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When facing complex mathematical challenges in template development, you have several powerful tools at your disposal. This guide helps you choose the right approach for your specific problem.

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Existing MathJS Functions

It’s always worth triple-checking what already exists in the MathJS Functions Reference.
Some functions have unexpected names - for example, compareNatural() can do matrix comparisons. Always search thoroughly!

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Pros

  • No new code required
  • More functions exist than you probably think!
  • Well-tested and documented

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Cons

  • Sometimes weird or hard-to-read function names (add a description or authorNote!)
  • Can be awkward making a function work that isn’t quite intended for your use case
  • Your specific solution may not exist

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Best Suited For

Being your first port of call for mild-to-moderate complexity problems.

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Temporary Custom Functions

MathJS allows you to define temporary custom functions within your templates.

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Pros

  • Programming with no dev help required 🙂
  • Particularly useful when creating or processing matrices
  • Works across multiple widgets in the same template

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Cons

  • Limited to MathJS capabilities
  • Doesn’t render correctly in LaTeX (can be fixed if needed)

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Best Suited For

Doing weird manipulation of matrices or creating simple custom operations.

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Examples

Custom functions DO work over multiple widgets! Define once, use anywhere in the template.

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Permanent Custom Functions

We have existing custom functions like iterate(), interpolate(), and more. New ones can be added as needed.

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Pros

  • Very fast (executed in users’ web browsers)
  • Can use both MathJS and native JavaScript libraries
  • Minimal code required
  • No network latency

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Cons

  • Engineers may be less familiar with JavaScript
  • Not well suited for calling external libraries or APIs
  • Bad for memory-intensive work (e.g., huge matrices)

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Best Suited For

Operations that require less than ~5 parameters of data and nothing outside MathJS or native JavaScript.

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Existing Custom Functions

  • iterate() - Iterative solving
  • interpolate() - Linear and non-linear interpolation
  • solveSecant() - Secant method solver
  • See full documentation

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Python Solvers

The big Python scripts that handle complex engineering calculations.

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Pros

  • Lots of external libraries available (check licenses for commercial use!)
  • Python is similar to Matlab and familiar to engineers
  • Few restrictions on memory or CPU
  • Can handle complex FEA and matrix operations

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Cons

  • Every solver call requires a network roundtrip (~100-300ms each)
  • Must always support history - hard to change once written
  • Requires careful consideration to write good-quality code

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Best Suited For

Super-complex calculations:
  • Finite Element Analysis (FEA)
  • Huge matrices
  • External library dependencies
  • API integrations
Solver calls add up quickly! Each call is 100-300ms, so minimize the number of calls in your template.

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Decision Tree

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Performance Considerations

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Best Practices

  1. Start Simple: Always check if MathJS already has what you need
  2. Minimize Solver Calls: Batch operations when possible
  3. Document Complex Functions: Add descriptions and author notes
  4. Consider User Experience: Balance accuracy with performance
  5. Test Edge Cases: Ensure your solution handles all scenarios

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Getting Help

  • Check existing functions documentation
  • Ask in engineering Slack channels
  • Review similar templates for inspiration
  • Consult with dev team for custom function needs