]> Maxima MathML Output Test Page

DONE

N ! N + 1 !

1 N + 1

N + 1 2 N ! 2

N + 1 ! 2

17 + 4

1

1 , 1 ,1 ,2

1 + 1 1 + 1 1 + 1 2

4

1 , 1 ,2 ,1 , 2 ,1 ,2 , 1 ,2

265 97 153 56

1.7321428571428572

1 , 1 ,1 ,2

1 + 1 1 + 1 1 + 1 2

4

1 , 1 ,2 ,1 , 2 ,1 ,2 , 1 ,2

265 97 153 56

1.7321428571428572

DONE

true

F B Z + F A Y + F X

1 X + 2 - 1 X + 1 + 1 X + 1 2 + X

Y + 1 X + 1 + 1

A = - 0.5 ,B = 3

G B G C + G A

G B C + G A

A + 3 ,4 , 4 , 3.5

A 2 + 2 A + 1 Y + X 2

A + 1 2 Y + X 2

U V A X + B + C

F F F U F F V F F F A F X + F B + F C

Y + X ,0 ,-3.2 , 2.5× 1020 ,X

UNION(X,Y):=IF X = [] THEN Y
       ELSE (IF MEMBER(T:FIRST(X),Y) THEN UNION(REST(X),Y)
		 ELSE CONS(T,UNION(REST(X),Y)));

B , 1 ,X 2 ,-X 2 ,A ,Y , 1 2

X 5 - 5 X 4 2 + 5 X 3 3 - X 6

1 ,- 5 2 ,5 3 ,-1 6

- 5 2

DONE

1 3 2 X - 2 1 3 2 3 2 2 3 + 1 - 2 X - 2 1 3 6 2 2 3 X 2 - 2 1 3 X + 2 2 3 + 1 3 2 2 3 X + 2 1 3

1 X 3 + 2

Negterm+ Quotient+ Quotient

G(L):=CATCH(MAP(LAMBDA([X],IF X < 0 THEN THROW(X) ELSE F(X)),L));

F 1 ,F 2 ,F 3 ,F 7

-3

Y 2 + B X

DONE

B X + #101Y 2

#101Y 2 - Y 2

Y

B X + A 2

DONE

_101A 2 + B X

_101A 2 - A 2

A

B X + A 2

DONE

_101A 2 + B X

_101A 2 - A 2

A

DONE

3 F B + 2 F A

F 1 ,X Y + 2 F X ,X

DONE

3 F B + 2 F A

DONE

2 F A

DONE

2 F A F B

DONE

G G G A ,B ,C ,D

0

DONE

G G G A ,B ,C ,D

0

DONE

H X ,Y , Z

DONE

H X ,Y , Z

DONE

-H X ,Y , Z

DONE

J A ,B , C ,D

DONE

-F X

DONE

G X

DONE

true

1

F

HASHED , 2 , 1 ,X

DECLARED ,2 , 2 , 3

HASH_TABLE ,true , 1 , x

System Function

VAR 1 > 0

Database Info, VAR 1 > 0

2

VALUE

R

R

DONE

R

R

R

DONE

R

TRANSCENDENTAL

TRANSCENDENTAL

false

TYPEOF(X):=BLOCK([Q],IF NUMBERP(X) THEN RETURN(ALGEBRAIC),
       IF NOT ATOM(X) THEN RETURN(MAPLIST(TYPEOF,X)),Q:GET(X,TYPE),
       IF Q = FALSE THEN ERROR("NOT NUMERIC") ELSE Q);

TRANSCENDENTAL ,false ,TRANSCENDENTAL

true

A > 1

true

false

true

DONE

^RULE1, SIMPEXPT

1 - cos 2 Y

DONE

NONZEROANDFREEOF(X,E):=IS(E # 0 AND FREEOF(X,E));

DONE

LINEAR

B = Y 2 , A = Y + 4 , X = Z

DONE

CONSTINTERVAL(L,H):=CONSTANTP(H-L);

DONE

DONE

DONE

X + π X + 2 π sin T T

B = X + 2 π ,A = X + π ,X = T , F = sin T

0 T sin T T

false

DONE

false

SINRULE 1 , SIMP-%SIN

sin X cos Y + cos X sinh Y

true

^RULE2, SIMPEXPT

1

^

^RULE3, SIMPEXPT

sin X + 1 2

2 sin X - cos 2 X + 2

1 - cos 2 X

DONE

DONE

^RULE4, SIMPEXPT

1 - cos 2 Y

DONE

NONZEROANDFREEOF(X,E):=IS(E # 0 AND FREEOF(X,E));

DONE

LINEAR

B = Y 2 , A = Y + 4 , X = Z

DONE

CONSTINTERVAL(L,H):=CONSTANTP(H-L);

DONE

DONE

DONE

X + π X + 2 π sin T T

B = X + 2 π ,A = X + π ,X = T , F = sin T

0 T sin T T

false

A , B ,F ,X

DONE

ONELESS(X,Y):=IS(X = Y-1);

MTEXT A 1 A 2 !, --> , A 1 !, WHERE ,ONELESS A 2 , A 1

MTEXT A 1 ! A 1 , --> , A 1 - 1 !

