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  • Committer: Bazaar Package Importer
  • Author(s): Camm Maguire
  • Date: 2006-10-18 14:52:42 UTC
  • mto: (1.1.5 upstream)
  • mto: This revision was merged to the branch mainline in revision 4.
  • Revision ID: james.westby@ubuntu.com-20061018145242-vzyrm5hmxr8kiosf
Import upstream version 5.10.0

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tests/rtest4.mac
6
6
***************************************************************************/
7
7
 
8
8
 
9
 
KILL(FUNCTIONS,ARRAYS,VALUES);
10
 
DONE$
11
 
EV(SIN(X),EXPONENTIALIZE);
12
 
-%I*(%E^(%I*X)-%E^-(%I*X))/2$
13
 
TAYLOR(SIN(X)/X,X,0,4);
14
 
1-X^2/6+X^4/120$
15
 
EV(COS(X)^2-SIN(X)^2,SIN(X)^2 = 1-COS(X)^2);
16
 
2*COS(X)^2-1$
17
 
(SQRT(-4)+SQRT(2.25))^2;
18
 
(2*%I+1.5)^2$
19
 
EXPAND(%);
20
 
6.0*%I-1.75$
21
 
EXPAND(SQRT(2*%I));
22
 
(-1)^(1/4)*SQRT(2)$
23
 
KILL(ALLBUT(PROPS));
24
 
DONE$
25
 
SIN(X)+COS(Y)+(W+1)^2+'DIFF(SIN(W),W);
26
 
COS(Y)+SIN(X)+'DIFF(SIN(W),W,1)+(W+1)^2$
27
 
EV(%,SIN,EXPAND,DIFF,X = 2,Y = 1);
28
 
COS(W)+W^2+2*W+COS(1)+1.909297426825682;
29
 
EV(X+Y,X:A+Y,Y:2);
30
 
Y+A+2$
31
 
'DIFF(Y^2+X*Y+X^2,X,2,Y,1);
32
 
'DIFF(Y^2+X*Y+X^2,X,2,Y,1)$
33
 
EV(%,DIFF);
 
9
kill(functions,arrays,values);
 
10
done$
 
11
ev(sin(x),exponentialize);
 
12
-%i*(%e^(%i*x)-%e^-(%i*x))/2$
 
13
taylor(sin(x)/x,x,0,4);
 
14
1-x^2/6+x^4/120$
 
15
ev(cos(x)^2-sin(x)^2,sin(x)^2 = 1-cos(x)^2);
 
16
2*cos(x)^2-1$
 
17
(sqrt(-4)+sqrt(2.25))^2;
 
18
(2*%i+1.5)^2$
 
19
expand(%);
 
20
6.0*%i-1.75$
 
21
expand(sqrt(2*%i));
 
22
(-1)^(1/4)*sqrt(2)$
 
23
kill(all);
 
24
done$
 
25
sin(x)+cos(y)+(w+1)^2+'diff(sin(w),w);
 
26
cos(y)+sin(x)+'diff(sin(w),w,1)+(w+1)^2$
 
27
ev(%,sin,expand,diff,x = 2,y = 1);
 
28
cos(w)+w^2+2*w+cos(1)+1.909297426825682;
 
29
ev(x+y,x:a+y,y:2);
 
30
y+a+2$
 
31
'diff(y^2+x*y+x^2,x,2,y,1);
 
32
'diff(y^2+x*y+x^2,x,2,y,1)$
 
33
ev(%,diff);
34
34
0$
35
 
EXP:2*X-3*Y = 3;
36
 
2*X-3*Y = 3$
37
 
-3*X+2*Y = -4;
38
 
2*Y-3*X = -4$
39
 
SOLVE([EXP,%]);
40
 
[[Y = -1/5,X = 6/5]]$
41
 
EV(EXP,%);
 
35
exp:2*x-3*y = 3;
 
36
2*x-3*y = 3$
 
37
-3*x+2*y = -4;
 
38
2*y-3*x = -4$
 
39
solve([exp,%]);
 
40
[[y = -1/5,x = 6/5]]$
 
41
ev(exp,%);
42
42
3 = 3$
43
 
X+1/X > GAMMA(1/2);
44
 
X+1/X > SQRT(%PI)$
45
 
EV(%,NUMER,X = 1/2);
 
