Mathematical software

Mathematical software is software used to model, analyze or calculate numeric, symbolic or geometric data.

It is a type of application software which is used for solving mathematical problems or mathematical study. There are various views to what is the mathematics, so there is various views of the category of mathematical software which used for them, over from narrow to wide sense.

A type of mathematical software (math library) also used by built in the part of an another scientific software. A most primary them (for example, to calculate elementary function by floating point arithmetic) may be in the category of mathematical software. They are often usually built in the general purpose systems as middleware. So to speak, mathematical software is not only an application software but also basis of the another scientific software. And that is its one of the characteristic of mathematical software as that mean.
Several mathematical software often have good user interface for educational purpose (see educational math software). But the core parts of solver of them direct dependent to the algorism by the mathematical knowledge. So it may be common sense that it does not process if it not well solved on mathematical construction at least. (There is physical limitation of hardware.) That is typical difference of mathematical software for another application software.
Specially, It may be sure common sense that to the attention that there is a such as next case in mathematical software using:

Encryption software apply the second case.

Numerical analysis and symbolic computation had been in most important place of the subject, but other kind of them is also growing now. An useful mathematical knowledge of such as algorism which exist before the invention of electronic computer, helped to mathematical software developing. On the other hand, by the growth of computing power (such as seeing on Moore's law), the new treatment (for example, a new kind of technique such as data assimilation which combined numerical analysis and statistics) needing conversely the progress of the mathematical science or applied mathematics.
The progress of mathematical information presentation such as TeX or MathML will demand to evolution form formula manipulation language to true mathematics manipulation language (notwithstanding the problem that whether mathematical theory is inconsistent or not). And popularization of general purpose mathematical software, special purpose mathematical software so called one purpose software which used special subject will alive with adapting for environment progress at normalization of platform. So the diversity of mathematical software will be keeped.

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Wikipedia