Manuals/calci/MOORE

From ZCubes Wiki
Revision as of 11:01, 30 April 2015 by Devika (talk | contribs)
Jump to navigation Jump to search
MATRIX("MOORE",order)


  • is the size of the Moore matrix.

Description

  • This function gives the moore matrix of order 3 with the element 1.
  • A moore matrix, is a square matrix over a finite field.
  • When moore matrix is a square matrix, then its deteminant is called a Moore determinant.
  • But it is unrelated to the Moore determinant of a quaternionic Hermitian matrix.
  • The Moore matrix has successive powers of the applied to the first column, so it is an mxn matrix of the form:

Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. TeX parse error: Double exponent: use braces to clarify"): {\displaystyle {\begin{bmatrix}\alpha _{1}&{\alpha _{1}}^{q}&\cdots &{\alpha _{1}}^{q}^{n-1}\\\alpha _{2}&{\alpha _{2}}^{q}&\cdots &{\alpha _{2}}^{q}^{n-1}\\\alpha _{3}&{\alpha _{3}}^{q}&\cdots &{\alpha _{3}}^{q}^{n-1}\\\vdots &\ddots &\vdots \\\alpha _{m}&{\alpha _{m}}^{q}&\cdots &{\alpha _{m}}^{q}^{n-1}\\\end{bmatrix}}}

  • In calci, MATRIX("moore") is giving the matrixwith the element 1 of order 3.
  • And MATRIX("moore",4,1..4) is giving Moore matrix starting element 1 to 4 of order 4.

Examples

  • 1.MATRIX("moore")
1 1 1
1 1 1
1 1 1
  • 2.MATRIX("moore",5,1..5)
1 1 1 1 1
2 4 16 256 65536
3 9 81 6561 43046721
4 16 256 65536 4294967296
5 25 625 390625 152587890625
  • 3.MATRIX("moore",4,3..7,"",2.3)
3 12.513502532843182 334.1730615222005 638460.9005874459
4 24.251465064166364 1530.7256306021752 21147737.669320222
5 40.51641491731905 4983.693475030862 319424366.94628483
6 61.623714938749366 13074.350231574774 2936069039.087338


See Also


References