43
x+1/x > gamma(1/2);
 
44
x+1/x > sqrt(%pi)$
 
45
ev(%,numer,x = 1/2);
46
46
2.5 > 1.772453850905516;
47
47
/* tops 20 :2.5 > 1.77245384$ */
48
 
EV(%,PRED);
49
 
TRUE$
50
 
ZEROEQUIV(SIN(2*X)-2*SIN(X)*COS(X),X);
51
 
TRUE$
52
 
ZEROEQUIV(%E^X+X,X);
53
 
FALSE$
54
 
ZEROEQUIV(LOG(A*B)-LOG(A)-LOG(B),A);
55
 
DONTKNOW$
56
 
(1/(X+Y)^4-3/(Y+Z)^3)^2;
57
 
(1/(Y+X)^4-3/(Z+Y)^3)^2$
58
 
EXPAND(%,2,0);
59
 
-6/((Y+X)^4*(Z+Y)^3)+9/(Z+Y)^6+1/(Y+X)^8$
60
 
EXPAND(A . (B+C . (D+E)+F));
61
 
A . F+A . C . E+A . C . D+A . B$
62
 
EXPAND((X+1)^3);
63
 
X^3+3*X^2+3*X+1$
64
 
EXP:(X+1)^7;
65
 
(X+1)^7$
66
 
EXPAND(%);
67
 
X^7+7*X^6+21*X^5+35*X^4+35*X^3+21*X^2+7*X+1$
68
 
EXPAND(EXP,7,7);
69
 
X^7+7*X^6+21*X^5+35*X^4+35*X^3+21*X^2+7*X+1$
70
 
EV(A*(B+C)+A*(B+C)^2,EXPOP:1);
71
 
A*(C+B)^2+A*C+A*B$
72
 
RATEXPAND((2*X-3*Y)^3);
73
 
-27*Y^3+54*X*Y^2-36*X^2*Y+8*X^3$
74
 
EXP:(X-1)/(X+1)^2+1/(X-1);
75
 
(X-1)/(X+1)^2+1/(X-1)$
76
 
EXPAND(%);
77
 
X/(X^2+2*X+1)-1/(X^2+2*X+1)+1/(X-1)$
78
 
RATEXPAND(EXP);
79
 
2*X^2/(X^3+X^2-X-1)+2/(X^3+X^2-X-1)$
80
 
SIN(X/(X^2+X)) = %E^((LOG(X)+1)^2-LOG(X)^2);
81
 
SIN(X/(X^2+X)) = %E^((LOG(X)+1)^2-LOG(X)^2)$
82
 
RATSIMP(%);
83
 
SIN(1/(X+1)) = %E*X^2$
84
 
B*(A/B-X)+B*X+A;
85
 
B*X+B*(A/B-X)+A$
86
 
RATSIMP(%);
87
 
2*A$
88
 
((X-1)^(3/2)-(X+1)*SQRT(X-1))/SQRT(X-1)/SQRT(X+1);
89
 
((X-1)^(3/2)-SQRT(X-1)*(X+1))/(SQRT(X-1)*SQRT(X+1))$
90
 
RATSIMP(%);
91
 
-2/SQRT(X+1)$
92
 
EV(X^(A+1/A),RATSIMPEXPONS);
93
 
X^((A^2+1)/A)$
94
 
(LOG(X^2+X)-LOG(X))^A/LOG(X+1)^(A/2);
95
 
(LOG(X^2+X)-LOG(X))^A/LOG(X+1)^(A/2)$
96
 
RADCAN(%);
97
 
LOG(X+1)^(A/2)$
98
 
LOG(A^(2*X)+2*A^X+1)/LOG(A^X+1);
99
 
LOG(A^(2*X)+2*A^X+1)/LOG(A^X+1)$
100
 
RADCAN(%);
 
48
ev(%,pred);
 
49
true$
 
50
zeroequiv(sin(2*x)-2*sin(x)*cos(x),x);
 
51
true$
 
52
zeroequiv(%e^x+x,x);
 