M - 1 !N !

MTEXT sin 2 A , --> ,1 - cos 2 A

sin 4 X

cos 4 X - 2 cos 2 X + 1

DONE

ONELESS(X,Y):=IS(X = Y-1);

MTEXT A 1 A 2 !, --> , A 1 !, WHERE ,ONELESS A 2 , A 1

MTEXT A 1 ! A 1 , --> , A 1 - 1 !

M - 1 !N !

MTEXT sin 2 A , --> ,1 - cos 2 A

sin 4 X

cos 4 X - 2 cos 2 X + 1

true

1 2 - 1 2 cos 2 X

2 A 2 - B cos 2 Y + X + A B + 5 sin 4 X - U

1 2 2 A 2 - B 2 cos 4 Y + 2 X - 2 A 2 - B -A B - 5 sin 2 Y + 5 X - U + 2 A 2 - B -A B - 5 sin 2 Y - 3 X + U - 1 2 - A B - 5 2 cos 8 X - 2 U + 1 2 -A B - 5 2 + 1 2 2 A 2 - B 2

DONE

1 8 2 A 2 - B 2 sin 4 Y + 2 X - 1 2 B - 2 A 2 -A B - 5 cos 2 Y + 5 X - U - 1 2 2 A 2 - B -A B - 5 cos 2 Y - 3 X + U

1 8 2 A 2 - B 2 sin 4 Y + 2 X - 1 2 B - 2 A 2 -A B - 5 cos 2 Y + 5 X - U - 1 2 2 A 2 - B -A B - 5 cos 2 Y - 3 X + U

1 16 sin 5 X + 1 16 cos 5 X - 5 16 sin 3 X + 5 16 cos 3 X + 5 8 sin X + 5 8 cos X

false

X 2 X Y + 3 X Y = sin X X

Y = %C - cos X X 3

Y = -cos X + 1 X 3

2 X 2 Y + Y X Y 3 = 0

Y 3 + 6 %K 1 Y 6 = X + %K 2

- 2 Y 3 - 3 Y 6 = X

Y 3 - 10 Y 6 = X - 3 2

- K 2 L 2 M 2 N 2 + K 2 M 2 N 2 - K 2 L 2 N 2 + K 2 N 2

L 2 + K 2 = 1

N 2 - M 2 = 1

K 4 N 4

K 1 K 4 - K 2 K 3 - K 1 K 2 K 3 2

K 1 K 4 - K 2 K 3 = 0

K 3 K 4 + K 1 K 2 = 0

K 4 K 3

Z + X Y + 2 X 2

-Z + 5 Y + 3 X - 1

Z 2 - Y 2 + X + 5

7425 X 8 - 1170 X 7 + 1299 X 6 + 12076 X 5 + 22887 X 4 - 5154 X 3 - 1291 X 2 + 7688 X + 15376

X F X = X G X + sin X

2 X 2 G X = X F X - cos X

A

1

{

|

{ | X ,X > 0

{ | X ,X < 2

OU

OI

OU { | X ,X > 0 ,{ | X ,X < 2

OU { | X ,X > 0 ,{ | X ,X < 2

{ 1 ,2 , 3

{ 3 ,4 , 5

OU OU { 1 ,2 ,3 ,{ 1 ,2 , 3 ,{ 3 ,4 , 5

OU

OI

OU OU { 1 ,2 ,3 ,{ 1 ,2 , 3 ,{ 7

DONE

true

true

3 Γ 3 4 b 7 8 b p 2 4 8 π %M -5 8 ,-1 4 (b p 2 2 ) 3 2 5 8 Γ 3 8 b 1 4 p - 2 3 8 π %M -5 8 ,1 4 (b p 2 2 ) Γ 7 8 b 1 4 p 4

2 A 2 p π A 2 p 2 - 2 π erf A p A 2 p 2 p

- π - p 2 + 2 A p + A 2 4 b 2 A p + A 2 2 b erf p + A 2 b - A 2 2 b erf p - A 2 b + p 2 + 2 A p 2 b erf p + A 2 b - p 2 2 b erf p - A 2 b + - A p b p 2 2 b - 2 A p + A 2 2 b + A 2 2 b 8 b

