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SRdeformations :: isTrivial

isTrivial -- Check whether a deformation is trivial.

Synopsis

Description

Check whether f is trivial, i.e., denominatorMonomial f has degree 1.

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 : isTrivial f

o6 = false
i7 : f1=firstOrderDeformation(mg, vector {-1,1,0,0,0})

     x
      1
o7 = --
     x
      0

o7 : first order deformation space of dimension 1
i8 : isTrivial f1

o8 = true

See also

Ways to use isTrivial :

For the programmer

The object isTrivial is a method function.