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Sat May 30 16:26:32 PDT 1992 REDUCE 3.4.1, 15-Jul-92 ... 1: 1: 2: 2: (COMPACT) 3: 3: Time: 34 ms 4: 4: % 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; 5: 5: Time: 1836 ms 6: 6: Quitting Sat May 30 16:26:35 PDT 1992