A -A p p 2

16 2 p p 2 + 1 + 2 p 2 9 π 3 2 p 4 2 p p 2 + 1 + 2 p 2 + 1

-1 4 p p 140 p + 10 1 4 p + π 140 erf 2 p p 2 + 20 erf 2 p p + 5 erf 2 p 8 π p 4

%IBES 0 ( A t 2 ) %IBES 1 (A t 2 ) p 2

2 1 2 p + 1 3 4 - 1 1 - 2 p 3 4 2 3 4 Γ 1 4 p 3 2

- 12 -3 π erf p p 5 2 -1 p 8 - π erf p p 3 2 - 1 p 2 - π erf p p -1 p 2 - 3 p 2 4 - p 2 p 2 + 2 π erf p p 3 2 -1 p 4 + π erf p p -1 p 2 + p 2 p - π erf p p -1 p 2 π p 4

- erf p -1 p π p 3 2

π %IBES 1 ( t ) 2 p 3 2

- 4 Γ 1 3 %M -3 2 ,1 3 (-1 4 p ) - 1 8 p 3 - 1 5 6 3 Γ 2 3 p 3 2 + 4 Γ 1 3 %M -3 2 ,1 3 (-1 4 p ) - 1 8 p 3 - 1 5 6 Γ 2 3 p 3 2 - 8 Γ 2 3 %M -3 2 ,-1 3 (-1 4 p ) - 1 8 p 3 - 1 1 6 3 Γ 1 3 p 3 2

5 Γ 1 4 %P -3 2 ,-3 4 (1 1 p 2 + 1 ) 1 p 4 - 1 3 8 p 9 4 18 - 1 1 4 2 Γ 2 3 4 + 5 Γ 1 4 %P -3 2 ,-3 4 (1 1 p 2 + 1 ) 1 p 4 - 1 3 8 p 9 4 18 - 1 1 4 2 Γ 2 3 4 + 4 Γ 3 4 %P -3 2 ,3 4 (1 1 p 2 + 1 ) p 3 4 - 1 3 4 Γ 2 1 4 1 p 4 - 1 3 8

4 2 π 1 p 2 + 1 2 p 3 - 2 1 1 p 2 + 1 - 1 1 p 2 + 1 2 p 2 π p 2

15 1 A 2 + 1 - 1 3 4 1 A 2 + 1 + 1 3 2 + 1 1 - A 2 + 1 3 2 16 A 2 + 1

3 A A 2 p 2 + 1 5 2 p 4

A -A p p 2

DONE

TR_OPTIMIZE_MAX_LOOP

3 1 log 3 + 1 log x 1 log 3 + 1 log 3

- 4 3

1 , 2 ,3 ,4 , 5 ,6 ,7 , 8 ,9 ,10

1

2

3

4

5

6

7

8

9

10

true

y f x ,y

x f x ,y

h(x,y):=x*y*DIFF(f(x,y),x,1,y,1);

x 2 x y f x ,y y x

x 2 x y f x ,y y y

F(X):=Y+X^2;

Y + 4

11

F(X):=1+SIN(X)^2;

sin 2 X + 1 + 1

G(Y,Z):=3*Y+F(Z);

3 Z + 14 + 1.2298488470659301

H(N):=SUM(I*X^I,I,0,N);

F X ,G Y ,Z ,H N

T[N](X):=RATEXPAND(2*X*T[N-1](X)-T[N-2](X));

T[0](X):=1;

T[1](X):=X;

8 Y 4 - 8 Y 2 + 1

G[N](X):=SUM(EV(X),I,N,2+N);

H(N,X):=SUM(EV(X),I,N,2+N);

3 I 2

29

P[N](X):=RATSIMP(DIFF((X^2-1)^N,X,N)/(2^N*N!));

Q(N,X):=RATSIMP(DIFF((X^2-1)^N,X,N)/(2^N*N!));

LAMBDA X ,3 X 2 - 1 2

3 Y + 1 2 - 1 2

3 Y 2 - 1 2

37

F[I,J](X,Y):=Y^J+X^I;

G(FUN,A,B):=PRINT(FUN," applied to ",A," and ",B," is ",FUN(A,B));

2 C

1.5403023064268146

DONE

A[N]:=N*A[N-1];

1

120

A[N]:=N;

6

24

LAMBDA X ,Y ,Z ,Z 2 + Y 2 + X 2

A 2 + 5

A + 3

X 2 ,Y 3 ,-2

X 3

A , X 2 ,Y 3 ,-2 ,X 3

A 0 B 1

A 2 0 B 2 1

A 2 0 A B + B 1

A 2 0 A B A

1 1 1 - B A

1 A 0 - B A 1

B Y + A X Y

A B C D E F G H I

C G + B D + A 2 C H + B E + A B C I + B F + A C F G + D E + A D F H + E 2 + B D F I + E F + C D G I + D H + A G H I + E H + B G I 2 + F H + C G

