Language and Compiler built for Mathematics

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Discussion Overview

The discussion revolves around identifying programming languages, compilers, and integrated development environments specifically designed for performing advanced mathematical computations. Participants explore various software tools and frameworks that may facilitate mathematical work, including their capabilities and limitations.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant inquires about specific names of compilers, languages, and integrated environments tailored for full-fledged mathematics.
  • Another participant suggests MATLAB as a self-sufficient tool that can integrate with C/C++/C# for extended functionality.
  • Multiple participants question the definition of "full-fledged mathematics," proposing that it encompasses various fields such as algebraic geometry, measure theory, and differential equations.
  • Mathematica is highlighted as a strong tool for symbolic mathematics, while MATLAB is noted for its strengths in linear algebra.
  • One participant mentions Magma as useful for abstract algebra, particularly in comparing Lie groups.
  • Maxima, Euler (for GTK), and SAGE are also proposed as relevant tools for mathematical work.
  • There is a suggestion that a full-fledged mathematics environment should enable the discovery or invention of custom mathematical frameworks.
  • Another participant argues that formulating a framework is essential for discovering new mathematics, implying that coding for calculations is challenging without a solid foundation.
  • Concerns are raised about the current limitations of AI in developing such frameworks for mathematics.

Areas of Agreement / Disagreement

Participants express differing views on what constitutes "full-fledged mathematics" and the tools that best serve this purpose. There is no consensus on a single tool or framework that meets all needs, indicating multiple competing perspectives.

Contextual Notes

Participants have not defined the specific criteria for "full-fledged mathematics," leading to ambiguity in the discussion. The effectiveness of the suggested tools may depend on the specific mathematical tasks or fields being addressed.

pairofstrings
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Hello,

I want to know:
1. Compiler name built especially for doing full-fledged mathematics.
2. language name built especially for doing full-fledged mathematics.
3. Integrated software development environment name built especially for doing full-fledged mathematics.
4. Language, compiler and integrated software development environment for full-fledged mathematics that gives access to device drivers, especially, display device driver.
5. Name of any software framework that gives access to device drivers with language, compiler compatibility and integrated software development environment support with that of:
  • Compiler name built especially for doing full-fledged mathematics. (1 from above)
  • language name built especially for doing full-fledged mathematics. (2 from above)
  • Integrated software development environment name built especially for doing full-fledged mathematics. (3 from above)
Thank you.
 
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MATLAB
Usually, it is self-sufficient.
If necessary, it can be integrated with C/C++/C# which gives any functionality you can imagine.
 
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What is "full-fledged mathematics"?

Algebraic geometry? Measure theory? Differential equations?

There is no one-tool-does-all for mathematics.
Mathematica is great for symbolic work
Matlab is great for anything involving linear algebra (and more)
A recent piece of software called magma is great for more abstract algebra (I used it to compare Lie groups for example)
 
JorisL said:
What is "full-fledged mathematics"?

Algebraic geometry? Measure theory? Differential equations?

There is no one-tool-does-all for mathematics.
Mathematica is great for symbolic work
Matlab is great for anything involving linear algebra (and more)
A recent piece of software called magma is great for more abstract algebra (I used it to compare Lie groups for example)

A full-fledged mathematics has an ability to help me discover or invent a custom mathematics.

A full-fledged mathematics gives me an ability to help me discover or invent a custom mathematics.
 
If you want to find new mathematics you have to formulate a framework you'll work with.
After that, you might be able to implement code to do calculations but that's hard.

Short version, most likely not since this would need AI which isn't developed enough.
 

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