Maths Toolkit for the Casio fx-CG100

A calculator app in stock MicroPython 1.9.4 using the built-in casioplot. Three parts: an expression calculator, a computer algebra system, and 263 tools mapped to OCR B (MEI) A-Level Maths (H640) and Further Maths (H645).

tests smoke runtime license

Install

Copy to the root of the calculator's storage:

maths.py, casui.py, casutil.py
caslex.py, caseng.py, casrender.py, cascalc.py, caspoly.py
pure640.py, purecalc.py, stat640.py, mech640.py, proof.py,

vcplx.py, matrix.py, vectors.py, polyroots.py, series.py, hyper.py, polar.py, diffeq.py, fmmech.py, fmstat.py, numeric.py, algos.py, xpure.py, fpt.py

Do not copy casioplot.py. It is a PC stub; the calculator has the real module built in and the stub would shadow it. Also skip tests.py, stress.py, devlint.py and casioshot.py, which are desktop-only.

Run maths.py.

Keys

Menu
up / down	move, wraps
1-9	jump to entry
page up / down	move seven
first / last	`\	<- `and` ->\	`
OK, EXE	choose
back	up one level; leaves the app at the top

Expression entry
left / right	move caret
start / end of line	`\	<- `and` ->\	`
up	recall last entry
down	clear
DEL	delete back
back	clear; again on an empty line cancels
ALPHA	letters a-z
SHIFT	`sin^-1`, `cos^-1`, `tan^-1`, `ln`, `log`, `pi`, `=`, log to a base
CATALOG	`!`, `abs(`, `nCr(`, `nPr(`, `sec(`, `cosec(`, `cot(`, the hyperbolics and their inverses, `sech(`, `cosech(`, `coth(`, `logb(`, `pi`, `ans`, `,`

Settings

Both are on the home menu and last for the session; the calculator cannot write files.

Angle mode: DEGREES / RADIANS. Applies to all trig.

Working: SHOWN / HIDDEN. Output lines are one of three kinds. Answers always show. Working shows only in SHOWN. Caveats always show, in both modes: warnings, domain restrictions, verification results, statements that a tool did not finish. 1213 lines are marked working, 640 caveat. tests.py asserts for all 263 tools that HIDDEN output is a subset of SHOWN and never empty.

Modes

Calculate. Type an expression, see a 2D preview, press OK. ans holds the last result. Exact fractions are shown under the decimal. Non-finite results report "undefined" or "overflow".

Calculus & Algebra. Enter f(x) once, then apply operations without retyping: differentiate, integrate, simplify, expand, factorise, collect, partial fractions, solve, definite integral, evaluate, table, graph. The first seven are symbolic; the rest are numeric and use the angle mode.

A-Level Maths and Further Maths hold the section tools below.

Tools

A-Level Maths

Section	n	Tools
Pure: algebra & trig	16	Quadratic solver, Simultaneous eqns, Arithmetic seq/sum, Geometric seq/sum, Binomial expansion, Logarithms, Coord geometry, Circle, Trig tools, Solve a triangle, Arc length & sector, Inequalities, Surds & rationalising, Line meets circle, Sequences & behaviour, Proportion k x, k/x
Pure: functions & calculus	17	Composite fg(x), Inverse function, Domain & range, Modulus \	f(x)\	, Graph transformations, Parametric d/dx, Parametric -> Cartesian, Implicit d/dx, Integration by substitution, Separation of variables, Stationary points, Constant of integration, Volume of revolution, Mean value of f, Improper integral, Small-angle approx, Exact trig values
Statistics	21	Summary stats, Freq table mean/var, Discrete RV E,Var, Binomial B(n,p), Normal P(a<X<b), Inverse Normal, HT binomial prop, HT Normal mean z, PMCC + regression, Probability rules, Tree diagram + Bayes, Sampling methods, Stratified sample, Factorial / nCr, Box plot, Histogram, Cumulative freq, Scatter + regression, Venn diagram, Reduce to linear form, Distribution shape
Mechanics	15	SUVAT solver, Projectiles, Resultant of forces, Resolve a force, Equilibrium check, Newton II F=ma, Friction F=mu R, Friction horiz plane, Friction incline, Pulley (connected), Moments / reactions, Projectile: find the launch, Variable acceleration, Distance vs displacement, Connected particles
Proof	5	Induction: a sum, Induction: divisibility, Induction: M^n, Disprove by counterexample, Proof methods reference

