SystemException["MemoryAllocationFailure"] Uncaught SystemException returned to top level from NSolve

Question

Bug introduced in 10.0.0 and fixed in 11.0.0

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When trying to solve 8 equations in 8 unknowns, I get SystemException["MemoryAllocationFailure"]. I am not sure if I am doing something wrong, or is this something that should not really happen. Here is the code:

f={w1 + w2 + w3 + w4 == 2, w1*x1 + w2*x2 + w3*x3 + w4*x4 == 0, 
 w1*x1^2 + w2*x2^2 + w3*x3^2 + w4*x4^2 == 2/3, 
 w1*x1^3 + w2*x2^3 + w3*x3^3 + w4*x4^3 == 0, 
 w1*x1^4 + w2*x2^4 + w3*x3^4 + w4*x4^4 == 2/5, 
 w1*x1^5 + w2*x2^5 + w3*x3^5 + w4*x4^5 == 0, 
 w1*x1^6 + w2*x2^6 + w3*x3^6 + w4*x4^6 == 2/7, 
 w1*x1^7 + w2*x2^7 + w3*x3^7 + w4*x4^7 == 0};

NSolve[f, {w1, w2, w3, w4, x1, x2, x3, x4}]

This is using Mathematica 10.4, on Windows 7, 16 GB RAM, 64 bits.

This happens only with NSolve. Using Solve does not generate this error, which is even more strange.

question is: Should this error be generated? Is this a user error, or a problem in NSolve?

Answer 1

This is a bug, for a possible workaround switch to a non-default method, for example

 f = {w1 + w2 + w3 + w4 == 2, w1*x1 + w2*x2 + w3*x3 + w4*x4 == 0, 
 w1*x1^2 + w2*x2^2 + w3*x3^2 + w4*x4^2 == 2/3, 
 w1*x1^3 + w2*x2^3 + w3*x3^3 + w4*x4^3 == 0, 
 w1*x1^4 + w2*x2^4 + w3*x3^4 + w4*x4^4 == 2/5, 
 w1*x1^5 + w2*x2^5 + w3*x3^5 + w4*x4^5 == 0, 
 w1*x1^6 + w2*x2^6 + w3*x3^6 + w4*x4^6 == 2/7, 
 w1*x1^7 + w2*x2^7 + w3*x3^7 + w4*x4^7 == 0};

NSolve[f, {w1, w2, w3, w4, x1, x2, x3, x4}, Method -> "EndomorphismMatrix"]