Initial population.

1 files changed, 763 insertions, 0 deletions

diff --git a/src/hyper/pages/INT.pht b/src/hyper/pages/INT.pht
new file mode 100644
index 00000000..4264dc2e
--- /dev/null
+++ b/src/hyper/pages/INT.pht
@@ -0,0 +1,763 @@
+\begin{patch}{ugxIntegerPrimesPagePatch1}
+\begin{paste}{ugxIntegerPrimesPageFull1}{ugxIntegerPrimesPageEmpty1}
+\pastebutton{ugxIntegerPrimesPageFull1}{\hidepaste}
+\tab{5}\spadcommand{factor 102400}
+\indentrel{3}\begin{verbatim}
+         12 2
+   (1)  2  5
+                                 Type: Factored Integer
+\end{verbatim}
+\indentrel{-3}\end{paste}\end{patch}
+
+\begin{patch}{ugxIntegerPrimesPageEmpty1}
+\begin{paste}{ugxIntegerPrimesPageEmpty1}{ugxIntegerPrimesPagePatch1}
+\pastebutton{ugxIntegerPrimesPageEmpty1}{\showpaste}
+\tab{5}\spadcommand{factor 102400}
+\end{paste}\end{patch}
+
+\begin{patch}{ugxIntegerPrimesPagePatch2}
+\begin{paste}{ugxIntegerPrimesPageFull2}{ugxIntegerPrimesPageEmpty2}
+\pastebutton{ugxIntegerPrimesPageFull2}{\hidepaste}
+\tab{5}\spadcommand{prime? 7}
+\indentrel{3}\begin{verbatim}
+   (2)  true
+                                          Type: Boolean
+\end{verbatim}
+\indentrel{-3}\end{paste}\end{patch}
+
+\begin{patch}{ugxIntegerPrimesPageEmpty2}
+\begin{paste}{ugxIntegerPrimesPageEmpty2}{ugxIntegerPrimesPagePatch2}
+\pastebutton{ugxIntegerPrimesPageEmpty2}{\showpaste}
+\tab{5}\spadcommand{prime? 7}
+\end{paste}\end{patch}
+
+\begin{patch}{ugxIntegerPrimesPagePatch3}
+\begin{paste}{ugxIntegerPrimesPageFull3}{ugxIntegerPrimesPageEmpty3}
+\pastebutton{ugxIntegerPrimesPageFull3}{\hidepaste}
+\tab{5}\spadcommand{prime? 8}
+\indentrel{3}\begin{verbatim}
+   (3)  false
+                                          Type: Boolean
+\end{verbatim}
+\indentrel{-3}\end{paste}\end{patch}
+
+\begin{patch}{ugxIntegerPrimesPageEmpty3}
+\begin{paste}{ugxIntegerPrimesPageEmpty3}{ugxIntegerPrimesPagePatch3}
+\pastebutton{ugxIntegerPrimesPageEmpty3}{\showpaste}
+\tab{5}\spadcommand{prime? 8}
+\end{paste}\end{patch}
+
+\begin{patch}{ugxIntegerPrimesPagePatch4}
+\begin{paste}{ugxIntegerPrimesPageFull4}{ugxIntegerPrimesPageEmpty4}
+\pastebutton{ugxIntegerPrimesPageFull4}{\hidepaste}
+\tab{5}\spadcommand{nextPrime 100}
+\indentrel{3}\begin{verbatim}
+   (4)  101
+                                  Type: PositiveInteger
+\end{verbatim}
+\indentrel{-3}\end{paste}\end{patch}
+
+\begin{patch}{ugxIntegerPrimesPageEmpty4}
+\begin{paste}{ugxIntegerPrimesPageEmpty4}{ugxIntegerPrimesPagePatch4}
+\pastebutton{ugxIntegerPrimesPageEmpty4}{\showpaste}
+\tab{5}\spadcommand{nextPrime 100}
+\end{paste}\end{patch}
+
+\begin{patch}{ugxIntegerPrimesPagePatch5}
+\begin{paste}{ugxIntegerPrimesPageFull5}{ugxIntegerPrimesPageEmpty5}
+\pastebutton{ugxIntegerPrimesPageFull5}{\hidepaste}
+\tab{5}\spadcommand{prevPrime 100}
