Is useful in solving recurrence relations.įor more information see hypersimp(). Similarity in hypergeometric sense means that a quotient ofį(k) and g(k) is a rational function in k. Returns True if f and g are hyper-similar. Journal of Symbolic Computation (1995) 20, 399-417 Koepf, Algorithms for m-fold Hypergeometric Summation, Otherwise Noneįor more information on the implemented algorithm refer to: Quotient of polynomials of minimal degree. If f(k) is hypergeometric then as result we arrive with a Perform simplification of nested fractions, powersĪnd if the resulting expression is a quotient of Of gamma and rising factorial with integer, absolute Rewrite all occurrences of gamma in terms of products Rewrite all functions in terms of gamma, if possible. The algorithm performs three basic steps: Integer sequences which have equivalent representation in terms The input term can be composed of functions and Given combinatorial term f(k) simplify its consecutive term ratio > from sympy import besselj, besseli, besselsimp, polar_lift, I, S > from sympy.abc import z, nu > besselsimp ( besselj ( nu, z * polar_lift ( - 1 ))) exp(I*pi*nu)*besselj(nu, z) > besselsimp ( besseli ( nu, z * polar_lift ( - I ))) exp(-I*pi*nu/2)*besselj(nu, z) > besselsimp ( besseli ( S ( - 1 ) / 2, z )) sqrt(2)*cosh(z)/(sqrt(pi)*sqrt(z)) > besselsimp ( z * besseli ( 0, z ) + z * ( besseli ( 2, z )) / 2 + besseli ( 1, z )) 3*z*besseli(0, z)/2 hypersimp ¶. Separated expressions may not necessarily be grouped together.Īlthough factoring is necessary to separate variables in someĮxpressions, it is not necessary in all cases, so one should notĬount on the returned factors being factored. The order of the factors is determined by Mul, so that the If force=True, then bases of powers will be separated regardless (Passing None for symbols will return theĮxpression in a dictionary keyed to ‘coeff’.) Other symbols or non-symbols will be returned keyed to the Keys if symbols are provided, then all those symbols willīe used as keys, and any terms in the expression containing In a dictionary keyed to their corresponding symbols.īy default, all symbols in the expression will appear as If dict=True then the separated terms will be returned Byĭefault, it separates with respect to all symbols in anĮxpression and collects constant coefficients that are Separates variables in an expression, if possible. separatevars ( expr, symbols =, dict = False, force = False ) ¶
Query for boolean expressions using assumptions. This inconsistency will be resolved in future version. Not reduce it and you should use refine() or ask()įunction. If the expression is notĮvaluated by default (such as Predicate()), simplification will If the expression prefers automatic evaluation (such asĮq() or Or()), simplification will return True orįalse if truth value can be determined. You can avoid this behavior by passing doit=False asĪlso, it should be noted that simplifying the boolian expression is not Note that simplify() automatically calls doit() on the finalĮxpression. X belongs to the set where this relation is true. If inverse=True, it will be assumed that a composition of inverseįunctions, such as sin and asin, can be cancelled in any order.įor example, asin(sin(x)) will yield x without checking whether If rational=False(default) then nothing will be done If rational=None, Floats will be recast as Rationals but the result willīe recast as Floats. If rational=True, Floats will be recast as Rationals before simplification. Simplification strategies and then compares them using the measureįunction, we get a completely different result that is still different Note that because simplify() internally tries many different 8 > 1.7 # 1.7 is the default ratio True > simplify ( g, measure = my_measure ) -log(a)*log(b) + log(a) + log(b) return count > my_measure ( g ) 8 > my_measure ( h ) 14 > 15.
# Every other operation gets a weight of 1 (the default). count = count_ops ( expr, visual = True ). # Discourage powers by giving POW a weight of 10. Educators earn digital badges that certify knowledge, skill, and experience.> from sympy import Symbol, S > def my_measure ( expr ). Save time lesson planning by exploring our library of educator reviews to over 550,000 open educational resources (OER).Īn all-in-one learning object repository and curriculum management platform that combines Lesson Planet’s library of educator-reviews to open educational resources with district materials and district-licensed publisher content.Ī comprehensive online edtech PD solution for schools and districts. Timely and inspiring teaching ideas that you can apply in your classroom
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