hrmt

Arguments

v

row of polynomials i.e. 1xk polynomial matrix

pg

polynomial

U

unimodular matrix polynomial.

Description

[pg,U]=hrmt(v) returns a unimodular matrix U and pg = gcd of row of polynomials v such that v*U = [pg,0].

Examples

x = poly(0,'x');
v = [x*(x+1), x^2*(x+1), (x-2)*(x+1), (3*x^2+2)*(x+1)]
[pg, U] = hrmt(v);
U = clean(U)
det(U)

--> v = [x*(x+1), x^2*(x+1), (x-2)*(x+1), (3*x^2+2)*(x+1)]
 v  =
  x +x²  x² +x³  -2 -x +x²  2 +2x +3x² +3x³

--> [pg, U] = hrmt(v);
--> U = clean(U)
 U  =
  x   -2 +x  1 +1.5x²   0.5
  -1  0      0          0
  0   -x     -1 -1.5x²  -0.5
  0   0      -1         0

--> det(U)
 ans  =
  1

See also

• gcd — Greatest (positive) Common Divisor
• htrianr — triangularization of polynomial matrix