Legend Position in Maxima Plots

Here’s something I just learned and want to share with others and record for my use the next time I need to do this and have already forgotten!

The position and appearance of the figure legend in Maxima plots drawn with plot() (by setting gnuplot_preamble) and in draw() (by setting user_preamble),  can be manipulated to any of the gnuplot options listed here.

Here are some examples:




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logabs, logarc: How to make integrate() return what you expect


In the back of my calculus book there is a table of famous integrals.  Here’s integral number 21 in that table:


From Maxima integrate(), I get



What’s going on?

Both forms give a workable antiderivative for the original integrand:


Furthermore, we believe that both forms are correct because of this helpful identity for hyperbolic sine:

 {\rm asinh}(z)=\ln(z+\sqrt{1+z^2}).  

Turns out (thanks to a Barton Willis for pointing me in the right direction) there’s a variable logarc that we can set to make Maxima return the logarithmic form instead of hyperbolic sine:


I haven’t yet encountered cases where this would be a bad idea in general, but I’ll update this if I do.


In the first week of my differential equations course, we study methods of direct integration and separation of variables.  I like to emphasize that the absolute values can lend an extra degree of generality to solutions with antiderivatives of the form

\int \frac{1}{u}\;du = \ln |u|+ C.   

As an example, for the initial value problem

 y' = \frac{x}{1-x^2}    ,  y(0)=1    ,

it is convenient for treating all possible initial conditions (x \ne \pm 1) in one step to use the antiderivative

y = -\frac{1}{2} \ln | 1-x^2 | + C.   

However, Maxima omits the absolute values.


For this case, we could consider only the needed interval -1<x<1, but still…

Turns out we can set the Maxima variable logabs to make integrate() include absolute values in cases like this:


But then later in the course, I saw that logabs also impacts the Ordinary Differential Equation solver ode2().  I encountered an example for which Maxima, in particular solve() applied to expressions involving absolute value,  didn’t do what I wanted with logabs:true

For the logistic equation

\frac{dP}{dt} = kP\left ( 1-\frac{P}{P_c} \right )    ,  P(0)=P_0   

we expect that by separating variables we can obtain the solution

P(t) = \frac{P_0 P_c}{(P_c-P_0)e^{-kt}+ P_0}.   

Here’s what happens when we use ode2() with and without logabs:true:





Student Projects in Maxima Vol 1, Num 4: ODE Systems for Epidemiological Models

Student Projects in Maxima is an online project to disseminate work by undergraduate students using Maxima to reproduce published results in the sciences and social sciences.

Volume 1, Number 4 (2017) is devoted to Systems of Ordinary Differential Equations for SIR models in epidemiology.



Emenheiser, Anna, Virus Dynamics and Drug Therapy

Radermacher, Erin, A Model of the 2014 Ebola Outbreak

Rafai, Sagar, Analysis of Communicable Disease Models


Student Projects in Maxima Vol 1, Num 3: ODE Systems for Interacting Population Models

Student Projects in Maxima is an online project to disseminate work by undergraduate students using Maxima to reproduce published results in the sciences and social sciences.

Volume 1, Number 3 (2017) is devoted to Systems of Ordinary Differential Equations for non-chaotic predator-prey and other interacting population models



