denseResultant -- dense resultant (classical resultant)

Usage:

denseResultant(d_0,d_1,...)

denseResultant(f_0,f_1,...)
Inputs:
- (d_0,d_1,...), a sequence of integers.
- (f_0,f_1,...), a sequence of $n+1$ Laurent polynomials in $n$ variables.
Optional inputs:
- Algorithm => ..., default value "Poisson"
- CoefficientRing => ..., default value ZZ
Outputs:
- for (d_0,d_1,...), this is the same as sparseResultant exponentsMatrix genericLaurentPolynomials(d_0,d_1,...);
- for (f_0,f_1,...), this is the same as affineResultant{f_0,f_1,...}.

Description

i1 : (f0,f1,f2) = genericLaurentPolynomials(1,2,2)

                           2               2                        2  
o1 = (a x  + a x  + a , b x  + b x x  + b x  + b x  + b x  + b , c x  +
       2 1    1 2    0   5 1    4 1 2    2 2    3 1    1 2    0   5 1  
     ------------------------------------------------------------------------
                 2
     c x x  + c x  + c x  + c x  + c )
      4 1 2    2 2    3 1    1 2    0

o1 : Sequence

i2 : time denseResultant(f0,f1,f2); -- using Poisson formula
 -- used 0.11212s (cpu); 0.112352s (thread); 0s (gc)

i3 : time denseResultant(f0,f1,f2,Algorithm=>"Macaulay"); -- using Macaulay formula
 -- used 0.306389s (cpu); 0.276649s (thread); 0s (gc)

i4 : time (denseResultant(1,2,2)) (f0,f1,f2); -- using sparseResultant
 -- used 0.504012s (cpu); 0.432772s (thread); 0s (gc)

i5 : assert(o2 == o3 and o3 == o4)

Ways to use denseResultant:

denseResultant(Thing)

For the programmer

The object denseResultant is a method function with a single argument.

The source of this document is in SparseResultants.m2:1257:0.

denseResultant -- dense resultant (classical resultant)

Description

See also

Ways to use denseResultant:

For the programmer