On Feb 23, 2014, at 9:58 AM, Anurag Sharma <anurag...@gmail.com> wrote:
Hi While going through some of the risch algorithm code, I couldn't understand few of the docstrings. One of them is quoted here: "DE.D is a list of the derivatives of x, t1, t2, ..., tn-1 = t, DE.T is the list [x, t1, t2, ..., tn-1], DE.t is the outer-most variable of the differential extension at the given level (the level can be adjusted using DE.increment_level() and DE.decrement_level()), k is the field C(x, t0, ..., tn-2), where C is the constant field. The numerator of a fraction is denoted by a and the denominator by d. If the fraction is named f, fa == numer(f) and fd == denom(f). Fractions are returned as tuples (fa, fd). DE.d and DE.t are used to represent the topmost derivation and extension variable, respectively." I do not understand what is the difference in DE.D and DE.T ? And also the last line. Kindly be lucid. The risch algorithm is implemented recursively. You work only with the top most variable, which is DE.t. I suggest creating some differential extensions to see how they work. Try DifferentialExtension(log(exp(x**2) + 1), x, dummy=False) (dummy=False will prevent it from using dummy variables, which will make it easier to manipulate). This extension will be, mathematically, Q(, x, t0, t1), where t0 = exp(x**2) and t1 = log(t0 + 1). These are really defined by their derivatives, so Dt0 = 2*x*t0 and Dt1 = 2*x*t0/(t0 + 1). These expressions are in the D list. They are used to take the derivative of other expressions in terms of x, t0, and t1 in derivation(). DE.t would be t1 and DE.d would be 2*x*t0/(t0 + 1). Usually you only care about the top level, i.e., DE.d and DE.t. Aaron Meurer These are hurriedly asked questions I might be able to get them after some more thought, but its better to put them on the mailing list maybe someone else stuck can also get help from these. :) Cheers -- You received this message because you are subscribed to the Google Groups "sympy" group. To unsubscribe from this group and stop receiving emails from it, send an email to sympy+unsubscr...@googlegroups.com. To post to this group, send email to sympy@googlegroups.com. Visit this group at http://groups.google.com/group/sympy. For more options, visit https://groups.google.com/groups/opt_out. -- You received this message because you are subscribed to the Google Groups "sympy" group. To unsubscribe from this group and stop receiving emails from it, send an email to sympy+unsubscr...@googlegroups.com. To post to this group, send email to sympy@googlegroups.com. Visit this group at http://groups.google.com/group/sympy. For more options, visit https://groups.google.com/groups/opt_out.
