Maple @ KTF (3/1999)

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simplify( ... )

> F:=(x^7-y^7)/(x-y);

> simplify(F);

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solve(f(x)=0,x); RootOf(...); allvalues(...);

> solve(exp(x)/x=y,x);

> evalf(eval(%,y=4));

> solve({z=s*x*y,rho=s*sqrt(1-y^2)*sqrt(x^2-1)},{x,y});
allvalues(%)[3];

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diff(f(x),x)

> F:=1/(x+1/(y+1/(x+y)));
diff(F,y,x)-diff(F,x,y);
simplify(%);

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int(f(x),x)

> Int((rho^2-z^2)/sqrt(z^2+rho^2),z) = int((rho^2-z^2)/sqrt(z^2+rho^2),z);

> Int(1/sqrt(a+b*cos(x)+c*sin(x)),x);

> int(1/sqrt(a+d*cos(x-x0)),x);

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dsolve(F(f '(x),f(x),x)=0, f(x) )

> dsolve( {diff(f(x),x)=x*f(x)*(1-f(x)),f(0)=3},f(x));

> rovnice:=diff(f(t),t,t)+b*diff(f(t),t)+Omega^2*f(t)=0;

> reseni:=dsolve({rovnice,f(0)=0,D(f)(0)=1},f(t));

> plot( subs(A=1,b=0.5,Omega=1,omega=2,rhs(reseni)),t=0..10);

> ddsolve:= ( F,f,x ) -> dsolve( subs( {f.2=diff(f(x),x,x),f.1=diff(f(x),x),f=f(x)},F), f(x) ):

> ddsolve(y1=x*y*(1-y),y,x);
ddsolve(f2+f=0,f,x);

> Order:=10:
dsolve( {x^2*diff(f(x),x,x)+x*diff(f(x),x)+(x^2-1)*f(x)=0,f(0)=0,D(f)(0)=1/2},f(x),type=series);

> series(BesselJ(1,x),x);

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value(f)

> F:=Diff(sin(x),x);
value(F);

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eval(f,x=a),limit(f,x=a)

> 'diff(sin(x),x)';

> eval(%);

> eval(cos(x),x=Pi);

> eval(x^a+y^b,{a=2,b=3});

> limit(sin(x)/x,x=0);

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Unevaluated expressions, 'expr'

> # 3D Laplace(x/r)
simplify(sum('diff( x1/sqrt(x1^2+x2^2+x3^2) , x.i, x.i )',i=1..3));

A special case of unevaluation is used to unassign a name

> x:=2;

> diff(sin(x),x);

Error, wrong number (or type) of parameters in function diff

> x:='x';

> diff(sin(x),x);

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expand(f)

> expand((x+y)^9);

> expand(exp(ln(cos(x+y))+a));

> expand(BesselJ(4,t));

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normal(f); simplify(f); factor(f)

> F:=1/(x+1)+3/(x+2)+3/(x+3)+1/(x+4):
F = simplify(F);

> factor(F);

> simplify(diff(1/(x^2-1),x$5));

> simplify(diff(1/(1-2*m/r+Q^2/r^2),r$3));
factor(%);

> normal(sin(x)^4-cos(x)^4);
simplify(sin(x)^4-cos(x)^4);
factor(sin(x)^4-cos(x)^4);

piecewise(...)

> plot(piecewise(x<0,1,x<Pi,cos(x),-1),x=-0.9..3.9);

> diff(piecewise(x<0,1,x<Pi,cos(x),-1),x,x);

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series(f)

> series(Si(x),x,11);

> int(series(sin(x)/x,x,11),x);

> simplify(series(sin(x)/x,x,7)^2+series(cos(x)/x,x,7)^2);
series(series(sin(x)/x,x,19)^2+series(cos(x)/x,x,19)^2,x,19);

> lprint(series(sin(x)/x,x,9)^2);

(series(1-1/6*x^2+1/120*x^4-1/5040*x^6+1/362880*x^8+O(x^10),x,10))^2

> Order:=8:
KR:=E=epsilon*sin(E)+M;

> RKR:=solve(KR,E);

> RRKR:=series(RKR,epsilon);

> factor(simplify(RRKR));

> RRR:=convert(combine(%),polynom);

>

>

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Funkce

> KepE2 := (M,epsilon)->M+sin(M)*epsilon+1/2*sin(2*M)*epsilon^2;

> KepE7 := unapply(RRR,M,epsilon);

> plot( {KepE2(x,0.7),KepE7(x,0.7)},x=0..2*Pi);

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with(linalg)

> restart;
with(linalg);

Warning, new definition for norm

Warning, new definition for trace

> matrix([ [1,0],[0,-1] ]) &* matrix([ [0,1],[1,0] ]) - matrix([ [0,1],[1,0] ])&*matrix([ [1,0],[0,-1] ]);
M1:=evalm(%);

> eigenvectors(M1);

> evalm(exponential(M1));

>

> N:=41;A:=5.0;P:=((N+1)/2/A)^2:

> V:=diag(seq(1/2/P*(i-(N+1)/2)^2,i=1..N)):

> T:=band([-P/2,P,-P/2],N):

>

> evalm(V):

> H:=evalm(T+V):

> VH:=eigenvectors(H):

> eigensort:=(x,y)->evalb(x[1]<y[1]);
VH2:=sort([VH],eigensort):

> plot({seq([seq([i,op(VH2[j,3])[i]],i=1..N)],j=1..5)});

> Digits:=16;
plot({seq(interp([seq(A*2/(N+1)*(i-(N+1)/2),i=1..N)],op(VH2[j,3]),z),j=1..5)},z=-4..4);

>