The PUDB Python debugger provides a colorful ncurses-based "text-GUI" debugger that can be called by the local Sage python interpreter to debug Python scripts that interface with built-in Sage functions and types. In this tutorial, we provide a small sample script that interfaces with Sage and detail howto debug with PUDB in this case. The separate non-math-related tutorial for PUDB located at this link is a primary reference here, though we only reproduce the highlights of that full introduction to PUDB in this tutorial. We also cover installation of the PUDB module with the separate local Python that comes bundled with Sage in the next section, which is somewhat different than installing the module with a package manager such as `apt`

. Another video tutorial giving a concise overview of the PUDB debugger is found at this link.

The actual installation of the PUDB module in Python is straightforward once you know a couple of tricks about how the Sage shell can be used to install new packages in its own local chroot-like environment. In particular, assuming you have the OpenSSL development libraries installed on your system (try `apt-get install libssl-dev`

on a Debian variant Linux box), we can issue the following commands in sequence to get Sage's local Python to recognize the PUDB add-on:

```
$ sage -i openssl
$ sage -f python2
$ sage -sh
(sage-sh) pip install --upgrade pip
(sage-sh) pip install pudb
(sage-sh) exit
```

This method also works to install other Python add-on modules into Sage's Python, for example, such as the useful `memory_profiler`

module that is not yet installed in Sage by default. To verify that the install of PUDB is working correctly, consider any fairly simple Python script `test-script.py`

and then issue the following command:

```
$ sage -python -m pudb test-script.py
```

This should bring up the colorful vim-like ncurses interface to our new GUI debugger for Sage. To exit this screen, type **q** and navigate to the `< Quit >`

link to leave the application (more on these shortcuts in the next sections).

Another convenience when using the long sage `-python`

command is to add an alias to your local `~/.bashrc`

file using the next commands.

```
$ echo "alias sage-debug='sage -python -m pudb'" >> ~/.bashrc
$ source ~/.bashrc
```

Then PUDB can be run on our sample test script from above by typing `sage-debug test-script.py`

from within your terminal. Additional information on customizing PUDB with themes, hacks, including other add-ons to PUDB itself (such as a custom "stringifier" for displaying variables) are detailed in the following blog posts:

SageMathCloud has PUDB available after a small amount of configuration. To setup PUDB for use in SMC large terminal application, first open up a new terminal and run the following:

```
$ pip install pudb
```

Once this operation is complete, it should be possible to start up PUDB by typing the command `pudb myscript.py`

(we notice that we can also call `import pudb`

from within the Python source file itself). Note that the full sage command `sage -python -m pudb myscript.py`

suggested in the previous install notes **does not** work in the SMC terminal.

```
from sage.all import Integer, golden_ratio, var, fibonacci, binomial, sgn
def AssertVType(obj, vtype, excpt = ValueError):
if not isinstance(obj, vtype):
raise excpt('Object should be of type ' + vtype)
return False
##
return True
##
def Assert(cond, excpt, emsg = ""):
if not cond:
raise excpt(emsg)
return False
##
return True
##
def IsInteger(iobj):
return isinstance(iobj, int) or iobj.is_integer()
##
class PhiPoly(object):
def __init__(self, a = Integer(0), b = Integer(0)):
self._a = a
self._b = b
##
@property
def a(self):
return self._a
##
@a.setter
def a(self, a):
self._a = a
##
@property
def b(self):
return self._b
##
@b.setter
def b(self, b):
self._b = b
##
def __str__(self):
str_sign_func = lambda i, pos, neg, zero: \
pos if sgn(i) == 1 else neg if sgn(i) == -1 else zero
rstr = "%s * phi %s %s" % (self.a, str_sign_func(self.b, "+", "-", ""), \
str_sign_func(self.b, self.b, abs(self.b), ""))
return rstr
##
def __float__(self):
return n(self.a * golden_ratio + self.b)
def __list__(self):
return [self.a, self.b]
##
def __tuple__(self):
return (self.a, self.b)
##
def __repr__(self):
return str([self.a, self.b])
##
def __radd__(self, rhs):
return self.__add__(rhs)
##
def __add__(self, rhs):
rop = PhiPoly(a = self.a, b = self.b)
if IsInteger(rhs):
rop.b += rhs
else:
rop.a += rhs.a
rop.b += rhs.b
return rop
##
def __pow__(self, p):
Assert(IsInteger(p), ValueError, "Exponent must be an integer")
coeffs = [ [binomial(p, r) * (self.a ** r) * (self.b ** (p-r)), r] \
for r in range(0, p + 1)]
return PhiPoly.fromcoeffs(coeffs)
##
def __xor__(self, p):
return self.__pow__(p)
##
def is_integer(self):
return self.a == 0
##
@classmethod
def fromexpr(ppcls, expr, phi = golden_ratio):
x = var('x')
coeffs = expr.subs(phi == x).coefficients()
return ppcls.fromcoeffs(coeffs)
##
@classmethod
def fromcoeffs(ppcls, coeffs):
from_pow_func = lambda (coeff, pexp): \
ppcls(a = coeff * fibonacci(pexp), b = coeff * fibonacci(pexp - 1))
pow2phipolylst = map(from_pow_func, coeffs)
return sum(pow2phipolylst)
##
## PhiPoly
```

```
from PhiPoly import *
if __name__ == "__main__":
mpowupper = 12
constant_term = 2
ppoly_pows_list = []
for m in range(1, mpowupper + 1):
phipoly_expr = (golden_ratio + constant_term) ** m
phipoly = PhiPoly.fromexpr(phipoly_expr)
ppoly_pows_list += [(m, phipoly)]
print "[m = %2d]: (phi + %s) ** %2d == %s" % \
(m, constant_term, m, phipoly)
##
print ppoly_pows_list
##
```

