Checking whether a real polynomial of 21 variables is non-negative

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Let $P$ be a real polynomial with $n$ variables.

Question 1: Is there a SageMath function deciding whether $P$ is non-negative?

By non-negative I mean that for all $v \in \mathbb{R}^n$ we have $P(v) \ge 0$.

Question 2: Is it workable for $n = 21$?

Here is the poIynomial I am interested in (where the variables are $x_{s,i}$, with $s = 1,2,3$ and $i = 1,2,\dots, \ell$):
$$P=\sum_{k=1}^{\ell} \frac{1}{n_k} \prod_{s=1}^3 (\sum_{i,j} n_{i,j}^k x_{s,i} x_{s,j})$$ where $n_i$ and $n_{i,j}^k$ are non-negative integers given by the following lists (here $\ell = 7$):
[for those interested it corresponds to a fusion ring, see here]

dim=[1,5,5,5,6,7,7]
M=[
[[1,0,0,0,0,0,0],[0,1,0,0,0,0,0],[0,0,1,0,0,0,0],[0,0,0,1,0,0,0],[0,0,0,0,1,0,0],[0,0,0,0,0,1,0],[0,0,0,0,0,0,1]],[[0,1,0,0,0,0,0],[1,1,0,1,0,1,1],[0,0,1,0,1,1,1],[0,1,0,0,1,1,1],[0,0,1,1,1,1,1],[0,1,1,1,1,1,1],[0,1,1,1,1,1,1]],[[0,0,1,0,0,0,0],[0,0,1,0,1,1,1],[1,1,1,0,0,1,1],[0,0,0,1,1,1,1],[0,1,0,1,1,1,1],[0,1,1,1,1,1,1],[0,1,1,1,1,1,1]],[[0,0,0,1,0,0,0],[0,1,0,0,1,1,1],[0,0,0,1,1,1,1],[1,0,1,1,0,1,1],[0,1,1,0,1,1,1],[0,1,1,1,1,1,1],[0,1,1,1,1,1,1]],[[0,0,0,0,1,0,0],[0,0,1,1,1,1,1],[0,1,0,1,1,1,1],[0,1,1,0,1,1,1],[1,1,1,1,1,1,1],[0,1,1,1,1,2,1],[0,1,1,1,1,1,2]],[[0,0,0,0,0,1,0],[0,1,1,1,1,1,1],[0,1,1,1,1,1,1],[0,1,1,1,1,1,1],[0,1,1,1,1,2,1],[1,1,1,1,2,1,2],[0,1,1,1,1,2,2]],[[0,0,0,0,0,0,1],[0,1,1,1,1,1,1],[0,1,1,1,1,1,1],[0,1,1,1,1,1,1],[0,1,1,1,1,1,2],[0,1,1,1,1,2,2],[1,1,1,1,2,2,1]]
]

Here is the code generating the polynomial:

cpdef ExplicitPolynomial(list dim,list M):
    cdef int l,i,j,k,s
    l=len(dim)
    return sum([prod([sum([sum([M[i][j][k]*var('x_%d' % int(l*s+i))*var('x_%d' % int(l*s+j)) for i in range(l)]) for j in range(l)]) for s in range(3)])/dim[k] for k in range(l)])

Here is the polynomial explicitly:

