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I often hit the "Detected access to protected memory ..." failure from maxima. In some cases it seems to go into a loop whereupon I receive the same message hundreds of times. I know which sage worksheet cell is failing, but cannot find what it is about that cell which causes the failure, because maxima does not tell me. Is it possible to set up the worksheet so that this error is trapped and triggers a stack trace?

I often hit the "Detected access to protected memory ..." failure from maxima. In some cases it seems to go into a loop whereupon I receive the same message hundreds of times. I know which sage worksheet cell is failing, but cannot find what it is about that cell which causes the failure, because maxima does not tell me. Is it possible to set up the worksheet so that this error is trapped and triggers a stack trace? trace?

I often hit the "Detected access to protected memory ..." failure from maxima. In some cases it seems to go into a loop whereupon I receive the same message hundreds of times. I know which sage worksheet cell is failing, but cannot find what it is about that cell which causes the failure, because maxima does not tell me. Is it possible to set up the worksheet so that this error is trapped and triggers a stack trace?trace in sage/python?

I often hit the "Detected access to protected memory ..." failure from maxima. In some cases it seems to go into a loop whereupon I receive the same message hundreds of times. I know which sage worksheet cell is failing, but cannot find what it is about that cell which causes the failure, because maxima does not tell me. Is it possible to set up the worksheet so that this error is trapped and triggers a stack trace in sage/python?

sage: version()
'SageMath version 7.6, Release Date: 2017-03-25'
sage: Parallelism().set(nproc=2)
sage: var('rho12,rho13,rho23', domain='real')
sage: assume(rho12>0, rho13>0, rho23>0)
sage: var('r12,r13,r23', domain='real')
sage: var('m1 m2 m3', domain='real')
sage: var('mu12,mu13,mu23', domain='real')
sage: ####
sage: #assume(m1>0, m2>0, m3>0) # !! This is a Maxima killer! (even though physically required)
sage: m1=1; m2=1; m3=1
sage: # !! With 'assume' above and with ANY m1,m2,m3 in SR, we seg-fault and core-dump when computing the connection.
sage: ####
sage: mu12 = (m1m2)/(m1+m2); mu23 = (m2m3)/(m2+m3); mu13 = (m1m3)/(m1+m3)
sage: # Contravariant metric tensor, per Turbiner et al., arXiv:1611.08157.
sage: Ginv = matrix([[2/mu12rho12, 1/m1(rho12+rho13-rho23), 1/m2(rho12+rho23-rho13)],\
... [1/m1(rho12+rho13-rho23), 2/mu13rho13, 1/m3(rho13+rho23-rho12)],\
... [1/m2(rho12+rho23-rho13), 1/m3(rho13+rho23-rho12), 2/mu23rho23]])
sage: G = Ginv.inverse();
sage: # Begin manifold creation
sage: M = Manifold(13,'R^3',field='real',start_index=1)
sage: U = M.open_subset('U')
sage: Rho.<rho12,rho13,rho23> = U.chart();
sage: Rho.add_restrictions([rho12>0, rho13>0, rho23>0])
sage: Rho.add_restrictions([sqrt(rho23)<sqrt(rho12)+sqrt(rho13),\ <br=""> ... sqrt(rho13)<sqrt(rho12)+sqrt(rho23), sqrt(rho12)<sqrt(rho13)+sqrt(rho23)])="" <br=""> ...
sage: g = M.riemannian_metric('g');
sage: g[:] = G[:].simplify_full()
sage: ginv = g.inverse()
sage: ### This will seg-fault and core-dump if ANY m1,m2,m3 are in SR, and the 'assume' statement active.
sage: nabla = g.connection()
sage: # Turbiner calculates the Ricci scalar.
sage: # Attempting to do so here causes seg fault if all m1,m2,m3=1!
sage: # (Is this because of singularities at all boundaries of rho-space? Regardless, code should *never crash.)
sage: Ric_g = g.ricci_scalar()

I often hit the "Detected access to protected memory ..." failure from maxima. In some cases it seems to go into a loop whereupon I receive the same message hundreds of times. I know which sage worksheet cell is failing, but cannot find what it is about that cell which causes the failure, because maxima does not tell me. Is it possible to set up the worksheet so that this error is trapped and triggers a stack trace in sage/python?

sage: version() 
 
