c DO NOT modify this file. Instead, run the mathematic script c ricci_calc.ma to generate this file. c here are the assignments for dxuxx et al dxuxx=-(dexgxx*uxx**2)-2.d0*dexgxy*uxx*uxy-dexgyy*uxy**2-2.d0*de & xgxz*uxx*uxz-2.d0*dexgyz*uxy*uxz-dexgzz*uxz**2 dxuxy=-(dexgxx*uxx*uxy)-dexgxy*uxy**2-dexgxz*uxy*uxz-dexgxy*uxx* & uyy-dexgyy*uxy*uyy-dexgyz*uxz*uyy-dexgxz*uxx*uyz-dexgyz*uxy*uyz- & dexgzz*uxz*uyz dxuxz=-(dexgxx*uxx*uxz)-dexgxy*uxy*uxz-dexgxz*uxz**2-dexgxy*uxx* & uyz-dexgyy*uxy*uyz-dexgyz*uxz*uyz-dexgxz*uxx*uzz-dexgyz*uxy*uzz- & dexgzz*uxz*uzz dxuyy=-(dexgxx*uxy**2)-2.d0*dexgxy*uxy*uyy-dexgyy*uyy**2-2.d0*de & xgxz*uxy*uyz-2.d0*dexgyz*uyy*uyz-dexgzz*uyz**2 dxuyz=-(dexgxx*uxy*uxz)-dexgxy*uxz*uyy-dexgxy*uxy*uyz-dexgxz*uxz & *uyz-dexgyy*uyy*uyz-dexgyz*uyz**2-dexgxz*uxy*uzz-dexgyz*uyy*uzz- & dexgzz*uyz*uzz dxuzz=-(dexgxx*uxz**2)-2.d0*dexgxy*uxz*uyz-dexgyy*uyz**2-2.d0*de & xgxz*uxz*uzz-2.d0*dexgyz*uyz*uzz-dexgzz*uzz**2 dyuxx=-(deygxx*uxx**2)-2.d0*deygxy*uxx*uxy-deygyy*uxy**2-2.d0*de & ygxz*uxx*uxz-2.d0*deygyz*uxy*uxz-deygzz*uxz**2 dyuxy=-(deygxx*uxx*uxy)-deygxy*uxy**2-deygxz*uxy*uxz-deygxy*uxx* & uyy-deygyy*uxy*uyy-deygyz*uxz*uyy-deygxz*uxx*uyz-deygyz*uxy*uyz- & deygzz*uxz*uyz dyuxz=-(deygxx*uxx*uxz)-deygxy*uxy*uxz-deygxz*uxz**2-deygxy*uxx* & uyz-deygyy*uxy*uyz-deygyz*uxz*uyz-deygxz*uxx*uzz-deygyz*uxy*uzz- & deygzz*uxz*uzz dyuyy=-(deygxx*uxy**2)-2.d0*deygxy*uxy*uyy-deygyy*uyy**2-2.d0*de & ygxz*uxy*uyz-2.d0*deygyz*uyy*uyz-deygzz*uyz**2 dyuyz=-(deygxx*uxy*uxz)-deygxy*uxz*uyy-deygxy*uxy*uyz-deygxz*uxz & *uyz-deygyy*uyy*uyz-deygyz*uyz**2-deygxz*uxy*uzz-deygyz*uyy*uzz- & deygzz*uyz*uzz dyuzz=-(deygxx*uxz**2)-2.d0*deygxy*uxz*uyz-deygyy*uyz**2-2.d0*de & ygxz*uxz*uzz-2.d0*deygyz*uyz*uzz-deygzz*uzz**2 dzuxx=-(dezgxx*uxx**2)-2.d0*dezgxy*uxx*uxy-dezgyy*uxy**2-2.d0*de & zgxz*uxx*uxz-2.d0*dezgyz*uxy*uxz-dezgzz*uxz**2 