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quotientRemainder' -- matrix quotient and remainder (opposite)

Synopsis

Usage:
(q,r) = quotientRemainder'(f,g)
Inputs:
- f, a matrix
- g, a Groebner basis or a matrix, with the same source as f
Outputs:
- q, the quotient of f upon (opposite) division by g
- r, the remainder of f upon (opposite) division by g

Description

The equation q*g+r == f will hold. The sources and targets of the maps should be free modules. This function is obtained from quotientRemainder 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} | y     -9x-9y |
     {-1} | 5x+2y 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} | 0 1 -9 -9 |, 0)
      {-1} | 5 2 0  7  |

o4 : Sequence

i5 : q*g+r == f

o5 = true

i6 : f = f + map(target f, source f, id_(R^2))

o6 = {-1} | y+1   -9x-9y |
     {-1} | 5x+2y 7y+1   |

             2       2
o6 : Matrix R  <--- R

i7 : (q,r) = quotientRemainder'(f,g)

o7 = ({-1} | 0 1 -9 -9 |, {-1} | 1 0 |)
      {-1} | 5 2 0  7  |  {-1} | 0 1 |

o7 : Sequence

i8 : q*g+r == f

o8 = true

See also

quotientRemainder -- matrix quotient and remainder

Ways to use `quotientRemainder'` :

quotientRemainder'(Matrix,Matrix)

Code

function 'quotientRemainder'': source code not available