exponentsMatrix -- exponents in one or more polynomials

Synopsis

• Usage:

  exponentsMatrix(f_0,f_1,...)

• Inputs:
  • (f_0,f_1,...) one or more Laurent polynomials in the same ring.
• Optional inputs:
  • Unmixed => ..., default value null
• Outputs:
  • (A_0,A_1,...) a sequence of matrices such that the columns of A_i are the exponents of f_i. If either the option Unmixed is set to true or all the matrices A_i are equal, then just one matrix is returned whose columns are all the exponents occurring in at least one of the polynomials.

Description

i1 : QQ[x,y,z];

i2 : f = (x^2 - 7 + x*y*z^11 + y, -3*y^7*z + x^3*y + 5*x^2);

i3 : exponentsMatrix(f_0)

o3 = | 0 0 1  2 |
     | 0 1 1  0 |
     | 0 0 11 0 |

              3        4
o3 : Matrix ZZ  <--- ZZ

i4 : exponentsMatrix(f_0,f_1)

o4 = (| 0 0 1  2 |, | 0 2 3 |)
      | 0 1 1  0 |  | 7 0 1 |
      | 0 0 11 0 |  | 1 0 0 |

o4 : Sequence

i5 : exponentsMatrix(f_0,f_1,Unmixed=>true)

o5 = | 0 0 0 1  2 3 |
     | 0 1 7 1  0 1 |
     | 0 0 1 11 0 0 |

              3        6
o5 : Matrix ZZ  <--- ZZ

See also

• exponents -- the exponents of a polynomial
• sparseResultant -- sparse resultant (A-resultant)
• genericLaurentPolynomials -- generic (Laurent) polynomials