a little off topic... SMP (precursor to Mathematica)...

[pilgrimdan]

this link goes to an article by Stephen Wolfram...

http://blog.stephenwolfram.com/2013/06/ ... #more-5192

about half way down he provides the following:

"It’s been years now, and I’d really like to see SMP run again. So here’s a challenge.

This is the source for a C program encrypted like the SMP source code.

Actually, it’s the source for the program that did the encryption: a version of the circa-1981 Unix crypt utility, “cleverly” modified by changing parameters etc.

Can someone break the encryption?

in the article he provides the output (for some reason the code would not paste here)...

[zullil]

SMP (the “Symbolic Manipulation Program”)

Not to be confused with

SMP ("Symmetric multiprocessing")

[Daniel Shawul]

Just curious, is this software used to be called MACSYMA by any chance? I read it is an SMP program developed in MIT whose core is used for Mathematica and Maple. I think symbolic manipulation (SMP) and stuff like theorem proving must benefit from AI, and also give back. I still remember the shock i had when i learned that the famous quadratic equation can be solved with a program symbolically!
Daniel

[Henk]

Just curious, is this software used to be called MACSYMA by any chance? I read it is an SMP program developed in MIT whose core is used for Mathematica and Maple. I think symbolic manipulation (SMP) and stuff like theorem proving must benefit from AI, and also give back. I still remember the shock i had when i learned that the famous quadratic equation can be solved with a program symbolically!
Daniel

Even solving small sets of linear equations symbolically can be impossible.
If no reductions or factoring can be applied, you may get length of expressions doubling for each operation.

[pilgrimdan]

Just curious, is this software used to be called MACSYMA by any chance? I read it is an SMP program developed in MIT whose core is used for Mathematica and Maple. I think symbolic manipulation (SMP) and stuff like theorem proving must benefit from AI, and also give back. I still remember the shock i had when i learned that the famous quadratic equation can be solved with a program symbolically!
Daniel

Daniel.... yes...

here's a quote from the same article...

"Then in the summer of 1977 I discovered the ARPANET, or what’s now the internet. There were only 512 hosts on it back then. And @O 236 went to an open computer at MIT that ran a program called Macsyma—that did algebra, and could be used interactively. I was amazed so few people used it. But it wasn’t long before I was spending most of my days on it. I developed a certain way of working—going back and forth with the machine, trying things out and seeing what happened. And routinely doing weird things like enumerating different algebraic forms for an integral—then just “experimentally” seeing which differentiated correctly.

My physics papers started containing all sorts of amazing formulas. And not imagining that I could be using a computer, people started thinking that I must be some kind of great human algebraic calculator. I got more and more ambitious, trying to do more and more with Macsyma. Pretty soon I think I was its largest user. But sometime in 1979 I hit the edge; I’d outgrown it.

And then it was November 1979. I was 20 years old, and I’d just gotten my PhD in physics. I was spending a few weeks at CERN, planning my future in (as I believed) physics. And one thing I concluded was that to do physics well, I’d need something better than Macsyma. And after a little while I decided that the only way I’d really have a chance to get what I wanted was if I built it myself."

[mar]

Even solving small sets of linear equations symbolically can be impossible.
If no reductions or factoring can be applied, you may get length of expressions doubling for each operation.

What are you talking about? Symbolic simplification using expression trees is not impossible at all. Just make sure you keep factors sorted and together - no magic there. Programs like Maple will solve any set of linear equations easily, except that you may not like the output. It seems to me you are just trolling here

[Henk]

Even solving small sets of linear equations symbolically can be impossible.
If no reductions or factoring can be applied, you may get length of expressions doubling for each operation.

What are you talking about? Symbolic simplification using expression trees is not impossible at all. Just make sure you keep factors sorted and together - no magic there. Programs like Maple will solve any set of linear equations easily, except that you may not like the output. It seems to me you are just trolling here

If I tried to solve 200 linear, even sparse equations symbolically. No numeric substitutions. You can wait forever. And if a solution is found it gives you pages of output.

If you are annoyed don't feed the troll. He is not hungry at all.

[Daniel Shawul]

@Martin, Let us give Henk some space even though I should be the last person to say that
I don't know much about symbolic solution of linear system of equations but I would guess it would be 'just' finding the inverse. It will probably require lots of assumptions to simplify the equations and test for all required properties of the matrix. With naive gauss elimination, i don't imagine it to be that hard but i wouldn't know much about it. Even numerical inversion of a matrix efficiently is so damn hard so iterative solutions using Krylov subspace methods is what is usually done.

[Daniel Shawul]

Thanks that was a nice coincidence. FYI the software had applications in chess too. The first people who analyzed alpha-beta, used Macsyma to solve some really tough integral equations (for up to depth 10 or so) and produced results. The integral format is recursive so they couldn't do it for more. Infact those equations from the page starting to look like the equations i see in the paper, but probably wishful thinking

[mar]

@Martin, Let us give Henk some space even though I should be the last person to say that
I don't know much about symbolic solution of linear system of equations but I would guess it would be 'just' finding the inverse. It will probably require lots of assumptions to simplify the equations and test for all required properties of the matrix. With naive gauss elimination, i don't imagine it to be that hard but i wouldn't know much about it. Even numerical inversion of a matrix efficiently is so damn hard so iterative solutions using Krylov subspace methods is what is usually done.

Ok
Well Daniel me neither, but I once wrote a program to simplify symbolic expressions (no functions) and (to some extent) it worked fine. Sometimes one has to take a step backwards (expand) to be able to simplify further (if possible). Using plain gauss-jordan and arbitrary precision rational numbers (no symbols), it started to choke on matrices larger than 10x10, so I guess something more clever has to be applied indeed. I wouldn't even think of solving a system of 200 equations without using sparse matrices and some clever algorithm. Not even without symbols. That'd be just plain insane.