symmetricPower -- symmetric power

Synopsis

Usage:

symmetricPower(i,f)
Inputs:
- i, an integer,
- M, a matrix, or a module
Outputs:
- a matrix, or a module, the $i$-th symmetric power of the matrix or module $f$

Description

There is currently one restriction: if $f$ is a matrix, then it must have only one row, and be a map of free modules, as in this example.

i1 : R = ZZ/101[a..d]

o1 = R

o1 : PolynomialRing

i2 : symmetricPower(2,vars R)

o2 = | a2 ab ac ad b2 bc bd c2 cd d2 |

             1      10
o2 : Matrix R  <-- R

If G --> F --> M --> 0 is a presentation for the module M = coker(f:G-->F), then symmetricPower(i,f) is the cokernel of the map symmetricPower(i-1,F) ** G --> symmetricPower(i,F).

i3 : R = ZZ/101[a,b]

o3 = R

o3 : PolynomialRing

i4 : symmetricPower(2,image vars R)

o4 = cokernel {2} | -b 0  |
              {2} | a  -b |
              {2} | 0  a  |

                            3
o4 : R-module, quotient of R

Ways to use symmetricPower :

symmetricPower(ZZ,Matrix)
symmetricPower(ZZ,Module)
symmetricPower(ZZ,CoherentSheaf) (missing documentation)

symmetricPower -- symmetric power

Synopsis

Description

See also

Ways to use symmetricPower :

For the programmer