X + 1 = Y 2

X - 1 = 2 Y + 1

2 X = Y 2 + 2 Y + 1

X + 1 Y = Y

Y X + 1 = 1 Y

FIB[N]:=IF N = 1 OR N = 2 THEN 1 ELSE FIB[N-2]+FIB[N-1];

2

2

5

ETA(MU,NU):=IF MU = NU THEN MU ELSE (IF MU > NU THEN MU-NU ELSE NU+MU);

11

4

A

DONE

HESSIAN(F):=BLOCK([DFXX,DFXY,DFXZ,DFYY,DFYZ,DFZZ],DFXX:DIFF(F,X,2),
	DFXY:DIFF(F,X,1,Y,1),DFXZ:DIFF(F,X,1,Z,1),DFYY:DIFF(F,Y,2),
	DFYZ:DIFF(F,Y,1,Z,1),DFZZ:DIFF(F,Z,2),
	DETERMINANT(MATRIX([DFXX,DFXY,DFXZ],[DFXY,DFYY,DFYZ],
			   [DFXZ,DFYZ,DFZZ])));

DONE

-3 A Y 9 A 2 X Z + 18 A Y 2 - 27 A 3 X Y Z - 54 A 2 X 3

Y 3 + A X Y + X 3

F(X):=BLOCK([A,Y],LOCAL(A),Y:4,A[Y]:X,DISPLAY(A[Y]));

2

0

DONE

0

DONE

0

DONE

55

1

sin X

DONE

X 7 90 - X 6 240 - X 5 15 - X 4 8 + X 2 2 + X + 1

0

DONE

5 X 5 + 9 X 4 + 12 X 3 + 14 X 2 + 15 X

-3.0

DONE

1000

DONE

2.2824290358878674

X

NEWTON(F,GUESS):=BLOCK([NUMER,Y],LOCAL(F,DF,X,GUESS),NUMER:TRUE,
       DEFINE(DF(X),DIFF(F(X),X)),
       DO (Y:DF(GUESS),IF Y = 0 THEN ERROR("derivative at",GUESS,"is zero"),
	   GUESS:GUESS-F(GUESS)/Y,
	   IF ABS(F(GUESS)) < 5.0E-6 THEN RETURN(GUESS)));

SQR(X):=X^2-5.0;

DONE

E 90

DONE

DONE

X X F X + F X

F(X):=SIN(X);

sin X + X cos X

X

3

3

X

F(X):=X^2;

F 2

4

F 2

4

33

I = 1 4 I !

X

A B X 2 X

DONE

S + 55

55

S + 110

I = 0 N G I

Z Z

X 2 X 2

I = 0 N G I

I = 0 N G I

I = 0 N G I + 1

DONE

A

DONE

Y 2 Y

Y 3 3

F(Y):=DIFF(Y*LOG(Y),Y,2);

F(Y):=1/Y;

tmp :%

Y + X 3

3 Y + X 2

X 2 + 1

sin X

sin π 12 + 1 3

sin 1

β 1 2 ,2 5

1 2 1 - X X

25

4.79425538604203000 2732879B-1

cos 2 X - sin 2 X

- 1 2

-4 cos X sin X

sin 2 X 2 + X 2 - X - sin 2 X 2 2

sin 2 X 2

cos X sin X

sin 2 X 2

cos 2 X

sech 2 X sinh X tanh X coth 2 X + cosh 2 X sech 2 X tanh X coth 2 X + sech 2 X tanh X coth 2 X

