will hold. The sources and targets of the maps should be free modules. This function is obtained from
by transposing the inputs and outputs.
i1 : R = ZZ[x,y]
o1 = R
o1 : PolynomialRing
|
i2 : f = random(R^{2:1},R^2)
o2 = {-1} | 8x+y 8x+3y |
{-1} | 3x+7y 3x+7y |
2 2
o2 : Matrix R <-- R
|
i3 : g = transpose (vars R ++ vars R)
o3 = {-1} | x 0 |
{-1} | y 0 |
{-1} | 0 x |
{-1} | 0 y |
4 2
o3 : Matrix R <-- R
|
i4 : (q,r) = quotientRemainder'(f,g)
o4 = ({-1} | 8 1 8 3 |, 0)
{-1} | 3 7 3 7 |
o4 : Sequence
|
i5 : q*g+r == f
o5 = true
|
i6 : f = f + map(target f, source f, id_(R^2))
o6 = {-1} | 8x+y+1 8x+3y |
{-1} | 3x+7y 3x+7y+1 |
2 2
o6 : Matrix R <-- R
|
i7 : (q,r) = quotientRemainder'(f,g)
o7 = ({-1} | 8 1 8 3 |, {-1} | 1 0 |)
{-1} | 3 7 3 7 | {-1} | 0 1 |
o7 : Sequence
|
i8 : q*g+r == f
o8 = true
|