On Saturday, March 15, 2014 5:28:33 AM UTC+5:30, Aaron Meurer wrote: > > On Mon, Mar 3, 2014 at 2:03 PM, RAJAT AGGARWAL > <rajatagg...@gmail.com <javascript:>> wrote: > > Hi > > I was working on the other parts of the sympy code, to understand the > much > > part of it so that i can have ideas for this project that how we can > reduce > > new step_eval functions to implement step-by-step expressions. I have > come > > up with new ideas and different kind of implementations. > > > > 1. In sympy we have different kind of implementations for different kind > of > > functions. In integration we already have the list of the steps. For > > example: If I evaluate > > > > integrate(asin(x) *log(x), x), we get the integral_steps > > PartsRule(u=log(x), dv=asin(x), v_step=PartsRule(u=asin(x), dv=1, > > v_step=ConstantRule(constant=1, context=1, symbol=x), second_step= > > URule(u_var=_u, u_func=-x**2 + 1,constant=1/2, substep= > > ConstantTimesRule(constant=1/2, other=-1/sqrt(_u), substep > > =ConstantTimesRule(constant=-1, other=1/sqrt(_u), substep= > > PowerRule(base=_u, exp=-1/2, context=1/sqrt(_u), symbol=_u), > > context=-1/sqrt(_u), symbol=_u), context=-1/sqrt(_u), symbol=x), > > context=x/sqrt(-x**2 + 1), symbol=x), context=asin(x), symbol=x), > > second_step=RewriteRule(rewritten=asin(x) + sqrt(-x**2 + 1)/x, > > substep=AddRule(substeps=[PartsRule(u=asin(x), dv=1, v_step= > > ConstantRule(constant=1, context=1, symbol=x), second_step= > > URule(u_var=_u, u_func=-x**2 + 1, constant=1/2, substep= > > ConstantTimesRule(constant=1/2, other=-1/sqrt(_u), substep > > =ConstantTimesRule(constant=-1, other=1/sqrt(_u), substep= > > PowerRule(base=_u, exp=-1/2, context=1/sqrt(_u), symbol=_u), > > context=-1/sqrt(_u), symbol=_u), context=-1/sqrt(_u), symbol=x), > > context=x/sqrt(-x**2 + 1), symbol=x), context=asin(x), symbol=x), > > DontKnowRule(context=sqrt(-x**2 + 1)/x, symbol=x)], > > context=asin(x) + sqrt(-x**2 + 1)/x, symbol=x), > > context=(x*asin(x) + sqrt(-x**2 + 1))/x, symbol=x), > > context=log(x)*asin(x), symbol=x) > > > > For such a big parts like integral, we can just parse this output and > change > > this into a tree to get the whole hierarchy and then we can print the > steps > > which are taken to do this integral. > > This is already done in SymPy Gamma. >
Step-by-step implementation includes all the modules. It is just an example to proceed with different modules. What I meant was, for Integration parts we can just use this already implemented feature to show the steps. > > > In Integrations, different algorithms have been used, we can use these > steps > > and it can be used to explain the algorithms to the users. Say if a user > > want to know about risch algorithm , we can use these steps to explain > the > > algorithm by taking one example of any function. > > Sure, though this will only be useful if you want to know how the > Risch algorithm works. It will not be useful for understanding the > integration, since the Risch algorithm uses methods that are far > different from the ones you learn in calculus. > > Yeah, I agree that this is different from what we learn in calculus. In steps we can show that the question can be solved using "risch algorith" and then the algorithm .This way we can use this functionality to tell the workflow of the algorithm. > > > > 2. For derivations, I had already implemented tree structures for having > > step by step expressions, as you can see in the commits. > > For the optimizations and addition of less functions, we can > > ````traceback```` for some functions and get the inputs and outputs of > the > > called function and put that in a tree like > > > > def goto_child(self, infunc): > > if len(infunc.args) == 0: > > return infunc > > temp = infunc > > infunc = list(infunc.args) > > for i in range(len(infunc)): > > if isinstance(infunc[i], Derivative): > > infunc[i] = diff(infunc[i].expr, infunc[i].args[-1], > > evaluate=True, step=True) > > else: > > infunc[i] = self.goto_child(infunc[i]) > > at = tuple(infunc) > > return temp.func(*at) > > def tracefunc(frame, event, arg, indent=[0]): > > if event == "call": > > if frame.f_code.co_name == "_eval_derivative": > > # make a parent with 'arg' and the send the child to > the > > next call > > elif event == "return": > > # store the resturn result and then go to next level of > tree > > return tracefunc > > > > This implementation will be same for many functions which have the > standard > > call for doit() or for _eval_derivative(). Same can be done for the > basic > > classes. > > > > According to me, if we use traceback, there is a need of step_derivation > > function at the end of for some parent classes, because sympy code is > very > > vast and if in future some change happens, then we may have to change > this > > parser for traceback functions . > > > > Conclusive thought which i have is, We can use traceback to form string > of > > steps for every called functions (similar to shown in integration ) and > > then we make parser for the main function( like Integrate() ) and since > for > > every function we can get the input argument and output argument, we can > > make a tree and then we output the results. > > Benefits: Very Less addition of new functions, parser will be able to > parse > > for every function including both simple and complex. Easy > Implementation. > > No need to use strings and a parser. Just store it in a normal Python > data structure. > > Yes, I tried showing the prototype of the "tree" to be used for the storage of the parent function and its child functions . and then its inorder traversal. > Aaron Meurer > > > > > -- > > 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+un...@googlegroups.com <javascript:>. > > To post to this group, send email to sy...@googlegroups.com<javascript:>. > > > Visit this group at http://groups.google.com/group/sympy. > > To view this discussion on the web visit > > > https://groups.google.com/d/msgid/sympy/6334e79b-0d97-4bed-92f9-61214bb88217%40googlegroups.com. > > > > > > 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. To view this discussion on the web visit https://groups.google.com/d/msgid/sympy/bace0132-bdc2-4176-a798-a006d03f5eaf%40googlegroups.com. For more options, visit https://groups.google.com/d/optout.
