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Maxima MathML Output Test Page
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)));
G(L):=CATCH(MAP(LAMBDA([X],IF X < 0 THEN THROW(X) ELSE F(X)),L));
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);
NONZEROANDFREEOF(X,E):=IS(E # 0 AND FREEOF(X,E));
CONSTINTERVAL(L,H):=CONSTANTP(H-L);
NONZEROANDFREEOF(X,E):=IS(E # 0 AND FREEOF(X,E));
CONSTINTERVAL(L,H):=CONSTANTP(H-L);
ONELESS(X,Y):=IS(X = Y-1);
ONELESS(X,Y):=IS(X = Y-1);
h(x,y):=x*y*DIFF(f(x,y),x,1,y,1);
F(X):=Y+X^2;
F(X):=1+SIN(X)^2;
G(Y,Z):=3*Y+F(Z);
H(N):=SUM(I*X^I,I,0,N);
T[N](X):=RATEXPAND(2*X*T[N-1](X)-T[N-2](X));
T[0](X):=1;
T[1](X):=X;
G[N](X):=SUM(EV(X),I,N,2+N);
H(N,X):=SUM(EV(X),I,N,2+N);
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!));
F[I,J](X,Y):=Y^J+X^I;
G(FUN,A,B):=PRINT(FUN," applied to ",A," and ",B," is ",FUN(A,B));
A[N]:=N*A[N-1];
A[N]:=N;
FIB[N]:=IF N = 1 OR N = 2 THEN 1 ELSE FIB[N-2]+FIB[N-1];
ETA(MU,NU):=IF MU = NU THEN MU ELSE (IF MU > NU THEN MU-NU ELSE NU+MU);
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])));
F(X):=BLOCK([A,Y],LOCAL(A),Y:4,A[Y]:X,DISPLAY(A[Y]));
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;
F(X):=SIN(X);
F(X):=X^2;
F(Y):=DIFF(Y*LOG(Y),Y,2);
F(Y):=1/Y;
TEST(F):=BLOCK([U],U:INTEGRATE(F,X),RATSIMP(F-DIFF(U,X)));
ISLINEAR(EXP,VAR):=BLOCK([C],C:BOTHCOEF(RAT(EXP,VAR),VAR),
IS(FREEOF(VAR,C) AND C[1] # 0));
H[I,J]:=1/(-1+J+I);