p_nf, p_nf_mod, p_true_nf, p_true_nf_mod

p_nf(poly,plist,vlist,order)

p_nf_mod(poly,plist,vlist,order,mod)

:: Computes the normal form of the given polynomial. (The result may be multiplied by a constant.)

p_true_nf(poly,plist,vlist,order)

p_true_nf_mod(poly,plist,vlist,order,mod)

:: Computes the normal form of the given polynomial. (The result is returned as a form of [numerator, denominator])

return

p_nf : polynomial, p_true_nf : list

poly

polynomial

plist,vlist

list

order

number, list or matrix

mod

prime

• Defined in the package `gr'.
• Obtains the normal form of a polynomial by a polynomial list.
• These are interfaces to dp_nf(), dp_true_nf(), dp_nf_mod(), dp_true_nf_mod
• The polynomial poly and the polynomials in plist is converted, according to the variable ordering vlist and type of term ordering otype, into their distributed polynomial counterparts and passed to dp_nf().
• dp_nf(), dp_true_nf(), dp_nf_mod() and dp_true_nf_mod() is called with value 1 for fullreduce.
• The result is converted back into an ordinary polynomial.
• As for p_true_nf(), p_true_nf_mod() refer to dp_true_nf() and dp_true_nf_mod().

[79] K = katsura(5)$
[80] V = [u5,u4,u3,u2,u1,u0]$
[81] G = hgr(K,V,2)$
[82] p_nf(K[1],G,V,2);
0
[83] L = p_true_nf(K[1]+1,G,V,2);
[-1503...,-1503...]
[84] L[0]/L[1];
1

References

section dp_ptod, section dp_dtop, section dp_ord, section dp_nf, dp_nf_mod, dp_true_nf, dp_true_nf_mod.

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