53
false$
 
54
zeroequiv(log(a*b)-log(a)-log(b),a);
 
55
dontknow$
 
56
(1/(x+y)^4-3/(y+z)^3)^2;
 
57
(1/(y+x)^4-3/(z+y)^3)^2$
 
58
expand(%,2,0);
 
59
-6/((y+x)^4*(z+y)^3)+9/(z+y)^6+1/(y+x)^8$
 
60
expand(a . (b+c . (d+e)+f));
 
61
a . f+a . c . e+a . c . d+a . b$
 
62
expand((x+1)^3);
 
63
x^3+3*x^2+3*x+1$
 
64
exp:(x+1)^7;
 
65
(x+1)^7$
 
66
expand(%);
 
67
x^7+7*x^6+21*x^5+35*x^4+35*x^3+21*x^2+7*x+1$
 
68
expand(exp,7,7);
 
69
x^7+7*x^6+21*x^5+35*x^4+35*x^3+21*x^2+7*x+1$
 
70
ev(a*(b+c)+a*(b+c)^2,expop:1);
 
71
a*(c+b)^2+a*c+a*b$
 
72
ratexpand((2*x-3*y)^3);
 
73
-27*y^3+54*x*y^2-36*x^2*y+8*x^3$
 
74
exp:(x-1)/(x+1)^2+1/(x-1);
 
75
(x-1)/(x+1)^2+1/(x-1)$
 
76
expand(%);
 
77
x/(x^2+2*x+1)-1/(x^2+2*x+1)+1/(x-1)$
 
78
ratexpand(exp);
 
79
2*x^2/(x^3+x^2-x-1)+2/(x^3+x^2-x-1)$
 
80
sin(x/(x^2+x)) = %e^((log(x)+1)^2-log(x)^2);
 
81
sin(x/(x^2+x)) = %e^((log(x)+1)^2-log(x)^2)$
 
82
ratsimp(%);
 
83
sin(1/(x+1)) = %e*x^2$
 
84
b*(a/b-x)+b*x+a;
 
85
b*x+b*(a/b-x)+a$
 
86
ratsimp(%);
 
87
2*a$
 
88
((x-1)^(3/2)-(x+1)*sqrt(x-1))/sqrt(x-1)/sqrt(x+1);
 
89
((x-1)^(3/2)-sqrt(x-1)*(x+1))/(sqrt(x-1)*sqrt(x+1))$
 
90
ratsimp(%);
 
91
-2/sqrt(x+1)$
 
92
ev(x^(a+1/a),ratsimpexpons);
 
93
x^((a^2+1)/a)$
 
94
(log(x^2+x)-log(x))^a/log(x+1)^(a/2);
 
95
(log(x^2+x)-log(x))^a/log(x+1)^(a/2)$
 
96
radcan(%);
 
97
log(x+1)^(a/2)$
 
98
log(a^(2*x)+2*a^x+1)/log(a^x+1);
 
