Co-efficients of Polynomial Rings

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Candid Pleasure

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Jun 8, 2022, 3:56:23 PM6/8/22
to Macaulay2
Hi,
I have been trying to obtain the resultant of some polynomials and I keep getting an error, the problem seems to be that it is treating my coefficients as variables. I tried to correct this by using coefficient Rings and also polynomial ring of a polynomial ring but it leads to another error when I call macaulayFormula. 
I've attached some codes generating the error and the error message of each.

loadPackage "EliminationMatrices"

R = QQ[a_0..a_5,b_0..b_5,c_0..c_5][x,y,z]

f1 = a_0*x^2+a_1*x*y+a_2*x*z+a_3*y^2+a_4*y*z+a_5*z^2

f2 = b_0*x^2+b_1*x*y+b_2*x*z+a_3*y^2+b_4*y*z+b_5*z^2

 f3 = c_0*x^2+c_1*x*y+c_2*x*z+a_3*y^2+c_4*y*z+c_5*z^2

 F = matrix{{f1,f2,f3}}

 G=macaulayFormula({x,y,z},F)

stdio:25:3:(3): error: not implemented yet: fraction fields of polynomial rings over rings other than ZZ, QQ, or a finite field

loadPackage"Resultants"

loadPackage "EliminationMatrices"

R=QQ[a_0..a_5,b_0..b_5,c_0..c_5,x,y,z]

f1 = a_0*x^2+a_1*x*y+a_2*x*z+a_3*y^2+a_4*y*z+a_5*z^2

f2 = b_0*x^2+b_1*x*y+b_2*x*z+a_3*y^2+b_4*y*z+b_5*z^2

 f3 = c_0*x^2+c_1*x*y+c_2*x*z+a_3*y^2+c_4*y*z+c_5*z^2

 F = matrix{{f1,f2,f3}}

 G=macaulayFormula({x,y,z},F)

resultant(F)

stdio:13:1:(3): error: the number of polynomials must be equal to the number of variables, but got 3 polynomials and 21 variables

Any help would be deeply appreciated.  Thank you.

 

Laurent Buse

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Jun 8, 2022, 4:48:30 PM6/8/22
to maca...@googlegroups.com
Hi,

These two packages use different ways of defining the ambient rings and you mixed them. You should proceed as follows:

loadPackage "EliminationMatrices"
R=QQ[a_0..a_5,b_0..b_5,c_0..c_5,x,y,z]
f1 = a_0*x^2+a_1*x*y+a_2*x*z+a_3*y^2+a_4*y*z+a_5*z^2
f2 = b_0*x^2+b_1*x*y+b_2*x*z+a_3*y^2+b_4*y*z+b_5*z^2
f3 = c_0*x^2+c_1*x*y+c_2*x*z+a_3*y^2+c_4*y*z+c_5*z^2
F = matrix{{f1,f2,f3}}
G=macaulayFormula({x,y,z},F)


loadPackage"Resultants"
R = QQ[a_0..a_5,b_0..b_5,c_0..c_5][x,y,z]
f1 = a_0*x^2+a_1*x*y+a_2*x*z+a_3*y^2+a_4*y*z+a_5*z^2
f2 = b_0*x^2+b_1*x*y+b_2*x*z+a_3*y^2+b_4*y*z+b_5*z^2
f3 = c_0*x^2+c_1*x*y+c_2*x*z+a_3*y^2+c_4*y*z+c_5*z^2
F = matrix{{f1,f2,f3}}
Res=resultant(F);
degree Res


Best regards,
Laurent.


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