From 92adfc5d4855288ee119cdae21d7912c73027d59 Mon Sep 17 00:00:00 2001 From: Antonio Jimenez Pastor Date: Tue, 12 Feb 2019 17:53:53 +0100 Subject: [PATCH] Added function for computing the inverse of a polynomial. --- ajpastor/dd_functions/ddExamples.py | 48 ++++++++++++++++++--- releases/diff_defined_functions__0.6.zip | Bin 139583 -> 139868 bytes ...f_defined_functions__0.6__19.02.12_17:53:52.zip | Bin 0 -> 139868 bytes 3 files changed, 43 insertions(+), 5 deletions(-) create mode 100644 releases/old/diff_defined_functions__0.6__19.02.12_17:53:52.zip diff --git a/ajpastor/dd_functions/ddExamples.py b/ajpastor/dd_functions/ddExamples.py index f398724..1f4a765 100644 --- a/ajpastor/dd_functions/ddExamples.py +++ b/ajpastor/dd_functions/ddExamples.py @@ -1908,6 +1908,40 @@ def DAlgebraic(polynomial, init=[], dR=None): ## Returning the DDFunction ################################################## return destiny_ring.element(equation, init); + +def polynomial_inverse(polynomial): + ''' + Method that computes the functional inverse for a polynomial. As the functional + inverse of a polynomial is an algebraic series, then it is D-finite. + + The polynomial provided must be univariate. + ''' + ## Local imports + from sage.rings.polynomial.polynomial_ring import is_PolynomialRing as isPolynomial; + from ajpastor.misc.sequence_manipulation import inv_lagrangian; + + ############################################### + ## Dealing with the polynomial input + ############################################### + parent = polynomial.parent(); + if(not (isPolynomial(parent) or isMPolynomial(parent))): + raise TypeError("The minimal polynomial is NOT a polynomial"); + + if(polynomial.constant_coefficient() != 0): + raise ValueError("Non-invertible polynomial given: %s" %polynomial); + + ## Building the extra variable needed for algebraicity + x = parent.gens()[0]; + y = str(x)+"_y"; + R = PolynomialRing(parent.fraction_field(), [y]); + y = R.gens()[0]; + + ## Building the initial conditions + coeffs = polynomial.coefficients(False); + inv = inv_lagrangian(lambda n : factorial(n)*coeffs[n]); + init = [inv(i) for i in range(len(coeffs))]; + + return DAlgebraic(polynomial(**{str(x):y})-x, init); ################################################################################## ################################################################################## @@ -1926,9 +1960,15 @@ def __decide_parent(input, parent = None, depth = 1): as the coefficient of a differential equation. If 'parent' is None, then several considerations are made: - - If 'input' is a Symbolic Expression, we take the variables of it, consider everyone but 'x' as parameters and create the corresponding ParametrizedDDRing of the depth given. The argument 'input' MUST be a polynomial in 'x' and a rational function in any other variable. - - If 'input' is a polynomial, then the first generator will be consider as the variable of a DDRing and the others as parameters. Then we create the corresponding ParametrizedDDRing with the depth given. - - Otherwise, we create the DDRing of the parent of 'input' of the given depth and try to work with that ring. + - If 'input' is a Symbolic Expression, we take the variables of it, consider + everyone but 'x' as parameters and create the corresponding ParametrizedDDRing + of the depth given. The argument 'input' MUST be a polynomial in 'x' and a + rational function in any other variable. + - If 'input' is a polynomial, then the first generator will be consider as the + variable of a DDRing and the others as parameters. Then we create the corresponding + ParametrizedDDRing with the depth given. + - Otherwise, we create the DDRing of the parent of 'input' of the given depth + and try to work with that ring. ''' dR = parent; if(dR is None): @@ -1997,5 +2037,3 @@ def __check_list(list_of_elements, invalid_vars=[]): list_of_elements = [parent(el) for el in list_of_elements]; return (parent, list_of_elements); - - diff --git a/releases/diff_defined_functions__0.6.zip b/releases/diff_defined_functions__0.6.zip index 3361f62f001cd842c48339de39b7b210d340f739..03648d092287ad8aeb49e02d13744bb27083487f 100644 GIT binary patch delta 11004 zcmZX4Wl$YU+bw(J1b24`?(PyG1a}QiaEFaEIKiDwaEBm)B)B`l-QC?iL2ll2uDoB} zshaLty&joaRr8~}R!29|N-q+cssbz=3e115rZ~k!Gzuj0-)4sYxf3Ue5|vosuyX%- zgc6{Eu@lRD;r^v?pvEj9gr5?iIBwX#dC8MJEdQ1GzgcqLuivo{tQD0#TdI)P#bIFl z(?Kva$?H5sP*q$o1~M`XtU{fcp}W;jw*rEGfo=Tbz+I%#?vXm06~r~m2MSBfKQ?qZ568%? zMXoHmQ|O(W{X+*MV>`9UI31_CN$>?Ul*eL;+{i@7QQ8h6^Xfz6G&FYmx`^VOdYiZ6 z)#-qkw~;Q^agsC3g;i6N_6Xz!hO)Ca-!j*$WuO&GUI8aZIv=q*=S!$D>=_1UEt`Cj z6!+=$zkeOQuJe{T@~b&criw?y!TXdy4eR^Fr7SUB9qn`{G0d)(!TeTU+(As_g@ud( zN2N>nkIg79%^V`1+7b_*l?^cZ%-yEICB`kzp7W(TBc1HY{FREKt^@dz-l1Q6J+0Tj 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