laurent -- Converts an exponent vector or a deformation into a Laurent monomial.

• Usage:
laurent(v,R)
laurent(f)
• Inputs:
• v, ,
• R, ,
• Outputs:
• ,

Description

Converts the exponent vector v into a Laurent monomial in the variables of R. The result lies in frac R. The number of variables of R has to match the length of v.

If given a FirstOrderDeformation it returns the corresponding laurent monomial.

 i1 : R=QQ[x_0..x_4] o1 = R o1 : PolynomialRing i2 : m=vector {1,-2,1,0,0} o2 = | 1 | | -2 | | 1 | | 0 | | 0 | 5 o2 : ZZ i3 : laurent(m,R) x x 0 2 o3 = ---- 2 x 1 o3 : frac R

 i4 : R=QQ[x_0..x_4] o4 = R o4 : PolynomialRing i5 : addCokerGrading(R); 5 4 o5 : Matrix ZZ <--- ZZ i6 : I=ideal(x_0*x_1,x_1*x_2,x_2*x_3,x_3*x_4,x_4*x_0) o6 = ideal (x x , x x , x x , x x , x x ) 0 1 1 2 2 3 3 4 0 4 o6 : Ideal of R i7 : mg=mingens I; 1 5 o7 : Matrix R <--- R i8 : f=firstOrderDeformation(mg, vector {-1,-1,0,2,0}) 2 x 3 o8 = ---- x x 0 1 o8 : first order deformation space of dimension 1 i9 : laurent f 2 x 3 o9 = ---- x x 0 1 o9 : frac R