+\indentrel{3}\begin{verbatim}
+   (5)  97
+                                  Type: PositiveInteger
+\end{verbatim}
+\indentrel{-3}\end{paste}\end{patch}
+
+\begin{patch}{ugxIntegerPrimesPageEmpty5}
+\begin{paste}{ugxIntegerPrimesPageEmpty5}{ugxIntegerPrimesPagePatch5}
+\pastebutton{ugxIntegerPrimesPageEmpty5}{\showpaste}
+\tab{5}\spadcommand{prevPrime 100}
+\end{paste}\end{patch}
+
+\begin{patch}{ugxIntegerPrimesPagePatch6}
+\begin{paste}{ugxIntegerPrimesPageFull6}{ugxIntegerPrimesPageEmpty6}
+\pastebutton{ugxIntegerPrimesPageFull6}{\hidepaste}
+\tab{5}\spadcommand{primes(100,175)}
+\indentrel{3}\begin{verbatim}
+   (6)
+   [173, 167, 163, 157, 151, 149, 139, 137, 131, 127,
+    113, 109, 107, 103, 101]
+                                     Type: List Integer
+\end{verbatim}
+\indentrel{-3}\end{paste}\end{patch}
+
+\begin{patch}{ugxIntegerPrimesPageEmpty6}
+\begin{paste}{ugxIntegerPrimesPageEmpty6}{ugxIntegerPrimesPagePatch6}
+\pastebutton{ugxIntegerPrimesPageEmpty6}{\showpaste}
+\tab{5}\spadcommand{primes(100,175)}
+\end{paste}\end{patch}
+
+\begin{patch}{ugxIntegerPrimesPagePatch7}
+\begin{paste}{ugxIntegerPrimesPageFull7}{ugxIntegerPrimesPageEmpty7}
+\pastebutton{ugxIntegerPrimesPageFull7}{\hidepaste}
+\tab{5}\spadcommand{factor(2 :: Complex Integer)}
+\indentrel{3}\begin{verbatim}
+                     2
+   (7)  - %i (1 + %i)
+                         Type: Factored Complex Integer
+\end{verbatim}
+\indentrel{-3}\end{paste}\end{patch}
+
+\begin{patch}{ugxIntegerPrimesPageEmpty7}
+\begin{paste}{ugxIntegerPrimesPageEmpty7}{ugxIntegerPrimesPagePatch7}
+\pastebutton{ugxIntegerPrimesPageEmpty7}{\showpaste}
+\tab{5}\spadcommand{factor(2 :: Complex Integer)}
+\end{paste}\end{patch}
+
+\begin{patch}{ugxIntegerNTPagePatch1}
+\begin{paste}{ugxIntegerNTPageFull1}{ugxIntegerNTPageEmpty1}
+\pastebutton{ugxIntegerNTPageFull1}{\hidepaste}
+\tab{5}\spadcommand{[fibonacci(k) for k in 0..]}
+\indentrel{3}\begin{verbatim}
+   (1)  [0,1,1,2,3,5,8,13,21,34,...]
+                                   Type: Stream Integer
+\end{verbatim}
+\indentrel{-3}\end{paste}\end{patch}
+
+\begin{patch}{ugxIntegerNTPageEmpty1}
+\begin{paste}{ugxIntegerNTPageEmpty1}{ugxIntegerNTPagePatch1}
+\pastebutton{ugxIntegerNTPageEmpty1}{\showpaste}
+\tab{5}\spadcommand{[fibonacci(k) for k in 0..]}
+\end{paste}\end{patch}
+
+\begin{patch}{ugxIntegerNTPagePatch2}
+\begin{paste}{ugxIntegerNTPageFull2}{ugxIntegerNTPageEmpty2}
+\pastebutton{ugxIntegerNTPageFull2}{\hidepaste}
+\tab{5}\spadcommand{[legendre(i,11) for i in 0..10]}
+\indentrel{3}\begin{verbatim}
+   (2)  [0,1,- 1,1,1,1,- 1,- 1,- 1,1,- 1]
+                                     Type: List Integer
+\end{verbatim}
+\indentrel{-3}\end{paste}\end{patch}
+
+\begin{patch}{ugxIntegerNTPageEmpty2}
+\begin{paste}{ugxIntegerNTPageEmpty2}{ugxIntegerNTPagePatch2}
