library(mosaicCalc)
## Loading required package: mosaic
## Registered S3 method overwritten by 'mosaic':
##   method                           from   
##   fortify.SpatialPolygonsDataFrame ggplot2
## 
## The 'mosaic' package masks several functions from core packages in order to add 
## additional features.  The original behavior of these functions should not be affected by this.
## 
## Attaching package: 'mosaic'
## The following objects are masked from 'package:dplyr':
## 
##     count, do, tally
## The following object is masked from 'package:Matrix':
## 
##     mean
## The following object is masked from 'package:ggplot2':
## 
##     stat
## The following objects are masked from 'package:stats':
## 
##     binom.test, cor, cor.test, cov, fivenum, IQR, median, prop.test,
##     quantile, sd, t.test, var
## The following objects are masked from 'package:base':
## 
##     max, mean, min, prod, range, sample, sum
## Loading required package: mosaicCore
## 
## Attaching package: 'mosaicCore'
## The following objects are masked from 'package:dplyr':
## 
##     count, tally
## The legacy packages maptools, rgdal, and rgeos, underpinning the sp package,
## which was just loaded, were retired in October 2023.
## Please refer to R-spatial evolution reports for details, especially
## https://r-spatial.org/r/2023/05/15/evolution4.html.
## It may be desirable to make the sf package available;
## package maintainers should consider adding sf to Suggests:.
## 
## Attaching package: 'mosaicCalc'
## The following object is masked from 'package:stats':
## 
##     D
## Loading required package: mosaic
## Registered S3 method overwritten by 'mosaic':
##   method                           from   
##   fortify.SpatialPolygonsDataFrame ggplot2
## 
## The 'mosaic' package masks several functions from core packages in order to add 
## additional features.  The original behavior of these functions should not be affected by this.
## 
## Attaching package: 'mosaic'
## The following objects are masked from 'package:dplyr':
## 
##     count, do, tally
## The following object is masked from 'package:Matrix':
## 
##     mean
## The following object is masked from 'package:ggplot2':
## 
##     stat
## The following objects are masked from 'package:stats':
## 
##     binom.test, cor, cor.test, cov, fivenum, IQR, median, prop.test,
##     quantile, sd, t.test, var
## The following objects are masked from 'package:base':
## 
##     max, mean, min, prod, range, sample, sum
## Loading required package: mosaicCore
## 
## Attaching package: 'mosaicCore'
## The following objects are masked from 'package:dplyr':
## 
##     count, tally
## The legacy packages maptools, rgdal, and rgeos, underpinning the sp package,
## which was just loaded, will retire in October 2023.
## Please refer to R-spatial evolution reports for details, especially
## https://r-spatial.org/r/2023/05/15/evolution4.html.
## It may be desirable to make the sf package available;
## package maintainers should consider adding sf to Suggests:.
## The sp package is now running under evolution status 2
##      (status 2 uses the sf package in place of rgdal)
## 
## Attaching package: 'mosaicCalc'
## The following object is masked from 'package:stats':
## 
##     D
library(ggplot2)

Integral mosaik adalah konsep kunci dalam mosaic calculus. Ini adalah generalisasi dari integral dalam kalkulus konvensional yang memungkinkan kita untuk memahami integral dalam konteks yang lebih umum dan fleksibel. Berikut ini adalah beberapa materi mengenai integral mosaik:

Konsep Integral Mosaik:

Interval Mosaik: Integral mosaik berfokus pada konsep interval mosaik, yang merupakan himpunan interval-real yang membentuk fungsi dalam konteks mosaic calculus. Interval-interval mosaik ini dapat tumpang tindih, bersinggungan, atau bahkan saling berpotongan. Integral Mosaik: Integral mosaik adalah cara untuk menghitung integral fungsi yang mempertimbangkan kontribusi dari berbagai interval mosaik. Dalam pendekatan ini, kita membagi domain fungsi menjadi berbagai interval mosaik dan menghitung integral dari masing-masing interval mosaik tersebut. Properti Integral Mosaik: Integral mosaik memiliki beberapa properti khusus: Linearitas: Integral mosaik bersifat linear, sehingga integral dari kombinasi linear dua fungsi adalah sama dengan kombinasi linear dari integral masing-masing fungsi. Indeks: Integral mosaik memiliki indeks yang memungkinkan perpanjangan domain dan penggunaan dalam berbagai konteks. Perpanjangan Domain: Dalam mosaic calculus, domain integral dapat diperluas untuk mengatasi situasi yang lebih kompleks. Penggunaan Integral Mosaik:

Kasus Khusus Integral Riemann: Integral Riemann dalam kalkulus konvensional adalah kasus khusus integral mosaik di mana interval mosaik adalah interval terbuka yang tidak tumpang tindih. Dengan kata lain, integral Riemann adalah metode integral dalam konteks mosaic calculus. Analisis Non-standar: Integral mosaik juga sering digunakan dalam analisis non-standar. Ini memungkinkan pemodelan yang lebih fleksibel dan formal terhadap bilangan infinitesimal dan non-standar. Contoh Penggunaan: Integral mosaik digunakan dalam berbagai konteks matematika, termasuk teori bilangan, analisis non-standar, dan pemodelan fenomena yang sulit dijelaskan oleh integral Riemann.

g <- makeFun(sin(x^2)*cos(sqrt(x^4 + 3 )-x^2) - x + 1 ~ x)
slice_plot(g(x) ~ x, domain(x = -3:3)) %>%
  gf_hline(yintercept  = 10, color = "red")

# Membuat data frame interval mosaik
mosaic_intervals <- data.frame(
  Lower = c(0, 1, 2, 3, 4),
  Upper = c(1, 2, 3, 4, 5)
)

# Membuat plot interval mosaik
ggplot(data = mosaic_intervals) +
  geom_segment(aes(x = Lower, xend = Upper, y = 0, yend = 0)) +
  geom_text(aes(x = (Lower + Upper) / 2, y = 0, label = paste("(", Lower, ",", Upper, ")"), vjust = -1)) +
  labs(x = "Interval Mosaik", y = "") +
  theme_minimal()

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