From 36dd46be1f59e3c65ec22adc178d5c96b52531ef Mon Sep 17 00:00:00 2001 From: Antonio Jimenez Pastor Date: Wed, 6 Feb 2019 08:51:27 +0100 Subject: [PATCH] Updated repository --- ajpastor/misc/sequence_manipulation.py | 33 ++++++++++++++++----- releases/diff_defined_functions__0.6.zip | Bin 139127 -> 139260 bytes ...f_defined_functions__0.6__19.02.06_08:51:26.zip | Bin 0 -> 139260 bytes 3 files changed, 25 insertions(+), 8 deletions(-) create mode 100644 releases/old/diff_defined_functions__0.6__19.02.06_08:51:26.zip diff --git a/ajpastor/misc/sequence_manipulation.py b/ajpastor/misc/sequence_manipulation.py index ce1b403..64eae8e 100644 --- a/ajpastor/misc/sequence_manipulation.py +++ b/ajpastor/misc/sequence_manipulation.py @@ -1,3 +1,6 @@ +from sage.functions.other import factorial; +from sage.combinat.combinat import bell_polynomial; +from sage.arith.misc import falling_factorial; ################################################################################ ################################################################################ @@ -11,6 +14,12 @@ def hadamard_product(f,g): def cauchy_product(f,g): return lambda n : sum(f(m)*g(n-m) for m in range(n+1)); + +def standard_derivation(f): + return lambda n : (n+1)*f(n+1); + +def shift(f): + return lambda n : f(n+1); def composition(f,g): if(g(0) != 0): @@ -30,6 +39,8 @@ def egf_ogf(f): ''' Method that receives a sequence in the form of a black-box function and return a sequence h(n) such that egf(f) = ogf(h). + + Then h(n) = f(n)/factorial(n) ''' return lambda n: f(n)/factorial(n); @@ -37,6 +48,8 @@ def ogf_egf(f): ''' Method that receives a sequence in the form of a black-box function and return a sequence h(n) such that egf(h) = ogf(f). + + Then h(n) = f(n)*factorial(n) ''' return lambda n: f(n)*factorial(n); @@ -45,8 +58,8 @@ def inv_lagrangian(f): raise ValueError("Power serie not invertible"); if(f(1) == 0): raise NotImplementedError("Case with order higher than 1 not implemented"); - f = egf_ogf(f); - def _inverse(n): + f = ogf_egf(f); + def _inverse_egf(n): if(n == 0): return 0; elif(n == 1): @@ -57,10 +70,14 @@ def inv_lagrangian(f): poly = bell_polynomial(n-1,k); #print poly; variables = poly.variables(); - #print variables; - extra = (-1)^k*falling_factorial(n+k-1,k); - result += extra*poly(**{str(variables[i]):f(i+1)/((i+1)*f(1)) for i in range(len(v -ariables))}); - return (1/((f(1)^n)*factorial(n))) * result; - return ogf_egf(_inverse); + extra = ((-1)**k)*falling_factorial(n+k-1, k); + if(k == n-1): + evaluation = poly(x=f(2)/2/f(1)); + else: + evaluation = poly(**{"x%d" %(i) : f(i+2)/(i+2)/f(1) for i in range(n-k)}); + + result += extra*evaluation; + + return (1/(f(1)**n)) * result; + return egf_ogf(_inverse_egf); diff --git a/releases/diff_defined_functions__0.6.zip b/releases/diff_defined_functions__0.6.zip index 009625cedbfc10fc201d5a11df346650c0e5fa2b..c492eb62dd9e4bfdc5e8c075aedde02ab5fc4e04 100644 GIT binary patch delta 6421 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