# Module ^** ZZ -- tensor power

## Synopsis

• Operator: ^**
• Usage:
M^**i
• Inputs:
• Outputs:
• , the i-th tensor power of M

## Description

The second symmetric power of the canonical module of the rational quartic:
 i1 : R = QQ[a..d]; i2 : I = monomialCurveIdeal(R,{1,3,4}) 3 2 2 2 3 2 o2 = ideal (b*c - a*d, c - b*d , a*c - b d, b - a c) o2 : Ideal of R i3 : M = Ext^1(I,R^{-4}) o3 = cokernel {1} | c 0 -d 0 -b | {1} | b c 0 a 0 | {1} | 0 d c b a | 3 o3 : R-module, quotient of R i4 : M^**2 o4 = cokernel {2} | c 0 -d 0 -b 0 0 0 0 0 0 0 0 0 0 c 0 -d 0 -b 0 0 0 0 0 0 0 0 0 0 | {2} | b c 0 a 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 c 0 -d 0 -b 0 0 0 0 0 | {2} | 0 d c b a 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 c 0 -d 0 -b | {2} | 0 0 0 0 0 c 0 -d 0 -b 0 0 0 0 0 b c 0 a 0 0 0 0 0 0 0 0 0 0 0 | {2} | 0 0 0 0 0 b c 0 a 0 0 0 0 0 0 0 0 0 0 0 b c 0 a 0 0 0 0 0 0 | {2} | 0 0 0 0 0 0 d c b a 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 b c 0 a 0 | {2} | 0 0 0 0 0 0 0 0 0 0 c 0 -d 0 -b 0 d c b a 0 0 0 0 0 0 0 0 0 0 | {2} | 0 0 0 0 0 0 0 0 0 0 b c 0 a 0 0 0 0 0 0 0 d c b a 0 0 0 0 0 | {2} | 0 0 0 0 0 0 0 0 0 0 0 d c b a 0 0 0 0 0 0 0 0 0 0 0 d c b a | 9 o4 : R-module, quotient of R