Pemanfaatan R untuk Komputasi Simbolik
[The Utilization of R for Symbolic Computation]
DOI:
https://doi.org/10.19166/jstfast.v9i1.9649Kata Kunci:
Numerical Methods, R Programming, Ryacas, Symbolic Computation, YacasAbstrak
One of the R packages for symbolic operations that is currently active and developing is Ryacas. This package is an interface between the yacas system and R, combining symbolic and numerical computation capabilities in one system. This study aims to explore and document R's capabilities in symbolic computation using Ryacas. There are three topics that will be discussed in this research, namely 1) precision of arithmetic calculations, 2) application to linear algebra, and 3) application of symbolic computation to solving Mathematics-Statistics cases. Ryacas is able to increase the precision of numerical calculations in simple arithmetic cases, and operations in linear algebra. The case of obtaining the probability distribution function and probability density function of a random variable U which is a function of a random variable Y, can be easily solved by Ryacas. The output of symbolic computation from this last case is further processed numerically by R in the form of a graphical appearance, with the ggplot2 package. Likewise, the simulation process is carried out to generate the values of the random variable U. These results illustrate the continuous process between symbolic and numerical computation in one system, in this case R.
Bahasa Indonesia Abstract: Paket R untuk operasi simbolik yang saat ini aktif dan berkembang salah satunya adalah Ryacas. Paket ini merupakan antarmuka antara sistem yacas dan R, sehingga menggabungkan kemampuan komputasi simbolik dan numerik dalam satu sistem. Penelitian ini bertujuan untuk mengeksplorasi dan mendokumentasikan kemampuan R dalam komputasi simbolik dengan menggunakan Ryacas. Ada tiga topik yang akan dibahas dalam penelitian ini, yaitu 1) presisi perhitungan aritmatika, 2) penerapan pada aljabar linear, dan 3) penerapan komputasi simbolik pada pemecahan kasus Matematika-Statistik. Ryacas mampu meningkatkan presisi perhitung-an numerik pada kasus aritmatika sederhana, dan operasi-operasi pada aljabar linear. Kasus mendapatkan fungsi sebaran peluang dan fungsi kepekatan peluang dari peubah acak U yang merupakan fungsi dari suatu peubah acak Y, dapat dengan mudah diselesaikan oleh Ryacas. Luaran komputsi simbolik dari kasus terakhir ini, diperoses lebih lanjut secara numerik oleh R berupa penampilan grafik, dengan paket ggplot2. Demikian pula proses simulasi dilakukan untuk membangkitkan nilai-nilai peubah acak U. Hasil ini mengilustrasikan proses bersinam-bungan antara komputasi simbolik dan numerik dalam satu sistem, dalam hal ini R.
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