MAT 305:
Mathematical
Computing
John Perry
Decision-
making
Boolean
statements
Having said all
that.. .
Summary
MAT 305: Mathematical Computing
Lecture 7: Decision-making in Sage
John Perry
University of Southern Mississippi
Fall 2009
Prepare for your exams
Study with the several resources on Docsity
Earn points to download
Earn points by helping other students or get them with a premium plan
Guidelines and tips
Prepare for your exams
Study with the several resources on Docsity
Earn points to download
Earn points by helping other students or get them with a premium plan
Community
Ask the community
Ask the community for help and clear up your study doubts
University Rankings
Discover the best universities in your country according to Docsity users
Free resources
Our save-the-student-ebooks!
Download our free guides on studying techniques, anxiety management strategies, and thesis advice from Docsity tutors
Decision Making in Mathematical Computing: Boolean Statements and Pseudocode - Prof. John , Study notes of Mathematics
A lecture note from mat 305: mathematical computing at the university of southern mississippi, fall 2009. It covers decision making in sage, including boolean statements, piecewise functions, and characterizing concavity. The lecture includes pseudocode examples and sage code implementation.
Typology: Study notes
2009/2010
1 / 54
This page cannot be seen from the preview
Don't miss anything!
Related documents
Partial preview of the text
Download Decision Making in Mathematical Computing: Boolean Statements and Pseudocode - Prof. John and more Study notes Mathematics in PDF only on Docsity!
Mathematical Computing John Perry
Decision- making Boolean statements Having said all that... Summary
MAT 305: Mathematical Computing
Lecture 7: Decision-making in Sage
John Perry
University of Southern Mississippi
Fall 2009
Mathematical Computing John Perry
Decision- making Boolean statements Having said all that... Summary
Outline
1 Decision-making
2 Boolean statements
3 Having said all that...
4 Summary
You should be in worksheet mode to repeat the examples.
Mathematical Computing John Perry
Decision- making Boolean statements Having said all that... Summary
Decision making?
A function may have to act in different ways, depending on the arguments.
Mathematical Computing John Perry
Decision- making Boolean statements Having said all that... Summary
Decision making?
A function may have to act in different ways, depending on the arguments.
Example
Piecewise functions:
f (x) =
f 1 (x) , x ∈
a 0 , a 1
f 2 (x)^ , x ∈
a 1 , a 2
Mathematical Computing John Perry
Decision- making Boolean statements Having said all that... Summary
if statements
if (condition): if-statement if-statement
... non-if statement
where
- condition: expression that evaluates to True or False
- (^) condition True? statement1, statement2, etc. performed
- (^) control passes finally to non-if statement
- condition False? statement1, statement2,... skipped
- control passes immediately to non-if statement
Mathematical Computing John Perry
Decision- making Boolean statements Having said all that... Summary
Example
sage: f = cos(x) sage: ddf = diff(f,2) sage: if (ddf(3pi/4) > 0): print 'concave up at', 3pi/ concave up at 3/4*pi
Mathematical Computing John Perry
Decision- making Boolean statements Having said all that... Summary
if-elif-else statements
if (condition1): if-statement
... elif (condition2): elif1-statement ... elif (condition3): elif2-statement ... ... else: else-statement ... non-if statement
where
- (^) statement block selected by condition
Mathematical Computing John Perry
Decision- making Boolean statements Having said all that... Summary
Pseudocode for if-elif-else
if condition if-statement
... else if condition elseif1-statement ... else if condition elseif2-statement ... ... else condition else-statement ...
Notice:
- (^) indentation
- no parentheses, colons
- else if, not elif
Mathematical Computing John Perry
Decision- making Boolean statements Having said all that... Summary
Example: concavity
Write a Sage function that tests whether a function f is concave up or down at a given point. Have it return the string ’concave up’, ’concave down’, or ’neither’.
Different choices =⇒ need to make a decision! =⇒ if
Mathematical Computing John Perry
Decision- making Boolean statements Having said all that... Summary
Example: concavity
Write a Sage function that tests whether a function f is concave up or down at a given point. Have it return the string ’concave up’, ’concave down’, or ’neither’.
Different choices =⇒ need to make a decision! =⇒ if
Start with pseudocode.
- What inputs are needed?
- (^) What output is expected?
- What has to be done?
- step by step
- Divide et impera! Divide and conquer!
Mathematical Computing John Perry
Decision- making Boolean statements Having said all that... Summary
Pseudocode for Example
algorithm check_concavity inputs a ∈ R f (x), a twice-differentiable function at x = a outputs
Mathematical Computing John Perry
Decision- making Boolean statements Having said all that... Summary
Pseudocode for Example
algorithm check_concavity inputs a ∈ R f (x), a twice-differentiable function at x = a outputs ’concave up’ if f is concave up at x = a ’concave down’ if f is concave down at x = a ’neither’ otherwise do
Mathematical Computing John Perry
Decision- making Boolean statements Having said all that... Summary
Try it!
sage: def check_concavity(a, f, x): ddf = diff(f, x, 2) if (ddf(x=a) > 0): return 'concave up' elif (ddf(x=a) < 0): return 'concave down' else: return 'neither'
Mathematical Computing John Perry
Decision- making Boolean statements Having said all that... Summary
Try it!
sage: def check_concavity(a, f, x): ddf = diff(f, x, 2) if (ddf(x=a) > 0): return 'concave up' elif (ddf(x=a) < 0): return 'concave down' else: return 'neither' sage: check_concavity(3*pi/4, cos(x), x) 'concave up' sage: check_concavity(pi/4, cos(x), x) 'concave down'