Exact workflows in SumWise 3.1
Use explicit Desktop input and Function Reference. Exact results remain distinct from approximate graph samples. These bounded operations do not turn all ordinary calculations or Ask questions into exact algebra.
poly_divrem(x^3-1,x-1,x)[x^2 + x + 1, 0]poly_gcd(x^3-x,x^2-1,x)x^2 - 1linear_solve_exact(matrix(2,2,2,1,1,-1),vector(1,0))[1/3, 1/3]interpolate_exact(vector(0,1,2),vector(1,3,7),x)x^2 + x + 1rational_simplify((x^2-1)/(x-1),x)x + 1, with x - 1 != 0solve_rational(x^2-2=0,x)[-sqrt(2), sqrt(2)]
Input and scope
Use supported exact integer/rational expressions and explicit case-sensitive formal variables. For the new exact vector/system/rational routes, use supported inline inputs; approximate named vectors and decimal/scientific literals are not exact inputs. Ordinary numerical operations retain their own meanings. Polynomial degree/intermediate degree is bounded by 8; the new linear solver accepts square 2x2–4x4 systems with a unique solution; interpolation accepts 2–8 distinct exact positions. Rational solving is over reals with reduced numerator degree at most two; identities return a non-finite-solution diagnostic rather than a fake finite set. Checked growth and resource limits can reject otherwise meaningful inputs.
Operation boundaries
Each operation is an explicit Desktop request. It validates the original supported input before simplification, uses checked rational arithmetic, and either completes the whole result or refuses it. A small eventual answer does not guarantee that intermediate growth fits.
| Operation | Accepted family | Important boundary |
|---|---|---|
poly_divrem(p,d,x) | Univariate rational-coefficient polynomials | Degree/intermediate degree ≤ 8; nonzero divisor; ordered quotient/remainder identity, not pointwise fraction cancellation. |
poly_gcd(p,q,x) | Univariate exact polynomial GCD | Degree/intermediate degree ≤ 8; normalized exact result, not general factorization. |
linear_solve_exact(A,b) | Inline matrix and vector, square 2×2–4×4 | Unique rational solution only. Singular consistent and inconsistent systems receive distinct diagnostics. Scalar entries use integer literals, signs and + − * /; no powers or named vectors. |
interpolate_exact(xs,ys,x) | Matching inline vectors of 2–8 exact rational constants | Pairwise distinct exact x positions; degree at most n−1 ≤ 7. Constants and zero are valid. This is interpolation, not regression. |
rational_simplify(expr,x) | One real variable, rational arithmetic and positive literal powers 1–8 | Original-domain predicates remain part of the value even when the reduced answer is 0 or 1. |
solve_rational(lhs=rhs,x) | The same bounded grammar on both sides | Reduced numerator degree ≤ 2; at most two distinct real roots, ordered exactly and filtered by the original domain. |
Integer literal magnitude is at most 1,000,000; checked rational numerator/denominator magnitudes are at most 1012. Each request has one 8,192 charged coefficient-operation allowance, not a fresh allowance per child expression. Applicable shared limits are 4,096 source/output bytes, 513 tokens, nesting 32, aggregate exact-input AST 192 nodes and depth 24 under each operation’s counting convention. Polynomial intermediates have at most nine coefficients. Rational-domain values retain at most 32 nonconstant polynomial predicates and at most 4,096 bytes of combined canonical formula/conditions. These are refusal boundaries, not performance guarantees or arbitrary precision.
Polynomial operations permit their supported literal powers 0–8; the two rational-expression routes deliberately accept only positive literal powers 1–8. Approximate/scientific coefficients, other variables, units, complex values, arbitrary functions and unsupported composition are rejected in these exact routes. Explicit case-sensitive formal variables are not replaced by stored numeric bindings.
solve_rational returns an exact symbolic empty set for no in-domain real roots, including negative-discriminant quadratics. An undefined original expression is an error. An identity reports infinitely many solutions on its original domain without publishing a fake finite set; higher reduced degree is unsupported. Irrational quadratic roots remain symbolic radicals. Copying a radical into an ordinary approximate evaluator is not an exact numeric round trip.
Domain conditions are part of the answer
For rational_simplify, canceled denominators still restrict the original domain. Copy Result and human-readable reports include conditions. Reuse the original invocation. Unsupported graph, CAS, assignment and machine export transfers reject; plotting the bare reduced formula does not preserve a removable hole.
Save and Open
Keep old originals. Old-only encoding remains supported and opening does not migrate it. After adding domain-qualified content, the first upgrade from a named legacy file requires Save As to a genuinely different file. Domain-qualified content uses workspace version 6. Older baseline readers cannot open this format; supported old workspaces remain readable in 3.1. Open performs bounded mathematical validation: at most 32 typed occurrences, four reconstruction passes, conservative 1,048,576 coefficient operations overall, not a time guarantee. No session command replay is performed.
Languages and Ask
English, Spanish, French and German are in one app. Interface choice applies next launch; Ask language is independently selected. Fourteen bounded sub-intents cover arithmetic, conversion, time/distance/speed, percentage-of/increase/decrease, factor/expand, derivative/integral, linear equations and bounded 2D plots. Interpret, review, insert and execute separately. No unrestricted prose or automatic exact-solver selection. Some historical/technical text remains English or canonical.
Translations are machine-assisted drafts; no fluent-human translation approval or accessibility certification is claimed.
SumWise on Microsoft Store · Release notes
Desktop purchase: US$24.99 one-time, with a full-featured seven-day Microsoft Store trial. Local prices and availability may vary. SumWise 3.1 is available now on Microsoft Store.