dp_nf
, dp_nf_mod
, dp_true_nf
, dp_true_nf_mod
[numerator, denominator]
)
dp_nf()
: distributed polynomial, dp_true_nf()
: list
dp_nf_mod()
and dp_true_nf_mod()
require
distributed polynomials with coefficients in a finite field as arguments.
dp_nf()
may be multiplied by a constant in the
ground field in order to make the result integral. The same is true
for dp_nf_mod()
, but it returns the true normal form if
the ground field is a finite field.
dp_true_nf()
and dp_true_nf_mod()
return
such a list as [nm,dn]
.
Here nm is a distributed polynomial whose coefficients are integral
in the ground field, dn is an integral element in the ground
field and nm/dn is the true normal form.
p_nf
and p_true_nf
are sufficient.
[0] load("gr")$ [64] load("katsura")$ [69] K=katsura(4)$ [70] dp_ord(2)$ [71] V=[u0,u1,u2,u3,u4]$ [72] DP1=newvect(length(K),map(dp_ptod,K,V))$ [73] G=gr(K,V,2)$ [74] DP2=newvect(length(G),map(dp_ptod,G,V))$ [75] T=dp_ptod((u0-u1+u2-u3+u4)^2,V)$ [76] dp_dtop(dp_nf([0,1,2,3,4],T,DP1,1),V); u4^2+(6*u3+2*u2+6*u1-2)*u4+9*u3^2+(6*u2+18*u1-6)*u3+u2^2+(6*u1-2)*u2+9*u1^2-6*u1+1 [77] dp_dtop(dp_nf([4,3,2,1,0],T,DP1,1),V); -5*u4^2+(-4*u3-4*u2-4*u1)*u4-u3^2-3*u3-u2^2+(2*u1-1)*u2-2*u1^2-3*u1+1 [78] dp_dtop(dp_nf([0,1,2,3,4],T,DP2,1),V); -1138087976845165778088612297273078520347097001020471455633353049221045677593 0005716505560062087150928400876150217079820311439477560587583488*u4^15+... [79] dp_dtop(dp_nf([4,3,2,1,0],T,DP2,1),V); -1138087976845165778088612297273078520347097001020471455633353049221045677593 0005716505560062087150928400876150217079820311439477560587583488*u4^15+... [80] @78==@79; 1
dp_dtop
,
section dp_ord
,
section dp_mod
, dp_rat
,
section p_nf
, p_nf_mod
, p_true_nf
, p_true_nf_mod
.
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