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### `gr_minipoly`, `minipoly`

gr_minipoly(plist,vlist,order,poly,v,homo)
:: Computation of the minimal polynomial of a polynomial modulo an ideal
minipoly(plist,vlist,order,poly,v)
:: Computation of the minimal polynomial of a polynomial modulo an ideal
return
polynomial
plist, vlist
list
order
number, list or matrix
poly
polynomial
v
indeterminate
homo
flag
• `gr_minipoly()` begins by computing a Groebner basis. `minipoly()` regards an input as a Groebner basis with respect to the variable order vlist and the order type order.
• Let K be a field. If an ideal I in K[X] is zero-dimensional, then, for a polynomial p in K[X], the kernel of a homomorphism from K[v] to K[X]/I which maps f(v) to f(p) mod I is generated by a polynomial. The generator is called the minimal polynomial of p modulo I.
• `gr_minipoly()` and `minipoly()` computes the minimal polynomial of a polynomial p and returns it as a polynomial of v.
• The minimal polynomial can be computed as an element of a Groebner basis. But if we are only interested in the minimal polynomial, `minipoly()` and `gr_minipoly()` can compute it more efficiently than methods using Groebner basis computation.
• It is recommended to use a degree reverse lex order as a term order for `gr_minipoly()`.
``` G=tolex(G0,V,0,V)\$
43.818sec + gc : 11.202sec
 GSL=tolex_gsl(G0,V,0,V)\$
17.123sec + gc : 2.590sec
 MP=minipoly(G0,V,0,u0,z)\$
4.370sec + gc : 780msec
```
References
section `lex_hensel`, `lex_tl`, `tolex`, `tolex_d`, `tolex_tl`.

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