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Complaints of the assembly held in Pavia, April eight and nine, 1976

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1007/978-3-319-00894-3 4, © Springer International Publishing Switzerland 2014 27 28 4 Patterns and Substitutions And this one—when the argument is a list. By the way, note what happens when a list is being squared. In[8] := { f [{x, y}], f [x + y]}/. f [x List]−>x∧ 2 Out[8] = x2 , y2 , f [x + y] One more example. In[9] := a √ = Sqrt[x]/Sqrt[y] x Out[9] = √ y In[10] := a/. {Sqrt[x]−>u, Sqrt[y]−>v} u Out[10] = √ y Why hasn’t the second substitution triggered? In[11] := FullForm[a] Out[11]//FullForm = Times[Power[x, Rational[1, 2]], Power[y, Rational[−1, 2]]] a does not contain y1/2 , only y−1/2 ; therefore, the substitution y1/2 → v does not work.

X + m . ∗ y−> f [n, m] Out[54] = 2 + x + z And here is our method which always works. In[55] := a = {x + y + z + 2, 2 ∗ x + y + z + 2, 2 ∗ x + 3 ∗ y + z + 2, 2 ∗ x − y + z + 2, x + z + 2, z + 2} Out[55] = {2 + x + y + z, 2 + 2x + y + z, 2 + 2x + 3y + z, 2 + 2x − y + z, 2 + x + z, 2 + z} In[56] := s = {l . ∗ x + f [n , m ]−> f [n + l, m], l . ∗ y + f [n , m ]−> f [n, m + l]} Out[56] = { f [n , m ] + x l . → f [l + n, m], f [n , m ] + y l . → f [n, l + m]} In[57] := a + f [0, 0]//. 5 Conditions Substitutions which apply only when an arbitrary variable satisfies some condition are often needed.

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 , {. }] (or f [{. }] where f is a Listable function) and some other cases.