LMOpGCRD¶

greatest common right divisor for linear Mahler operators¶

Calling sequence:¶

$\operatorname{LMOpGCRD}(S, x, M, b)$

Parameters:¶

  • $S$, a set or list of linear Mahler operators,
  • $x$, a name
  • $M$, the name of the Mahler operator
  • $b$, a radix

Description:¶

  • $\operatorname{LMOpGCRD}$ computes the greatest common right divisor of a set or list of linear Mahler operators.
  • It is an implementation of Algorithm $12$ in the cited article.

References:¶

  • Frédéric Chyzak, Thomas Dreyfus, Philippe Dumas, and Marc Mezzarobba (2018). Computing solutions of linear Mahler equations. Mathematics of Computation 87.314, pp. 2977–3021.

Example:¶

In [1]:
libname := libname, FileTools:-JoinPath(["maple","lib","dcfun.mla"],base=homedir):
In [2]:
 with(dcfun):
Out[2]:

We compute the greatest common right divisor of two linear Mahler operators.

In [3]:
 L1 := LMOpLCLM([ 1- x*M, x^2 - M], x, M, 3);
Out[3]:

$$x^{3} M^{2}+\left(-x^{9}-x^{6}-x^{3}-1\right) M +x^{8}+x^{5}+x^{2}$$

In [4]:
 L2 := LMOpLCLM([1 - x*M, x^3 - M^2], x, M, 3);
Out[4]:

$$x^{9} M^{3}+\left(-x^{14}-x^{7}-1\right) M^{2}-x^{18} M +x^{17}+x^{10}+x^{3}$$

In [5]:
 LMOpGCRD([L1, L2], x, M, 3);
Out[5]:

$$-M x +1$$