quotient(Matrix,GroebnerBasis) -- matrix quotient

Synopsis

• Function: quotient

• Usage:

  q = quotient(f,g)

• Inputs:
  • f, a matrix
  • g, a Gröbner basis, a Gröbner basis or a matrix, with the same target as f
• Optional inputs:
  • BasisElementLimit => ..., default value infinity,
  • DegreeLimit => ..., default value {},
  • MinimalGenerators => ..., default value true,
  • PairLimit => ..., default value infinity,
  • Strategy => ..., default value null,
• Outputs:
  • q, a matrix, the quotient of f upon division by g

Description

i1 : R = ZZ[x,y]

o1 = R

o1 : PolynomialRing

i2 : f = random(R^2,R^{2:-1})

o2 = | 8x+y  8x+3y |
     | 3x+7y 3x+7y |

             2      2
o2 : Matrix R  <-- R

i3 : g = vars R ++ vars R

o3 = | x y 0 0 |
     | 0 0 x y |

             2      4
o3 : Matrix R  <-- R

i4 : quotient(f,g)

o4 = {1} | 8 8 |
     {1} | 1 3 |
     {1} | 3 3 |
     {1} | 7 7 |

             4      2
o4 : Matrix R  <-- R

i5 : f = f + map(target f, source f, id_(R^2))

o5 = | 8x+y+1 8x+3y   |
     | 3x+7y  3x+7y+1 |

             2      2
o5 : Matrix R  <-- R

i6 : quotient(f,g)

o6 = {1} | 8 8 |
     {1} | 1 3 |
     {1} | 3 3 |
     {1} | 7 7 |

             4      2
o6 : Matrix R  <-- R

See also

• quotientRemainder -- matrix quotient and remainder
• quotient' -- matrix quotient (opposite)