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### `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()`.
``` K = katsura(5)\$
 V = [u5,u4,u3,u2,u1,u0]\$
 G = hgr(K,V,2)\$
 p_nf(K,G,V,2);
0
 L = p_true_nf(K+1,G,V,2);
[-1503...,-1503...]
 L/L;
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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