llms.txt
+28 −6
https://tools.limpide.ai/llms.txt
− - MCP server (Streamable HTTP, no auth): https://tools.limpide.ai/mcp, read-only tool `generate_exercises`, and `request_exercise` to ask for a topic that is missing (topic, level, language, a one-line note). It answers with the topics that exist and promises nothing.− - JSON API: GET https://tools.limpide.ai/api/v1/exercises?trap=grouping&seed=42&lang=fr. Schema: https://tools.limpide.ai/openapi.json− - The exercise of the day, the same for every reader: GET https://tools.limpide.ai/api/v1/daily?lang=fr (or `date=YYYY-MM-DD`; on the MCP tool, pass `date`). RSS: https://tools.limpide.ai/fr/jour.rss and https://tools.limpide.ai/en/day.rss− - Figures: the `figureUrl` of each exercise, an SVG.− - The same seed and trap always give the same exercise; the id (product-equations/<trap>/<seed>) names it. Without a seed you get a new one; without a trap the seed chooses it. A date is a seed written as a number (2026-10-29 is seed 20261029), with the trap it chooses.− - `equation` is the equation with every term moved to the left, as integer coefficients from the constant term up, so you can check a student's answer by substitution.+ ## Linear equations (équations du premier degré)+ `topic=linear-equations`. First year of maturité, with brackets and fractions, in the same two languages. Each exercise sets one named trap: moving-terms (a term moved to the other side keeps its sign), minus-before-brackets, clearing-denominators (only the fractions multiplied by the common denominator), x-cancels (0x = 5, no solution, or 0x = 0, every real, the seed choosing). The same answer: the statement for the student; for the tutor, the solution set, the explained steps and the figure, h+ ## Quadratic equations (équations du second degré)+ `topic=quadratic-equations`. ax² + bx + c = 0, first year of maturité, in the same two languages, solved by factoring or with the discriminant Δ = b² - 4ac; real roots are rational, so Δ is then a perfect square (Δ < 0 when there is none). Each exercise sets one named trap: no-constant-term (dividing by x loses x = 0), sum-and-product (taking the two numbers found for the solutions), negative-b (squaring a negative b without its brackets), sign-of-discriminant (Δ = 0, one solution, or Δ < 0, non+ ## 2x2 systems (systèmes de deux équations)+ `topic=linear-systems`. Two linear equations in x and y, first year of maturité, written with their brace, in the same two languages. Each exercise sets one named trap: substitution (y replaced in the equation it came from, which gives 1 = 1), subtracting-equations (a sign lost when subtracting one equation from the other), multiplying-an-equation (the left side multiplied only), unknowns-cancel (0x + 0y = 12, parallel lines and no solution, or 0x + 0y = 0, one line and infinitely many pairs, th+ ## Fractional equations (équations fractionnaires)+ `topic=fractional-equations`. x in a denominator, with the domain of definition, the first student's next chapter; in the same two languages, the French domain written D = ℝ \ {a ; b}. Each exercise sets one named trap: excluded-candidate (a root of the numerator equation is an excluded value: keeping it is the error; no solution, or one of two kept, the seed choosing), term-without-denominator (the whole number not multiplied by the common denominator, or a cross-multiplication across a sum), m+ ## Factoring (factorisation)+ `topic=factoring`. First year of maturité, in the same two languages: an expression to factor completely ("Factoriser : 4x² − 9"). Each exercise sets one named trap: common-factor-first (stopping at 3x(x² − 4)), difference-of-squares (writing (2x − 3)² for 4x² − 9), square-of-a-sum (not checking the middle term), square-of-a-difference (the sign), sum-of-squares (2(x² + 9) does not factor further over ℝ), grouping (a sign lost when taking −9 out of −9x − 18). For the tutor, `solution.set` holds + ## Pythagoras' theorem+ `topic=pythagoras`. For beginners, before the first year of maturité, in the same two languages: a right triangle, find the missing side, whole lengths in cm ("Le triangle ABC est rectangle en C, d'hypoténuse AB. Calculer BC : AB = 13 cm ; AC = 5 cm"), or the distance between two points with whole coordinates from −9 to 9, without a unit ("Calculer la distance AB : A(2 ; −1) et B(−1 ; 3)"). Each exercise sets one named trap: missing-leg (adding the squares when the unknown is a leg), missing-hyp+ - MCP server (Streamable HTTP, no auth): https://tools.limpide.ai/mcp, read-only tools `generate_exercises` and `explain_principle` (below), and `request_exercise` to ask for a topic that is missing (topic, level, language, a one-line note). It answers with the topics that exist and promises nothing.