By Andrey Grozin
The fundamentals of desktop algebra and the language of Mathematica are defined. This name will lead towards an knowing of Mathematica that permits the reader to unravel difficulties in physics, arithmetic, and chemistry. Mathematica is the main normal method for doing mathematical calculations via computing device, together with symbolic and numeric calculations and photos. it really is utilized in physics and different branches of technological know-how, in arithmetic, schooling and plenty of different components. Many very important ends up in physics may by no means be acquired with no broad use of laptop algebra.
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Example text
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.