dzuxy=-(dezgxx*uxx*uxy)-dezgxy*uxy**2-dezgxz*uxy*uxz-dezgxy*uxx* & uyy-dezgyy*uxy*uyy-dezgyz*uxz*uyy-dezgxz*uxx*uyz-dezgyz*uxy*uyz- & dezgzz*uxz*uyz dzuxz=-(dezgxx*uxx*uxz)-dezgxy*uxy*uxz-dezgxz*uxz**2-dezgxy*uxx* & uyz-dezgyy*uxy*uyz-dezgyz*uxz*uyz-dezgxz*uxx*uzz-dezgyz*uxy*uzz- & dezgzz*uxz*uzz dzuyy=-(dezgxx*uxy**2)-2.d0*dezgxy*uxy*uyy-dezgyy*uyy**2-2.d0*de & zgxz*uxy*uyz-2.d0*dezgyz*uyy*uyz-dezgzz*uyz**2 dzuyz=-(dezgxx*uxy*uxz)-dezgxy*uxz*uyy-dezgxy*uxy*uyz-dezgxz*uxz & *uyz-dezgyy*uyy*uyz-dezgyz*uyz**2-dezgxz*uxy*uzz-dezgyz*uyy*uzz- & dezgzz*uyz*uzz dzuzz=-(dezgxx*uxz**2)-2.d0*dezgxy*uxz*uyz-dezgyy*uyz**2-2.d0*de & zgxz*uxz*uzz-2.d0*dezgyz*uyz*uzz-dezgzz*uzz**2 c here are the assignments for the x-x component of the 3-ricci t1=5.d-1*dexgxx*dxuxx+dexgxy*dxuxy-5.d-1*deygxx*dxuxy+dexgxz*dxu & xz-5.d-1*dezgxx*dxuxz+5.d-1*dexgxx*dyuxy+dexgxy*dyuyy-5.d-1*deyg & xx*dyuyy+dexgxz*dyuyz-5.d-1*dezgxx*dyuyz+5.d-1*dexgxx*dzuxz+dexg & xy*dzuyz-5.d-1*deygxx*dzuyz+dexgxz*dzuzz-5.d-1*dezgxx*dzuzz+5.d- & 1*d2xxgxx*uxx+d2xxgxy*uxy+d2xxgxz*uxz+5.d-1*(-(dexgxx*dxuxx)-2.d & 0*dexgxy*dxuxy+deygxx*dxuxy-2.d0*dexgxz*dxuxz+dezgxx*dxuxz-d2xxg & xx*uxx-2.d0*d2xxgxy*uxy+d2xygxx*uxy-2.d0*d2xxgxz*uxz+d2xzgxx*uxz & ) t2=d2xygxy*uyy-5.d-1*d2yygxx*uyy+d2xygxz*uyz+d2xzgxy*uyz-d2yzgxx & *uyz-2.5d-1*(deygxx*uxx+dexgyy*uxy+(dexgyz+deygxz-dezgxy)*uxz)*( & dexgxx*uxy+2.d0*dexgxy*uyy-deygxx*uyy+2.d0*dexgxz*uyz-dezgxx*uyz & )+2.5d-1*(dexgxx*uxx+2.d0*dexgxy*uxy-deygxx*uxy+2.d0*dexgxz*uxz- & dezgxx*uxz)*(deygxx*uxy+dexgyy*uyy+(dexgyz+deygxz-dezgxy)*uyz)-2 & .5d-1*(deygxx*uxy+dexgyy*uyy+(dexgyz+deygxz-dezgxy)*uyz)**2+2.5d & -1*(-(dexgxx*uxy)-2.d0*dexgxy*uyy+deygxx*uyy-2.d0*dexgxz*uyz+dez & gxx*uyz)*(dexgyy*uxy-2.d0*deygxy*uxy-deygyy*uyy-2.d0*deygyz*uyz+ & dezgyy*uyz)+5.d-1*(-(deygxx*dxuxy)-dexgyy*dxuyy-(dexgyz+deygxz-d & ezgxy)*dxuyz-d2xygxx*uxy-d2xxgyy*uyy-(d2xxgyz+d2xygxz-d2xzgxy)*u & yz) t3=d2xzgxz*uzz-5.d-1*d2zzgxx*uzz+2.5d-1*(dexgxx*uxx+2.d0*dexgxy* & uxy-deygxx*uxy+2.d0*dexgxz*uxz-dezgxx*uxz)*(dezgxx*uxz+(dexgyz-d & eygxz+dezgxy)*uyz+dexgzz*uzz)-2.5d-1*(dezgxx*uxz+(dexgyz-deygxz+ & dezgxy)*uyz+dexgzz*uzz)**2+2.5d-1*(dexgxx*uxy+2.d0*dexgxy*uyy-de & ygxx*uyy+2.d0*dexgxz*uyz-dezgxx*uyz)*((-dexgyz+deygxz+dezgxy)*ux & z+dezgyy*uyz+deygzz*uzz)-2.5d-1*(dezgxx*uxx+(dexgyz-deygxz+dezgx & y)*uxy+dexgzz*uxz)*(dexgxx*uxz+2.d0*dexgxy*uyz-deygxx*uyz+2.d0*d & exgxz*uzz-dezgxx*uzz)+2.5d-1*((-dexgyz+deygxz+dezgxy)*uxy+dezgyy & *uyy+deygzz*uyz)*(dexgxx*uxz+2.d0*dexgxy*uyz-deygxx*uyz+2.d0*dex & gxz*uzz-dezgxx*uzz)-5.d-1*(dezgxx*uxy+(dexgyz-deygxz+dezgxy)*uyy & +dexgzz*uyz)*(deygxx*uxz+dexgyy*uyz+(dexgyz+deygxz-dezgxy)*uzz)+ & 2.5d-1*(dexgxx*uxz+2.d0*dexgxy*uyz-deygxx*uyz+2.d0*dexgxz*uzz-de & zgxx*uzz)*(-(dexgzz*uxz)+2.d0*dezgxz*uxz-deygzz*uyz+2.d0*dezgyz* & uyz+dezgzz*uzz)+5.d-1*(-(dezgxx*dxuxz)-(dexgyz-deygxz+dezgxy)*dx & uyz-dexgzz*dxuzz-d2xzgxx*uxz-(d2xxgyz-d2xygxz+d2xzgxy)*uyz-d2xxg & zz*uzz) riccixx=t1+t2+t3 c here are the assignments for the x-y component of the 3-ricci t1=5.d-1*(-(deygxx*dxuxx)-dexgyy*dxuxy-(dexgyz+deygxz-dezgxy)*dx & uxz-d2xygxx*uxx-d2xxgyy*uxy-(d2xxgyz+d2xygxz-d2xzgxy)*uxz)+5.d-1 & *(deygxx*dxuxx+dexgyy*dxuxy+(dexgyz+deygxz-dezgxy)*dxuxz+d2xygxx & *uxx+d2xxgyy*uxy+(d2xxgyz+d2xygxz-d2xzgxy)*uxz)+2.5d-1*(-(dexgyy & *uxx)+2.d0*deygxy*uxx+deygyy*uxy+2.d0*deygyz*uxz-dezgyy*uxz)*(-( & dexgxx*uxy)-2.d0*dexgxy*uyy+deygxx*uyy-2.d0*dexgxz*uyz+dezgxx*uy & z)+2.5d-1*(deygxx*uxx+dexgyy*uxy+(dexgyz+deygxz-dezgxy)*uxz)*(de & ygxx*uxy+dexgyy*uyy+(dexgyz+deygxz-dezgxy)*uyz)+5.d-1*(dexgyy*dx & uxy-2.d0*deygxy*dxuxy-deygyy*dxuyy-2.d0*deygyz*dxuyz+dezgyy*dxuy & z+d2xxgyy*uxy-2.d0*d2xygxy*uxy-d2xygyy*uyy-2.d0*d2xygyz*uyz+d2xz & gyy*uyz)+5.d-1*(deygxx*dyuxy+dexgyy*dyuyy+(dexgyz+deygxz-dezgxy) & *dyuyz+d2yygxx*uxy+d2xygyy*uyy+(d2xygyz+d2yygxz-d2yzgxy)*uyz)+2. & 