"Source: Text/Ring/RngSlope.text";
"Line: 1107";
"Date: Fri Sep 26 12:10:11 2025";
"Main: Fri Sep 26 14:29:19 2025";
// original file: Text/Ring/RngSlope.text, line: 1107
// Example: H57E6 ()
print "Example: H57E6";
ei := GetEchoInput();
SetEchoInput(true);
S<u> := SpRing (pAdicField (7, 30), 1); // slope 1
M := SpMatrix(3,5,[S|1,0,u,u^2,u,  u^2/7,0,1,0,0, 0,0,1,0,u^4/7^2]);
ROWS := Rows(M);
V := u * ROWS[1] + u^2/7 * ROWS[3]; // create a kernel
MAT := SpMatrix(ROWS cat [Universe(ROWS)|V]); // 4 x 5
Dimension (SpSpace (MAT)); // 3
assert $1 eq 3;
K := Kernel (MAT); K;
KK := Kernel(BasisMatrix(K)); KK;
assert ZeroVector(Ambient(KK)) in KK;
SetEchoInput(ei);
