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 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 zerodimensional, 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()
.
[117] G=tolex(G0,V,0,V)$
43.818sec + gc : 11.202sec
[118] GSL=tolex_gsl(G0,V,0,V)$
17.123sec + gc : 2.590sec
[119] 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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