5d-1*(deygxx*uxx+dexgyy*uxy+(dexgyz+deygxz-dezgxy)*uxz)*(dezgxx* & uxz+(dexgyz-deygxz+dezgxy)*uyz+dexgzz*uzz) t2=2.5d-1*(deygxx*uxy+dexgyy*uyy+(dexgyz+deygxz-dezgxy)*uyz)*((- & dexgyz+deygxz+dezgxy)*uxz+dezgyy*uyz+deygzz*uzz)-2.5d-1*(dezgxx* & uxz+(dexgyz-deygxz+dezgxy)*uyz+dexgzz*uzz)*((-dexgyz+deygxz+dezg & xy)*uxz+dezgyy*uyz+deygzz*uzz)-2.5d-1*((-dexgyz+deygxz+dezgxy)*u & xx+dezgyy*uxy+deygzz*uxz)*(dexgxx*uxz+2.d0*dexgxy*uyz-deygxx*uyz & +2.d0*dexgxz*uzz-dezgxx*uzz)+2.5d-1*(dezgxx*uxy+dexgyz*uyy-deygx & z*uyy+dezgxy*uyy+dexgzz*uyz)*(dexgyy*uxz-2.d0*deygxy*uxz-deygyy* & uyz-2.d0*deygyz*uzz+dezgyy*uzz)+2.5d-1*(deygxx*uxz+dexgyy*uyz+(d & exgyz+deygxz-dezgxy)*uzz)*(-(dexgzz*uxz)+2.d0*dezgxz*uxz-deygzz* & uyz+2.d0*dezgyz*uyz+dezgzz*uzz)+5.d-1*((dexgyz-deygxz-dezgxy)*dx & uxz-dezgyy*dxuyz-deygzz*dxuzz+(d2xxgyz-d2xygxz-d2xzgxy)*uxz-d2xz & gyy*uyz-d2xygzz*uzz)+5.d-1*(deygxx*dzuxz+dexgyy*dzuyz+(dexgyz+de & ygxz-dezgxy)*dzuzz+d2yzgxx*uxz+d2xzgyy*uyz+(d2xzgyz+d2yzgxz-d2zz & gxy)*uzz) riccixy=t1+t2 c here are the assignments for the x-z component of the 3-ricci t1=5.d-1*(-(dezgxx*dxuxx)-(dexgyz-deygxz+dezgxy)*dxuxy-dexgzz*dx & uxz-d2xzgxx*uxx-(d2xxgyz-d2xygxz+d2xzgxy)*uxy-d2xxgzz*uxz)+5.d-1 & *(dezgxx*dxuxx+(dexgyz-deygxz+dezgxy)*dxuxy+dexgzz*dxuxz+d2xzgxx & *uxx+(d2xxgyz-d2xygxz+d2xzgxy)*uxy+d2xxgzz*uxz)-2.5d-1*((-dexgyz & +deygxz+dezgxy)*uxx+dezgyy*uxy+deygzz*uxz)*(dexgxx*uxy+2.d0*dexg & xy*uyy-deygxx*uyy+2.d0*dexgxz*uyz-dezgxx*uyz)+2.5d-1*(dezgxx*uxx & +(dexgyz-deygxz+dezgxy)*uxy+dexgzz*uxz)*(deygxx*uxy+dexgyy*uyy+( & dexgyz+deygxz-dezgxy)*uyz)-2.5d-1*((-dexgyz+deygxz+dezgxy)*uxy+d & ezgyy*uyy+deygzz*uyz)*(deygxx*uxy+dexgyy*uyy+(dexgyz+deygxz-dezg & xy)*uyz)+2.5d-1*(dezgxx*uxy+(dexgyz-deygxz+dezgxy)*uyy+dexgzz*uy & z)*(-(dexgyy*uxy)+2.d0*deygxy*uxy+deygyy*uyy+2.d0*deygyz*uyz-dez & gyy*uyz)+5.d-1*((dexgyz-deygxz-dezgxy)*dxuxy-dezgyy*dxuyy-deygzz & *dxuyz+(d2xxgyz-d2xygxz-d2xzgxy)*uxy-d2xzgyy*uyy-d2xygzz*uyz) t2=5.d-1*(dezgxx*dyuxy+(dexgyz-deygxz+dezgxy)*dyuyy+dexgzz*dyuyz & +d2yzgxx*uxy+(d2xygyz-d2yygxz+d2yzgxy)*uyy+d2xygzz*uyz)+2.5d-1*( & dezgxx*uxx+(dexgyz-deygxz+dezgxy)*uxy+dexgzz*uxz)*(dezgxx*uxz+(d & exgyz-deygxz+dezgxy)*uyz+dexgzz*uzz)+2.5d-1*((-dexgyz+deygxz+dez & gxy)*uxy+dezgyy*uyy+deygzz*uyz)*(dezgxx*uxz+(dexgyz-deygxz+dezgx & y)*uyz+dexgzz*uzz)+2.5d-1*(-(dexgzz*uxx)+2.d0*dezgxz*uxx-deygzz* & uxy+2.d0*dezgyz*uxy+dezgzz*uxz)*(-(dexgxx*uxz)-2.d0*dexgxy*uyz+d & eygxx*uyz-2.d0*dexgxz*uzz+dezgxx*uzz)-2.5d-1*(-(dexgzz*uxy)+2.d0 & *dezgxz*uxy-deygzz*uyy+2.d0*dezgyz*uyy+dezgzz*uyz)*(deygxx*uxz+d & exgyy*uyz+(dexgyz+deygxz-dezgxy)*uzz)+5.d-1*(dexgzz*dxuxz-2.d0*d & ezgxz*dxuxz+deygzz*dxuyz-2.d0*dezgyz*dxuyz-dezgzz*dxuzz+d2xxgzz* & uxz-2.d0*d2xzgxz*uxz+d2xygzz*uyz-2.d0*d2xzgyz*uyz-d2xzgzz*uzz)+5 & .d-1*(dezgxx*dzuxz+(dexgyz-deygxz+dezgxy)*dzuyz+dexgzz*dzuzz+d2z & zgxx*uxz+(d2xzgyz-d2yzgxz+d2zzgxy)*uyz+d2xzgzz*uzz) riccixz=t1+t2 c here are the assignments for the y-y component of the 3-ricci t1=-5.d-1*dexgyy*dxuxx+deygxy*dxuxx+5.d-1*deygyy*dxuxy+deygyz*dx & uxz-5.d-1*dezgyy*dxuxz-5.d-1*dexgyy*dyuxy+deygxy*dyuxy+5.d-1*dey & gyy*dyuyy+deygyz*dyuyz-5.d-1*dezgyy*dyuyz-5.d-1*dexgyy*dzuxz+dey & gxy*dzuxz+5.d-1*deygyy*dzuyz+deygyz*dzuzz-5.d-1*dezgyy*dzuzz-5.d & -1*d2xxgyy*uxx+d2xygxy*uxx+d2yygxy*uxy+d2xygyz*uxz t2=-(d2xzgyy*uxz)+d2yzgxy*uxz-2.5d-1*(deygxx*uxx+dexgyy*uxy+(dex & gyz+deygxz-dezgxy)*uxz)**2+2.5d-1*(-(dexgxx*uxx)-2.d0*dexgxy*uxy & +deygxx*uxy-2.d0*dexgxz*uxz+dezgxx*uxz)*(dexgyy*uxx-2.d0*deygxy* & uxx-deygyy*uxy-2.d0*deygyz*uxz+dezgyy*uxz)+5.d-1*(-(deygxx*dyuxx & )-dexgyy*dyuxy-(dexgyz+deygxz-dezgxy)*dyuxz-d2yygxx*uxx-d2xygyy* & uxy-(d2xygyz+d2yygxz-d2yzgxy)*uxz)+5.d-1*d2yygyy*uyy+d2yygyz*uyz & -2.5d-1*(-(dexgyy*uxx)+2.d0*deygxy*uxx+deygyy*uxy+2.d0*deygyz*ux & z-dezgyy*uxz)*(deygxx*uxy+dexgyy*uyy+(dexgyz+deygxz-dezgxy)*uyz) & +2.5d-1*(deygxx*uxx+dexgyy*uxy+(dexgyz+deygxz-dezgxy)*uxz)*(-(de & xgyy*uxy)+2.d0*deygxy*uxy+deygyy*uyy+2.d0*deygyz*uyz-dezgyy*uyz) & +5.d-1*(dexgyy*dyuxy-2.d0*deygxy*dyuxy-deygyy*dyuyy-2.d0*deygyz* & dyuyz+dezgyy*dyuyz+d2xygyy*uxy-2.d0*d2yygxy*uxy-d2yygyy*uyy-2.d0 & *d2yygyz*uyz+d2yzgyy*uyz) t3=d2yzgyz*uzz-5.d-1*d2zzgyy*uzz+2.5d-1*(-(dexgyy*uxx)+2.d0*deyg & xy*uxx+deygyy*uxy+2.d0*deygyz*uxz-dezgyy*uxz)*(dezgxx*uxz+(dexgy & z-deygxz+dezgxy)*uyz+dexgzz*uzz)+2.5d-1*(-(dexgyy*uxy)+2.d0*deyg & xy*uxy+deygyy*uyy+2.d0*deygyz*uyz-dezgyy*uyz)*((-dexgyz+deygxz+d & ezgxy)*uxz+dezgyy*uyz+deygzz*uzz)-2.5d-1*((-dexgyz+deygxz+dezgxy & )*uxz+dezgyy*uyz+deygzz*uzz)**2-5.d-1*((-dexgyz+deygxz+dezgxy)*u & xx+dezgyy*uxy+deygzz*uxz)*(deygxx*uxz+dexgyy*uyz+(dexgyz+deygxz- & dezgxy)*uzz)+2.5d-1*(dezgxx*uxx+(dexgyz-deygxz+dezgxy)*uxy+dexgz & z*uxz)*(-(dexgyy*uxz)+2.d0*deygxy*uxz+deygyy*uyz+2.d0*deygyz*uzz & -dezgyy*uzz)-2.5d-1*((-dexgyz+deygxz+dezgxy)*uxy+dezgyy*uyy+deyg & zz*uyz)*(-(dexgyy*uxz)+2.d0*deygxy*uxz+deygyy*uyz+2.d0*deygyz*uz & z-dezgyy*uzz)+2.5d-1*(-(dexgyy*uxz)+2.d0*deygxy*uxz+deygyy*uyz+2 & .d0*deygyz*uzz-dezgyy*uzz)*(-(dexgzz*uxz)+2.d0*dezgxz*uxz-deygzz & *uyz+2.d0*dezgyz*uyz+dezgzz*uzz)+5.d-1*((dexgyz-deygxz-dezgxy)*d & yuxz-dezgyy*dyuyz-deygzz*dyuzz+(d2xygyz-d2yygxz-d2yzgxy)*uxz-d2y & zgyy*uyz-d2yygzz*uzz) ricciyy=t1+t2+t3 c here are the assignments for the y-z component of the 3-ricci t1=2.5d-1*((-dexgyz+deygxz+dezgxy)*uxx+dezgyy*uxy+deygzz*uxz)*(d & exgxx*uxx+2.d0*dexgxy*uxy-deygxx*uxy+2.d0*dexgxz*uxz-dezgxx*uxz) & -2.5d-1*(dezgxx*uxx+(dexgyz-deygxz+dezgxy)*uxy+dexgzz*uxz)*(deyg & xx*uxx+dexgyy*uxy+(dexgyz+deygxz-dezgxy)*uxz)+5.d-1*(-(dezgxx*dy & uxx)-(dexgyz-deygxz+dezgxy)*dyuxy-dexgzz*dyuxz-d2yzgxx*uxx-(d2xy & gyz-d2yygxz+d2yzgxy)*uxy-d2xygzz*uxz)+5.d-1*((-dexgyz+deygxz+dez & gxy)*dxuxx+dezgyy*dxuxy+deygzz*dxuxz+(-d2xxgyz+d2xygxz+d2xzgxy)* & uxx+d2xzgyy*uxy+d2xygzz*uxz)+2.5d-1*(dexgyy*uxx-2.d0*deygxy*uxx- & deygyy*uxy-2.d0*deygyz*uxz+dezgyy*uxz)*(dezgxx*uxy+dexgyz*uyy-de & ygxz*uyy+dezgxy*uyy+dexgzz*uyz)+2.5d-1*(deygxx*uxx+dexgyy*uxy+(d & exgyz+deygxz-dezgxy)*uxz)*((-dexgyz+deygxz+dezgxy)*uxy+dezgyy*uy & y+deygzz*uyz)+5.d-1*((dexgyz-deygxz-dezgxy)*dyuxy-dezgyy*dyuyy-d & eygzz*dyuyz+(d2xygyz-d2yygxz-d2yzgxy)*uxy-d2yzgyy*uyy-d2yygzz*uy & z) t2=5.d-1*((-dexgyz+deygxz+dezgxy)*dyuxy+dezgyy*dyuyy+deygzz*dyuy & z+(-d2xygyz+d2yygxz+d2yzgxy)*uxy+d2yzgyy*uyy+d2yygzz*uyz)+2.5d-1 & *(dezgxx*uxx+(dexgyz-deygxz+dezgxy)*uxy+dexgzz*uxz)*((-dexgyz+de & ygxz+dezgxy)*uxz+dezgyy*uyz+deygzz*uzz)+2.5d-1*((-dexgyz+deygxz+ & dezgxy)*uxy+dezgyy*uyy+deygzz*uyz)*((-dexgyz+deygxz+dezgxy)*uxz+ & dezgyy*uyz+deygzz*uzz)-2.5d-1*(-(dexgzz*uxx)+2.d0*dezgxz*uxx-dey & gzz*uxy+2.d0*dezgyz*uxy+dezgzz*uxz)*(deygxx*uxz+dexgyy*uyz+(dexg & yz+deygxz-dezgxy)*uzz)+2.5d-1*(-(dexgzz*uxy)+2.d0*dezgxz*uxy-dey & gzz*uyy+2.d0*dezgyz*uyy+dezgzz*uyz)*(dexgyy*uxz-2.d0*deygxy*uxz- & deygyy*uyz-2.d0*deygyz*uzz+dezgyy*uzz)+5.d-1*(dexgzz*dyuxz-2.d0* & dezgxz*dyuxz+deygzz*dyuyz-2.d0*dezgyz*dyuyz-dezgzz*dyuzz+d2xygzz & *uxz-2.d0*d2yzgxz*uxz+d2yygzz*uyz-2.d0*d2yzgyz*uyz-d2yzgzz*uzz)+ & 5.d-1*((-dexgyz+deygxz+dezgxy)*dzuxz+dezgyy*dzuyz+deygzz*dzuzz+( & -d2xzgyz+d2yzgxz+d2zzgxy)*uxz+d2zzgyy*uyz+d2yzgzz*uzz) ricciyz=t1+t2 c here are the assignments for the z-z component of the 3-ricci t1=-5.d-1*dexgzz*dxuxx+dezgxz*dxuxx-5.d-1*deygzz*dxuxy+dezgyz*dx & uxy+5.d-1*dezgzz*dxuxz-5.d-1*dexgzz*dyuxy+dezgxz*dyuxy-5.d-1*dey & gzz*dyuyy+dezgyz*dyuyy+5.d-1*dezgzz*dyuyz-5.d-1*dexgzz*dzuxz+dez & gxz*dzuxz-5.d-1*deygzz*dzuyz+dezgyz*dzuyz+5.d-1*dezgzz*dzuzz-5.d & -1*d2xxgzz*uxx+d2xzgxz*uxx-d2xygzz*uxy+d2xzgyz*uxy