algebrite

# mini test for distribution builds mini_test = -> run_test [ # static spherical metric "clear", "", "gdd=((-exp(2*Phi(r)),0,0,0),(0,exp(2*Lambda(r)),0,0),(0,0,r^2,0),(0,0,0,r^2*sin(theta)^2))", "", "X=(t,r,theta,phi)", "", "guu=inv(gdd)", "", "gddd=d(gdd,X)", "", "GAMDDD=1/2*(gddd+transpose(gddd,2,3)-transpose(transpose(gddd,2,3),1,2))", "", "GAMUDD=contract(outer(guu,GAMDDD),2,3)", "", "T1=d(GAMUDD,X)", "", "T2=contract(outer(GAMUDD,GAMUDD),2,4)", "", "RUDDD=transpose(T1,3,4)-T1+transpose(T2,2,3)-transpose(transpose(T2,2,3),3,4)", "", "RDD=contract(RUDDD,1,3)", "", "R=contract(contract(outer(guu,RDD),2,3),1,2)", "", "GDD=RDD-1/2*gdd*R", "", "Gtt=1/r^2*exp(2 Phi(r)) d(r (1 - exp(-2 Lambda(r))),r)", "", "Grr=-1/r^2*exp(2*Lambda(r))*(1-exp(-2*Lambda(r)))+2/r*d(Phi(r),r)", "", "Gthetatheta=r^2*exp(-2*Lambda(r))*(d(d(Phi(r),r),r)+d(Phi(r),r)^2+d(Phi(r),r)/r-d(Phi(r),r)*d(Lambda(r),r)-d(Lambda(r),r)/r)", "", "Gphiphi=sin(theta)^2*Gthetatheta", "", "T=((Gtt,0,0,0),(0,Grr,0,0),(0,0,Gthetatheta,0),(0,0,0,Gphiphi))", "", "GDD-T", "((0,0,0,0),(0,0,0,0),(0,0,0,0),(0,0,0,0))", # surface integral example from the manual "clear", "", "z=1-x^2-y^2", "", "F=(x*y^2*z,-2*x^3,y*z^2)", "", "S=(x,y,z)", "", "s=dot(F,cross(d(S,x),d(S,y)))", "", "defint(s,y,-sqrt(1-x^2),sqrt(1-x^2),x,-1,1)", "1/48*pi", # hydrogen wavefunction example "clear", "", "laplacian(f)=1/r^2*d(r^2*d(f,r),r)+1/(r^2*sin(theta))*d(sin(theta)*d(f,theta),theta)+1/(r*sin(theta))^2*d(f,phi,phi)", "", "n=7", "", "l=3", "", "m=1", "", "R=r^l*exp(-r/n)*laguerre(2*r/n,n-l-1,2*l+1)", "", "Y=legendre(cos(theta),l,abs(m))*exp(i*m*phi)", "", "psi=R*Y", "", "E=psi/n^2", "", "K=laplacian(psi)", "", "V=2*psi/r", "", "circexp(sin(theta)*(E-K-V))", "0", # Green's theorem (surface integral) "clear", "", "P=2x^3-y^3", "", "Q=x^3+y^3", "", "f=d(Q,x)-d(P,y)", "", "x=r*cos(theta)", "", "y=r*sin(theta)", "", "defint(f*r,r,0,1,theta,0,2pi)", "3/2*pi", # Green's theorem (line integral) "clear", "", "x=cos(t)", "", "y=sin(t)", "", "P=2x^3-y^3", "", "Q=x^3+y^3", "", "f=P*d(x,t)+Q*d(y,t)", "", "f=circexp(f)", "", "defint(f,t,0,2pi)", "3/2*pi", # Stokes' theorem (surface integral) "clear", "", "z=9-x^2-y^2", "", "F=(3y,4z,-6x)", "", "S=(x,y,z)", "", "f=dot(curl(F),cross(d(S,x),d(S,y)))", "", "x=r*cos(theta)", "", "y=r*sin(theta)", "", "defint(f*r,r,0,3,theta,0,2pi)", "-27*pi", # Stokes' theorem (line integral) "clear", "", "x=3*cos(t)", "", "y=3*sin(t)", "", "z=9-x^2-y^2", "", "P=3y", "", "Q=4z", "", "R=-6x", "", "f=P*d(x,t)+Q*d(y,t)+R*d(z,t)", "", "f=circexp(f)", "", "defint(f,t,0,2pi)", "-27*pi", ]