% Tests of the COMPACT package.
% Author: Anthony C. Hearn.
% First some simple examples.
aa := {cos(x)^2+sin(x)^2-1};
xx := 2*cos(x)^2+2*sin(x)^2-2;
compact(xx,aa);
xx := (1-cos(x)^2)^4;
compact(xx,aa);
% These examples are from Lars Hornfeldt.
% This should be cos x^10*sin x^10.
compact(((1-(sin x)**2)**5)*((1-(cos x)**2)**5)
*(((sin x)**2+(cos x)**2)**5),
{cos x^2+sin x^2=1});
% This example illustrates the problem in the above. It is cos(x)^6.
compact(-3cos(x)^2*sin(x)^2-sin(x)^6+1,{cos x^2+sin x^2-1});
compact(s*(1-(sin x**2))+c*(1-(cos x)**2)+(sin x)**2+(cos x)**2,
{cos x^2+sin x^2=1});
xx := s*(1-(sin x**2))+c*(1-(cos x)**2)+(sin x)**2+(cos x)**2
*((sin x)**2+(cos x)**2)*(sin x)**499*(cos x)**499;
compact(xx,{cos(x)^2+sin(x)^2=1});
compact((s*(1-(sin x**2))+c*(1-(cos x)**2)+(sin x)**2+(cos x)**2)
*((sin x)**2+(cos x)**2)*(sin x)**499*(cos x)**499,
{cos x^2+sin x^2=1});
compact(df((1-(sin x)**2)**4,x),{cos x^2+sin x^2=1});
% End of Lars Hornfeld examples.
xx := a*(cos(x)+2*sin(x))^3-w*(cos(x)-sin(x))^2;
compact(xx,aa);
xx := (1-cos(x)^2)^2+(1-sin(x)^2)^2;
compact(xx,aa);
xx := (c^2-1)^6+7(s-1)^4+23(c+s)^5;
compact(xx,{c+s=1});
yy := (c+1)^6*s^6+7c^4+23;
compact(yy,{c+s=1});
zz := xx^3+c^6*s^6$
compact(zz,{c+s=1});
xx := (c+s)^5 - 55(1-s)^2 + 77(1-c)^3 + (c+2s)^8;
% This should reduce to something like:
yy := 1 - 55c^2 + 77s^3 + (1+s)^8;
% The result contains the same number but different terms.
compact(xx,{c+s=1});
compact(yy,{c+s=1});
% Test showing order of expressions is important.
d2:= - 4*r3a**2 - 4*r3b**2 - 4*r3c**2 + 3*r3**2$
d1:= 4 * r3a**2 * r3
+ 4 * r3b**2 * r3
+ 4 * r3c**2 * r3
+ 16 * r3a * r3b * r3c
- r3**3$
d0:= 16 * r3a**4
+ 16 * r3b**4
+ 16 * r3c**4
+ r3**4
- 32 * r3a**2 * r3b**2
- 32 * r3a**2 * r3c**2
- 32 * r3b**2 * r3c**2
- 8 * r3a**2 * r3**2
- 8 * r3b**2 * r3**2
- 8 * r3c**2 * r3**2
- 64 * r3a * r3b * r3c * r3$
alist := { c0 = d0, c1 = d1, c2 = d2}$
blist := { c2 = d2, c1 = d1, c0 = d0}$
d:= d2 * l*l + d1 * l + d0;
compact(d,alist); % Works fine.
compact(d,blist); % Only c2=d2 is applied.
% This example illustrates why parallel application of the individual
% side relations is necessary.
lst:={x1=a+b+c, x2=a-b-c, x3=-a+b-c, x4=-a-b+c};
z1:=(a+b+c)*(a-b-c)*(-a+b-c); % This is x1*x2*x3.
z2:=(a+b+c)*(a-b-c)*(-a+b-c)*(-a-b+c); % This is x1*x2*x3*x4.
compact(z1,lst); % Not the best solution but better than nothing.
compact(z2,lst); % Does nothing.
end;