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SymPy: Symbolic Mathematics in Python

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Re: SymPy: Symbolic Mathematics in Python

#131

Post by wakawaka28 »

taeric wrote: post #129
wakawaka28 wrote: post #122

Earlier quoted context omitted.

No it's not silly. A Lamborghini might be a better performing vehicle that could solve problems I didn't even know I had, but if I don't have the money for it and/or a Ford Pinto covers 99% of the cases I need, the Pinto is better. I'm not arguing that SymPy is going to beat Mathematica on benchmarks. But if both of them meet your needs, and you like having money and/or control of the code, SymPy wins.

So, in this we don't really disagree. But, I would only agree that it is an objectively better choice for you. It is not an objectively better CAS. Demonstrably so, per that benchmark. Similarly, a lamborghini is almost certainly an objectively faster car. Such that if you were discussing fast vehicles and someone pointed out that their ebike was good enough for them, it would be a statement out of nowhere that is no…

We are essentially in agreement. I just don't think Mathematica is worth the money unless you need it for something specific like solving tricky problems. As much shade as you can throw on Python, there are lots more possibilities to use Python with SymPy than to use Mathematica. Unfortunately, the cutting edge FOSS math scene will always lag behind the commercial tools, as it is incredibly hard for them to get donations. I remember hearing a story about the developer of Octave (the most popular Matlab clone). He had worked on it for years and hardly got any donations, despite probably having hundreds of thousands of downloads and constant feature requests.

Re: SymPy: Symbolic Mathematics in Python

#132

Post by manojlds »

jlokier wrote: post #102
manojlds wrote: post #41

As an aside - I have a bunch of logical expressions and I need to see if they are mutually exclusive. As in, if one is true given some combination of the variables, none of the other expressions must be true for the same combination. For example Country="US" and Type="Sales" is not exclusive with Type in ("Sales", "Purchase") What would be an approach to solving this?

If your logical expressions aren't too strange, and there aren't too many, that's well suited to an SMT solver, such as Z3. You might, for example, create a new logical expression for each pair of your original expressions, joining each pair with AND, and then join those AND pairs with OR. Then ask the SMT solver to generate an unsatisfiability proof.

Thanks the suggestion was very useful and I am even close to having a prototype. Z3 is cool!

Re: SymPy: Symbolic Mathematics in Python

#133

Post by taeric »

wakawaka28 wrote: post #131
taeric wrote: post #129

Earlier quoted context omitted.

So, in this we don't really disagree. But, I would only agree that it is an objectively better choice for you. It is not an objectively better CAS. Demonstrably so, per that benchmark. Similarly, a lamborghini is almost certainly an objectively faster car. Such that if you were discussing fast vehicles and someone pointed out that their ebike was good enough for them, it would be a statement out of nowhere that is no…

We are essentially in agreement. I just don't think Mathematica is worth the money unless you need it for something specific like solving tricky problems. As much shade as you can throw on Python, there are lots more possibilities to use Python with SymPy than to use Mathematica. Unfortunately, the cutting edge FOSS math scene will always lag behind the commercial tools, as it is incredibly hard for them to get donat…

Indeed, I think we are fairly aligned.

I also think the math systems will lag for more than just donations. The work to make a good CAS is pretty intense. A lot like a good SAT system. Or really anything that is deep in the weeds of computer science. A lot of us are so far removed from the math that they focus on, that it can be mind bending to try and get back into it. (Indeed, for a lot like me, we were probably never really great at it, in the first place.)

Mathematica and Matlab are interesting to consider, as they are likely very well integrated into older workflow systems from the mainframe era. In particular, I'd expect the high end simulations for car and vehicle designs are much more integrated with those than anything open source. And a lot of that is largely availability of what they are integrating with. Most of us do not have the science labs and all of the equipment that goes with it.

Which, I think, is a bad feedback loop on this. For folks without those labs, Mathematica/Matlab are prohibitively expensive. For those with the labs, they are probably a rounding error. And there is no real path from the current equilibrium to one that can get it to more people. (The old path was free access in college. But that is becoming less of a thing in modern programming jobs.)

Re: SymPy: Symbolic Mathematics in Python

#134

Post by thebiss »

toolslive wrote: post #89
whyever wrote: post #21

Earlier quoted context omitted.

Why are you calculating the Jacobian symbolically? AFAIK, for complex cases, the numerical Jacobian is often faster / more numerically stable.

There are plenty of situations where the scenario goes like this: you first do symbolical calculations. then fill in some of the free variables, your resulting expression will simplify a lot. Then you compile that resulting expression to native code and evaluate the simplified specialized code for a zillion parameter vectors. Anyway,if your day job needs something like this you're better off using a lisp than python.

For those of us that have never touched lisp - can you explain why?

Re: SymPy: Symbolic Mathematics in Python

#135

Post by mixedmath »

bmitc wrote: post #128
mixedmath wrote: post #125

Earlier quoted context omitted.

I'm a mathematician. One reason it matters to me is that if I write a program that computes something in a proof, I need to be able to understand and verify (or possibly check that other people I trust have verified) the source and algorithms. I have also modified and extended open source implementations in sage to work with cases I needed. And I've added some of this back to sage. It is undeniable that Mathematica e…

> One reason it matters to me is that if I write a program that computes something in a proof, I need to be able to understand and verify (or possibly check that other people I trust have verified) the source and algorithms Do you actually do this verification? How do you accomplish this? The software stacks are huge. Why do you trust other people over the people who develop Mathematica, who just happened to be paid?

Yes, I do. And open source software can have papers and algorithms documenting various aspects. This is very much like using results of other math research papers, in that there is communal review and trees of dependencies and everything can be cross-verified.

It is also true that, just like with a generic math research paper, that I don't check every claim of every step of every implementation of every algorithm in the process. But checking is possible, and when we find errors (which we do frequently) we can look and try to explain what it happening.

But when we find errors in tools such as Mathematica, we cannot. We report the errors and then know nothing more. (And sometimes the errors are never fixed).

Re: SymPy: Symbolic Mathematics in Python

#136

Post by fho »

6gvONxR4sf7o wrote: post #85
fho wrote: post #83

Earlier quoted context omitted.

Funfact: you can probably JIT compile that using JAX for an easy performance gain.

But then they would have to compile the jit-optimized XLA to C. Do you know if that’s straightforwardly doable?

Hmm ... Good question. I would assume that JAX and XLA is based on LLVM (like everything else these days) and that you could probably grab the IR at some point to compile it to your target.

Re: SymPy: Symbolic Mathematics in Python

#137

Post by toolslive »

thebiss wrote: post #134
toolslive wrote: post #89

Earlier quoted context omitted.

There are plenty of situations where the scenario goes like this: you first do symbolical calculations. then fill in some of the free variables, your resulting expression will simplify a lot. Then you compile that resulting expression to native code and evaluate the simplified specialized code for a zillion parameter vectors. Anyway,if your day job needs something like this you're better off using a lisp than python.

For those of us that have never touched lisp - can you explain why?

Lisp has quote, unquote, and friends allowing you to turn code into data, then manipulate it and then turn it back into code. These are all the tools you need to create on-the-fly compilers. Here's an article explaining the lost art:

http://gms.freeshell.org/peval.html

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