sinh 4 X + cosh 2 X + 1 sinh 3 X cosh 5 X

DONE

- X - - X 2

1 - X 2 6 + X 4 120 +

2 cos 2 X - 1

2 + 1.5 2

6.0 - 1.75

-1 1 4 2

DONE

cos Y + sin X + W sin W + W + 1 2

Y + A + 2

3 X 2 Y Y 2 + X Y + X 2

0

2 X - 3 Y = 3

2 Y - 3 X = -4

Y = - 1 5 ,X = 6 5

3 = 3

X + 1 X > π

true

true

false

DONTKNOW

1 Y + X 4 - 3 Z + Y 3 2

- 6 Y + X 4 Z + Y 3 + 9 Z + Y 6 + 1 Y + X 8

A F + A C E + A C D + A B

X 3 + 3 X 2 + 3 X + 1

X + 1 7

X 7 + 7 X 6 + 21 X 5 + 35 X 4 + 35 X 3 + 21 X 2 + 7 X + 1

X 7 + 7 X 6 + 21 X 5 + 35 X 4 + 35 X 3 + 21 X 2 + 7 X + 1

A C + B 2 + A C + A B

-27 Y 3 + 54 X Y 2 - 36 X 2 Y + 8 X 3

X - 1 X + 1 2 + 1 X - 1

X X 2 + 2 X + 1 - 1 X 2 + 2 X + 1 + 1 X - 1

2 X 2 X 3 + X 2 - X - 1 + 2 X 3 + X 2 - X - 1

sin X X 2 + X = log X + 1 2 - log 2 X

sin 1 X + 1 = X 2

B X + B A B - X + A

2 A

X - 1 3 2 - X - 1 X + 1 X - 1 X + 1

- 2 X + 1

X A 2 + 1 A

log X 2 + X - log X A log X + 1 A 2

log X + 1 A 2

log A 2 X + 2 A X + 1 log A X + 1

2

X - 1 X 2 + 1

X 2 - 1

DONE

B + A Y + B + A X

- 1 X - Y + X X - Y 2 - F X X - Y 3

- X - Y 2 + X X - Y - F X

- Y 2 + X Y - F X

B + A 10 S 2 + 2 A B S + A 2 B 2 A B S 2

2 S + A B S 2 + B + A 10 A B

A F + A C E + D + A B

1 Y + X 19 + X + 2 20 - 2 Y Y + X 20 - X Y + X 20

X + 2 20 - Y Y + X 20

2 X + 2 - 2 X + 1 + 1 X + 1 2

- X X 3 + 4 X 2 + 5 X + 2

2 X + 2 - 2 X + 1 + 1 X + 1 2

7 2 73 127 337 92737 649657

2 Y + X Z - 2 Z + 2

X 2 Y 2 + 2 X Y 2 + Y 2 - X 2 - 2 X - 1

X 2 + 2 X + 1 Y - 1 36 Y + 1

X + 1 2 X - X + 1

X 2 - A X + 1 X 2 + A X + 1

- Y 2 + X Z - X Z + X

X + 2 X + 3 X + B X + C 2

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

- 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 X + C - C - 2 C 2 + -B - 3 C + 3 B X + C 2 + B - 2 B - 3 C 2 + 6 B - 2 B 2 C + B 3 - 3 B 2 X + B - 1 B - 3 C 2 + 18 - 6 B C + 9 B - 27 X + 3

- C 2 - 4 C - B + 6 C - 3 2 C - B 2 X + C - C - 2 C - 3 C - B X + C 2 + B - 2 B - 3 C - B 2 X + B - 1 B - 3 C - 3 2 X + 3

X 4 + X 3 + X 2 + X + 1

A 4 + A 3 + A 2 + A + 1

X - A X - A 2 X - A 3 X + A 3 + A 2 + A + 1

X 4 + 1 X 8 - X 4 + 1

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 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 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

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 + U 2

X + 1 A Z + W 2 + V + U 2

2 X + 1 2 X 2 - 1

X - 1 X + 1 X - X +

Y 8 - Y 7 - 11 Y 6 - 19 Y 5 + 101 Y 4 + 76 Y 3 - 176 Y 2 + 64 Y + 256 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 + 2496 Y 3 + 4096 Y 2 + 6144 Y + 4096

DONE

2 A ,X F X

B + A ,0

2 2 A log Y + A log X

A log X 2 Y 4

0

false

X Y 3

X Y 1 4

true

X Y

X Y 1 3

ALL

X 2 Y 1 4

X 3 Y 2 1 6

false

1

true

0

DONE

cos X + 3 X 2 + 4 X

cos 2 X - sin 2 X

-4 cos X sin X

true

F X 2 X 2 F X + F X X F X 2

G X H X F X ,Y Y

G X H X X F X ,Y Y + F X ,H X X H X - F X ,G X X G X

DONE

A X

X A A + A X A

F X ,Y ,X T ,Y T

Y F T Y + X F T X

Y X

DONE

F X ,Y

G X ,Y X Y + X 2

J N ,Z

J 0 ,X X 2 - 3 J 1 ,X X + 6 J 2 ,X X 2

TEST(F):=BLOCK([U],U:INTEGRATE(F,X),RATSIMP(F-DIFF(U,X)));