+\pastebutton{ugxIntegerNTPageEmpty2}{\showpaste}
+\tab{5}\spadcommand{[legendre(i,11) for i in 0..10]}
+\end{paste}\end{patch}
+
+\begin{patch}{ugxIntegerNTPagePatch3}
+\begin{paste}{ugxIntegerNTPageFull3}{ugxIntegerNTPageEmpty3}
+\pastebutton{ugxIntegerNTPageFull3}{\hidepaste}
+\tab{5}\spadcommand{[jacobi(i,15) for i in 0..9]}
+\indentrel{3}\begin{verbatim}
+   (3)  [0,1,1,0,1,0,0,- 1,1,0]
+                                     Type: List Integer
+\end{verbatim}
+\indentrel{-3}\end{paste}\end{patch}
+
+\begin{patch}{ugxIntegerNTPageEmpty3}
+\begin{paste}{ugxIntegerNTPageEmpty3}{ugxIntegerNTPagePatch3}
+\pastebutton{ugxIntegerNTPageEmpty3}{\showpaste}
+\tab{5}\spadcommand{[jacobi(i,15) for i in 0..9]}
+\end{paste}\end{patch}
+
+\begin{patch}{ugxIntegerNTPagePatch4}
+\begin{paste}{ugxIntegerNTPageFull4}{ugxIntegerNTPageEmpty4}
+\pastebutton{ugxIntegerNTPageFull4}{\hidepaste}
+\tab{5}\spadcommand{[eulerPhi i for i in 1..]}
+\indentrel{3}\begin{verbatim}
+   (4)  [1,1,2,2,4,2,6,4,6,4,...]
+                                   Type: Stream Integer
+\end{verbatim}
+\indentrel{-3}\end{paste}\end{patch}
+
+\begin{patch}{ugxIntegerNTPageEmpty4}
+\begin{paste}{ugxIntegerNTPageEmpty4}{ugxIntegerNTPagePatch4}
+\pastebutton{ugxIntegerNTPageEmpty4}{\showpaste}
+\tab{5}\spadcommand{[eulerPhi i for i in 1..]}
+\end{paste}\end{patch}
+
+\begin{patch}{ugxIntegerNTPagePatch5}
+\begin{paste}{ugxIntegerNTPageFull5}{ugxIntegerNTPageEmpty5}
+\pastebutton{ugxIntegerNTPageFull5}{\hidepaste}
+\tab{5}\spadcommand{[moebiusMu i for i in 1..]}
+\indentrel{3}\begin{verbatim}
+   (5)  [1,- 1,- 1,0,- 1,1,- 1,0,0,1,...]
+                                   Type: Stream Integer
+\end{verbatim}
+\indentrel{-3}\end{paste}\end{patch}
+
+\begin{patch}{ugxIntegerNTPageEmpty5}
+\begin{paste}{ugxIntegerNTPageEmpty5}{ugxIntegerNTPagePatch5}
+\pastebutton{ugxIntegerNTPageEmpty5}{\showpaste}
+\tab{5}\spadcommand{[moebiusMu i for i in 1..]}
+\end{paste}\end{patch}
+
+\begin{patch}{ugxIntegerNTPagePatch6}
+\begin{paste}{ugxIntegerNTPageFull6}{ugxIntegerNTPageEmpty6}
+\pastebutton{ugxIntegerNTPageFull6}{\hidepaste}
+\tab{5}\spadcommand{a := roman(78)\bound{a }}
+\indentrel{3}\begin{verbatim}
+   (6)  LXXVIII
+                                     Type: RomanNumeral
+\end{verbatim}
+\indentrel{-3}\end{paste}\end{patch}
+
+\begin{patch}{ugxIntegerNTPageEmpty6}
+\begin{paste}{ugxIntegerNTPageEmpty6}{ugxIntegerNTPagePatch6}
+\pastebutton{ugxIntegerNTPageEmpty6}{\showpaste}
+\tab{5}\spadcommand{a := roman(78)\bound{a }}
+\end{paste}\end{patch}
+
+\begin{patch}{ugxIntegerNTPagePatch7}
+\begin{paste}{ugxIntegerNTPageFull7}{ugxIntegerNTPageEmpty7}
+\pastebutton{ugxIntegerNTPageFull7}{\hidepaste}
+\tab{5}\spadcommand{b := roman(87)\bound{b }}
+\indentrel{3}\begin{verbatim}
+   (7)  LXXXVII
