# Algebraic and geometric topology. Proceedings of symposia in by James R. Milgram PDF

By James R. Milgram

ISBN-10: 0821814338

ISBN-13: 9780821814338

**Read or Download Algebraic and geometric topology. Proceedings of symposia in pure mathematics, V.32, Part.2 PDF**

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**Additional resources for Algebraic and geometric topology. Proceedings of symposia in pure mathematics, V.32, Part.2**

**Example text**

In[3]:= f 2 1 Out[3]= In[4]:= Out[4]= x 1 x 1 x 2 g 2 1 x 1 x 2 3. Create a piecewise-defined function g x based on the following and then plot the function from 2 to 0. 3 Predicates and Boolean operations Predicates When working with data sets, you are often presented with the problem of extracting those data points that meet certain criteria. Similarly, when you write programs, oftentimes what to do next at any particular point in your program will depend upon some test or condition being met.

In[24]:= Out[24]= Part a b, 1 a The second part is b. In[25]:= Out[25]= Part a b, 2 b This should be clearer from looking at the internal representation of this expression. In[26]:= FullForm a b Out[26]//FullForm= Plus a, b So Part[a+b,1] is another way of asking for the first element of Plus[a,b], which is just a. In general Part[expr,n] gives the nth element of expr. 36 An Introduction to Programming with Mathematica It is worth noting that the 0th part is the Head of the expression. In[27]:= Out[27]= Part a b, 0 Plus As we stated above, atomic expressions have no parts.

Similarly, the expression 1+2 is represented internally by Plus[1,2]; its assignment tag is Plus. Occasionally you will encounter the Tag expression when you try to evaluate some incorrect input. In[23]:= 1 2 4 Set::write : Tag Plus in 1 Out[23]= 2 is Protected. More… 4 For user-defined functions, the tag basically refers to the name of the function. So, for example, the following assignment associates the rule 1 x x2 with the tag f. In[24]:= f x_ : 1 x x2 There can be many evaluation rules associated with one tag.

### Algebraic and geometric topology. Proceedings of symposia in pure mathematics, V.32, Part.2 by James R. Milgram

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