# totalSpace -- Total space of a deformation.

## Description

Compute the total space of a first order deformation f or a list of first order deformations. The polynomial ring T is used for the base. The number of variables of T should match dim(FirstOrderDeformation) f (respectively the sum over the deformations in L).

 i1 : R=QQ[x_0..x_4]; i2 : addCokerGrading(R); 5 4 o2 : Matrix ZZ <--- ZZ i3 : I=ideal(x_0*x_1,x_1*x_2,x_2*x_3,x_3*x_4,x_4*x_0) o3 = ideal (x x , x x , x x , x x , x x ) 0 1 1 2 2 3 3 4 0 4 o3 : Ideal of R i4 : mg=mingens I; 1 5 o4 : Matrix R <--- R i5 : f=firstOrderDeformation(mg, vector {-1,-1,0,2,0}) 2 x 3 o5 = ---- x x 0 1 o5 : first order deformation space of dimension 1 i6 : S=QQ[t] o6 = S o6 : PolynomialRing i7 : totalSpace(f,S) 2 o7 = ideal (x x , x x , x x , x x , t*x + x x ) 3 4 0 4 2 3 1 2 3 0 1 o7 : Ideal of QQ[t, x ..x ] 0 4 i8 : f1=firstOrderDeformation(mg, vector {0,-1,-1,0,2}) 2 x 4 o8 = ---- x x 1 2 o8 : first order deformation space of dimension 1 i9 : S=QQ[t1,t2] o9 = S o9 : PolynomialRing i10 : totalSpace({f,f1},S) 2 2 o10 = ideal (x x , x x , x x , t2*x + x x , t1*x + x x ) 3 4 0 4 2 3 4 1 2 3 0 1 o10 : Ideal of QQ[t1, t2, x ..x ] 0 4