Sat Jun 29 14:15:42 PDT 1991
REDUCE 3.4, 15-Jul-91 ...
1: 1:
2: 2:
3: 3: % Tests of the COMPACT package.
% Author: Anthony C. Hearn.
% First some simple examples.
aa := {cos(x)^2+sin(x)^2-1};
2 2
AA := {SIN(X) + COS(X) - 1}
xx := 2*cos(x)^2+2*sin(x)^2-2;
2 2
XX := 2*(SIN(X) + COS(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.
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 10
SIN(X) *COS(X)
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
SIN(X) *C + COS(X) *S + 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;
501 501 499 503 2 2
XX := SIN(X) *COS(X) + SIN(X) *COS(X) - SIN(X) *S + SIN(X)
2
- COS(X) *C + C + S
compact(xx,{cos(x)^2+sin(x)^2=1});
499 501 2 2 2
SIN(X) *COS(X) + SIN(X) *C + SIN(X) + COS(X) *S
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
SIN(X) *COS(X) *(SIN(X) *C + COS(X) *S + 1)
compact(df((1-(sin x)**2)**4,x),{cos x^2+sin x^2=1});
7
- 8*SIN(X)*COS(X)
% End of Lars Hornfeld examples.
xx := a*(cos(x)+2*sin(x))^3-w*(cos(x)-sin(x))^2;
3 2 2
XX := 8*SIN(X) *A + 12*SIN(X) *COS(X)*A - SIN(X) *W
2 3
+ 6*SIN(X)*COS(X) *A + 2*SIN(X)*COS(X)*W + COS(X) *A
2
- COS(X) *W
compact(xx,aa);
2 3
- 2*SIN(X)*COS(X) *A + 2*SIN(X)*COS(X)*W + 8*SIN(X)*A - 11*COS(X) *A
+ 12*COS(X)*A - W
xx := (1-cos(x)^2)^2+(1-sin(x)^2)^2;
4 2 4 2
XX := SIN(X) - 2*SIN(X) + COS(X) - 2*COS(X) + 2
compact(xx,aa);
2 2
- 2*SIN(X) *COS(X) + 1
xx := (c^2-1)^6+7(s-1)^4+23(c+s)^5;
12 10 8 6 5 4 4
XX := C - 6*C + 15*C - 20*C + 23*C + 115*C *S + 15*C
3 2 2 3 2 4 5 4
+ 230*C *S + 230*C *S - 6*C + 115*C*S + 23*S + 7*S
3 2
- 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
YY := C *S + 6*C *S + 15*C *S + 7*C + 20*C *S + 15*C *S
6 6
+ 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
C - 18*C + 153*C - 816*C + 3081*C - 8820*C + 20019*C
22 20 18 16 14
- 37272*C + 58854*C - 81314*C + 100488*C - 111840*C
12 11 10 9 8 7
+ 111341*C - 6*C - 97545*C - 20*C + 80439*C - 6*C
6 4 2
- 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
+ 1792*C *S + 10*C *S - 77*C + 1792*C *S + 10*C *S
2 7 4 8 5 2
+ 231*C + 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 2
D := - 4*L *R3A - 4*L *R3B - 4*L *R3C + 3*L *R3 + 4*L*R3A *R3
2 2 3
+ 16*L*R3A*R3B*R3C + 4*L*R3B *R3 + 4*L*R3C *R3 - L*R3
4 2 2 2 2 2 2
+ 16*R3A - 32*R3A *R3B - 32*R3A *R3C - 8*R3A *R3
4 2 2 2 2
- 64*R3A*R3B*R3C*R3 + 16*R3B - 32*R3B *R3C - 8*R3B *R3
4 2 2 4
+ 16*R3C - 8*R3C *R3 + R3
compact(d,alist);
2
L *C2 + L*C1 + C0
% Works fine.
compact(d,blist);
2 3 2 2
L *C2 + 16*L*R3A*R3B*R3C + 2*L*R3 - L*R3*C2 - 64*R3A *R3B
2 2 2 2 4 2
- 64*R3A *R3C - 64*R3A*R3B*R3C*R3 - 64*R3B *R3C + 4*R3 - 4*R3 *C2
2
+ C2
% 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);
Z1 :=
3 2 2 2 2 3 2 2 3
- 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;
4: 4:
Quitting
Sat Jun 29 14:15:50 PDT 1991