Pages created and updated by Terry Sturtevant Date Posted: May 12, 2017

Maxima Logic Tutorial

Maxima is a GPL program, available for Windows, Mac, and Linux. It is a computer algebra system (CAS) like Maple or Mathematica.
There are various tutorials out there on how to use Maxima; this one is designed to focus on its use for digital circuit analysis; i.e. lots of use of Boolean algebra.

Sample Digital Logic Circuit

Here is a simple circuit:
Prime Number Indentifier Circuit

It gives us the following boolean Sum-Of-Products (SOP) equation :
prime = a₃ a₂ a₁ + a₃ a₂ a₀ + a₂ a₁ a₀ + a₂ a₁ a₀

A computer algebra system can be very useful for analyzing circuits like this.

1. Opening Maxima

2. Entering Equations

3. Saving a Session

4. Quitting Maxima

5. Loading a Previous Session

6. Redefining Variables

7. Checking all Possible Input Combinations

8. Links

---

1. Opening Maxima:
   • At a command prompt, type maxima

     bash-4.1$ maxima
     Maxima 5.25.1 http://maxima.sourceforge.net
     using Lisp CLISP 2.49 (2010-07-07)
     Distributed under the GNU Public License. See the file COPYING.
     Dedicated to the memory of William Schelter.
     The function bug_report() provides bug reporting information.
     (%i1) 
     

     
     
     
2. Entering Equations:
   • To enter a boolean equation,
     At the prompt, type in the the command as shown:
     

     (%i1)  (not a3) and (not a2 and a1); 
     (%o1)                    (not a3) and (not a2) and a1
     
     

     
     This is the first term in the equation; we can type in each term separately to keep them all straight.
     We could also assign each term to its own variable, like this:
     

     (%i1) t1: (not a3) and (not a2 and a1); 
     (%o1)                    (not a3) and (not a2) and a1
     
     

     
     
     The remaining terms can be entered similarly:
     

     (%i2) (not a3) and (a2 and a0); 
     (%o2)                       (not a3) and a2 and a0
     (%i3) (not a2) and (a1 and a0); 
     (%o3)                       (not a2) and a1 and a0
     (%i4) (not a1) and (a2 and a0); 
     (%o4)                       (not a1) and a2 and a0
     

     
     If we wanted to use assignments for each it would look like this:
     

     (%i2) t2: (not a3) and (a2 and a0); 
     (%o2)                       (not a3) and a2 and a0
     (%i3) t3: (not a2) and (a1 and a0); 
     (%o3)                       (not a2) and a1 and a0
     (%i4) t4: (not a1) and (a2 and a0); 
     (%o4)                       (not a1) and a2 and a0
     

     
     
     We can combine the individual terms easily by their results numbers, like this:
     

     (%i5)  %o1 or %o2 or %o3 or %o4;
     (%o5) ((not a3) and (not a2) and a1) or ((not a3) and a2 and a0)
                             or ((not a2) and a1 and a0) or ((not a1) and a2 and a0)
     

     
     This ability to recall previous results is very useful, and we'll use it a lot.
     
     For instance, now %o5 represents the complete expression for the function.
     
     If we used assignments for the terms, we would combine them like this:
     

     (%i5)  t1 or t2 or t3 or t4;
     (%o5) ((not a3) and (not a2) and a1) or ((not a3) and a2 and a0)
                             or ((not a2) and a1 and a0) or ((not a1) and a2 and a0)
     

     
     
   • You can substitute in specific component values:
     

     (%i6) %o5, a0=false, a1=false,a2=false, a3=false;
     (%o6)                                false
     

     
     
     
3. Saving a Session:
   • Saving a session: (The "all" means to save all variables from this session.)
     

     (%i6) %o5, a0=false, a1=false,a2=false, a3=false;
     (%o6)                                false
     (%i7) save("test",all);
     (%o7)                       /home/terry/maxima/test
     
     

     
     
     
4. Quitting Maxima:
   • Quitting maxima:
     

     (%o7)                       /home/terry/maxima/test
     (%i8) quit();
     
     

     
     
     
5. Loading a Previous Session:
   • It's nice to be able to pick up where you left off, so you can keep developing an analysis over time.
     To loading a previous session:
     

     bash-4.1$ maxima
     Maxima 5.25.1 http://maxima.sourceforge.net
     using Lisp CLISP 2.49 (2010-07-07)
     Distributed under the GNU Public License. See the file COPYING.
     Dedicated to the memory of William Schelter.
     The function bug_report() provides bug reporting information.
     (%i1) load("test");
     (%o7)                                test
     

     Notice that the statement number has jumped ahead; all of the statements from the previous session have been included in this one.
     
