MultiplicationMat

MultiplicationMat -- multiplication matrix of a ringelem

Syntax

MultiplicationMat(X: RINGELEM, I: IDEAL): MAT
MultiplicationMat(X: RINGELEM, I: IDEAL, QB: LIST): MAT

Description

This function computes the multiplication matrix of a ringelem f modulo a zero-dimensional ideal I with respect to a quotient basis of I.

In the second form it is computed with respect to the given quotient basis QB.

Example

/**/  use QQ[x,y];
/**/  I := ideal(x*y +y^2 -x -4*y +3, x^2 -y^2 -4*x +2*y +3, y^3 -4*y^2 +5*y -2);
/**/  MultiplicationMat(x, I);
matrix(QQ,
 [[0, -3, -5, -3],
  [0, 4, 6, -2],
  [0, -1, -1, 1],
  [1, 1, 1, 4]])

/**/  MultiplicationMat(x, I, [one(CurrentRing), x, y, y^2]);
matrix(QQ,
 [[0, -3, -3, -5],
  [1, 4, 1, 1],
  [0, -2, 4, 6],
  [0, 1, -1, -1]])