There is an issue discussing adding something like this to SymPy: https://github.com/sympy/sympy/issues/26177
> and compute sp.resultant(p, sp.diff(p,x), x) > computing this takes around the ballpark of 50 seconds, maple takes 4 Are you saying that Maple takes 4 seconds for this and with SymPy it takes 50 seconds? If so then I think that is to be expected because Maple will do this operation in its kernel which means it is basically using a C implementation whereas SymPy hee uses a Python implementation. The algorithms might also be different but I would expect that the SymPy implementation would be at least 10x faster if it were in C. For some polynomial operations SymPy can now make use of python-flint meaning that the FLINT library which is written in C for operations like this. Using python-flint for multivariate polynomials is not implemented in SymPy yet but when it is it will be possible to use FLINT's resultant routines for this. In the meantime it might make sense to implement the solver using python-flint directly since it only requires multivariate polynomials with rational coefficients and python-flint provides a faster implementation of those already for direct use. Oscar On Sun, 3 Aug 2025 at 18:34, William Zhang (mintIceCream_) <[email protected]> wrote: > > Hello, undergrad here, i found an old chinese paper/maple script which seemed > kind of interesting so i decided to port it to sympy > Heres the code and everything > https://github.com/iceCreamMint/inqeuality-prover/tree/main > Its an prover for non-strict multivariable polynomial inequalities with > rational coefficents and positive real variables > Theres also one for geometric inequalities involving one triangle but that > part seems really complicated so i havent done anything with it yet > In my opinion the way it works is rather interesting, it does cad but ignores > lower dimensional cells to avoid having to solve for roots(i think this is > why it can only deal with unstrict inequalities?) > Other than that, it does some preprocessing to radicals and rationals to make > them valid for cad > > Currently the main bottleneck seems to be that resultants are painfully slow > For example, take > p = 6561*x**8*y**4*z**4 - 26244*x**8*y**3*z**3 + 39366*x**8*y**2*z**2 - > 26244*x**8*y*z + 6561*x**8 - 26244*x**7*y**5*z**4 - 26244*x**7*y**4*z**5 + > 78732*x**7*y**4*z**3 + 78732*x**7*y**3*z**4 - 78732*x**7*y**3*z**2 - > 78732*x**7*y**2*z**3 + 26244*x**7*y**2*z + 26244*x**7*y*z**2 + > 39366*x**6*y**6*z**4 + 26244*x**6*y**5*z**5 - 52488*x**6*y**5*z**3 + > 39366*x**6*y**4*z**6 - 52488*x**6*y**4*z**4 - 39366*x**6*y**4*z**2 - > 52488*x**6*y**3*z**5 + 49572*x**6*y**3*z**3 + 78732*x**6*y**3*z - > 39366*x**6*y**2*z**4 - 69984*x**6*y**2*z**2 - 26244*x**6*y**2 + > 78732*x**6*y*z**3 + 69984*x**6*y*z - 26244*x**6*z**2 - 23328*x**6 - > 26244*x**5*y**7*z**4 + 26244*x**5*y**6*z**5 - 52488*x**5*y**6*z**3 + > 26244*x**5*y**5*z**6 - 52488*x**5*y**5*z**4 + 157464*x**5*y**5*z**2 - > 26244*x**5*y**4*z**7 - 52488*x**5*y**4*z**5 + 29160*x**5*y**4*z**3 - > 78732*x**5*y**4*z - 52488*x**5*y**3*z**6 + 29160*x**5*y**3*z**4 + > 20412*x**5*y**3*z**2 + 157464*x**5*y**2*z**5 + 20412*x**5*y**2*z**3 - > 23328*x**5*y**2*z - 78732*x**5*y*z**4 - 23328*x**5*y*z**2 + > 6561*x**4*y**8*z**4 - 26244*x**4*y**7*z**5 + 78732*x**4*y**7*z**3 + > 39366*x**4*y**6*z**6 - 52488*x**4*y**6*z**4 - 39366*x**4*y**6*z**2 - > 26244*x**4*y**5*z**7 - 52488*x**4*y**5*z**5 + 29160*x**4*y**5*z**3 - > 78732*x**4*y**5*z + 6561*x**4*y**4*z**8 - 52488*x**4*y**4*z**6 + > 312012*x**4*y**4*z**4 + 46656*x**4*y**4*z**2 + 39366*x**4*y**4 + > 78732*x**4*y**3*z**7 + 29160*x**4*y**3*z**5 - 285768*x**4*y**3*z**3 - > 46656*x**4*y**3*z - 39366*x**4*y**2*z**6 + 46656*x**4*y**2*z**4 + > 57348*x**4*y**2*z**2 + 23328*x**4*y**2 - 78732*x**4*y*z**5 - > 46656*x**4*y*z**3 - 62208*x**4*y*z + 39366*x**4*z**4 + 23328*x**4*z**2 + > 31104*x**4 - 26244*x**3*y**8*z**3 + 78732*x**3*y**7*z**4 - > 78732*x**3*y**7*z**2 - 52488*x**3*y**6*z**5 + 49572*x**3*y**6*z**3 + > 78732*x**3*y**6*z - 52488*x**3*y**5*z**6 + 29160*x**3*y**5*z**4 + > 20412*x**3*y**5*z**2 + 78732*x**3*y**4*z**7 + 29160*x**3*y**4*z**5 - > 285768*x**3*y**4*z**3 - 46656*x**3*y**4*z - 26244*x**3*y**3*z**8 + > 49572*x**3*y**3*z**6 - 285768*x**3*y**3*z**4 + 254016*x**3*y**3*z**2 - > 78732*x**3*y**2*z**7 + 20412*x**3*y**2*z**5 + 254016*x**3*y**2*z**3 - > 20736*x**3*y**2*z + 78732*x**3*y*z**6 - 46656*x**3*y*z**4 - 20736*x**3*y*z**2 > + 39366*x**2*y**8*z**2 - 78732*x**2*y**7*z**3 + 26244*x**2*y**7*z - > 39366*x**2*y**6*z**4 - 69984*x**2*y**6*z**2 - 26244*x**2*y**6 + > 157464*x**2*y**5*z**5 + 20412*x**2*y**5*z**3 - 23328*x**2*y**5*z - > 39366*x**2*y**4*z**6 + 46656*x**2*y**4*z**4 + 57348*x**2*y**4*z**2 + > 23328*x**2*y**4 - 78732*x**2*y**3*z**7 + 20412*x**2*y**3*z**5 + > 254016*x**2*y**3*z**3 - 20736*x**2*y**3*z + 39366*x**2*y**2*z**8 - > 69984*x**2*y**2*z**6 + 57348*x**2*y**2*z**4 - 233280*x**2*y**2*z**2 + > 20736*x**2*y**2 + 26244*x**2*y*z**7 - 23328*x**2*y*z**5 - 20736*x**2*y*z**3 + > 18432*x**2*y*z - 26244*x**2*z**6 + 23328*x**2*z**4 + 20736*x**2*z**2 - > 18432*x**2 - 26244*x*y**8*z + 26244*x*y**7*z**2 + 78732*x*y**6*z**3 + > 69984*x*y**6*z - 78732*x*y**5*z**4 - 23328*x*y**5*z**2 - 78732*x*y**4*z**5 - > 46656*x*y**4*z**3 - 62208*x*y**4*z + 78732*x*y**3*z**6 - 46656*x*y**3*z**4 - > 20736*x*y**3*z**2 + 26244*x*y**2*z**7 - 23328*x*y**2*z**5 - 20736*x*y**2*z**3 > + 18432*x*y**2*z - 26244*x*y*z**8 + 69984*x*y*z**6 - 62208*x*y*z**4 + > 18432*x*y*z**2 + 6561*y**8 - 26244*y**6*z**2 - 23328*y**6 + 39366*y**4*z**4 + > 23328*y**4*z**2 + 31104*y**4 - 26244*y**2*z**6 + 23328*y**2*z**4 + > 20736*y**2*z**2 - 18432*y**2 + 6561*z**8 - 23328*z**6 + 31104*z**4 - > 18432*z**2 + 4096 > and compute sp.resultant(p, sp.diff(p,x), x) > computing this takes around the ballpark of 50 seconds, maple takes 4 > In some cases factoring the polynomial and computing resultant between all > pairs of factors is significantly faster than calling sp.resultant, but im > not sure if its still the resultant at that point, program still seems to > work and be correct though > So currently im trying to implement the modular resultant algorithm as > described by Collins(1971) to see if it gets any faster > Other than that im trying to look for ways to allow equalities in conditions > and figure out a way to deal with strict inequalites, reading about grobner > bases right now and hoping that might help > > In the program there are two inequality solvers, first one is > xprove(statement, condition) which tries to prove condition -> statement for > positive real variables, there are a bunch of tests for this > yprove just calls xprove a bunch of times to try and prove inequalities in > real non-zero variables, there are no tests for this > > The script/paper also seems to be related to the maple RegularChains package, > i dont know if the sympy agca library does anything similar(i have a lot of > reading to do) > > Its my first time doing anything like this, any feedback is appreciated, > thank you > > -- > 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 [email protected]. > To view this discussion visit > https://groups.google.com/d/msgid/sympy/04911951-4b31-4208-a083-f950e8524f11n%40googlegroups.com. -- You received this message because you are subscribed to the Google Groups "sympy" group. 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