     
   • Previous statements can be recalled:
     

     (%i1) load("test");
     (%o7)                                test
     (%i8) %o5;
     (%o8) ((not a3) and (not a2) and a1) or ((not a3) and a2 and a0)
                             or ((not a2) and a1 and a0) or ((not a1) and a2 and a0)
     

     
     
     
6. Redefining Variables:
   • Variables can be changed:
     

     (%i9) %o5, a0=true, a1=false,a2=false, a3=false;
     (%o9)                                false
     (%i10) %o5, a0=false, a1=true,a2=false, a3=false;
     (%o10)                                true
     

     
     
     We can continue on, substituting all of the input variable combinations.
7. Checking all Possible Input Combinations:
   • Loops can be used to check all possible input combinations to an equation:
     

     (%i11) for a0 in [false,true]
     do for a1 in [false,true]
     do for a2 in [false,true]
     do for a3 in [false,true]
     do (t1:(not a3) and (not a2 and a1),
     t2:(not a3) and (a2 and a0),
     t3:(not a2) and (a1 and a0),
     t4:(not a1) and (a2 and a0),
     result:t1 or t2 or t3 or t4,
     display(a0,a1,a2,a3,result));
      
     

     
     This sets up four nested loops, (one for each variable), to check all of the combinations. Note: When multiple statements are performed inside loops, the statments are separated by commas, not semicolons, and the entire set is enclosed in parentheses.
     The output looks like this:

                                       a0 = false
     
                                       a1 = false
     
                                       a2 = false
     
                                       a3 = false
     
                                     result = false
     
                                       a0 = false
     
                                       a1 = false
     
                                       a2 = false
     
                                        a3 = true
     
                                     result = false
     
                                       a0 = false
     
                                       a1 = false
     
                                        a2 = true
     
                                       a3 = false
     
                                     result = false
     
                                       a0 = false
     
                                       a1 = false
     
                                        a2 = true
     
                                        a3 = true
     
                                     result = false
     
                                       a0 = false
     
                                        a1 = true
     
                                       a2 = false
     
                                       a3 = false
     
                                      result = true
     
                                       a0 = false
     
                                        a1 = true
     
                                       a2 = false
     
                                        a3 = true
     
                                     result = false
     
                                       a0 = false
     
                                        a1 = true
     
                                        a2 = true
     
                                       a3 = false
     
                                     result = false
     
                                       a0 = false
     
                                        a1 = true
     
                                        a2 = true
     
                                        a3 = true
     
                                     result = false
     
                                        a0 = true
     
                                       a1 = false
     
                                       a2 = false
     
                                       a3 = false
     
                                     result = false
     
                                        a0 = true
     
                                       a1 = false
     
                                       a2 = false
     
                                        a3 = true
     
                                     result = false
     
                                        a0 = true
     
                                       a1 = false
     
                                        a2 = true
     
                                       a3 = false
     
                                      result = true
     
                                        a0 = true
     
                                       a1 = false
     
                                        a2 = true
     
                                        a3 = true
     
                                      result = true
     
                                        a0 = true
     
                                        a1 = true
     
                                       a2 = false
     
                                       a3 = false
     
                                      result = true
     
                                        a0 = true
     
                                        a1 = true
     
                                       a2 = false
     
                                        a3 = true
     
                                      result = true
     
                                        a0 = true
     
                                        a1 = true
     
                                        a2 = true
     
                                       a3 = false
     
                                      result = true
     
                                        a0 = true
     
                                        a1 = true
     
                                        a2 = true
     
                                        a3 = true
     
                                     result = false
     
     (%o11)                              done
     

8. Links:
   • Maxima Manual [HTML; ]
     The official documentation
   • Maxima Overview [HTML; Burkhard Bunk]
     A good shorthand reference to commands and syntax
   • Maxima tutorial [HTML; Boris Gaertner]
     The "First Steps" and "Getting Started" sections are very useful introductions to the basics.

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