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