Multiple algebraic roots
var x,y
x^2 + y^2 = 25
x*y = 12Four real solution pairs: (±3,±4) with consistent signs, in both variable orders.
Worked examples
See Version 4.0 solve real mathematical tasks.
A set of concise examples with executable-style input and screenshots captured from the desktop application. Open images to inspect results at full resolution.
A journey across different numerical models
These nine captures show the software rather than conceptual artwork. They illustrate distinct activities: nonlinear root search, workflow execution, ODE and PDE results, quadrature, differentiation, limits, integral equations and mathematical model generation.
01. Multiple solutions
Inspect distinct roots of a nonlinear system and their residual information.
02. Birthday paradox with workflow
A while loop calculates the 23-person probability threshold.
03. Initial-value ODE
Inspect a computed trajectory on its output grid.
04. Partial differential equation
A field model with domain, boundary conditions and numerical output.
05. Numerical quadrature
Accepted integral with error and evaluation diagnostics.
06. Gradient and Hessian
Multivariable numerical differentiation results.
07. Limits
Compare limit estimates and status near an indeterminate expression.
08. Integral equations
Numerical results from a Fredholm/Volterra-style model.
09. Equation Generator
Generate systems with known constructed solutions for exploration.
Three starting scripts
Numerical integration
quad
expr = x^2
var = x
range = [0,3]Reference definite integral: 9.
Workflow iteration
workflow
s = 0
for i in 1..5
s += i
end
report sReference report: 15.
All solver scripts on this site should be checked against the installed Version 4.0 build before being used for external validation. A screenshot is evidence of one reported run, not of exhaustive correctness for every problem.
Discover additional worked problems
The 100 Challenging Numerical Problems PDF is available to read or download. Browse all six documents on the Resources page.
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