eigenmath/mini-test.cpp

238 lines
2.8 KiB
C++

// mini test for distribution builds
#include "stdafx.h"
#include "defs.h"
static char *s[] = {
// 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)",
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"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",
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"Q=x^3+y^3",
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"f=d(Q,x)-d(P,y)",
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"x=r*cos(theta)",
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"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)",
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"P=2x^3-y^3",
"",
"Q=x^3+y^3",
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"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)",
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"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)",
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"z=9-x^2-y^2",
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"P=3y",
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"Q=4z",
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"R=-6x",
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"f=P*d(x,t)+Q*d(y,t)+R*d(z,t)",
"",
"f=circexp(f)",
"",
"defint(f,t,0,2pi)",
"-27*pi",
};
void
mini_test(void)
{
test(__FILE__, s, sizeof (s) / sizeof (char *));
}