dsolv_dual

dsolv_dual(f,v)

:: Grobner dual of f.

return

List

f, v

List

• It returns the Grobner dual of f in the ring of polynomials with variables v.
• The ideal generated by f must be primary to the maximal ideal generated by v. If it is not primary to the maximal ideal, then this function falls into an infinite loop.
• This is an implementation of Algorithm 2.3.14 of the book [SST]. If we replace variables x, y, ... in the output by log(x), log(y), ..., then these polynomials in log are solutions of the system of differential equations f_(x->x*dx, y->y*dy, ...).

[435] dsolv_dual([y-x^2,y+x^2],[x,y]);
[x,1]
[436] dsolv_act(y*dy-sm1_mul(x*dx,x*dx,[x,y]),log(x),[x,y]);
0
[437] dsolv_act(y*dy+sm1_mul(x*dx,x*dx,[x,y]),log(x),[x,y]);
0

[439] primadec([y^2-x^3,x^2*y^2],[x,y]);
[[[y^2-x^3,y^4,x^2*y^2],[y,x]]]
[440] dsolv_dual([y^2-x^3,x^2*y^2],[x,y]);
[x*y^3+1/4*x^4*y, x^2*y, x*y^2+1/12*x^4, y^3+x^3*y,
 x^2, x*y, y^2+1/3*x^3, x, y, 1]

[441] dsolv_test_dual();
  Output is  omitted.

• dsolv_starting_term

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