REDUCE 3.6, 15-Jul-95, patched to 6 Mar 96 ...
% Tests of the COMPACT package.
% Author: Anthony C. Hearn.
% First some simple examples.
aa := {cos(x)^2+sin(x)^2-1};
2 2
aa := {cos(x) + sin(x) - 1}
xx := 2*cos(x)^2+2*sin(x)^2-2;
2 2
xx := 2*(cos(x) + sin(x) - 1)
compact(xx,aa);
0
xx := (1-cos(x)^2)^4;
8 6 4 2
xx := cos(x) - 4*cos(x) + 6*cos(x) - 4*cos(x) + 1
compact(xx,aa);
8
sin(x)
% 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});
10 2 4 10 8 2
sin(x) *(10*cos(x) *sin(x) - sin(x) + 5*sin(x) - 5*sin(x) + 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});
2 2 6
- 3*cos(x) *sin(x) - sin(x) + 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});
2 2
cos(x) *s + sin(x) *c + 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;
503 499 501 501 2 2
xx := cos(x) *sin(x) + cos(x) *sin(x) - cos(x) *c - sin(x) *s
2
+ sin(x) + c + s
compact(xx,{cos(x)^2+sin(x)^2=1});
501 499 2 2 2
cos(x) *sin(x) + cos(x) *s + sin(x) *c + sin(x)
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});
499 499 2 2
cos(x) *sin(x) *(cos(x) *s + sin(x) *c + 1)
compact(df((1-(sin x)**2)**4,x),{cos x^2+sin x^2=1});
2 2 6
8*cos(x)*sin(x)*(3*cos(x) *sin(x) + sin(x) - 1)
% End of Lars Hornfeld examples.
xx := a*(cos(x)+2*sin(x))^3-w*(cos(x)-sin(x))^2;
3 2 2 2
xx := cos(x) *a + 6*cos(x) *sin(x)*a - cos(x) *w + 12*cos(x)*sin(x) *a
3 2
+ 2*cos(x)*sin(x)*w + 8*sin(x) *a - sin(x) *w
compact(xx,aa);
2 3
11*cos(x)*sin(x) *a + 2*cos(x)*sin(x)*w + cos(x)*a + 2*sin(x) *a + 6*sin(x)*a
- w
xx := (1-cos(x)^2)^2+(1-sin(x)^2)^2;
4 2 4 2
xx := cos(x) - 2*cos(x) + sin(x) - 2*sin(x) + 2
compact(xx,aa);
2 2
- 2*cos(x) *sin(x) + 1
xx := (c^2-1)^6+7(s-1)^4+23(c+s)^5;
12 10 8 6 5 4 4 3 2
xx := c - 6*c + 15*c - 20*c + 23*c + 115*c *s + 15*c + 230*c *s
2 3 2 4 5 4 3 2
+ 230*c *s - 6*c + 115*c*s + 23*s + 7*s - 28*s + 42*s - 28*s + 8
compact(xx,{c+s=1});
12 10 8 6 4 2
c - 6*c + 15*c - 20*c + 22*c - 6*c + 24
yy := (c+1)^6*s^6+7c^4+23;
6 6 5 6 4 6 4 3 6 2 6 6 6
yy := c *s + 6*c *s + 15*c *s + 7*c + 20*c *s + 15*c *s + 6*c*s + s + 23
compact(yy,{c+s=1});
6 6 5 6 4 6 4 3 6 2 6 6 6
c *s + 6*c *s + 15*c *s + 7*c + 20*c *s + 15*c *s + 6*c*s + s + 23
zz := xx^3+c^6*s^6$
compact(zz,{c+s=1});
36 34 32 30 28 26 24 22
c - 18*c + 153*c - 816*c + 3081*c - 8820*c + 20019*c - 37272*c
20 18 16 14 12 11
+ 58854*c - 81314*c + 100488*c - 111840*c + 111341*c - 6*c
10 9 8 7 6 4 2
- 97545*c - 20*c + 80439*c - 6*c - 53783*c + 40608*c - 10368*c + 13824
xx := (c+s)^5 - 55(1-s)^2 + 77(1-c)^3 + (c+2s)^8;
8 7 6 2 5 3 5 4 4 4
xx := c + 16*c *s + 112*c *s + 448*c *s + c + 1120*c *s + 5*c *s
3 5 3 2 3 2 6 2 3 2
+ 1792*c *s + 10*c *s - 77*c + 1792*c *s + 10*c *s + 231*c
7 4 8 5 2
+ 1024*c*s + 5*c*s - 231*c + 256*s + s - 55*s + 110*s + 22
% This should reduce to something like:
yy := 1 - 55c^2 + 77s^3 + (1+s)^8;
2 8 7 6 5 4 3 2
yy := - 55*c + s + 8*s + 28*s + 56*s + 70*s + 133*s + 28*s + 8*s + 2
% The result contains the same number but different terms.
compact(xx,{c+s=1});
8 7 6 5 4 3 2
s + 8*s + 28*s + 56*s + 70*s + 133*s - 27*s + 118*s - 53
compact(yy,{c+s=1});
8 7 6 5 4 3 2
s + 8*s + 28*s + 56*s + 70*s + 133*s - 27*s + 118*s - 53
% 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;
2 2 2 2 2 2 2 2 3 2
d := 3*l *r3 - 4*l *r3a - 4*l *r3b - 4*l *r3c - l*r3 + 4*l*r3*r3a
2 2 4 2 2
+ 4*l*r3*r3b + 4*l*r3*r3c + 16*l*r3a*r3b*r3c + r3 - 8*r3 *r3a
2 2 2 2 4 2 2
- 8*r3 *r3b - 8*r3 *r3c - 64*r3*r3a*r3b*r3c + 16*r3a - 32*r3a *r3b
2 2 4 2 2 4
- 32*r3a *r3c + 16*r3b - 32*r3b *r3c + 16*r3c
compact(d,alist);
2
c0 + c1*l + c2*l
% Works fine.
compact(d,blist);
2 2 2 3 4
c2*l - c2*l*r3 + 2*c2*r3 + 8*c2*r3a + 2*l*r3 + 16*l*r3a*r3b*r3c - 5*r3
2 2 4 4 2 2 4
- 24*r3 *r3a - 64*r3*r3a*r3b*r3c + 48*r3a + 16*r3b - 32*r3b *r3c + 16*r3c
% 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};
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);
3 2 2 2 2 3 2 2 3
z1 := - a + a *b - a *c + a*b + 2*a*b*c + a*c - b - b *c + b*c + c
% This is x1*x2*x3.
z2:=(a+b+c)*(a-b-c)*(-a+b-c)*(-a-b+c);
4 2 2 2 2 4 2 2 4
z2 := a - 2*a *b - 2*a *c + b - 2*b *c + c
% This is x1*x2*x3*x4.
compact(z1,lst);
2
x1*(4*a*b + 2*c*x1 - x1 )
% Not the best solution but better than nothing.
compact(z2,lst);
4 2 2 2 2 4 2 2 4
a - 2*a *b - 2*a *c + b - 2*b *c + c
% Does nothing.
end;
(TIME: compact 710 710)