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rtest_operator_algebra.mac
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(kill(all), load('operator_algebra),0);
0$
(reset(dot0nscsimp, dot1simp, dot0simp, dot1simp, dotassoc, dotconstrules, dotdistrib,
dotexptsimp, dotident,dotscrules),0);
0$
(declare([F,G,H], operator),0);
0$
map('operatorp,[F,G,H]);
[true,true,true]$
map('operatorp,[f,Y,I]);
[false,false,false]$
map('operatorp,[F[x],G[%pi],H[6,28]]);
[true,true,true]$
operator_apply(0,x);
0$
operator_apply(1,x);
x$
operator_apply(107,x);
107*x$
operator_apply(107,-x);
-107*x$
operator_apply(F,x);
F(x)$
operator_apply(42*F,x);
42*F(x)$
operator_apply(-F,x);
-F(x)$
operator_apply(%pi*F,x);
%pi*F(x)$
operator_apply(-%pi*F,x);
-%pi*F(x)$
operator_apply(-%pi*F,-x);
-%pi*F(-x)$
operator_apply(-2*sqrt(3)*F,-x);
-2*sqrt(3)*F(-x)$
(declare([a,b],constant),0);
0$
operator_apply(a*F,x);
a*F(x)$
operator_apply(F/sqrt(5), X);
F(X)/sqrt(5)$
operator_apply(a*b*F,x);
a*b*F(x)$
operator_apply(F+G,x);
F(x)+G(x)$
operator_apply(F-G,x);
F(x)-G(x)$
operator_apply(F+G,x+y);
F(x+y)+G(x+y)$
operator_apply(a*F+b*G,x);
a*F(x)+b*G(x)$
operator_apply(a*(F-G),x);
a*(F(x) - G(x))$
(declare([F,G], linear),0);
0$
operator_apply(F.(F-G),x);
F(F(x)) - F(G(x))$
operator_apply(F.(F-a*G),x);
F(F(x)) - a*F(G(x))$
(remove([F,G], linear),0);
0$
errcatch(operator_apply(F*G,x));
[]$
errcatch(operator_apply(F^2,x));
[]$
errcatch(operator_apply(F/G,x));
[]$
operator_apply(F.G,x);
F(G(x))$
operator_apply(G.F,x);
G(F(x))$
operator_apply(F.F,x);
F(F(x))$
operator_apply(F.G - G.F,x);
F(G(x)) - G(F(x))$
operator_apply(F.G.F,x);
F(G(F(x)))$
operator_apply(F^^3,x);
F(F(F(x)))$
operator_apply(F^^(3/2),x);
(F^^(3/2))(x)$
operator_apply(F^^a,x);
(F^^(a))(x)$
dot_form(F(x));
F.x$
dot_form(107*F(x));
107*F.x$
dot_form(107*F(x)/46);
107*F.x / 46$
dot_form(F(%pi));
F.%pi$
dot_form(F(-x));
F.-x$
dot_form(F(aa-bb));
F . (aa-bb)$
dot_form(F(F(x)));
F^^2 . x$
dot_form(F(G(x)));
F.G.x$
dot_form(F(G(x)) - G(F(x)));
F.G.x - G.F.x$
dot_form(F(G(x)) + G(F(x)));
F.G.x + G.F.x$
dot_form(23*F(G(x)) + 42*G(F(x)));
23*F.G.x + 42*G.F.x$
dot_form(23*F(G(x)) + 42*G(F(x)));
23*F.G.x + 42*G.F.x$
dot_form(F(G(F(G(x)))));
(F.G)^^2 . x$
/* subscripted operators */
xx : operator_apply(F[%pi], x);
F[%pi](x)$
dot_form(xx);
F[%pi] . x$
xx : operator_apply(F[%pi,5], x);
F[%pi,5](x)$
dot_form(xx);
F[%pi,5] . x$
xx : operator_apply(F[%pi,5], x);
F[%pi,5](x)$
dot_form(xx);
F[%pi,5] . x$
(declare(σ,operator),0);
0$
xx : operator_apply(σ[x], x);
σ[x](x)$
dot_form(xx);
σ[x] . x$
xx : operator_apply(σ[x].σ[y], X);
σ[x](σ[y](X))$
dot_form(xx);
σ[x].σ[y] . X$
