Jupyter¶
- Language-independent part of IPython
- Provides user interfaces (console, notebook)
- browser is UI for notebook server
- convenient cell editing (markdown / code) and evaluation
- notebook provides checkpoint functions in addition to create/save/load
- manage kernel (stop / restart / reconnect)
- Provides document generators (nbconvert)
- HTML, PDF, markdown, code-only, reStructuredText, LaTeX
Maxima¶
- Computer algebra == formal (ignoring content) manipulation of expressions
- Maxima covers undergraduate math, more or less
- Started in 1968 as part of Project MAC ("machine-aided cognition")
- Written in Lisp, now open source, active community
- Standard UI is ASCII-art console (useful, not pretty)
- I'd like to use Jupyter as a UI to compose math + text documents
Jupyter architecture¶
- Client (front end) separated from kernel (back end)
- Client and kernel talk through sockets provided by ZeroMQ
Jupyter architecture diagram¶
Messages¶
- Evaluation:
- Client reads user input, sends string to kernel, e.g.:
"diff(exp(a*x), x)" - Kernel parses input, calls Maxima function to evaluate, returns result in two forms:
- as the printed form of a Maxima expression
- as LaTeX
- Client chooses an appropriate form to display
- Client reads user input, sends string to kernel, e.g.:
- Plot output:
- Same as evaluation, but result is returned as SVG
- Maxima-initiated questions (
asksign):- Maxima wants to ask user about the sign of some expression
- Kernel sends input prompt to client
- Client prints prompt, reads user input, sends string to kernel
- Kernel passes user input to Maxima
- Maxima completes whatever it was working on before
Examples¶
Formulate an expression¶
In [1]:
foo : 'diff (1/(1 + sqrt(1 - a*x^2)), x, 2);
Out[1]:
\[\tag{${\it \%o}_{0}$}\frac{d^2}{d\,x^2}\,\left(\frac{1}{\sqrt{1-a\,x^2}+1}\right)\]
Evaluate¶
In [2]:
bar : ev (foo, nouns);
Out[2]:
\[\tag{${\it \%o}_{1}$}\frac{a}{\sqrt{1-a\,x^2}\,\left(\sqrt{1-a\,x^2}+1\right)^2}+\frac{a^2\,x^2}{\left(1-a\,x^2\right)^{\frac{3}{2}}\,\left(\sqrt{1-a\,x^2}+1\right)^2}+\frac{2\,a^2\,x^2}{\left(1-a\,x^2\right)\,\left(\sqrt{1-a\,x^2}+1\right)^3}\]
asksign prompt¶
In [3]:
integrate (x^k, x);
Out[3]:
\[\tag{${\it \%o}_{2}$}\log x\]
In [4]:
integrate (x^k, x);
Out[4]:
\[\tag{${\it \%o}_{3}$}\frac{x^{k+1}}{k+1}\]
Plot output¶
In [5]:
plot2d (subst (a = 1, bar), [x, -2, 2], [y, -10, 10], [svg_file, "maxplot.svg"],[plot_format, gnuplot])$
expt: undefined: 0 to a negative exponent. expt: undefined: 0 to a negative exponent. plot2d: expression evaluates to non-numeric value somewhere in plotting range. plot2d: some values will be clipped.
Minor features¶
- Code syntax highlighting
- In browser via CodeMirror
- In HTML output via Pygments
- Maxima-specific stuff is encapsulated in a function which only does some regex matching
Links¶
- Jupyter
- Maxima
- Maxima-Jupyter
- About the author