By A A Sokolov
Booklet by means of Sokolov, A. A.
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In[43] := a = 2 ∗ x ∗ y/(3 ∗ z) 2xy Out[43] = 3z In[44] := FullForm[a] Out[44]//FullForm = Times[Rational[2, 3], x, y, Power[z, −1]] Nevertheless, the functions Numerator and Denominator work as expected. In[45] := {Numerator[a], Denominator[a]} Out[45] = {2xy, 3z} In[46] := Clear[a] We have already handled lists many times. A list appears to be just the function List with arguments—elements of the list. In[47] := FullForm[{x, y, z}] Out[47]//FullForm = List[x, y, z] Any Mathematica command can be written as a function with arguments (sometimes, it can also be written in some other way).
If the user has not given such a substitution, the left /. will do nothing, and the right one will replace opt1 by the default value of this option. In[41] := Options[ f ] = {opt1−>1, opt2−>2} Out[41] = {opt1 → 1, opt2 → 2} In[42] := f [x , opts ] := g[x, opt1/. {opts}/. Options[ f ], opt2/. {opts}/. 8 Attributes A function can have attributes which affect simplification of expressions with this function. , Plus and Times have this attribute). In[49] := Attributes[ f ] = {Flat} Out[49] = {Flat} In[50] := f [x, f [y, z], u] Out[50] = f [x, y, z, u] The attribute Orderless means that the function is symmetric in all arguments, and Mathematica may interchange them at will (Plus and Times have also this attribute).
5], f [3/2], f [x/2]}/. f [x ? 25, , f 4 2 But this method is not very general. It checks a condition depending on a single variable. The operator /; can be applied to a pattern (or its part). ” The condition in it can depend on several arbitrary variables. In[60] := s = {fac[0]−>1, fac[n Integer/; n > 0]−>n ∗ fac[n − 1]} Out[60] = {fac[0] → 1, fac[n Integer/; n > 0] → n fac[−1 + n]} In[61] := {fac[10], fac[−10]}//. s Out[61] = {3628800, fac[−10]} Internally, this operator is the function Condition.