Multiprocessing of Tensors is not working for Macintosh. show(version()) #MacBook Pro dual core i5, hyper-threaded. Should support 4 ply multiprocessing.
%display latex # LaTeX rendering turned on
Parallelism().set('tensor',4) #Only works if set to one.
Parallelism().set('linbox',4)
Parallelism()
M = Manifold(4, 'M')
MChart = M.open_subset('MChart')
Chart.<u,v,x,y> = MChart.chart(r'u:(-oo,+oo) v:(-oo,+oo) x:(-oo,+oo)
y:(-oo,+oo)')
gT= MChart.riemannian_metric('gT')
var('du','dv','dx','dy')
dsds= -du*dv+dx*dx+dy*dy+e^(x*y)*du*du
dsds=dsds.expand()
g00=dsds.coefficient(du,2)
g11=dsds.coefficient(dv,2)
g22=dsds.coefficient(dx,2)
g33=dsds.coefficient(dy,2)
g01=dsds.coefficient(du*dv,1)
g01=g01/2
g10=g01
gT[0,0] = g00.factor() #du du
gT[1,1] = g11.factor() #dv dv
gT[2,2] = g22.factor() #dx dx
gT[3,3] = g33.factor() #dy dy
gT[0,1] = g01.factor() #du dv
%display latex
show(gT.display())
Metric=gT
Nabla = Metric.connection()
#https://arxiv.org/pdf/gr-qc/0309008.pdf equation 54
%time
Bach=(Nabla(Metric.cotton()).up(Metric,3)['^u_aub'])+((Metric.schouten().up(Metric))*(Metric.weyl().down(Metric)))['^uv_aubv']
show(Bach.display())
%time
Bach=Nabla(Nabla(Metric.weyl().down(Metric))).up(Metric,4).up(Metric,5)['^bd_abcd']-(1/2)*((Metric.ricci().up(Metric))*(Metric.weyl().down(Metric)))['^bd_abcd']
show(Bach.display())
%time
Bach=-(Metric.schouten()*(Metric.weyl().down(Metric))).up(Metric,1).up(Metric,2)['^cd_cdab']
- Nabla(Nabla(Metric.schouten())).up(Metric,3)['^c_cab'] +
Nabla(Nabla(Metric.schouten())).up(Metric,3)['^c_abc']
Cotton=-Nabla(Metric.ricci())['_i[jk]']-1/(2*(4-1))*Nabla(Metric.ricci_scalar()*Metric)['_i[kj]']
%time
Bach=(Nabla(Cotton).up(Metric,3)['^u_aub'])+((Metric.schouten().up(Metric))*(Metric.weyl().down(Metric)))['^uv_aubv']
show(Bach.display())
--
You received this message because you are subscribed to the Google Groups
"sage-support" group.
To unsubscribe from this group and stop receiving emails from it, send an email
to sage-support+unsubscr...@googlegroups.com.
To view this discussion on the web visit
https://groups.google.com/d/msgid/sage-support/3720394c-2f01-47f5-a838-56946d0adda3%40googlegroups.com.
BachTensor.ipynb
Description: Binary data