t2=d2yzgxz*uxy+d2zzgxz*uxz-2.5d-1*(dezgxx*uxx+(dexgyz-deygxz+dez & gxy)*uxy+dexgzz*uxz)**2+2.5d-1*(dexgxx*uxx+2.d0*dexgxy*uxy-deygx & x*uxy+2.d0*dexgxz*uxz-dezgxx*uxz)*(-(dexgzz*uxx)+2.d0*dezgxz*uxx & -deygzz*uxy+2.d0*dezgyz*uxy+dezgzz*uxz)+5.d-1*(-(dezgxx*dzuxx)-( & dexgyz-deygxz+dezgxy)*dzuxy-dexgzz*dzuxz-d2zzgxx*uxx-(d2xzgyz-d2 & yzgxz+d2zzgxy)*uxy-d2xzgzz*uxz)-5.d-1*d2yygzz*uyy+d2yzgyz*uyy+d2 & zzgyz*uyz-5.d-1*((-dexgyz+deygxz+dezgxy)*uxx+dezgyy*uxy+deygzz*u & xz)*(dezgxx*uxy+(dexgyz-deygxz+dezgxy)*uyy+dexgzz*uyz)-2.5d-1*(( & -dexgyz+deygxz+dezgxy)*uxy+dezgyy*uyy+deygzz*uyz)**2 t3=2.5d-1*(-(dexgzz*uxx)+2.d0*dezgxz*uxx-deygzz*uxy+2.d0*dezgyz* & uxy+dezgzz*uxz)*(deygxx*uxy+dexgyy*uyy+(dexgyz+deygxz-dezgxy)*uy & z)+2.5d-1*(deygxx*uxx+dexgyy*uxy+(dexgyz+deygxz-dezgxy)*uxz)*(-( & dexgzz*uxy)+2.d0*dezgxz*uxy-deygzz*uyy+2.d0*dezgyz*uyy+dezgzz*uy & z)+2.5d-1*(-(dexgyy*uxy)+2.d0*deygxy*uxy+deygyy*uyy+2.d0*deygyz* & uyz-dezgyy*uyz)*(-(dexgzz*uxy)+2.d0*dezgxz*uxy-deygzz*uyy+2.d0*d & ezgyz*uyy+dezgzz*uyz)+5.d-1*((dexgyz-deygxz-dezgxy)*dzuxy-dezgyy & *dzuyy-deygzz*dzuyz+(d2xzgyz-d2yzgxz-d2zzgxy)*uxy-d2zzgyy*uyy-d2 & yzgzz*uyz)+5.d-1*d2zzgzz*uzz+2.5d-1*(dexgzz*uxx-2.d0*dezgxz*uxx+ & deygzz*uxy-2.d0*dezgyz*uxy-dezgzz*uxz)*(dezgxx*uxz+dexgyz*uyz-de & ygxz*uyz+dezgxy*uyz+dexgzz*uzz)+2.5d-1*(dexgzz*uxy-2.d0*dezgxz*u & xy+deygzz*uyy-2.d0*dezgyz*uyy-dezgzz*uyz)*(-(dexgyz*uxz)+deygxz* & uxz+dezgxy*uxz+dezgyy*uyz+deygzz*uzz)+2.5d-1*(dezgxx*uxx+(dexgyz & -deygxz+dezgxy)*uxy+dexgzz*uxz)*(-(dexgzz*uxz)+2.d0*dezgxz*uxz-d & eygzz*uyz+2.d0*dezgyz*uyz+dezgzz*uzz)+2.5d-1*((-dexgyz+deygxz+de & zgxy)*uxy+dezgyy*uyy+deygzz*uyz)*(-(dexgzz*uxz)+2.d0*dezgxz*uxz- & deygzz*uyz+2.d0*dezgyz*uyz+dezgzz*uzz)+5.d-1*(dexgzz*dzuxz-2.d0* & dezgxz*dzuxz+deygzz*dzuyz-2.d0*dezgyz*dzuyz-dezgzz*dzuzz+d2xzgzz & *uxz-2.d0*d2zzgxz*uxz+d2yzgzz*uyz-2.d0*d2zzgyz*uyz-d2zzgzz*uzz) riccizz=t1+t2+t3