xx : operator_apply(σ[x].σ[y] - σ[y].σ[x], X);
σ[x](σ[y](X)) - σ[y](σ[x](X))$
dot_form(xx);
σ[x].σ[y] . X - σ[y].σ[x] . X$
(remvalue(xx), declare(W, operator), declare(W, linear), 0);
0$
operator_apply([W, W.W, W^^4], 107);
[W(107), W(W(107)), W(W(W(W(107))))]$
operator_apply([W, W.W], a-b);
[W(a)-W(b), W(W(a)) - W(W(b))]$
(declare(Wc, operator), declare(Wc, linear),0);
0$
(put(W,Wc, 'operator_adjoint), put(Wc, W, 'operator_adjoint),0);
0$
operator_adjoint(%pi);
%pi$
operator_adjoint(%i);
-%i$
operator_adjoint(%i*%pi);
-%i * %pi$
operator_adjoint(W);
Wc$
operator_adjoint(Wc);
W$
operator_adjoint(W+Wc);
W+Wc$
operator_adjoint(W-Wc);
Wc-W$
operator_adjoint(W-Wc);
Wc-W$
operator_adjoint(W.Wc);
W.Wc$
operator_adjoint(W + %i*Wc);
Wc - %i*W$
operator_adjoint(5*W + 7*Wc);
5*Wc + 7*W$
operator_adjoint(W^^4);
Wc^^4$
operator_adjoint(23*W^^4);
23*Wc^^4$
operator_adjoint(operator_adjoint(F));
F$
(declare(F,operator, G, operator),0);
0$
(M : matrix([0,F],[G,0]), 0);
0$
M : operator_adjoint(M);
matrix([0,operator_adjoint(G)],[operator_adjoint(F),0])$
operator_adjoint(M);
matrix([0,F],[G,0])$
/* operator_adjoint of some constant multiples of operators #1 */
(declare(f,operator), operator_adjoint(f/sqrt(2)));
operator_adjoint(f)/sqrt(2)$
(forget(f,operator),0);
0$
(remvalue(M),0);
0$
(declare([f,g,h],operator), declare([a,b,c], constant), declare(n,integer), 0);
0$
extended_operatorp(f);
true$
extended_operatorp(f.g);
true$
extended_operatorp(f.g.h);
true$
extended_operatorp(f.g + g.f);
true$
extended_operatorp(f^^2);
true$
extended_operatorp(f^^n);
true$
extended_operatorp(42*f^^n / sqrt(2));
true$
extended_operatorp(a*f^^n / sqrt(2) - h);
true$
extended_operatorp(a*b*f.g + c*h);
true$
extended_operatorp(f*g);
false$
extended_operatorp(f^a);
false$
extended_operatorp(cos(f));
false$
bch(f,g,1);
f+g$
bch(f,g,2);
(f . g - g . f)/2 + g + f$
bch(f,g,3);
(g^^2 . f+g . f^^2-2*g . f . g+f^^2 . g+f . g^^2-2*f . g . f)/12 +(f . g-g . f)/2+g+f$
bch(f,g,4);
-((-(2*(g . f)^^2)+g^^2 . f^^2+2*(f . g)^^2-f^^2 . g^^2)/24)
+(g^^2 . f+g . f^^2-2*g . f . g+f^^2 . g+f . g^^2-2*f . g . f)/12
+(f . g - g . f)/2+g+f$
bch(f,f,4);
2*f$
bch(f,1,4);
1+f$
bch(f,0,4);
f$
bch(0,f,4);
f$
bch(f+g,f+g,4);
2*f+2*g$
errcatch(bch(f,g,5));
[]$
errcatch(bch(ff,gg,5));
[]$
bch_extended([],2);
0$
bch_extended([f],2);
f$
bch_extended([f,g],2) - bch(f,g,2);
0$
bch_extended([f,f,f],2);
3*f$
bch_extended([f,2*f,-3*f],2);
0$
bch_extended([f,g,f],2);
((f . g . f-g . f^^2)/2+g . f-((f^^2 . g-f . g . f)/2)-f . g)/2+((f . g-g . f)/2)+g+2*f$
(remove([f,g,h],operator), remove(n,integer), 0);
0$
values;
[]$
contexts;
[initial,global]$