sage: ExplicitPolynomial(dim,M)
(x_0^2 + x_1^2 + x_2^2 + x_3^2 + x_4^2 + x_5^2 + x_6^2)*(x_10^2 + x_11^2 + x_12^2 + x_13^2 + x_7^2 + x_8^2 + x_9^2)*(x_14^2 + x_15^2 + x_16^2 + x_17^2 + x_18^2 + x_19^2 + x_20^2) + 1/5*(2*x_0*x_1 + x_1^2 + x_2^2 + 2*x_1*x_3 + 2*x_2*x_4 + 2*x_3*x_4 + x_4^2 + 2*x_1*x_5 + 2*x_2*x_5 + 2*x_3*x_5 + 2*x_4*x_5 + x_5^2 + 2*x_1*x_6 + 2*x_2*x_6 + 2*x_3*x_6 + 2*x_4*x_6 + 2*x_5*x_6 + x_6^2)*(2*x_10*x_11 + x_11^2 + 2*x_10*x_12 + 2*x_11*x_12 + x_12^2 + 2*x_10*x_13 + 2*x_11*x_13 + 2*x_12*x_13 + x_13^2 + 2*x_10*x_8 + 2*x_12*x_8 + 2*x_13*x_8 + 2*x_7*x_8 + x_8^2 + 2*x_11*x_9 + 2*x_12*x_9 + 2*x_13*x_9 + x_9^2)*(2*x_14*x_15 + x_15^2 + x_16^2 + 2*x_15*x_17 + 2*x_16*x_18 + 2*x_17*x_18 + x_18^2 + 2*x_15*x_19 + 2*x_16*x_19 + 2*x_17*x_19 + 2*x_18*x_19 + x_19^2 + 2*x_15*x_20 + 2*x_16*x_20 + 2*x_17*x_20 + 2*x_18*x_20 + 2*x_19*x_20 + x_20^2) + 1/7*(x_1^2 + 2*x_1*x_2 + x_2^2 + 2*x_1*x_3 + 2*x_2*x_3 + x_3^2 + 2*x_1*x_4 + 2*x_2*x_4 + 2*x_3*x_4 + x_4^2 + 2*x_0*x_5 + 2*x_1*x_5 + 2*x_2*x_5 + 2*x_3*x_5 + 4*x_4*x_5 + x_5^2 + 2*x_1*x_6 + 2*x_2*x_6 + 2*x_3*x_6 + 2*x_4*x_6 + 4*x_5*x_6 + 2*x_6^2)*(x_10^2 + 2*x_10*x_11 + x_11^2 + 2*x_10*x_12 + 4*x_11*x_12 + x_12^2 + 2*x_10*x_13 + 2*x_11*x_13 + 4*x_12*x_13 + 2*x_13^2 + 2*x_12*x_7 + 2*x_10*x_8 + 2*x_11*x_8 + 2*x_12*x_8 + 2*x_13*x_8 + x_8^2 + 2*x_10*x_9 + 2*x_11*x_9 + 2*x_12*x_9 + 2*x_13*x_9 + 2*x_8*x_9 + x_9^2)*(x_15^2 + 2*x_15*x_16 + x_16^2 + 2*x_15*x_17 + 2*x_16*x_17 + x_17^2 + 2*x_15*x_18 + 2*x_16*x_18 + 2*x_17*x_18 + x_18^2 + 2*x_14*x_19 + 2*x_15*x_19 + 2*x_16*x_19 + 2*x_17*x_19 + 4*x_18*x_19 + x_19^2 + 2*x_15*x_20 + 2*x_16*x_20 + 2*x_17*x_20 + 2*x_18*x_20 + 4*x_19*x_20 + 2*x_20^2) + 1/7*(x_1^2 + 2*x_1*x_2 + x_2^2 + 2*x_1*x_3 + 2*x_2*x_3 + x_3^2 + 2*x_1*x_4 + 2*x_2*x_4 + 2*x_3*x_4 + x_4^2 + 2*x_1*x_5 + 2*x_2*x_5 + 2*x_3*x_5 + 2*x_4*x_5 + 2*x_5^2 + 2*x_0*x_6 + 2*x_1*x_6 + 2*x_2*x_6 + 2*x_3*x_6 + 4*x_4*x_6 + 4*x_5*x_6 + x_6^2)*(x_10^2 + 2*x_10*x_11 + x_11^2 + 2*x_10*x_12 + 2*x_11*x_12 + 2*x_12^2 + 2*x_10*x_13 + 4*x_11*x_13 + 4*x_12*x_13 + x_13^2 + 2*x_13*x_7 + 2*x_10*x_8 + 2*x_11*x_8 + 2*x_12*x_8 + 2*x_13*x_8 + x_8^2 + 2*x_10*x_9 + 2*x_11*x_9 + 2*x_12*x_9 + 2*x_13*x_9 + 2*x_8*x_9 + x_9^2)*(x_15^2 + 2*x_15*x_16 + x_16^2 + 2*x_15*x_17 + 2*x_16*x_17 + x_17^2 + 2*x_15*x_18 + 2*x_16*x_18 + 2*x_17*x_18 + x_18^2 + 2*x_15*x_19 + 2*x_16*x_19 + 2*x_17*x_19 + 2*x_18*x_19 + 2*x_19^2 + 2*x_14*x_20 + 2*x_15*x_20 + 2*x_16*x_20 + 2*x_17*x_20 + 4*x_18*x_20 + 4*x_19*x_20 + x_20^2) + 1/5*(x_1^2 + 2*x_0*x_3 + 2*x_2*x_3 + x_3^2 + 2*x_1*x_4 + 2*x_2*x_4 + x_4^2 + 2*x_1*x_5 + 2*x_2*x_5 + 2*x_3*x_5 + 2*x_4*x_5 + x_5^2 + 2*x_1*x_6 + 2*x_2*x_6 + 2*x_3*x_6 + 2*x_4*x_6 + 2*x_5*x_6 + x_6^2)*(x_10^2 + x_11^2 + 2*x_10*x_12 + 2*x_11*x_12 + x_12^2 + 2*x_10*x_13 + 2*x_11*x_13 + 2*x_12*x_13 + x_13^2 + 2*x_10*x_7 + 2*x_11*x_8 + 2*x_12*x_8 + 2*x_13*x_8 + x_8^2 + 2*x_10*x_9 + 2*x_11*x_9 + 2*x_12*x_9 + 2*x_13*x_9)*(x_15^2 + 2*x_14*x_17 + 2*x_16*x_17 + x_17^2 + 2*x_15*x_18 + 2*x_16*x_18 + x_18^2 + 2*x_15*x_19 + 2*x_16*x_19 + 2*x_17*x_19 + 2*x_18*x_19 + x_19^2 + 2*x_15*x_20 + 2*x_16*x_20 + 2*x_17*x_20 + 2*x_18*x_20 + 2*x_19*x_20 + x_20^2) + 1/5*(x_10^2 + 2*x_10*x_11 + x_11^2 + 2*x_10*x_12 + 2*x_11*x_12 + x_12^2 + 2*x_10*x_13 + 2*x_11*x_13 + 2*x_12*x_13 + x_13^2 + 2*x_11*x_8 + 2*x_12*x_8 + 2*x_13*x_8 + 2*x_12*x_9 + 2*x_13*x_9 + 2*x_7*x_9 + 2*x_8*x_9 + x_9^2)*(2*x_14*x_16 + 2*x_15*x_16 + x_16^2 + x_17^2 + 2*x_15*x_18 + 2*x_17*x_18 + x_18^2 + 2*x_15*x_19 + 2*x_16*x_19 + 2*x_17*x_19 + 2*x_18*x_19 + x_19^2 + 2*x_15*x_20 + 2*x_16*x_20 + 2*x_17*x_20 + 2*x_18*x_20 + 2*x_19*x_20 + x_20^2)*(2*x_0*x_2 + 2*x_1*x_2 + x_2^2 + x_3^2 + 2*x_1*x_4 + 2*x_3*x_4 + x_4^2 + 2*x_1*x_5 + 2*x_2*x_5 + 2*x_3*x_5 + 2*x_4*x_5 + x_5^2 + 2*x_1*x_6 + 2*x_2*x_6 + 2*x_3*x_6 + 2*x_4*x_6 + 2*x_5*x_6 + x_6^2) + 1/6*(2*x_10*x_11 + x_11^2 + 2*x_10*x_12 + 2*x_11*x_12 + 2*x_12^2 + 2*x_10*x_13 + 2*x_11*x_13 + 2*x_12*x_13 + 2*x_13^2 + 2*x_11*x_7 + 2*x_10*x_8 + 2*x_11*x_8 + 2*x_12*x_8 + 2*x_13*x_8 + 2*x_10*x_9 + 2*x_11*x_9 + 2*x_12*x_9 + 2*x_13*x_9 + 2*x_8*x_9)*(2*x_15*x_16 + 2*x_15*x_17 + 2*x_16*x_17 + 2*x_14*x_18 + 2*x_15*x_18 + 2*x_16*x_18 + 2*x_17*x_18 + x_18^2 + 2*x_15*x_19 + 2*x_16*x_19 + 2*x_17*x_19 + 2*x_18*x_19 + 2*x_19^2 + 2*x_15*x_20 + 2*x_16*x_20 + 2*x_17*x_20 + 2*x_18*x_20 + 2*x_19*x_20 + 2*x_20^2)*(2*x_1*x_2 + 2*x_1*x_3 + 2*x_2*x_3 + 2*x_0*x_4 + 2*x_1*x_4 + 2*x_2*x_4 + 2*x_3*x_4 + x_4^2 + 2*x_1*x_5 + 2*x_2*x_5 + 2*x_3*x_5 + 2*x_4*x_5 + 2*x_5^2 + 2*x_1*x_6 + 2*x_2*x_6 + 2*x_3*x_6 + 2*x_4*x_6 + 2*x_5*x_6 + 2*x_6^2)