+                                     Type: RomanNumeral
+\end{verbatim}
+\indentrel{-3}\end{paste}\end{patch}
+
+\begin{patch}{ugxIntegerNTPageEmpty7}
+\begin{paste}{ugxIntegerNTPageEmpty7}{ugxIntegerNTPagePatch7}
+\pastebutton{ugxIntegerNTPageEmpty7}{\showpaste}
+\tab{5}\spadcommand{b := roman(87)\bound{b }}
+\end{paste}\end{patch}
+
+\begin{patch}{ugxIntegerNTPagePatch8}
+\begin{paste}{ugxIntegerNTPageFull8}{ugxIntegerNTPageEmpty8}
+\pastebutton{ugxIntegerNTPageFull8}{\hidepaste}
+\tab{5}\spadcommand{a + b\free{a }\free{b }}
+\indentrel{3}\begin{verbatim}
+   (8)  CLXV
+                                     Type: RomanNumeral
+\end{verbatim}
+\indentrel{-3}\end{paste}\end{patch}
+
+\begin{patch}{ugxIntegerNTPageEmpty8}
+\begin{paste}{ugxIntegerNTPageEmpty8}{ugxIntegerNTPagePatch8}
+\pastebutton{ugxIntegerNTPageEmpty8}{\showpaste}
+\tab{5}\spadcommand{a + b\free{a }\free{b }}
+\end{paste}\end{patch}
+
+\begin{patch}{ugxIntegerNTPagePatch9}
+\begin{paste}{ugxIntegerNTPageFull9}{ugxIntegerNTPageEmpty9}
+\pastebutton{ugxIntegerNTPageFull9}{\hidepaste}
+\tab{5}\spadcommand{a * b\free{a }\free{b }}
+\indentrel{3}\begin{verbatim}
+   (9)  MMMMMMDCCLXXXVI
+                                     Type: RomanNumeral
+\end{verbatim}
+\indentrel{-3}\end{paste}\end{patch}
+
+\begin{patch}{ugxIntegerNTPageEmpty9}
+\begin{paste}{ugxIntegerNTPageEmpty9}{ugxIntegerNTPagePatch9}
+\pastebutton{ugxIntegerNTPageEmpty9}{\showpaste}
+\tab{5}\spadcommand{a * b\free{a }\free{b }}
+\end{paste}\end{patch}
+
+\begin{patch}{ugxIntegerNTPagePatch10}
+\begin{paste}{ugxIntegerNTPageFull10}{ugxIntegerNTPageEmpty10}
+\pastebutton{ugxIntegerNTPageFull10}{\hidepaste}
+\tab{5}\spadcommand{b rem a\free{a }\free{b }}
+\indentrel{3}\begin{verbatim}
+   (10)  IX
+                                     Type: RomanNumeral
+\end{verbatim}
+\indentrel{-3}\end{paste}\end{patch}
+
+\begin{patch}{ugxIntegerNTPageEmpty10}
+\begin{paste}{ugxIntegerNTPageEmpty10}{ugxIntegerNTPagePatch10}
+\pastebutton{ugxIntegerNTPageEmpty10}{\showpaste}
+\tab{5}\spadcommand{b rem a\free{a }\free{b }}
+\end{paste}\end{patch}
+
+\begin{patch}{ugxIntegerBasicPagePatch1}
+\begin{paste}{ugxIntegerBasicPageFull1}{ugxIntegerBasicPageEmpty1}
+\pastebutton{ugxIntegerBasicPageFull1}{\hidepaste}
+\tab{5}\spadcommand{2**(5678 - 4856 + 2 * 17)}
+\indentrel{3}\begin{verbatim}
+   (1)
+  480481077043500814718154092512592439123952613987168226_
+   34738556100880842000763082930863425270914120837430745_
+   72278211496076276922026433435687527334980249539302425_
+   42523045817764949544214392905306388478705146745768073_
+   877141698859815495632935288783334250628775936
+                                  Type: PositiveInteger
+\end{verbatim}
+\indentrel{-3}\end{paste}\end{patch}
+
+\begin{patch}{ugxIntegerBasicPageEmpty1}
+\begin{paste}{ugxIntegerBasicPageEmpty1}{ugxIntegerBasicPagePatch1}
