Sergio Parreiras

Dr. Sergio Parreiras

135 Reputation

16 years, 341 days
UNC Chapel Hill
Associate Professor

How to get intermediary calculations fro...

Maple

Two questions:

The algortihms that Groebner[Basis] uses at each step computes some "tentative" or "pseudo-basis". The "tentative" basis is not a Groebner basis but it is in the ideal generated by the original system of polynomial eq.

1) Is this correct ? Provided this is correct, then

2) How can one retrive the last "tentative" basis?
If I just use timelimit I can abort the computations but how can one retrive the last computation?

How to write a PDE system in a Weyl Alge...

I have been struggling (reading Ore/Weyl Algebra documentation) to understand how to input a PDE system with polynomial coeff. in Weyl algebra notation so I can compute a Groebner basis for it. I would be very grateful if someone could  show, using the simple example below, which differential operators in Ore_algebra[diff_algebra] should one declare to express the system in Weyl algebra notation. The systems I'm working are more complicated but all have many dependent variables, f and g functions in this example:

pdesys:= [ x*diff( f(x,y,z),x)- z*diff( g(x,y,z),y) = 0, (x^2-y)*diff( f(x,y,z),z)- y*diff( g(x,y,z),z) = 0 ]

Weird behavior of subs and isolate in PD...

Maple

Hi folks, I'm running Maple 17.02 and getting very different behaviors from subs and isolate. My actual expressions are way more complicated but this simple example illustrates the problem:

restart; with(PDEtools); F := diff_table(f(x, y, w, z, a, b));

subs(F[x] = Z(x, y, w, z, a, b), F[x]+F[x, b]-10);

subs(F[x] = Z(x, y, w, z, a, b), F[x]+F[x, y]-10);

The last line gives me what I want  Z+Z[y]-10 but the second line gives me Z+F[x,b]-10....

Copy and past PDEtools simplified notati...

Maple

Hi folks, the package PDEtools has a nice command declare that allow us to display PDEs using jet notation: say f[x]-g[y] instead of diff(f(x,y),x)-diff(g(x,y),y) but when I try to export it to LaTeX or just trying to copy and paste the display in a text file, I always get the long expression. If I try to copy as MathML I got junk... Any ideas on how to copy an expression displayed in jet notation to a text document?

simplify problem, global versus local va...

Maple

Hello folks,

simplify(max(x[1],y[1])) assuming x[1]>y[1] produces thr correct result but if we do f:=k->max(x[k],y[k]);

and try simplify(f(1)) assuming x[1]>y[1] we do not get any result.

I suspect that is something related to global versus local variables, any ideas?

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