Hi,

If I have boolean variable x1

And assuming multiplication means "AND" for boolean expressions;

and that addition means "OR"

Then

  x1 = x1^2 = x1^3 = ...=x1^k, k >= 1

Since "x1 and x1 and x1 ... and x1" = x1;

it is true if x1 is true and false if x1 is false.

How can a boolean expression with variables taken

to various powers be simplified?

I can't take credit for this; but Dave Rusin showed

Suppose you want to solve a large dense linear system AX=B over the rationals - what should you do? Well, one thing you should probably not do is directly apply Gaussian elimination. It does O(n^3) arithmetic operations, but the size of the numbers blow up, leading to an exponential bit complexity. Don't believe me? Try it:

Some time ago I was asked the question: do you know how to do a change of variables in a multi-dimensional definite integral?  I thought I knew, but I was wrong.  I only know how to do a change of variable in a multi-dimensional indefinite integral. 

On his blog, Jaime Zawinski (of Netscape and XEmacs fame) relates a tale of finding limits in the (supposedly) unlimited big number representation on a TI Lisp machine in the early 1990s. It is an amusing story, and it makes me wonder if GnuMP is has a similar limit on a different scale.  Or in other words, is there a positive integer small enough to fit into memory  (assuming 64 bit address space) but that cannot actually be constructed in GnuMP due to limits in the implementation? Does someone here know enough about the GnuMP internals to give the answer?

In the following worksheet, evalf[4997](... does what I expected and evalf[4998](... does not.

View 4937_Page147.mw on MapleNet or Download 4937_Page147.mw
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See (3) and (10) in the worksheet.

This workshop is focused on the intersection of programming languages (PL) and mechanized mathematics systems (MMS). The latter category subsumes present-day computer algebra systems (CAS), interactive proof assistants (PA), and automated theorem provers (ATP), all heading towards fully integrated mechanized mathematical assistants that are expected to emerge eventually (cf. the objective of Calculemus).

This is the second PLMMS workshop, with the first workshop held with Calculemus 2007 in Hagenberg, Austria.

Why isn't answer (2) the same as answer (4) in the following:

View 4937_Page 2.mw on MapleNet or Download 4937_Page 2.mw
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This is from page 2 of When Least Is Best by Paul J. Nahin.

Why doesn't Maple do what I want in the following:

View 4937_Rational.mw on MapleNet or Download 4937_Rational.mw
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A few weeks ago I mentioned the ncrunch comparison of "mathematical programs for data analysis" in a comment in another thread.  There is now a new, 5th release of that review. The systems reviewed are:

• GAUSS
• Maple
• Mathematica
• Matlab
• O-Matrix
• Ox
• SciLab

The review is skewed towards statistical computation and data manipulation, but it includes several interesting comparisons of the major computer algebra systems (CAS).

There is a comparative performance section, and the worksheets used for that benchmarking are available for download. Here is the Maple worksheet, which was used with Maple 11.

All this week:

• friCAS 1.0.2 released
• Sage 2.10.2 released
• OpenAxiom 1.1.0 released