By D M Brink; G R Satchler

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**Example text**

By Total Degree than Reverse Lexicographic First we compare the total degrees. If they are equal, then we begin from the junior variable xn : if its degree in s is larger than in t (nn > mn ), then s < t; if it is smaller (nn < mn ), then s > t; if nn = mn , we compare the degrees of the previous variable xn−1 ; and so on, that is, this is (within some total degree) the reverse lexicographic order with respect to the reverse list of variables. 3 Reduction of Polynomials Let’s fix some admissible monomial order.

An immediate assignment to the pattern fac[n] (for a specific n, namely, the value of the actual argument with which the function fac was called). What happens when we call fac[10]? If the function was never calculated with this argument, then this definition for an arbitrary argument will be used. The right-hand side with 10 substituted for n will be calculated, namely, an immediate assignment fac[10] = · · ·. Its right-hand side is calculated (it is the factorial of 10), and it is remembered as the value of fac[10].

In[81] := Table[x + i, {i, 0, 4}]/. 7 Parallelization Now most computers have multi-core processors. The function Parallelize tries to calculate its argument faster by starting several Mathematica kernels and ordering them to calculate parts of the expression and then collecting these parts together. In[82] := Parallelize[Table[$KernelID, {n, 0, 7}]] Out[82] = {4, 4, 3, 3, 2, 2, 1, 1} ($KernelID is the number of the kernel in which a particular list element has been evaluated). In addition to Table, it can handle Map[ f , {.

### Angular momentum by D M Brink; G R Satchler

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