The `PhiPoly`

class represents a polynomial in the `golden_ratio`

constant with integer coefficients.
Since we know the identity that `golden_ratio ** p = fibonacci(p) * golden_ratio + fibonacci(p-1)`

whenever `p >= 1`

is integer-valued, we can always reduce the polynomial expansions of this type as an integer linear combination of the `golden_ratio`

. The main runner function `pudb-main-runner.py`

is loop-based (as opposed to using, say, `map`

to obtain the same result) to demonstrate the debugging features of PUDB when interfacing with code using built-in Sage types and functions. It computes a list of the first `12`

mth powers of `golden_ratio + 2`

and stores these resulting linear combinations of the `golden_ratio`

as tuples of the form `(m, (golden_ratio+2) ** m)`

. Notice that at the top of the `PhiPoly.py`

file we are particularly selective about which built-in Sage types and functions we allow in our program (instead of, say, including them all with `from sage.all import *`

). The reason for this is that the variables list in the PUDB interface is far to long for the purposes of instruction when all of the built-in Sage machinery is imported at once.

To enter the PUDB debugger, we issue the following command at our terminal (or use the alias `sage-debug`

defined above):

```
$ sage -python -m pudb pudb-main-runner.py # Local Sage install
$ pudb pudb-main-runner.py # SMC Sage install
```

Once inside PUDB, we can tweak several initial settings in the preferences menu with the shortcut `<CTRL+p>`

. The image below shows an example of setting the theme for PUDB and turning on line numbers in the display of our working code. The preferences dialog also appears at runtime the first time PUDB is started.

The execution of PUDB is easy enough to follow if you are familiar with another debugger application (otherwise see the user-friendly links cited in the first section of this tutorial). The following list provides a reference of keyboard shortcuts for some of the most useful and common operations available in PUDB:

**n:**Execute next command**s:**Step into a function**c:**Continue execution**b:**Set a breakpoint on the current line**e:**Show the traceback from a thrown exception**q:**Opens dialog to either quit or to restart the running program**o:**Show the original console / standard output screen**m:**Open a module in a different file**!:**Go to the Python command line subwindow at the bottom of the screen**?:**Display the help dialog which includes a complete listing of shortcut commands**<SHIFT+V>:**Switch context to the variables subwindow on the right of the screen**<SHIFT+B>:**Switch context to the breakpoints subwindow on the right of the screen**<CTRL+X>:**Toggle contexts between the lines of code and the Python command line

Once focused on a line of code in the PUDB display, pressing **b** will set a breakpoint at that line where execution stops after continuing with the **c** shortcut. By navigating to the Breakpoints subwindow by pressing **<SHIFT+B>**, we can press enter on each of the set breakpoints to configure additional properties about them. One particularly useful option is to setup a variable condition under which the breakpoint applies. The next image shows one example of configuring such a condition.

The user can use the shortcut **!** to shift into the built-in Python command line at the bottom of the screen. Once in the command line, any Python command may be run, including those that involve initialized variables in the local context of the program. The next terminal screenshot provides an example.

One last matter of configuration in PUDB to cover is how to setup the way that individual variables are displayed in the right-hand-side subwindow. In particular, the default behavior is not nearly as informative in our case as having the Variables window display the corresponding string representations of the local objects. Once we press **<SHIFT+V>** and use the arrow keys to focus on an individual variable, pressing **<ENTER>** brings up the configuration dialog shown in the next screenshot (try viewing the `str()`

representations and expanding the view on a `list`

object).

The next screenshot image provides a view into the new displays for the `PhiPoly`

and Sage `Expression`

objects after we change the `phipoly`

, `phipoly_expr`

, and `ppoly_pows_list`

variables using the previous dialog. Note that in order for these variables to appear in the Variables subwindow, we need to have started the execution of the program into the loop by repeatedly pressing **n**, or by pressing **c** in conjunction with set breakpoints in the source.

- Interactively tracing execution of a command
- Handling errors and exceptions in Sage with
`pdb`

- Step-by-step debugging with IPython
- pdb — The Python Debugger documentation
- The pykdedebugger utility