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dotProduct -- entry by entry dot product of two Betti diagrams

Description

In the first version (M, lowestDeg) refers to mat2betti(M, lowestDeg), and in the second version (M,B) refers to (M,0,B). 
i1 : d = {0,1,3,4}

o1 = {0, 1, 3, 4}

o1 : List
 
i2 : M = facetEquation(d,1,-5,5)

o2 = | 45 -32 21 -12 |
     | 32 -21 12 -5  |
     | 21 -12 5  0   |
     | 12 -5  0  3   |
     | 5  0   -3 4   |
     | 0  3   -4 3   |
     | 0  0   0  0   |
     | 0  0   0  0   |
     | 0  0   0  0   |
     | 0  0   0  0   |
     | 0  0   0  0   |

              11       4
o2 : Matrix ZZ   <-- ZZ
 
i3 : B = pureBettiDiagram d

            0 1 2 3
o3 = total: 1 2 2 1
         0: 1 2 . .
         1: . . 2 1

o3 : BettiTally
 
i4 : dotProduct(M,-5,B)

o4 = 6
 
i5 : A = matrix"1,1,0; 0,1,1; 0,1,1"

o5 = | 1 1 0 |
     | 0 1 1 |
     | 0 1 1 |

              3       3
o5 : Matrix ZZ  <-- ZZ
 
i6 : B = matrix"0,1,-2;0,0,0;0,0,0"

o6 = | 0 1 -2 |
     | 0 0 0  |
     | 0 0 0  |

              3       3
o6 : Matrix ZZ  <-- ZZ
 
i7 : dotProduct(A, B)

o7 = 1
 
i8 : A1 = mat2betti A

            0 1 2
o8 = total: 1 3 2
         0: 1 1 .
         1: . 1 1
         2: . 1 1

o8 : BettiTally
 
i9 : B1 = mat2betti B

            1  2
o9 = total: 1 -2
         0: 1 -2

o9 : BettiTally
 
i10 : dotProduct(A1, B1)

o10 = 1
 
i11 : dotProduct(A, 0, B1)

o11 = 1
 
i12 : dotProduct(A, B1)

o12 = 1

See also

Ways to use dotProduct:

  • dotProduct(BettiTally,BettiTally)
  • dotProduct(Matrix,BettiTally)
  • dotProduct(Matrix,Matrix)
  • dotProduct(Matrix,ZZ,BettiTally)

For the programmer

The object dotProduct is a method function.

The source of this document is in /build/macaulay2-88fgJW/macaulay2-1.25.11+ds/M2/Macaulay2/packages/BoijSoederberg.m2:2354:0.