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rational simplification


[N1,D1] = simp(N,D)
H1 = simp(H)


N, D

real polynomials or real matrix polynomials


rational matrix (i.e matrix with entries n/d ,n and d real polynomials)


[n1,d1]=simp(n,d) calculates two polynomials n1 and d1 such that n1/d1 = n/d.

If N and D are polynomial matrices the calculation is performed element-wise.

H1=simp(H) is also valid (each entry of H is simplified in H1).

  • no threshold is given, i.e. simp cannot forces a simplification.
  • For linear dynamic systems which include integrator(s) simplification changes the static gain. (H(0) for continuous systems or H(1) for discrete systems).
  • For complex data, simp returns its input(s).
  • Rational simplification is called after nearly each operations on rationals. It is possible to toggle simplification on or off using simp_mode function.


s = poly(0,'s');
[n,d] = simp((s+1)*(s+2),(s+1)*(s-2))

simp_mode(%F); hns = s/s
simp_mode(%T); hns = s/s

See also

  • simp_mode — toggle rational simplification
  • clean — cleans matrices (round to zero small entries)
  • roots — roots of a polynomial
  • trfmod — poles and zeros display
  • poly — Polynomial definition from given roots or coefficients, or characteristic to a square matrix.
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Last updated:
Tue Mar 07 09:28:45 CET 2023