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getIdeals -- get component ideals from a monomial module

Synopsis

Description

Let M be a submodule of F and let $\{g_1,g_2,\ldots,g_r\}$ be a graded basis of F. This method returns a list $L=\{I_1,I_2,\ldots,I_r\}$ such that $M=I_i g_i \oplus I_2 g_2 \oplus \cdots \oplus I_r g_r$.

Example:

i1 : E = QQ[e_1..e_4, SkewCommutative => true]

o1 = E

o1 : PolynomialRing, 4 skew commutative variable(s)
 
i2 : m=matrix {{e_1*e_2,e_3*e_4,0,0,0},{0,0,e_1*e_2,e_2*e_3*e_4,0},{0,0,0,0,e_2*e_3*e_4}}

o2 = | e_1e_2 e_3e_4 0      0         0         |
     | 0      0      e_1e_2 e_2e_3e_4 0         |
     | 0      0      0      0         e_2e_3e_4 |

             3      5
o2 : Matrix E  <-- E
 
i3 : M=image m

o3 = image | e_1e_2 e_3e_4 0      0         0         |
           | 0      0      e_1e_2 e_2e_3e_4 0         |
           | 0      0      0      0         e_2e_3e_4 |

                             3
o3 : E-module, submodule of E
 
i4 : getIdeals M

o4 = {ideal (e e , e e ), ideal (e e , e e e ), ideal(e e e )}
              3 4   1 2           1 2   2 3 4          2 3 4

o4 : List

See also

Ways to use getIdeals :

For the programmer

The object getIdeals is a method function.