'SageMath version 7.6, Release Date: 2017-03-25' 
 
sage: Parallelism().set(nproc=2) 
 
sage: var('rho12,rho13,rho23', domain='real') 
 
sage: assume(rho12>0, rho13>0, rho23>0) 
 
sage: var('r12,r13,r23', domain='real') 
 
sage: var('m1 m2 m3', domain='real') 
 
sage: var('mu12,mu13,mu23', domain='real') 
 
sage: #### 
 
sage: #assume(m1>0, m2>0, m3>0)    # !! This is a Maxima killer! (even though physically required) 
 
sage: m1=1; m2=1; m3=1 
 
sage: # !! With 'assume' above and with ANY m1,m2,m3 in SR, we seg-fault and core-dump when computing the connection. 
 
sage: #### 
 
sage: mu12 = (m1m2)/(m1+m2); (m1*m2)/(m1+m2); mu23 = (m2m3)/(m2+m3); (m2*m3)/(m2+m3); mu13 = (m1m3)/(m1+m3) 
(m1*m3)/(m1+m3)  
sage: # Contravariant metric tensor, per Turbiner et al., arXiv:1611.08157. 
 
sage: Ginv = matrix([[2/mu12rho12, 1/m1(rho12+rho13-rho23), 1/m2(rho12+rho23-rho13)],\ 
matrix([[2/mu12*rho12, 1/m1*(rho12+rho13-rho23), 1/m2*(rho12+rho23-rho13)],\  
...           [1/m1(rho12+rho13-rho23), 2/mu13rho13, 1/m3(rho13+rho23-rho12)],\ 
[1/m1*(rho12+rho13-rho23), 2/mu13*rho13, 1/m3*(rho13+rho23-rho12)],\  
...           [1/m2(rho12+rho23-rho13), 1/m3(rho13+rho23-rho12), 2/mu23rho23]]) 
[1/m2*(rho12+rho23-rho13), 1/m3*(rho13+rho23-rho12), 2/mu23*rho23]])  
sage: G = Ginv.inverse(); 
 
sage: # Begin manifold creation 
 
sage: M = Manifold(13,'R^3',field='real',start_index=1) 
Manifold(1*3,'R^3',field='real',start_index=1)  
sage: U = M.open_subset('U') 
 
sage: Rho.<rho12,rho13,rho23> = U.chart(); 
 
sage: Rho.add_restrictions([rho12>0, rho13>0, rho23>0]) 
 
sage: Rho.add_restrictions([sqrt(rho23)<sqrt(rho12)+sqrt(rho13),\ <br="">
 ...       sqrt(rho13)<sqrt(rho12)+sqrt(rho23), sqrt(rho12)<sqrt(rho13)+sqrt(rho23)])="" <br="">
sqrt(rho12)<sqrt(rho13)+sqrt(rho23)])  
... 
 
sage: g = M.riemannian_metric('g'); 
 
sage: g[:] = G[:].simplify_full() 
 
sage: ginv = g.inverse() 
 
sage: ### This will seg-fault and core-dump if ANY m1,m2,m3 are in SR, and the 'assume' statement active. 
 
sage: nabla = g.connection() 
 
sage: # Turbiner calculates the Ricci scalar. 
 
sage: # Attempting to do so here causes seg fault if all m1,m2,m3=1! 
 
sage: #  (Is this because of singularities at all boundaries of rho-space? Regardless, code should *never *never* crash.) 
 
sage: Ric_g = g.ricci_scalar()
g.ricci_scalar()

I often hit the "Detected access to protected memory ..." failure from maxima. In some cases it seems to go into a loop whereupon I receive the same message hundreds of times. I know which sage worksheet cell is failing, but cannot find what it is about that cell which causes the failure, because maxima does not tell me. Is it possible to set up the worksheet so that this error is trapped and triggers a stack trace in sage/python?