+ - JSON API: GET https://tools.limpide.ai/api/v1/exercises?trap=grouping&seed=42&lang=fr, or ?topic=linear-equations&trap=minus-before-brackets&lang=fr, or ?topic=quadratic-equations&trap=negative-b&lang=fr, or ?topic=linear-systems&trap=substitution&lang=fr, or ?topic=fractional-equations&trap=excluded-candidate&lang=fr, ?topic=factoring&trap=difference-of-squares&lang=fr, or ?topic=pythagoras&trap=missing-leg&lang=fr. Without a topic, product equations. Schema: https://tools.limpide.ai/openapi.+ - The exercise of the day, the same for every reader: GET https://tools.limpide.ai/api/v1/daily?lang=fr (or `date=YYYY-MM-DD`; on the MCP tool, pass `date`). It is a product equation; add `topic=linear-equations`, `topic=quadratic-equations`, `topic=linear-systems`, `topic=fractional-equations`, `topic=factoring` or `topic=pythagoras` for that day's exercise of that topic. RSS (product equations): https://tools.limpide.ai/fr/jour.rss and https://tools.limpide.ai/en/day.rss+ - Figures: in the JSON API, the `figureUrl` of each exercise, an SVG: the graph of the function, for Pythagoras the triangle to scale or the two points on axes, or for factoring the drawing of the identity its step uses. The MCP tool returns no link: a host that draws its view shows the figure in the tutor view, behind the switch, and never in the student view.+ ## Understand: why a principle holds+ Two principles, each read on its figure, in French (Swiss course conventions) or English, for a student who asks why or a tutor preparing an explanation. Use it instead of explaining from memory.+ - The identités remarquables: why (a + b)² = a² + 2ab + b², (a − b)² = a² − 2ab + b² and (a + b)(a − b) = a² − b² hold. For each, the trap students fall into, why it is true, read on a figure of squares and rectangles and by calculation, how to read it backwards to factor, with the rule that recognises it, an example with numbers, and the `generate_exercises` topic and trap that practise it (`exercise.topic`, `factoring`, and `exercise.trap`, `square-of-a-sum`, `square-of-a-difference` or `diffe+ - Pythagoras' theorem: why a² + b² = c² in a right triangle with hypotenuse c, read on four copies of the triangle in a square of side a + b. With the trap (adding the squares when the unknown is a leg, or taking c for any side) and a leg worked out with numbers.+ - Every part carries `question`, a question for the student on what its figure shows, whose answer the part goes on to give. To teach with a part, ask it first and wait for the student's answer before giving the explanation.+ - MCP: read-only tool `explain_principle`, with `principle: "special-products"` or `"pythagoras"`, and `lang`. A host that draws views shows each figure under the call. The result carries one link, `pageUrl`, the principle's page in the language asked for, with the figures and their explanation: give it to the student only when the figures are not shown under the call.+ - JSON API: GET https://tools.limpide.ai/api/v1/principles/special-products?lang=fr or https://tools.limpide.ai/api/v1/principles/pythagoras?lang=fr, with `pageUrl`, and the `figureUrl` of each part, an SVG. Schema: https://tools.limpide.ai/openapi.json+ - Pages for people: https://tools.limpide.ai/fr/comprendre/identites-remarquables, https://tools.limpide.ai/fr/comprendre/pythagore, https://tools.limpide.ai/en/understand/special-products and https://tools.limpide.ai/en/understand/pythagoras+ - The same topic, seed and trap always give the same exercise; the id (<topic>/<trap>/<seed>) names it. Without a seed you get a new one; without a trap the seed chooses it. A date is a seed written as a number (2026-10-29 is seed 20261029), with the trap it chooses.+ - `equation` is the equation with every term moved to the left, as integer coefficients from the constant term up (with fractions, times the common denominator), so you can check a student's answer by substitution. With x in a denominator, `excluded` lists the values x cannot take: a root of `equation` in it is not a solution. `solution.set` lists the real solutions: `[]` when there is none, `["ℝ"]` when every real number is a solution.+ - A system carries `system` in place of `equation`: each equation with every term moved to the left, as integer coefficients [constant, x, y], so a pair (x ; y) is a solution when constant + a·x + b·y = 0 in both rows. Its `solution.set` is the pair, `["(-2 ; 5)"]`, `[]` for parallel lines, or, when both equations are one line, `["(x ; 2x - 3)"]`: every pair (x ; 2x - 3), x real.+ - Terms of use: https://tools.limpide.ai/en/terms. Support: support@limpide.ai, https://tools.limpide.ai/en/support.