99
log(a^(2*x)+2*a^x+1)/log(a^x+1)$
 
100
radcan(%);
101
101
2$
102
 
(%E^X-1)/(%E^(X/2)+1);
103
 
(%E^X-1)/(%E^(X/2)+1)$
104
 
RADCAN(%);
105
 
%E^(X/2)-1$
106
 
KILL(ALLBUT(PROPS));
107
 
DONE$
108
 
COMBINE(A/X+B/X+A/Y+B/Y);
109
 
(B+A)/Y+(B+A)/X$
110
 
X/(X-Y)^2-1/(X-Y)-F(X)/(X-Y)^3;
111
 
-1/(X-Y)+X/(X-Y)^2-F(X)/(X-Y)^3$
112
 
MULTTHRU((X-Y)^3,%);
113
 
-(X-Y)^2+X*(X-Y)-F(X)$
114
 
RATEXPAND(%);
115
 
-Y^2+X*Y-F(X)$
116
 
((A+B)^10*S^2+2*A*B*S+(A*B)^2)/(A*B*S^2);
117
 
((B+A)^10*S^2+2*A*B*S+A^2*B^2)/(A*B*S^2)$
118
 
MULTTHRU(%);
119
 
2/S+A*B/S^2+(B+A)^10/(A*B)$
120
 
MULTTHRU(A . (B+C . (D+E)+F));
121
 
A . F+A . C . (E+D)+A . B$
122
 
((X+2)^20-2*Y)/(X+Y)^20+(X+Y)^-19-X/(X+Y)^20;
123
 
1/(Y+X)^19+((X+2)^20-2*Y)/(Y+X)^20-X/(Y+X)^20$
124
 
XTHRU(%);
125
 
((X+2)^20-Y)/(Y+X)^20$
126
 
2/(X+2)-2/(X+1)+1/(X+1)^2;
127
 
2/(X+2)-2/(X+1)+1/(X+1)^2$
128
 
RATSIMP(%);
129
 
-X/(X^3+4*X^2+5*X+2)$
130
 
PARTFRAC(%,X);
131
 
2/(X+2)-2/(X+1)+1/(X+1)^2$
132
 
FACTOR(2^63-1);
 
102
(%e^x-1)/(%e^(x/2)+1);
 
103
(%e^x-1)/(%e^(x/2)+1)$
 
104
radcan(%);
 
105
%e^(x/2)-1$
 
106
kill(all);
 
107
done$
 
108
combine(a/x+b/x+a/y+b/y);
 
109
(b+a)/y+(b+a)/x$
 
110
x/(x-y)^2-1/(x-y)-f(x)/(x-y)^3;
 
111
-1/(x-y)+x/(x-y)^2-f(x)/(x-y)^3$
 
112
multthru((x-y)^3,%);
 
113
-(x-y)^2+x*(x-y)-f(x)$
 
114
ratexpand(%);
 
115
-y^2+x*y-f(x)$
 
116
((a+b)^10*s^2+2*a*b*s+(a*b)^2)/(a*b*s^2);
 
117
((b+a)^10*s^2+2*a*b*s+a^2*b^2)/(a*b*s^2)$
 
118
multthru(%);
 
119
2/s+a*b/s^2+(b+a)^10/(a*b)$
 
120
multthru(a . (b+c . (d+e)+f));
 
121
a . f+a . c . (e+d)+a . b$
 
122
((x+2)^20-2*y)/(x+y)^20+(x+y)^-19-x/(x+y)^20;
 
123
1/(y+x)^19+((x+2)^20-2*y)/(y+x)^20-x/(y+x)^20$
 
124
xthru(%);
 
125
((x+2)^20-y)/(y+x)^20$
 
126
2/(x+2)-2/(x+1)+1/(x+1)^2;
 
127
2/(x+2)-2/(x+1)+1/(x+1)^2$
 
128
ratsimp(%);
 
129
-x/(x^3+4*x^2+5*x+2)$
 
130
partfrac(%,x);
 
