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# Chapter 19.  Glossary of Commands
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# MAPLE SESSION 1
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>   (sin@cos)(x); 
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# MAPLE SESSION 2
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>    int(1/(1+x^3),x);   diff(%,x);
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# MAPLE SESSION 3
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>   with(plots): animate(sin(x*t),x=-10..10,t=1..2); 
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# MAPLE SESSION 4
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>   with(plots): animate3d(cos(x+t*y),x=0..Pi,y=-Pi..Pi,t=1..2);
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# MAPLE SESSION 5
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>    S:={y=-1,x=2}: assign(%); x,y; 
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# MAPLE SESSION 6
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>   asympt(GAMMA(x)^2/GAMMA(2*x)*4^x/sqrt(Pi),x,3);
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# MAPLE SESSION 7
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>    with(codegen): F:=exp((1+x+x^2)^3); C(F);
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# MAPLE SESSION 8
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>    with(student): Int(x^2/sqrt(1-x^6),x):
>    changevar(u=x^3,%,u); 
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# MAPLE SESSION 9
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>    expand((1+x+x^2)^10): coeff(%,x,10); 
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# MAPLE SESSION 10
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>    (x+1)^3*y-(y+1)^3*x: collect(%,x); 
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# MAPLE SESSION 11
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>   combine(exp(2*x)^3*exp(y));
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# MAPLE SESSION 12
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>    with(plots): contourplot(sin(x*y),x=0..Pi, y=0..Pi); 
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# MAPLE SESSION 13
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>   series(sqrt(1-x),x,4): convert(%,polynom); 
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# MAPLE SESSION 14
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>    degree((x+y)^6*(y-x^2)^10,x); 
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# MAPLE SESSION 15
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>    denom((x*sin(x)-cos(x))/x^2); 
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# MAPLE SESSION 16
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>    with(linalg): A:=matrix(4,4,(i,j)->x^(i*j));  
>    det(A); factor(%);
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# MAPLE SESSION 17
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>    diff(sin(x^2*y),x); 
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# MAPLE SESSION 18
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>   with(plots): P1:=plot(sin(x),x=0..Pi,style=POINT):
>   P2:=plot(x,x=0..Pi): display([P1,P2]);
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# MAPLE SESSION 19
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>    dsolve(diff(y(x),x$2)-y(x)=sin(x), y(x)); 
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# MAPLE SESSION 20
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>    evalf(exp(-Pi),20); 
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# MAPLE SESSION 21
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>   expand((2*x+1)*(3*x-5)); 
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# MAPLE SESSION 22
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>   factor(x^3+x^2*y-x*y^2-y^3); 
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# MAPLE SESSION 23
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>   floor(-11/3); 
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# MAPLE SESSION 24
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>    with(codegen): F:=exp((1+x+x^2)^3); fortran(F);
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# MAPLE SESSION 25
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>   fsolve(cos(x)=x/2,x); 
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# MAPLE SESSION 26
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>    with(linalg): A:=matrix([[1,2,3,4],[2,3,4,5],[5,6,7,8]]); 
>    gausselim(A);
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# MAPLE SESSION 27
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>   ifactor(999); 
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# MAPLE SESSION 28
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>   with(plots):
>   implicitplot((x^2)^(1/3)+(y^2)^(1/3)=1, x=-1..1, y=-1..1); 
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# MAPLE SESSION 29
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>   with(plots):
>   implicitplot3d(x^2+y^2+z^2=1,x=-1..1,y=-1..1,z=-1..1);
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# MAPLE SESSION 30
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>   int(x^2/sqrt(1+x^2),x=1..sqrt(3)); 
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# MAPLE SESSION 31
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>    with(linalg): A:=matrix(3,3,(i,j)->1/2^(i*j)); inverse(A);
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# MAPLE SESSION 32
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>   isolve({x^3+x*y=2,x^2+y^2=2},{x,y}); 
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# MAPLE SESSION 33
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>    with(linalg): A:=matrix(5,5,(i,j)->7^(i+j)); kernel(A);
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# MAPLE SESSION 34
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>   latex(Int(1/x,x)); 
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# MAPLE SESSION 35
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>   e:=x^2+y^2=r^2: lhs(e); 
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# MAPLE SESSION 36
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>   limit((cos(x)-1)/x^2,x=0); 
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# MAPLE SESSION 37
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>    L := [seq(10^i-1,i=1..6)]; map(ifactor,L);
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# MAPLE SESSION 38
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>    A:=matrix(4,4,(i,j)->x^(i+j));
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# MAPLE SESSION 39
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>    modp(13*19^5,34);
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# MAPLE SESSION 40
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>   normal((1-q^7)*(1-q^6)/(1-q^2)/(1-q)); 
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# MAPLE SESSION 41
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>   numer((x*sin(x)-cos(x))/x^2); 
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# MAPLE SESSION 42
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>   w:=x^3+x*y+y: op(w); op(2,w); 
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# MAPLE SESSION 43
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>   plot(x*sin(x),x=0..Pi); 
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# MAPLE SESSION 44
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>   plot3d(sin(x*y),x=0..Pi,y=0..Pi); 
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# MAPLE SESSION 45
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>   with(plots): polarplot(sin(t),t=0..2*Pi);
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# MAPLE SESSION 46
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>   product((a+i-1),i=1..6); 
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# MAPLE SESSION 47
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>   radsimp(sqrt(3)*sqrt(15)); 
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# MAPLE SESSION 48
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>    R9 := rand(0..9); R9(); R9(); R9();
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# MAPLE SESSION 49
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>   (1+sqrt(2))/(sqrt(2)-sqrt(3)): rationalize(%); 
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# MAPLE SESSION 50
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>   e:=x^2+y^2=r^2: rhs(e); 
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# MAPLE SESSION 51
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>   seq(x+(y-x)*i/4,i=0..4);
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# MAPLE SESSION 52
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>   simplify((sin(x)+cos(x))^2); 
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# MAPLE SESSION 53
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>   solve({x^2+x*y-y=17,y^2-x-y=9},{x,y}); 
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# MAPLE SESSION 54
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>   with(plots): spacecurve([sin(t),cos(t),t,t=0..2*Pi]);
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# MAPLE SESSION 55
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>   t^2+t+1: subs(t=1+sqrt(5),%); 
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# MAPLE SESSION 56
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>   sum(i^2,i=1..100); 
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# MAPLE SESSION 57
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>   taylor(tan(x),x=0,10); 
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# MAPLE SESSION 58
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>    R := (1-q^6)*(1-q^5)*(1-q^4)/(1-q)/(1-q^2)/(1-q^3); 
>    P := normal(R); type(P, polynom);
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# MAPLE SESSION 59
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>   Int(1/x,x): value(%); 
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# MAPLE SESSION 60
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>    F:=expand((1+x+x^2)^10): f:=unapply(F,x); f(x);
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# MAPLE SESSION 61
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>    L := [seq(i,i=1..10)]; whattype(L);