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remainder' -- matrix remainder (opposite)

Description

The equation q*g+r == f will hold, where q is the map provided by quotient'. The sources and targets of the maps should be free modules. This function is obtained from remainder 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 : remainder'(f,g)

o4 = 0

             2      2
o4 : Matrix R  <-- R
 
i5 : f = f + map(target f, source f, id_(R^2))

o5 = {-1} | 8x+y+1 8x+3y   |
     {-1} | 3x+7y  3x+7y+1 |

             2      2
o5 : Matrix R  <-- R
 
i6 : remainder'(f,g)

o6 = {-1} | 1 0 |
     {-1} | 0 1 |

             2      2
o6 : Matrix R  <-- R

Code

method function remainder':  source code not available

See also

Ways to use remainder':

  • remainder'(Matrix,Matrix)

For the programmer

The object remainder' is a method function.

The source of this document is in Macaulay2Doc/functions/quotient-remainder-doc.m2:270:0.