Synopsis

• Usage:
adjoint'(f,G,H)
• Inputs:
• f, , a homomorphism F --> Hom(G,H) between modules
• G, , a free module
• H, , a free module
• Outputs:
• , the adjoint homomorphism F ** G --> H

Description

Recall that ** refers to the tensor product of modules. If f is homogeneous, then the resulting matrix will be homogeneous.

 i1 : R = QQ[x_1 .. x_12]; i2 : f = genericMatrix(R,6,2) o2 = | x_1 x_7 | | x_2 x_8 | | x_3 x_9 | | x_4 x_10 | | x_5 x_11 | | x_6 x_12 | 6 2 o2 : Matrix R <--- R i3 : g = adjoint'(f,R^2,R^3) o3 = | x_1 x_4 x_7 x_10 | | x_2 x_5 x_8 x_11 | | x_3 x_6 x_9 x_12 | 3 4 o3 : Matrix R <--- R i4 : isHomogeneous g o4 = true