Sergio Parreiras

Dr. Sergio Parreiras

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16 years, 154 days
UNC Chapel Hill
Associate Professor

MaplePrimes Activity

These are questions asked by Sergio Parreiras

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?


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 ]

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....

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?

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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