131
2/(x+2)-2/(x+1)+1/(x+1)^2$
 
132
factor(2^63-1);
133
133
7^2*73*127*337*92737*649657$
134
 
FACTOR(Z^2*(X+2*Y)-4*X-8*Y);
135
 
(2*Y+X)*(Z-2)*(Z+2)$
136
 
X^2*Y^2+2*X*Y^2+Y^2-X^2-2*X-1;
137
 
X^2*Y^2+2*X*Y^2+Y^2-X^2-2*X-1$
138
 
BLOCK([DONTFACTOR:[X]],FACTOR(%/36/(Y^2+2*Y+1)));
139
 
(X^2+2*X+1)*(Y-1)/(36*(Y+1))$
140
 
FACTOR(%E^(3*X)+1);
141
 
(%E^X+1)*(%E^(2*X)-%E^X+1)$
142
 
FACTOR(X^4+1,A^2-2);
143
 
(X^2-A*X+1)*(X^2+A*X+1)$
144
 
FACTOR(X^3+X^2*Y^2-X*Z^2-Y^2*Z^2);
145
 
-((Y^2+X)*(Z-X)*(Z+X))$
146
 
(X+2)/(X+3)/(X+B)/(X+C)^2;
147
 
(X+2)/((X+3)*(X+B)*(X+C)^2)$
148
 
RATSIMP(%);
149
 
(X+2)/(X^4+(2*C+B+3)*X^3+(C^2+(2*B+6)*C+3*B)*X^2+((B+3)*C^2+6*B*C)*X+3*B*C^2)$
150
 
PARTFRAC(%,X);
151
 
-(C^2-4*C-B+6)/((C^4+(-2*B-6)*C^3+(B^2+12*B+9)*C^2+(-6*B^2-18*B)*C+9*B^2)
152
 
               *(X+C))
153
 
 -(C-2)/((C^2+(-B-3)*C+3*B)*(X+C)^2)
154
 
 +(B-2)/(((B-3)*C^2+(6*B-2*B^2)*C+B^3-3*B^2)*(X+B))
155
 
 -1/(((B-3)*C^2+(18-6*B)*C+9*B-27)*(X+3))$
156
 
MAP('FACTOR,%);
157
 
-((C^2-4*C-B+6)/((C-3)^2*(C-B)^2*(X+C)))-((C-2)/((C-3)*(C-B)*(X+C)^2))
158
 
                                      +(B-2)/((B-3)*(C-B)^2*(X+B))
159
 
                                      -(1/((B-3)*(C-3)^2*(X+3)))$
160
 
EXP:RATSIMP((X^5-1)/(X-1));
161
 
X^4+X^3+X^2+X+1$
162
 
SUBST(A,X,%);
163
 
A^4+A^3+A^2+A+1$
164
 
FACTOR(EXP,%);
165
 
(X-A)*(X-A^2)*(X-A^3)*(X+A^3+A^2+A+1)$
166
 
FACTOR(X^12+1);
167
 
(X^4+1)*(X^8-X^4+1)$
168
 
FACTOR(X^99+1);
169
 
(X+1)*(X^2-X+1)*(X^6-X^3+1)*(X^10-X^9+X^8-X^7+X^6-X^5+X^4-X^3+X^2-X+1)
170
 
     *(X^20+X^19-X^17-X^16+X^14+X^13-X^11-X^10-X^9+X^7+X^6-X^4-X^3+X+1)
171
 
     *(X^60+X^57-X^51-X^48+X^42+X^39-X^33-X^30-X^27+X^21+X^18-X^12-X^9+X^3+1)$
172
 
EV((X+1)*((U+V)^2+A*(W+Z)^2),EXPAND);
173
 
A*X*Z^2+A*Z^2+2*A*W*X*Z+2*A*W*Z+A*W^2*X+V^2*X+2*U*V*X+U^2*X+A*W^2+V^2+2*U*V
174
 
       +U^2$
175
 
FACTORSUM(%);
176
 
(X+1)*(A*(Z+W)^2+(V+U)^2)$
177
 
SQFR(4*X^4+4*X^3-3*X^2-4*X-1);
178
 
(2*X+1)^2*(X^2-1)$
179
 
GFACTOR(X^4-1);
180
 
(X-1)*(X+1)*(X-%I)*(X+%I)$
181
 
factor(Y^20-7*Y^19+11*Y^18-8*Y^17+59*Y^16-461*Y^15+1694*Y^14+198*Y^13-3541*
182
 
 Y^12+2818*Y^11-33327*Y^10-11272*Y^9-56656*Y^8-12672*Y^7+433664*Y^6+472064*Y^5
183
 
 +241664*Y^4+131072*Y^3+720896*Y^2+1835008*Y+1048576);
184
 
(Y^8-Y^7-11*Y^6-19*Y^5+101*Y^4+76*Y^3-176*Y^2+64*Y+256)
185
 
      *(Y^12-6*Y^11+16*Y^10-39*Y^9-19*Y^8-75*Y^7-315*Y^6+300*Y^5-304*Y^4
186
 
            +2496*Y^3+4096*Y^2+6144*Y+4096)$
 
134
factor(z^2*(x+2*y)-4*x-8*y);
 
135
(2*y+x)*(z-2)*(z+2)$
 
136
x^2*y^2+2*x*y^2+y^2-x^2-2*x-1;
 
137
x^2*y^2+2*x*y^2+y^2-x^2-2*x-1$
 
138
block([dontfactor:[x]],factor(%/36/(y^2+2*y+1)));
 
139
(x^2+2*x+1)*(y-1)/(36*(y+1))$
 
140
factor(%e^(3*x)+1);
 
