/*
 * inverse.maxima
 *
 * (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule
 */
n: 5;
m: X^5 + 15*X^3 - 30*X^2 + 45;

M: matrix(
	[ 0, 0, 0, 0, -45 ],
	[ 1, 0, 0, 0,   0 ],
	[ 0, 1, 0, 0,  30 ],
	[ 0, 0, 1, 0, -15 ],
	[ 0, 0, 0, 1,   0 ]
);
M2: M.M;
M3: M.M2;
M4: M.M3;

y: a0 + a1*X + a2*X^2 + a3*X^3 + a4*X^4;
Y: a0*identfor(M) + a1*M + a2*M2 + a3*M3 + a4*M4;

B: invert(Y);

b0: B[1,1];
b1: B[2,1];
b2: B[3,1];
b3: B[4,1];
b4: B[5,1];

Z: b0*identfor(M) + b1*M + b2*M2 + b3*M3 + b4*M4;
z: b0 + b1*X + b2*X^2 + b3*X^3 + b4*X^4;

w: expand(y*z);
remainder(w, m, X);