpastor/dd_functions/toDiffAlgebraic.py b/ajpastor/dd_functions/toDiffAlgebraic.py index 72cdf10..41bca2c 100644 --- a/ajpastor/dd_functions/toDiffAlgebraic.py +++ b/ajpastor/dd_functions/toDiffAlgebraic.py @@ -273,48 +273,107 @@ def inverse_DA(poly, vars=None): ## Computing the final equation return poly(**{str(g[i]): derivatives[i] for i in range(len(g))}).numerator(); -def guess_DA_DDfinite(poly): +def guess_DA_DDfinite(poly, init=[], bS=None, bd = None, all=True): ''' Method that tries to compute a DD-finite differential equation for a DA-function with constant coefficients. It just tries all the possibilities. It uses the Composition class to get the possibilities of the orders for the coefficients. + + INPUT: + - poly: polynomial with the differential equation we want to mimic with DD-finite elements + - init: initial values of the solution of poly + - bS: bound to the sum of orders in the DD-finite equation + - db: bound to the order of the DD-finite equation + - all: compute all the posibles equations ''' if(not poly.is_homogeneous()): raise TypeError("We require a homogeneous polynomial"); - S = poly.degree(); d = S - poly.parent().ngens() + 2; + if(bS is None): + S = poly.degree(); + else: + S = bS; + if(bd is None): + d = S - poly.parent().ngens() + 2; + else: + d = bd; compositions = Compositions(S, length = d+1); coeffs = [["a_%d_%d" %(i,j) for j in range(S)] for i in range(d+1)]; - R = ParametrizedDDRing(DFinite, sum(coeffs, [])); + cInit = [["i_%d_%d" %(i,j) for j in range(S-1)] for i in range(d+1)]; + R = ParametrizedDDRing(DFinite, sum(coeffs, [])+sum(cInit,[])); R2 = R.to_depth(2); coeffs = [[R.parameter(coeffs[i][j]) for j in range(S)] for i in range(d+1)]; + cInit = [[R.parameter(cInit[i][j]) for j in range(S-1)] for i in range(d+1)]; + sols = []; + for c in compositions: ## Building the parametrized guess - e = [R.element([coeffs[i][j] for j in range(c[i])] + [1],[1] + (c[i]-1)*[0]) for i in range(d+1)]; + e = [R.element([coeffs[i][j] for j in range(c[i])] + [1],cInit[i]) for i in range(d+1)]; f = R2.element(e); + if(len(init) > 0): + try: + f = f.change_init_values([init[i] for i in range(min(len(init), f.equation.jp_value+1))]); + except ValueError: + continue; ## Computing the DA equation poly2 = diff_to_diffalg(f); - ## Comparing the algebraic equations + ############################################### + ### Comparing the algebraic equations + ## Getting a possible constant difference m = poly.monomials(); m2 = poly2.monomials(); - eqs = []; + C = None; + for mon in m2: + c2 = poly2.coefficient(mon); + if(poly2.parent().base()(poly2.coefficient(mon)).is_constant()): + C = poly.coefficient(poly.parent()(mon))/c2; + break; + if(C is None): + C = 1; + elif(C == 0): + continue; + + ### Building all equations from the algebraic equation for mon in m2: - if(mon in m): - eqs += [poly2.coefficient(mon) - poly.coefficient(mon)]; + c2 = poly2.coefficient(mon); c = poly.coefficient(poly.parent()(mon)); + eqs += [C*c2 - c]; + + ################################################## + ### Comparing the initial values + for i in range(min(len(init), f.equation.jp_value+1),len(init)): + try: + eqs += [f.getInitialValue(i) - init[i]]; + except TypeError: + break; ## Case when no initial value can be computed + + ################################################## + ### Solving the system (groebner basis) + P = R.base_field.base(); + fEqs = []; + for el in eqs: + if(el.parent().is_field()): + fEqs += [P(str(el.numerator()))]; else: - eqs += [poly2.coefficient(mon)]; - P = R.base_field.base(); eqs = [P(str(el)) for el in eqs]; - gb = ideal(eqs).groebner_basis(); + fEqs += [P(str(el))]; + + gb = ideal(fEqs).groebner_basis(); if(1 not in gb): - return f,gb; - raise ValueError("No relation of the coefficients found for the polynomial %s" %poly); + sols += [(f,gb)]; + if(not all): + break; + + + if(len(sols) > 0 and not all): + return sols[0]; + + return sols; #################################################################################################### #### PACKAGE ENVIRONMENT VARIABLES #################################################################################################### -__all__ = ["is_InfinitePolynomialRing", "get_InfinitePolynomialRingGen", "get_InfinitePolynomialRingVaribale", "infinite_derivative", "toDifferentiallyAlgebraic_Below", "diff_to_diffalg", "inverse_DA"]; +__all__ = ["is_InfinitePolynomialRing", "get_InfinitePolynomialRingGen", "get_InfinitePolynomialRingVaribale", "infinite_derivative", "toDifferentiallyAlgebraic_Below", "diff_to_diffalg", 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