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Mathematica v12.1

writings.stephenwolfram.com

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Re: Mathematica v12.1

#81

Post by bloaf »

saboot wrote: post #53

I'm a physicist and I've used mathematica sparingly off and on for several years, mostly manipulating symbolic formulas. I still do not understand what I'm doing half the time. Mostly just googling and stackoverflow answers get me by. For example, I don't understand why I can't use subscripts as symbols? Any recommendations on trying to 'get' mathematica?

I think the reason Mathematica hasn't "caught on" is that it doesn't look like fortran/matlab type programming that scientists/engineers are more traditionally exposed to. I find that if I'm trying to write an explicit loop (as opposed to a map or vector operation) in Mathematica I am most likely doing something wrong.

You'll drive yourself crazy trying to understand subscripts as a beginner, I would advise against getting too fancy with them unless you are fairly advanced. They work reasonably transparently in most cases, but there are a handful of situations where they are really frustrating (e.g. in With/Module/Block constructs). You can actually use them as symbols if you import the Symbolize package and Symbolize them, but then you lose the ability to "do math" to the subscript (e.g. you won't be able to use Table[] won't generate the symbolized variables.)

Re: Mathematica v12.1

#82

Post by jiggawatts »

Does anyone know of a good, strongly-typed computer algebra system similar to Mathematica?

By strongly typed, I mean that Mathematica is weakly typed in the sense that it simply assumes that all expressions are Complex numbers. At most, it can restrict itself to some subset such as the Reals or Integers, but that's it.

It can't, for example, perform general simplifications over non-associative types such as most Matrix algebras, the quaternions, or any geometric algebra. Most built-in functions operate only on Complex numbers, or expressions over the Complex numbers, etc...

I'm looking for something I can use to do symbolic expression manipulation for physics equations in terms of geometric algebra, but as far as I know there's nothing out there with the capability.

Re: Mathematica v12.1

#83

Post by wdkrnls »

jiggawatts wrote: post #82

Does anyone know of a good, strongly-typed computer algebra system similar to Mathematica? By strongly typed, I mean that Mathematica is weakly typed in the sense that it simply assumes that all expressions are Complex numbers. At most, it can restrict itself to some subset such as the Reals or Integers, but that's it. It can't, for example, perform general simplifications over non-associative types such as most Matr…

FriCAS and Axiom

Re: Mathematica v12.1

#84

Post by rayhem_ »

reikonomusha wrote: post #58
ChrisLomont wrote: post #31

Earlier quoted context omitted.

Quite often it gives you a result that you can then prove directly, or check with other tools. The benefit of MMA is that it has a lot of tools and a good interface, good documentation, and a large community. In practice, pretty much no one doing science has the expertise or time to completely verify the science they are doing - they are building on centuries of knowledge across many disciplines, and for the most par…

The “cosmic rays” argument, to me, is inane. It simply doesn’t practically apply and is certainly not an argument against the benefits of open source code. You’re castigating the whole practice of code review, computer-aided proofs, automated theorem proving, etc.

And how many people doing "science" do code review, computer-aided proofs, or automated theorem proving to verify their code is correct? Very, very, very few.

Re: Mathematica v12.1

#85

Post by vtail »

steveklabnik wrote: post #79
vtail wrote: post #64

Earlier quoted context omitted.

Swift is a great example, but don't forget that is essentially funded by Apple. It would look very different if it would be a true community effort. Rust I'm not very familiar with: how much of their funding is dependent on Mozilla, at least for the core developer(s)? Also, a language + a standard library has a (much!) smaller surface comparing to Wolfram's vision.

Mozilla funds a few things. Some stuff is funded by other companies. Mozilla pays the most folks to work full time, but the amount is tiny compared to the overall set of teams, let alone contributors.

Thanks Steve for the answer! HN is an amazing place where a random comment asking a question about Rust can get an answer from a core developer. I hope we will always keep it that way.

Re: Mathematica v12.1

#86

Post by david38 »

rayhem_ wrote: post #84
reikonomusha wrote: post #58

Earlier quoted context omitted.

The “cosmic rays” argument, to me, is inane. It simply doesn’t practically apply and is certainly not an argument against the benefits of open source code. You’re castigating the whole practice of code review, computer-aided proofs, automated theorem proving, etc.

And how many people doing "science" do code review, computer-aided proofs, or automated theorem proving to verify their code is correct? Very, very, very few.

