dp_mbase

dp_mbase(dplist)

:: Computes the monomial basis

return

list of distributed polynomial

dplist

list of distributed polynomial

• Assuming that dplist is a list of distributed polynomials which is a Groebner basis with respect to the current ordering type and that the ideal I generated by dplist in K[X] is zero-dimensional, this function computes the monomial basis of a finite dimenstional K-vector space K[X]/I.
• The number of elements in the monomial basis is equal to the K-dimenstion of K[X]/I.

[215] K=katsura(5)$
[216] V=[u5,u4,u3,u2,u1,u0]$
[217] G0=gr(K,V,0)$
[218] H=map(dp_ptod,G0,V)$
[219] map(dp_ptod,dp_mbase(H),V)$
[u0^5,u4*u0^3,u3*u0^3,u2*u0^3,u1*u0^3,u0^4,u3^2*u0,u2*u3*u0,u1*u3*u0,
u1*u2*u0,u1^2*u0,u4*u0^2,u3*u0^2,u2*u0^2,u1*u0^2,u0^3,u3^2,u2*u3,u1*u3,
u1*u2,u1^2,u4*u0,u3*u0,u2*u0,u1*u0,u0^2,u4,u3,u2,u1,u0,1]

References

section gr, hgr, gr_mod, dgr.

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