DefParam -- deformation parameter

Description

DefParam is the name of an optional argument. Its value is a symbol, which specifies the name of the deformation parameter. Its default value is determined by the loadtime configuration Option DefaultDefParam, which has default value t.

For example, we may use the deformation parameter s:

i1 : S=QQ[x_0..x_4];

i2 : I=minors(2,matrix {{x_0,x_1,x_2,x_3},{x_1,x_2,x_3,x_4}});

o2 : Ideal of S

i3 : F0=gens I

o3 = | -x_1^2+x_0x_2 -x_1x_2+x_0x_3 -x_2^2+x_1x_3 -x_1x_3+x_0x_4
     ------------------------------------------------------------------------
     -x_2x_3+x_1x_4 -x_3^2+x_2x_4 |

             1      6
o3 : Matrix S  <-- S

i4 : (F,R,G,C)=versalDeformation(F0,DefParam=>s);

i5 : sum F

o5 = | x_1s_1+x_0s_2-x_1^2+x_0x_2 -s_1s_3+x_0s_4-x_1x_2+x_0x_3
     ------------------------------------------------------------------------
     -s_2s_3+s_3^2-s_1s_4-x_3s_1-x_2s_2+x_1s_4-x_2^2+x_1x_3
     ------------------------------------------------------------------------
     s_2s_3-s_3^2+x_2s_3-x_1x_3+x_0x_4 -x_4s_1-x_3s_2+x_3s_3-x_2x_3+x_1x_4
     ------------------------------------------------------------------------
     x_4s_3-x_3s_4-x_3^2+x_2x_4 |

                       1                6
o5 : Matrix (S[s ..s ])  <-- (S[s ..s ])
                1   4            1   4

Functions with optional argument named DefParam:

firstOrderDeformations(...,DefParam=>...) -- see firstOrderDeformations -- use tangent space to create first order perturbations and find relations
localHilbertScheme(...,DefParam=>...) -- see localHilbertScheme -- computes a power series representation of the local Hilbert scheme
versalDeformation(...,DefParam=>...) -- see versalDeformation(Matrix) -- computes a power series representation of a versal deformation

For the programmer

The object DefParam is a symbol.

The source of this document is in VersalDeformations.m2:1279:0.

DefParam -- deformation parameter

Description

See also

Functions with optional argument named DefParam:

For the programmer