Bhullar, Abhjeet,  Lions, Wildebeest and Zebras

Goodin Aunic, Parasitic Nematodes in Grouse

DeFore, Brandon, Breeding Suppression in Predator-Prey

Jerez, Emilio, Predator-Prey with Hawk and Dove Tactics

Bontrager, Eric, Predator-Prey with Prey Switching

Beatty, Ethan, Analysis of Logistic Growth Models

Rice, Gabriel, Pharmacokinetic Mechanism of Ethanol-Benzodiazepine Interactions

Kay, Ian, Radioactive Isotopes

Wile, Jessica, Ebola in Western Lowlands Gorillas

Bailey, John,  Kinetic Modeling for Interconnected Reactions

Piet, Joe, Elephant and Tree Population Dynamics

Kim, Judy, A Model for West Nile Virus

Kamalaldin, Kamalaldin, Infected Prey in Polluted Environment

Park, Kayla, Ratio-Dependent Predator Prey Model

Lundy, Liam, Predator Prey in a Single Species with Cannibalism

Orwin, Michael, Interactions of Model Neurons

Schultz, Pete, Photosynthetic Oscillations

Wadhwa, Raoul, Dynamics in an Inflammation Model

Del Olmo, Ricardo, Population Growth and Technological Change

Network Model of Cocaine Traffic in Spain Edited

Kill, Sean, A Logistic Model with Varying Carrying Capacity 

McFadden-Keesling, Sophia,  Predator Prey Model with a Refuge

Samson, Tanush,  Lions and Wildebeest Model

Morales, Zach,  Game Theory Models

Student Projects in Maxima Vol 1, Num 1: Systems of ODEs and Chaos

Student Projects in Maxima is an online project to disseminate work by undergraduate students using Maxima to reproduce published results in the sciences and social sciences.

Volume 1, Number 1 (2017) is devoted to Chaotic Systems of Ordinary Differential Equations.


Thornburg, Eric, Simple Pendulum and Chaos

Bhimani, Kevin, Chaos in a 3-Species Food Chain

York, Lily, A Lattice Model of Epilepsy

Andrews, Steven, 3D Chaotic Model

Rutledge, Tim,  A Model of Neuronal Bursting



Student Projects in Maxima Vol 1, Num 2: Systems of ODEs with Impulses and Switching Functions

Student Projects in Maxima is an online project to disseminate work by undergraduate students using Maxima to reproduce published results in the sciences and social sciences.

Volume 1, Number 2 (2017) is devoted to Systems of Ordinary Differential Equations with time-dependent forcing terms, non-continuous inputs, and forcing terms that require knowledge of a past state of the system.


Chumley, Qynce, An Office Heating and Cooling Model

Williams, Nick, Baseball Pitch Dynamics

Rizzolo, Skylar, BAC Model for alcohol consumption

Barth, Eric, A model of bladder bacteria proliferation in prostate disease

Barth, Eric, A Model of Pulse Vaccination Strategyi


A pause() function for Maxima

In MATLAB, pause interrupts execution of a loop until the user strikes a key, and pause(<n>) pauses for <n> seconds before resuming execution.
Here’s my attempt at a pause() function for Maxima that works in a similar way to MATLAB.  It uses Maxima’s read() to stop everything and wait for user input, and it uses the lisp function sleep to stop for a fixed number of seconds.
**note that a lisp function
     (function-name argument)
can be called inside Maxima as
I’m not happy that in order to resume after the pause, the user needs to enter a valid character (space or nothing results in an error) followed by CTRL-SHIFT.  I hope to either figure something else out or even better hear suggestions from other Maxima users!
    if tsecs=0 then
       read("Execution Paused...enter any character then CTRL-ENTER")
        disp(sconcat("paused for ", tsecs," seconds")),
call this either as
or, for a three second pause

Multiple plots in a single Maxima figure

In MATLAB, I often use the subplot() command to make an array of multiple plots in a single figure.

In Maxima, we can achieve that by generating each of the subplots using gr2d(),  and then putting them all together with a call to draw() or wxdraw():


There’s an optional columns argument — the subplots are drawn row-wise in an array with the specified number of columns:


And of course all this works for 3d plots using gr3d():


My Two Favorite wxMaxima Keyboard Shortcuts

Alt Up to recall previous commands to the current input line

In Matlab and RStudio, I love the ability to recall a command I’ve already typed using the up arrow key.  Today I discovered alt up arrow to do the same in wxMaxima!

Ctrl Shift K  for autocompletion and function template

This is really the best implementation of function templates I’ve seen in an IDE:

In wxMaxima, if I type inte  and then ctrl shift k, I see a popup menu of possible completions.  Choosing integrate results in an input cell template that looks like:


Pressing Tab highlights <expr> and I simply type the expression to be integrated.   A second press of Tab key highlights <x> and I type the name of the independent variable.

But wait, there’s more:  this works for any currently defined function—including user defined functions.

**UPDATE**  In the newer versions  of wxMaxima (since v15.10)   Ctrl+Tab and Shift+Ctrl+Tab also trigger autocompletion.