Further Maths core

Section	n	Tools
Complex numbers	10	Arithmetic z, w, Modulus & argument, Polar / exp form, From polar (r,theta), Power z^n (De Moivre), nth roots of z, Quadratic complex roots, Argand plot, Loci in the Argand plane, de Moivre identities
Matrices	15	Enter A, Enter B, Show A and B, A + B, A - B, k A, A B, Transpose A, Determinant A, Inverse A, Solve A x = b, Eigenvalues 2x2, 2D transform builder, 3D transform builder, Invariant points/lines
Vectors & 3-D	13	Magnitude \	a\	, Dot product a.b, Angle between, Cross product a x b, Unit vector, Scalar projection, Parallel / perp test, Point to line dist, Equation of a line, Line meets plane, Point to plane dist, Angle between planes, Skew lines distance
Roots of polynomials	6	Vieta quadratic, Vieta cubic, Vieta quartic, Quadratic roots, Numeric roots (x), Shift roots by k
Series & Maclaurin	7	Sum of r, Sum of r^2, Sum of r^3, Maclaurin of f(x), Approx + error, Method of differences, Reference card
Hyperbolic functions	8	Evaluate sinh, Evaluate cosh, Evaluate tanh, All three at x, arsinh (inverse), arcosh (inverse), artanh (inverse), Reference card
Polar coordinates	5	(r,theta) -> (x,y), (x,y) -> (r,theta), Plot polar curve, Preset curves, Polar area
Differential equations	6	First-order linear (IF), Second-order const-coeff, Particular integral, Coupled dx/dt, dy/dt, SHM recogniser, Damping classifier

Further Maths options

Section	n	Tools
Mechanics (FM)	19	Momentum & impulse, Restitution, Oblique impact: wall, Oblique impact: spheres, Work/Energy/Power, Projectile path (cartesian), Projectile on an incline, Circular motion, Hookes law / EPE, Elastic equilibrium/energy, Centre of mass, COM by calculus, COM standard bodies, Slide or topple, Couple, Triangle of forces, Relative motion 2-D, Dimensional analysis, Units & conversion
Statistics (FM)	25	Discrete RV E/Var, Discrete uniform, Poisson pmf/cdf, Binomial pmf/cdf, Geometric dist, Continuous RV E/Var, cdf, median, quartiles, Mode of a pdf, Piecewise pdf, Normal P(a<X<b), Standardise z, Inverse Normal, aX+bY+c combination, nX vs X1+..+Xn, Normal prob plot, PMCC r + test, Spearman rs + test, Regression y=a+bx, Chi-squared GOF, Chi-sq association, CI for mean (z), t interval / paired, CI for proportion, z-test for mean, Simulation
Numerical Methods	20	Newton-Raphson, Fixed-point iteration, Fixed-point diagnosis, Relaxation iteration, Cobweb / staircase, Order of convergence, Bisection, Integration (trap/mid/Simp), Integration error table, Richardson extrapolation, Aitken acceleration, Numerical derivative, Derivative error table, Newton forward differences, Euler method, Error abs/relative, Error propagation, Error in f(x), Round to s.f., Chop vs round
Modelling w/ Algorithms	15	Bubble sort, Insertion sort, Quick sort, Bin: first-fit, Bin: first-fit decr, Graph: degrees/incidence, Dijkstra shortest, Prim MST, Kruskal MST, Max flow / min cut, Cut capacity, Critical path, Simplex (max, <=), Simplex 2-stage (>=, =), LP graph 2-D
Extra Pure	16	Recurrence relation, Recurrence 1st order, Recurrence 2nd order, Verify a recurrence, Recurrence behaviour, Sets and notation, Group theory, Subgroups & Lagrange, Group isomorphism, 2x2 Eigen/diag, Modular arithmetic, Partial derivatives, Surface stationary pts, Tangent plane / normal, Contours & sections, 3x3 Eigen/diag
Further Pure w/ Tech	24	Plot f(x) curve, De Moivre z^n, nth roots of z, Euler dy/dx=f(x), Runge-Kutta RK2/RK4, Tangent field, Verify a DE solution, Limit of f(x), Asymptotes incl oblique, Stationary pts & cusps, Family of curves, Envelope of a family, Arc length, gcd & lcm, Prime test, Prime factorise, Euler totient phi(n), a^b mod m, Modular inverse, Fermat & Wilson, Pythagorean triples, Pell x^2-n y^2=1, Linear Diophantine, Base -> bin/hex

Device facts

Measured on hardware with hwcheck.py, 2026-08-09.