0

0

0

cos 3 X 3 - cos X

DONE

log X + 2

log log X

- cos 2 X + 3 2

X erf X - 1 4 erf X - 1 2

log X 2 - X + 1 6 + arctan 2 X - 1 3 3 - log X + 1 3

2 3 2 X - 1 2 3 + 1 + 2 X - 1 6 X 2 - X + 1 - 1 3 X + 1

X X 3 + 1

P > 0

%J 1 (2 A T ) T -P T

%J 1 (2 A T ) T -P T

¬ EQUAL I ,- 1

1 X 2 + 2

1 X 3 2 + 2

27 Y 3 + 54 X Y 2 + 36 X 2 Y + Y + 8 X 3 + X + 1

3 Y + 2 X 3 + Y + X + 1

- 1 Z + Y X + 1 X

Y + 1 X - 1 Z

- 1 Z + Y + X + 1

K 2 X 2 - 1 cos X + EPS K 2 X 2 - EPS 15 K 2 + 5 N 1 - 3 N 2 K - N 1 N 2

K X - 1 K X + 1 cos X + EPS 3 K + N 1 5 K - N 2

K 2 X 2 - 1 cos X + EPS 3 K + N 1 5 K - N 2

- 1 - K 2 X 2 cos X + EPS 3 K + N 1 5 K - N 2

B X Y + B + A X + 1 + A

B X Y + B + A X 2 + 1 + A

X 2 X 2 F X

X D 2

F 1 X + 1

DONE

A 2

@2+ 1

DONE

8 F X ,Y X F X ,Y - 2 U X ,Y X U X ,Y

16 A 2 - 2 U 0 ,1 X U X ,Y X = 0 ,Y = 1

A 2

@2+ 1

DONE

8 F X ,Y X F X ,Y - 2 U X ,Y X U X ,Y

16 A 2 - 2 U 0 ,1 X U X ,Y X = 0 ,Y = 1

G , A ,X 1 ,Y

2 A + 1 = 5

Y + 1

B X + A X + 5

X

ISLINEAR(EXP,VAR):=BLOCK([C],C:BOTHCOEF(RAT(EXP,VAR),VAR),
	 IS(FREEOF(VAR,C) AND C[1] # 0));

true

B + A 4 X 2 X + D + C 2 + 1

E 2 X 2 X + E 1 + 1

2 E 2 X 2 + E 1 E 2 X + E 2

2 B + A 4 X 2 + B + A 4 D + C 2 X + B + A 4

B + A X + B + A 2 X 2 + A X + B

E 3 E 4 X + E 3 2 X 2 + A X

- log X 2 - 2 1 3 X + 2 2 3 6 2 2 3 + arctan 2 X - 2 1 3 2 1 3 3 2 2 3 3 + log X + 2 1 3 3 2 2 3

E 7 + E 6 + E 5

15 π 8

15 8

2 3 Z 3 Y + 2 X 2 Y + X 2 X Y

2

V + U F + E + α

E V + F U F 2 + E 2 + cos α

cosh 2 sin X + sinh 2 cos X

cosh 2 2 sin 2 X + sinh 2 2 cos 2 X ATAN 2 sinh 2 cos X ,cosh 2 sin X

log 5 + arctan 4 3

log 2 5 + arctan 2 4 3 arctan arctan 4 3 log 5

Y + X

0

X 10 - 2 X 4 + 1 2

4

X = 612003 524288

X = 1.1673030853271484

2 X + 1 3 = 13.5 X 5 + 1

Z + X = Y

2 A X - Y = 2 A 2

Y - 2 Z = 2

X = A + 1 ,Y = 2 A , Z = A - 1

2 1 - L 1 X - 2 L 2 X - 1

L 2 - L 1

L 1 -Y - X 2 + 1

L 2 Y - X - 1 2

X = 0 ,Y = %R 1 , L 1 = 0 , L 2 = 0 ,X = 1 ,Y = 0 ,L 1 = 1 ,L 2 = 1

X 2 - Y 2

2 Y 2 - Y + X 2 - X - 1

X = - 1 3 ,Y = 1 3 , X = 1 3 ,Y = - 1 3 , X = - 1 3 ,Y = -1 3 , X = 1 ,Y = 1

X = π 6 ,F X = 1

F X = log 125 log 5

4 X 2 - Y 2 = 12 ,X Y - X = 2

X = -3 2 - 1 2 4 A 3 + 27 6 3 - 1 2 1 3 - 3 2 - 1 2 A 3 4 A 3 + 27 6 3 - 1 2 1 3 ,X = 3 2 - 1 2 4 A 3 + 27 6 3 - 1 2 1 3 - - 3 2 - 1 2 A 3 4 A 3 + 27 6 3 - 1 2 1 3 ,X = 4 A 3 + 27 6 3 - 1 2 1 3 - A 3 4 A 3 + 27 6 3 - 1 2 1 3

X = 3 - 1 2 , X = -3 + 1 2 , X = 1

X = 3 + 1 2 , X = 3 - 1 2 , X = -1 ,X = - 3 + 1 2 , X = -3 - 1 2 , X = 1

3 + 1 6 64 - 1

0

X 2 - 1

X = - 1 ,X = 1

0

H[I,J]:=1/(-1+J+I);

