Mr. Roman Pearce

## 1673 Reputation

18 years, 66 days
CECM/SFU
Research Associate

I am a research associate at Simon Fraser University and a member of the Computer Algebra Group at the CECM.

## Generators...

Try Generators(quotientlist);

## bug in RootFinding:-Isolate...

This is a bug in RootFinding:-Isolate.  I don't know the technical details of how the root is missed.  I will report it.

## x+y+z is the correct output for sor...

x+y+z is the correct output for sort( x+y+z, order = tdeg(x,y,z));  The monomials are compared first by total degree, then ties are broken by the smallest power in z being first, then by the smallest power in y being first.  So x is the largest monomial in tdeg(x,y,z) followed by y followed by z.

## @Markiyan Hirnyk Make that  Ba...

@Markiyan Hirnyk Make that

Basis(J, grlex(z,y,x));

The option 'tord' is to allow Groebner:-Basis to choose the term ordering.

## all languages ok...

Eventually we may want an option to filter by language, but we should be encouraging users in any language.  Maybe add a button to run it through google translate for readers.

## can you post the equations?...

Can you post the Maple input?  It is probably trying to compute a Groebner basis and failing.

## can you post the equations?...

Can you show us the equations?  We are very interested in problems that Maple can not do, especially Groebner basis problems, because we are working to improve that area of the system.  It sounds like Maple can not solve your polynomial system.

## parallela...

90 GFLOPS at 5 watts is impressive, but this is a niche product.  The current Intel cpus offer about 75 GFLOPS.  I think the point of the Parallela is to provide higher throughput at lower power.  It would be interesting for embedded systems.

## use coeffs...

You would use the coeffs command to find the coefficients, as in

vars := [seq(x[i], i=1..60)]:

C := [coeffs(f, vars, 'M')];  # list of coefficients

M := [M];  # list of corresponding monomials

But I'm not sure if your system is solvable.  Can you post the full system?

## It is almost certainly legitimate.  ...

It is almost certainly legitimate.  For one, Maple's arbitary precision routines will allocate and garbage collect memory.

## too hard...

@rodneykg I'm trying it but I'm not getting anywhere.  I think this problem is too hard for Maple.  I'm not sure how other software will fare.  We'll keep it as a benchmark problem.

## system is hard...

The complexity of solving non-linear systems increases rapidly with the number of variables.  Can you give us the values for sig1, sig2, etc?  Are they exact or approximate?  Because if we leave them as unknowns I think the problem is too hard.

As for alternatives to Maple, it depends on the approach.  A common approach for exact problems is to use Groebner bases, and for that Magma is generally the fastest software, followed by Singular, although Maple is usually not too bad.  Another approach is to use triangular sets (called RegularChains in Maple).  To my knowledge Maple has the best implementation of that approach.

I can run various methods against your system but if you have values for some of the parameters it will greatly improve the chances of success.

## use degree...

c := rand(0..10):

m := mul(j[i]^c(), i=0..15);