Recursion ceiling	92 frames. `tests.py` caps at 38 as a margin.
`getkey()` idle	`None`, not 0, over 400 samples. `casui.readkey` treats anything outside `KEYCODES` as idle.
Screen	384 x 192
`math` members	24 of 43 present. `atan2` yes; `factorial`, `asinh`, `acosh`, `atanh`, `log2`, `trunc`, `degrees`, `radians`, `isnan`, `isinf`, `isfinite`, `copysign` no. `devlint.MATH_OK` is pinned to the measured set.
Section modules	All 19 fit in RAM at once. `casui` still loads on demand.
Key codes	`row*10 + col`, 48 readable. `[ON]` and `[AC]` have no code.
`getkey()` cost	About 0 ms held, 8.3 ms idle (TI-Planet). Polling loops need no delay.

Source: fx-CG100/fx-1AU GRAPH Software User's Guide v2.10, pages 141-143.

Screen layout is checked by casioshot.py, which renders any screen to PNG on a PC using the toolkit's own char_w metric and flags overruns of the 384 px width. It draws with a desktop font at matched advances, so it catches overflow, not letterforms.

Constraints

Stock MicroPython 1.9.4. No f-strings, walrus, type annotations, async or yield from. ASCII only. Only math, random and casioplot are importable. No file writes. Recursion is on expression nesting, never input length. devlint.py enforces all of this.

Structure

File
`maths.py`	launcher
`casui.py`	keys, menus, input editor, result screens, settings
`casrender.py`	2D typesetter; owns the font metric
`caslex.py`	tokeniser and iterative parser
`caseng.py`	simplify, differentiate, evaluate, print
`cascalc.py`	integrate, solve, definite integral
`caspoly.py`	exact rational polynomial algebra
`casutil.py`	shared prompts, formatting, charts
19 section modules	`TOOLS` list of `(label, function)` plus `run()`

Expressions are tuples: ('n', 2), ('v', 'x'), ('+', a, b), ('sin', a). The parser is iterative shunting-yard. Rationals are (numerator, denominator) pairs.

Development

Runs unmodified under desktop CPython; casioplot.py stubs the graphics.

python3 tests.py       # 7108 checks
python3 stress.py      # 443 checks, drives every tool
python3 devlint.py     # MicroPython compliance, 32 files

tests.py auto-discovers tests_*.py, each exposing SECTIONS = [(label, fn)] where fn takes the harness object.

Adding a tool: add it to the module's TOOLS, add assertions to tests.py, add help text to casui.HELP, add it to the table above. Tests enforce the first and the last.

Not covered

SPEC_AUDIT.md checks all 730 H640 and H645 content statements against the code. Nine have nothing behind them.

Code	Statement	Reason
`D14`	Clean data: missing values, errors, outliers	Not a calculator task
`SH5`	Hypothesis test for an average using the Wilcoxon signed rank test	Needs an exact critical-value table that could not be verified to the standard the PMCC and Spearman tables were held to
`L5`	Recognise when a linear programming problem requires an integer solution	Not a calculator task
`L6`	Formulate a range of network problems as linear programming problems	Not a calculator task
`N13`	Explore network algorithms through their LP formulations	Not a calculator task, for the same reason as `L6`
`L11`	Use a visualisation of a three-dimensional linear programming problem	Out of scope for the hardware
`L16`	Handle variables which may be negative	Not built
`c2`	Use software to produce a tangent to a curve at a variable point	Out of scope for the hardware
`T10`	Solve other Diophantine equations	Partly, and open-ended as stated

Probes

hwcheck.py, keyprobe.py, calib_screen.py, fontmetrics.py and fontmetrics2.py are one-off hardware probes, not part of the app.

License

MIT.