1 1 2 1 3 1 2 1 3 1 4 1 3 1 4 1 5

2 X - A - 1 Y = 5 B ,B Y + A X + C = 0

2 1 - A - 5 B A B C

2 1 - A - 5 B A B C

1 -A - 1 2 - 5 B 2 0 1 2 C + 5 A B 2 B + A 2 - A

2 1 - A - 5 B A B C

2 1 - A - 5 B 0 2 B + A 2 - A 2 C + 5 A B

2 1 - A - 5 B A B C

2

3 1 2 4

LAMBDA 2 - 7 LAMBDA + 10

LAMBDA = 5 ,LAMBDA = 2

X 1 X 2

X 2 - 2 X 1 2 X 1 - X 2

X 2 - 2 X 1 = 0

X 2 2 + X 1 2 = 1

X 1 = - 1 5 ,X 2 = - 2 5 , X 1 = 1 5 ,X 2 = 2 5

F

1 + X + X 2 2 + 3073 X 3 18432 + 12817 X 4 307200 +

I 1 = 1 -1 I 1 2 2 I 1 BERN 2 I 1 X 2 I 1 I 1 2 I 1 ! 2

- sin 2 X + 3 cos 2 X + X

cos 10 X sin Y + sin 10 X cos Y

- sin 2 X + 3 cos 2 X + X

2 cos 2 X + X + 1

DONE

cos X

-cos X

4 X 2 Y + X 2 Y + X + 2 Y + X 2 Y + X - 4 X Y + X 2 Y + X 2 + 2 Y + X 2 Y + X 3

BLOCK([%1,%2,%3,%4],%1:Y+X,%2:X^2,%3:%E^(Y+%2),%4:1/%1,4*%2*%4*%3+2*%4*%3-4*X*%3/%1^2+2*%3/%1^3)

79

A 2 S - 4 S 2 - 4 S + 5 2

0 T F T - X sinh A X X + B F T = T 2

B F T ,T ,S + A F T ,T ,S S 2 - A 2 = 2 S 3

F T ,T ,S = 2 S 2 - 2 A 2 B S 5 + A - A 2 B S 3

DONE

-L M 3 + L 2 M 2 M 3 - L M 2 + L 2 M 1 M 3 - L 3 M 1 M 2 M 3 + L 2 M 1 M 2 - L M 1 + 1

- M 1 M 2 M 3 L 3 + M 2 M 3 + M 1 M 3 + M 1 M 2 L 2 + - M 3 - M 2 - M 1 L + 1

X 2

X F X 2

Y + A 2 Y + X X - 2 Y 4 X 2 - 4 Y 2 2 + 1 4 Y 2 + X 2

2 A + 2 Y X + 2 Y

X + 3 20

X 20 + 60 X 19 + 1710 X 18 + 30780 X 17 + 392445 X 16 + 3767472 X 15 + 28256040 X 14 + 169536240 X 13 + 826489170 X 12 + 3305956680 X 11 + 10909657044 X 10 + 29753610120 X 9 + 66945622770 X 8 + 123591918960 X 7 + 185387878440 X 6 + 222465454128 X 5 + 208561363245 X 4 + 147219785820 X 3 + 73609892910 X 2 + 23245229340 X + 3486784401

20 X 19 + 1140 X 18 + 30780 X 17 + 523260 X 16 + 6279120 X 15 + 56512080 X 14 + 395584560 X 13 + 2203971120 X 12 + 9917870040 X 11 + 36365523480 X 10 + 109096570440 X 9 + 267782491080 X 8 + 535564982160 X 7 + 865143432720 X 6 + 1112327270640 X 5 + 1112327270640 X 4 + 834245452980 X 3 + 441659357460 X 2 + 147219785820 X + 23245229340

