1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
|
document {
Key => {
modulo,
(modulo, Matrix, Matrix),
(modulo, Matrix, Nothing),
(modulo, Nothing, Matrix)
},
Headline => "find the pre-image (pullback) of image of a map (low level version)",
Usage => "modulo(f,g)",
Inputs => { "f", "g" },
Outputs => {
Matrix => { " whose image is the pre-image (pullback) of the image of ", TT "g", " under ", TT "f" }
},
PARA {
"The maps ", TT "f", " and ", TT "g", " must have the same target, and their sources and targets must be free.
If ", TT "f", " is ", TO "null", ", then it is taken to be the identity. If ", TT "g", " is ", TO "null", ", it is taken to be zero."
},
PARA {"This function is mainly for internal use."},
EXAMPLE lines ///
R = QQ[x,y,z]
f = matrix {{x,y}}
g = matrix {{y,z}}
modulo(f,g)
kernel( inducedMap(coker g, target g) * f )
///,
}
|