This. In theory it’s open, but in reality, people just want to get this work done mostly.

Also, if something is that important, people can and do perform the same calculations using different packages or different algorithms.

Write two algorithms in MMA, or one in MMA and one in something else, and every so often spot check a few cases by hand.

Re: Mathematica v12.1

#87

Post by ChrisLomont »

reikonomusha wrote: post #58
ChrisLomont wrote: post #31

Earlier quoted context omitted.

Quite often it gives you a result that you can then prove directly, or check with other tools. The benefit of MMA is that it has a lot of tools and a good interface, good documentation, and a large community. In practice, pretty much no one doing science has the expertise or time to completely verify the science they are doing - they are building on centuries of knowledge across many disciplines, and for the most par…

The “cosmic rays” argument, to me, is inane. It simply doesn’t practically apply and is certainly not an argument against the benefits of open source code. You’re castigating the whole practice of code review, computer-aided proofs, automated theorem proving, etc.

> The "cosmic rays" argument, to me, is inane.

Have you ever looked at the rates, or you just dismiss it without looking at it? Note that the current rate is higher than older references since the feature sizes have shrunk, and lower energy events can change bits on newer hardware.

Scientific computation, especially at the level of most researchers, is affected by cosmic ray bitflips, without question.

Since the OP was complaining about not being able to check everything ad absurdium, then this effect is certainly on the table. It's more likely to affect research than the difference between closed and open source if a researcher is ignorant of it.

It's also why good researchers, who know this is a real effect, tries to run a computation in multiple methods over different times, until they feel a consensus on the calculations is robust enough.

If you've never done it, write a program to watch memory for bit flips, and be amazed.

Here's an intro - do a back of the envelope calculation and see if you still think these events are rare enough that they don't affect common scientific work.

https://en.wikipedia.org/wiki/Soft_error#Cosmic_rays_creatin...

Re: Mathematica v12.1

#88

Post by ChrisLomont »

reikonomusha wrote: post #58
ChrisLomont wrote: post #31

Earlier quoted context omitted.

Quite often it gives you a result that you can then prove directly, or check with other tools. The benefit of MMA is that it has a lot of tools and a good interface, good documentation, and a large community. In practice, pretty much no one doing science has the expertise or time to completely verify the science they are doing - they are building on centuries of knowledge across many disciplines, and for the most par…

The “cosmic rays” argument, to me, is inane. It simply doesn’t practically apply and is certainly not an argument against the benefits of open source code. You’re castigating the whole practice of code review, computer-aided proofs, automated theorem proving, etc.

>You’re castigating the whole practice of code review, computer-aided proofs, automated theorem proving, etc.

No I'm not. Those are but one avenue of reducing the probability of error during computation. All of those only ensure that the code part is solid - there is an entire other world on the physical part that needs incredible engineering, noise reduction, error correction, defect mitigation, thermal issues, quantum issues, physical data decay, memory leakage, and so on.

I think by focusing only on aspects for code, you miss a large part of ensuring modern computing is accurate.

Re: Mathematica v12.1

#89

Post by tonyarkles »

billfruit wrote: post #51
veer-chah wrote: post #17

I have tried Mathematica for small duration and in general was wowed by it. For free CAS I would recommend to give Axiom or FriCAS(more actively developed) a run. http://fricas.sourceforge.net/ https://en.wikipedia.org/wiki/Axiom_(computer_algebra_system...

Or Maxima, which has a long heritage.

There’s a bit of a learning curve for sure, but in the last year Maxima has become an indispensable tool for me. Symbolically writing out multiple equations, putting them together, and solving for a variable buried deep inside is dramatically more repeatable and less error-prone. Pretty much anything I’m working on now that involves algebra or calculus gets a Maxima file that starts with first principals and derives the final equation.

Re: Mathematica v12.1

#90

Post by 0-_-0 »

wdkrnls wrote: post #83
jiggawatts wrote: post #82

Does anyone know of a good, strongly-typed computer algebra system similar to Mathematica? By strongly typed, I mean that Mathematica is weakly typed in the sense that it simply assumes that all expressions are Complex numbers. At most, it can restrict itself to some subset such as the Reals or Integers, but that's it. It can't, for example, perform general simplifications over non-associative types such as most Matr…

FriCAS and Axiom

Does that mean I can solve a system of equations in vector form, e.g. solve this for X:

A·X=d1

B·X=d2

(A⨯B)·X=(A⨯B)·C

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