The Castiel manual · 69 chapters
The Castiel manual
One calculator with six modes — Simple, School, Engineer, Financial, Programming, and Programming+ — sharing a single computation engine and one editable paper tape. Every mode, surface, and function is documented here, along with the full Catena language reference.
01
Getting started
What Castiel is, the window, switching modes, and the everyday calculator.
2 chapters02
School
Textbook entry, graphing, statistics, and the full set of learning sub-apps.
13 chapters01 The School apps the School home launcher and how the sub-apps fit together.02 The School calculator natural textbook entry, exact vs decimal, and the scientific keypad.03 Graph plotting functions, tracing, and the value table.04 3D graph surfaces `z = f(x, y)` you can rotate and inspect.05 Statistics data lists, one- and two-variable statistics, and regression.06 Distributions probability distributions with density, cumulative, and inverse forms.07 Spreadsheet a cell grid with formulas, charts, and multiple sheets.08 Equation solver linear systems, quadratics, polynomials, and numeric roots.09 Inequality solver solving and graphing inequalities on the number line.10 Base-N binary, octal, decimal, and hex integer arithmetic with bitwise tools.11 Recursion recurrence sequences, the term graph, and convergence.12 Geometry dynamic construction, measurement, and dragging.13 Probability simulation random-trial experiments and the law of large numbers.
03
Engineer
The scientific keypad, a CAS notebook, matrices, units, and constants.
6 chapters01 Engineer overview the mode and its advanced calculator with mode chips.02 CAS the computer-algebra notebook for symbolic work.03 Matrices & vectors the matrix and vector editors and their operations.04 Units & constants unit conversion and the physical-constants catalog.05 Numerical methods numeric root-finding.06 Plot Cartesian, polar, and parametric plotting.
04
Financial
Money over time — TVM, cash flow, amortization, bonds, and depreciation.
8 chapters01 Financial overview the mode, the TVM registers, and the printing tape.02 Time value of money solving among N, I/Y, PV, PMT, and FV.03 Cash flow (NPV & IRR) uneven cash flows, net present value, and internal rate of return.04 Amortization a payment-by-payment loan breakdown.05 Bonds bond price and yield with day-count conventions.06 Depreciation straight-line, sum-of-years-digits, and declining-balance schedules.07 Breakeven & margin breakeven analysis and profit margin.08 Interest conversion converting between nominal and effective rates.
05
Programming
Author, record, block, debug, and share Catena sequences.
7 chapters01 Programming overview the three views of a sequence and the mode's layout.02 Recorder building a sequence by recording calculator steps.03 Blocks authoring a sequence as visual blocks.04 Listing the text editor with value previews and diagnostics.05 Debugger stepping through a running sequence and inspecting state.06 Library saving, importing, exporting, and trusting sequence packs.07 AI assistant the Programming+ panel that drafts sequences with your own provider.
06
The Catena language
The sequencing language behind every mode — from first line to full reference.
13 chapters01 Getting started what Catena is, its safety model, and your first sequence.02 Language basics lines, comments, literals, and variables.03 Types & formatting the type system and the `AS` operator.04 Expressions & operators arithmetic, comparison, logic, and units.05 Bags the single container type and its queries.06 Control flow decisions, loops, and checkpoints.07 Reactivity rules that respond when values change.08 Sequences & functions defining, calling, and reusing sequences as functions.09 Commands & stdlib input, output, the answer register, and the math functions.10 Connectors & the API reaching outside services safely.11 Engine settings per-sequence `ESET` settings.12 Files & sharing the `.cat`, `.cats`, `.catx`, and `.nex` file types.13 Reference the keyword list, the full function catalog, and a grammar cheat-sheet.
07
Math basics
The mathematics behind the functions, from arithmetic to calculus.
13 chapters08
Features & settings
The paper tape, themes, connectors, licensing, and accessibility.
7 chapters01 The paper tape the shared, editable running log in every mode.02 Settings a walkthrough of every settings pane.03 Connectors currency rates, LLM providers, and receipt printing.04 Appearance & themes light and dark themes, accent colour, and skins.05 Free tier & licensing what is free, the advanced-mode timer, and buying the full version.06 File types every file Castiel reads and writes.07 Accessibility keyboard operation, screen-reader support, and contrast.