LMOpMul

multiplication of linear Mahler operators

Calling sequence:

$\operatorname{LMOpMul}(L_1, L_2, x, M, b)$

Parameters:

• $L_1$, a linear Mahler operator with rational functions coefficients
  
• $L_2$, a linear Mahler operator with rational functions coefficients
  
• $x$, a name
  
• $M$, the name of the Mahler operator
  
• $b$, the radix of the Mahler operator

Description:

• $\operatorname{LMOpMul}(L_1, L_2, x, M, b)$ computes the product of the linear Mahler operators $L_1$ and $L_2$.

References:

• Alin Bostan, Frédéric Chyzak, Bruno Le Roux (2008). Products of Ordinary Differential Operators by Evaluation and Interpolation. ISSAC '08.

Example:

libname := libname, FileTools:-JoinPath(["maple","lib","dcfun.mla"],base=homedir):

 with(dcfun):

We multiply two linear Mahler operators. Note that $L = (x - M)\times M$ is equivalent to $L = \operatorname{LMOpMul}(L, M, x, M, b)$ in view of the operators representation mode.

 b := 3;

$$3$$

 L1 := (x-M)*M;

$$\left(x -M \right) M$$

 L2 := add(M^k, k = 0..2);

$$M^{2}+M +1$$

 LMOpMul(L1, L2, x, M, b);

$$M x +\left(-1+x \right) M^{2}+\left(-1+x \right) M^{3}-M^{4}$$