sage: version()  
'SageMath version 7.6, Release Date: 2017-03-25'  
sage: Parallelism().set(nproc=2)  
sage: var('rho12,rho13,rho23', domain='real')  
sage: assume(rho12>0, rho13>0, rho23>0)  
sage: var('r12,r13,r23', domain='real')  
sage: var('m1 m2 m3', domain='real')  
sage: var('mu12,mu13,mu23', domain='real')  
sage: ####  
sage: #assume(m1>0, m2>0, m3>0)    # !! This is a Maxima killer! (even though physically required)  
sage: m1=1; m2=1; m3=1     
sage: # !! With 'assume' above and with ANY m1,m2,m3 in SR, we seg-fault and core-dump when computing the connection.  
sage: ####  
sage: mu12 = (m1*m2)/(m1+m2); mu23 = (m2*m3)/(m2+m3); mu13 = (m1*m3)/(m1+m3)  
sage: # Contravariant metric tensor, per Turbiner et al., arXiv:1611.08157.  
sage: Ginv = matrix([[2/mu12*rho12, 1/m1*(rho12+rho13-rho23), 1/m2*(rho12+rho23-rho13)],\  
...           [1/m1*(rho12+rho13-rho23), 2/mu13*rho13, 1/m3*(rho13+rho23-rho12)],\  
...           [1/m2*(rho12+rho23-rho13), 1/m3*(rho13+rho23-rho12), 2/mu23*rho23]])  
sage: G = Ginv.inverse();  
sage: # Begin manifold creation  
sage: M = Manifold(1*3,'R^3',field='real',start_index=1)  
sage: U = M.open_subset('U')  
sage: Rho.<rho12,rho13,rho23> = U.chart();  
sage: Rho.add_restrictions([rho12>0, rho13>0, rho23>0])  
sage: Rho.add_restrictions([sqrt(rho23)<sqrt(rho12)+sqrt(rho13),\  
...       sqrt(rho13)<sqrt(rho12)+sqrt(rho23), sqrt(rho12)<sqrt(rho13)+sqrt(rho23)])  
...  
sage: g = M.riemannian_metric('g');  
sage: g[:] = G[:].simplify_full()  
sage: ginv = g.inverse()  
 sage: ### This will seg-fault and core-dump if ANY m1,m2,m3 are in SR, and the 'assume' statement active.  
sage: nabla = g.connection()  g.connection()

sage: # Turbiner calculates the Ricci scalar.  
sage: # Attempting to do so here causes seg fault if all m1,m2,m3=1!   
sage: #  (Is this because of singularities at all boundaries of rho-space? Regardless, code should *never* crash.)  
sage: Ric_g = g.ricci_scalar()

I often hit the "Detected access to protected memory ..." failure from maxima. In some cases it seems to go into a loop whereupon I receive the same message hundreds of times. I know which sage worksheet cell is failing, but cannot find what it is about that cell which causes the failure, because maxima does not tell me. Is it possible to set up the worksheet so that this error is trapped and triggers a stack trace in sage/python?

sage: version()  
'SageMath version 7.6, Release Date: 2017-03-25'  
sage: Parallelism().set(nproc=2)  
sage: var('rho12,rho13,rho23', domain='real')  
sage: assume(rho12>0, rho13>0, rho23>0)  
sage: var('r12,r13,r23', domain='real')  
sage: var('m1 m2 m3', domain='real')  
sage: var('mu12,mu13,mu23', domain='real')  domain='real')

sage: ####  
sage: #assume(m1>0, m2>0, m3>0)   # !! This is a Maxima killer! killer (even though physically required)  required)! 
sage: m1=1; m2=1; m3=1     
sage: # !! With 'assume' above and with ANY m1,m2,m3 in SR, we seg-fault and core-dump when computing the connection.  
sage: ####  
 sage: mu12 = (m1*m2)/(m1+m2); mu23 = (m2*m3)/(m2+m3); mu13 = (m1*m3)/(m1+m3)  
sage: # Contravariant metric tensor, per Turbiner et al., arXiv:1611.08157.  
sage: Ginv = matrix([[2/mu12*rho12, 1/m1*(rho12+rho13-rho23), 1/m2*(rho12+rho23-rho13)],\  
...           [1/m1*(rho12+rho13-rho23), 2/mu13*rho13, 1/m3*(rho13+rho23-rho12)],\  
...           [1/m2*(rho12+rho23-rho13), 1/m3*(rho13+rho23-rho12), 2/mu23*rho23]])  
sage: G = Ginv.inverse();  
sage: # Begin manifold creation  
sage: M = Manifold(1*3,'R^3',field='real',start_index=1)  
sage: U = M.open_subset('U')  
sage: Rho.<rho12,rho13,rho23> = U.chart();  
sage: Rho.add_restrictions([rho12>0, rho13>0, rho23>0])  
sage: Rho.add_restrictions([sqrt(rho23)<sqrt(rho12)+sqrt(rho13),\  
...       sqrt(rho13)<sqrt(rho12)+sqrt(rho23), sqrt(rho12)<sqrt(rho13)+sqrt(rho23)])  
...  
sage: g = M.riemannian_metric('g');  
sage: g[:] = G[:].simplify_full()  
sage: ginv = g.inverse()  

sage: ### This will seg-fault and core-dump if ANY m1,m2,m3 are in SR, and the 'assume' statement active.  
sage: nabla = g.connection()

sage: # Turbiner calculates the Ricci scalar.  
sage: # ### Attempting to do so here causes seg fault if all m1,m2,m3=1!   
sage: #  (Is this because of singularities at all boundaries of rho-space? Regardless, 
sage: # (Regardless, code should *never* crash.)  
sage: Ric_g = g.ricci_scalar()