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Divisor :: moduleWithSectionToIdeal

moduleWithSectionToIdeal -- Turn a module to an ideal of a ring and keep track of a module element

Synopsis

Description

Tries to embed the target of the module map as an ideal in R, it will also return the image of 1 under the module map. These are returned as a list, the element first, and then the ideal. It uses MTries=>n (the default n value is 10) in the same way as moduleToIdeal.

i1 : R = QQ[x,y];
i2 : M = (ideal(x^2,x*y))*R^1;
i3 : mat = map(M, R^1, {{1}, {1}});

o3 : Matrix
i4 : moduleWithSectionToIdeal(mat)

o4 = {x + y, ideal (y, x)}

o4 : List

Like moduleToIdeal, if ReturnMap is set to true, then the method will also return the map from M to R1.

i5 : R = QQ[x,y];
i6 : M = (ideal(x^2,x*y))*R^1;
i7 : mat = map(M, R^1, {{1}, {1}});

o7 : Matrix
i8 : L = moduleWithSectionToIdeal(mat, ReturnMap=>true)

o8 = {x + y, ideal (y, x), | x y |}

o8 : List
i9 : target L#2

      1
o9 = R

o9 : R-module, free
i10 : source L#2

o10 = image | x2 xy |

                              1
o10 : R-module, submodule of R

See also

Ways to use moduleWithSectionToIdeal :