141
(%e^x+1)*(%e^(2*x)-%e^x+1)$
 
142
factor(x^4+1,a^2-2);
 
143
(x^2-a*x+1)*(x^2+a*x+1)$
 
144
factor(x^3+x^2*y^2-x*z^2-y^2*z^2);
 
145
-((y^2+x)*(z-x)*(z+x))$
 
146
(x+2)/(x+3)/(x+b)/(x+c)^2;
 
147
(x+2)/((x+3)*(x+b)*(x+c)^2)$
 
148
ratsimp(%);
 
149
(x+2)/(x^4+(2*c+b+3)*x^3+(c^2+(2*b+6)*c+3*b)*x^2+((b+3)*c^2+6*b*c)*x+3*b*c^2)$
 
150
partfrac(%,x);
 
151
-(c^2-4*c-b+6)/((c^4+(-2*b-6)*c^3+(b^2+12*b+9)*c^2+(-6*b^2-18*b)*c+9*b^2)
 
152
               *(x+c))
 
153
 -(c-2)/((c^2+(-b-3)*c+3*b)*(x+c)^2)
 
154
 +(b-2)/(((b-3)*c^2+(6*b-2*b^2)*c+b^3-3*b^2)*(x+b))
 
155
 -1/(((b-3)*c^2+(18-6*b)*c+9*b-27)*(x+3))$
 
156
map('factor,%);
 
157
-((c^2-4*c-b+6)/((c-3)^2*(c-b)^2*(x+c)))-((c-2)/((c-3)*(c-b)*(x+c)^2))
 
158
                                      +(b-2)/((b-3)*(c-b)^2*(x+b))
 
159
                                      -(1/((b-3)*(c-3)^2*(x+3)))$
 
160
exp:ratsimp((x^5-1)/(x-1));
 
161
x^4+x^3+x^2+x+1$
 
162
subst(a,x,%);
 
163
a^4+a^3+a^2+a+1$
 
164
factor(exp,%);
 
165
(x-a)*(x-a^2)*(x-a^3)*(x+a^3+a^2+a+1)$
 
166
factor(x^12+1);
 
167
(x^4+1)*(x^8-x^4+1)$
 
168
factor(x^99+1);
 
169
(x+1)*(x^2-x+1)*(x^6-x^3+1)*(x^10-x^9+x^8-x^7+x^6-x^5+x^4-x^3+x^2-x+1)
 
170
     *(x^20+x^19-x^17-x^16+x^14+x^13-x^11-x^10-x^9+x^7+x^6-x^4-x^3+x+1)
 
171
     *(x^60+x^57-x^51-x^48+x^42+x^39-x^33-x^30-x^27+x^21+x^18-x^12-x^9+x^3+1)$
 
172
ev((x+1)*((u+v)^2+a*(w+z)^2),expand);
 
173
a*x*z^2+a*z^2+2*a*w*x*z+2*a*w*z+a*w^2*x+v^2*x+2*u*v*x+u^2*x+a*w^2+v^2+2*u*v
 
174
       +u^2$
 
175
factorsum(%);
 
176
(x+1)*(a*(z+w)^2+(v+u)^2)$
 
177
sqfr(4*x^4+4*x^3-3*x^2-4*x-1);
 
178
(2*x+1)^2*(x^2-1)$
 
179
gfactor(x^4-1);
 
180
(x-1)*(x+1)*(x-%i)*(x+%i)$
 
181
factor(y^20-7*y^19+11*y^18-8*y^17+59*y^16-461*y^15+1694*y^14+198*y^13-3541*
 
182
 y^12+2818*y^11-33327*y^10-11272*y^9-56656*y^8-12672*y^7+433664*y^6+472064*y^5
 
183
 +241664*y^4+131072*y^3+720896*y^2+1835008*y+1048576);
 
184
(y^8-y^7-11*y^6-19*y^5+101*y^4+76*y^3-176*y^2+64*y+256)
 
185
      *(y^12-6*y^11+16*y^10-39*y^9-19*y^8-75*y^7-315*y^6+300*y^5-304*y^4
 
186
            +2496*y^3+4096*y^2+6144*y+4096)$
187
187