20 X + 3 19

A , 1 ,B ,1

B + A + 1

B 2 + 2 A + 2 B + A 2 + 2 A + 1

1.0× 10-20 X 2 - 5.5 X + 5.2× 1020

1.0× 10-20 X - 5.5 X + 5.2× 1020

1 , 2 Y

-1 , 2 X

2 X ,2 X Y 2 + Y

Y 4 + A Y 3 + 2 B + 1 Y 2 + B 2

Y 2 + B -A Y 2 - Y Y Y 2 + B

Y 4 + A Y 3 + 2 B Y 2 + Y 2 + B 2

0

B - A 2 C - A 2 C - B 2

4 X 3 + 10 X - 11 X 5 + 5

X 2 + X - 1 X 4 + X 3 + X 2 + X + 1

- 8 X 7 + 40 X 5 - 55 X 4 - 60 X 2 - 50 X 10 + 10 X 5 + 25

10 + 1 + 3 1 3

4 3 2 3 - 2 3 1 3 - 4 + 2 3 2 3 + 4 3 1 3 - 2

A 2 + A + 1

1 2 A - 1 + A 3 + 2

7 3 - 10 2 + 2 A - 2 2 - 1 7

Y 2 - X 2 ,A 2 + A + 1

1 + X +

1 - X + X 2 - X 3 +

Z - 2 + 4 + + Y - 1 + + X +

- Z - 2 16 + 1 4 + + -1 16 + Z - 2 32 + Y - 1 + 1 64 - 3 Z - 2 256 + Y - 1 2 + + -1 16 + Z - 2 32 + + 1 32 - 3 Z - 2 128 + Y - 1 + - 3 256 + 3 Z - 2 256 + Y - 1 2 + X + 1 64 - 3 Z - 2 256 + + -3 256 + 3 Z - 2 256 + Y - 1 + 3 512 - 15 Z - 2 2048 + Y - 1 2 + X 2 + - 1 256 + Z - 2 256 + + 1 256 - 5 Z - 2 1024 + Y - 1 + -5 2048 + 15 Z - 2 4096 + Y - 1 2 + X 3 +

Z + 1 + + Y + + X +

- Z 3 + Z 2 - Z + 1 + + -1 + 2 Z - 3 Z 2 + 4 Z 3 + Y + 1 - 3 Z + 6 Z 2 - 10 Z 3 + Y 2 + -1 + 4 Z - 10 Z 2 + 20 Z 3 + Y 3 + + -1 + 2 Z - 3 Z 2 + 4 Z 3 + + 2 - 6 Z + 12 Z 2 - 20 Z 3 + Y + -3 + 12 Z - 30 Z 2 + 60 Z 3 + Y 2 + 4 - 20 Z + 60 Z 2 - 140 Z 3 + Y 3 + X + 1 - 3 Z + 6 Z 2 - 10 Z 3 + + -3 + 12 Z - 30 Z 2 + 60 Z 3 + Y + 6 - 30 Z + 90 Z 2 - 210 Z 3 + Y 2 + -10 + 60 Z - 210 Z 2 + 560 Z 3 + Y 3 + X 2 + -1 + 4 Z - 10 Z 2 + 20 Z 3 + + 4 - 20 Z + 60 Z 2 - 140 Z 3 + Y + -10 + 60 Z - 210 Z 2 + 560 Z 3 + Y 2 + 20 - 140 Z + 560 Z 2 - 1680 Z 3 + Y 3 + X 3 +

2 N + 1 + 2 N 3 + 3 N 2 + N 6 - 1

1 2

5 π 2

55

X + 1 X + 3 X + 6 X + 10

0

IND

N + 1 !- 1

2 N + 1 63 N 4 + 112 N 3 + 18 N 2 - 22 N + 3 4 N 693 2 N N - 2 3 11 7

N 4 4 N 2 N N

I = 1 N - 1 I 2 N - 1 N + 1

I = 1 N I 2 - 1

F N = N N + 1 N + 2

DONE

1 2

- A 3 6

1 + A + 1 X 2 - A 2 + 2 A + 1 X 2 8 + 3 A 3 + 9 A 2 + 9 A - 1 X 3 48 +

1 + A + 1 X - X 3 6 +

1 + X 2 - X 2 8 + X 3 16 - 5 X 4 128 + 7 X 5 256 +

1 + X +

I = 1 X I + 1 2.5 X 2 + 1

1 + 2.5 X + 3.375 X 2 + 6.5625 X 3 +

1 X + 1 2 - X 12 + X 2 24 - 19 X 3 720 +

- X 2 - X 4 6 +

+ 0 +

- 1 X 6 + 1 2 X 4 + 11 120 X 2 - 347 15120 - 6767 X 2 604800 - 15377 X 4 7983360 +

1 - K 2 X 2 2 - 3 K 4 - 4 K 2 X 4 24 - 45 K 6 - 60 K 4 + 16 K 2 X 6 720 +

1 + N X + N 2 - N X 2 2 + N 3 - 3 N 2 + 2 N X 3 6 + N 4 - 6 N 3 + 11 N 2 - 6 N X 4 24 +

Y - Y 3 6 + + 1 - Y 2 2 + X + -Y 2 + Y 3 12 + X 2 + - 1 6 + Y 2 12 + X 3 +

Y + X - X 3 + 3 Y X 2 + 3 Y 2 X + Y 3 6 +

1 Y + Y 6 + + - 1 Y 2 + 1 6 + X ++ 1 Y 3 + X 2 ++ -1 Y 4 + X 3 +

END