Solving exact linear systems

Runnable RiXRun cell

.Plugin.Load("solve"); system := {#a,b:x,y# x + y == a; x - y == b }; answer := .solve.System(system, {= values={= a=3, b=1 } }); answer.solution;

Explore a parametric family

Runnable RiXRun cell

.Plugin.Load("solve"); family := .solve.System({#:x,y# x+y==2 },{= parameters=["s"] }); chosen := family.Substitute({= s=3 }); {: family[:kind],family[:directions],chosen,family.Residuals(chosen),family.Check(chosen) };

The particular solution is (2,0) and the retained null direction is (-1,1), so s=3 gives (-1,3).

Mix definitions, constraints, and an objective

Runnable RiXRun cell

.Plugin.Load("solve"); answer := .solve.System({#:x,y# y=x+1; x>=0; y<=3 },{= objective={= x=1 },sense=:max }); {: answer[:kind], answer[:solution], answer.Check(), answer[:optimizationresult][:certificate].Verify() };

The output definition is normalized to an equality and the inequalities go to the exact two-phase LP solver. No direction is inferred from statement order.

Exact and assumption-dependent scalar roots

Runnable RiXRun cell

.Plugin.Load("solve"); exact := .solve.Polynomial(.p`x^2-2`,1:2); numerical := .solve.Numerical((x)->x^2-2,1:2,{= absoluteWidth=1/100,maxWork=20 }); {: exact[:solution],exact.Check(), numerical[:status],numerical[:isolation],numerical[:assumptions] };

The Polynomial path returns an exact AlgebraicReal after a Sturm root-count check. The arbitrary callable path retains :continuityOrTrustedRootCount and does not claim certification from finite evaluations alone.