+\pastebutton{ugxIntegerBasicPageEmpty1}{\showpaste}
+\tab{5}\spadcommand{2**(5678 - 4856 + 2 * 17)}
+\end{paste}\end{patch}
+
+\begin{patch}{ugxIntegerBasicPagePatch2}
+\begin{paste}{ugxIntegerBasicPageFull2}{ugxIntegerBasicPageEmpty2}
+\pastebutton{ugxIntegerBasicPageFull2}{\hidepaste}
+\tab{5}\spadcommand{x := -101\bound{x }}
+\indentrel{3}\begin{verbatim}
+   (2)  - 101
+                                          Type: Integer
+\end{verbatim}
+\indentrel{-3}\end{paste}\end{patch}
+
+\begin{patch}{ugxIntegerBasicPageEmpty2}
+\begin{paste}{ugxIntegerBasicPageEmpty2}{ugxIntegerBasicPagePatch2}
+\pastebutton{ugxIntegerBasicPageEmpty2}{\showpaste}
+\tab{5}\spadcommand{x := -101\bound{x }}
+\end{paste}\end{patch}
+
+\begin{patch}{ugxIntegerBasicPagePatch3}
+\begin{paste}{ugxIntegerBasicPageFull3}{ugxIntegerBasicPageEmpty3}
+\pastebutton{ugxIntegerBasicPageFull3}{\hidepaste}
+\tab{5}\spadcommand{abs(x)\free{x }}
+\indentrel{3}\begin{verbatim}
+   (3)  101
+                                  Type: PositiveInteger
+\end{verbatim}
+\indentrel{-3}\end{paste}\end{patch}
+
+\begin{patch}{ugxIntegerBasicPageEmpty3}
+\begin{paste}{ugxIntegerBasicPageEmpty3}{ugxIntegerBasicPagePatch3}
+\pastebutton{ugxIntegerBasicPageEmpty3}{\showpaste}
+\tab{5}\spadcommand{abs(x)\free{x }}
+\end{paste}\end{patch}
+
+\begin{patch}{ugxIntegerBasicPagePatch4}
+\begin{paste}{ugxIntegerBasicPageFull4}{ugxIntegerBasicPageEmpty4}
+\pastebutton{ugxIntegerBasicPageFull4}{\hidepaste}
+\tab{5}\spadcommand{sign(x)\free{x }}
+\indentrel{3}\begin{verbatim}
+   (4)  - 1
+                                          Type: Integer
+\end{verbatim}
+\indentrel{-3}\end{paste}\end{patch}
+
+\begin{patch}{ugxIntegerBasicPageEmpty4}
+\begin{paste}{ugxIntegerBasicPageEmpty4}{ugxIntegerBasicPagePatch4}
+\pastebutton{ugxIntegerBasicPageEmpty4}{\showpaste}
+\tab{5}\spadcommand{sign(x)\free{x }}
+\end{paste}\end{patch}
+
+\begin{patch}{ugxIntegerBasicPagePatch5}
+\begin{paste}{ugxIntegerBasicPageFull5}{ugxIntegerBasicPageEmpty5}
+\pastebutton{ugxIntegerBasicPageFull5}{\hidepaste}
+\tab{5}\spadcommand{x < 0\free{x }}
+\indentrel{3}\begin{verbatim}
+   (5)  true
+                                          Type: Boolean
+\end{verbatim}
+\indentrel{-3}\end{paste}\end{patch}
+
+\begin{patch}{ugxIntegerBasicPageEmpty5}
+\begin{paste}{ugxIntegerBasicPageEmpty5}{ugxIntegerBasicPagePatch5}
+\pastebutton{ugxIntegerBasicPageEmpty5}{\showpaste}
+\tab{5}\spadcommand{x < 0\free{x }}
+\end{paste}\end{patch}
+
+\begin{patch}{ugxIntegerBasicPagePatch6}
+\begin{paste}{ugxIntegerBasicPageFull6}{ugxIntegerBasicPageEmpty6}
+\pastebutton{ugxIntegerBasicPageFull6}{\hidepaste}
+\tab{5}\spadcommand{x <= -1\free{x }}
+\indentrel{3}\begin{verbatim}
+   (6)  true
+                                          Type: Boolean
+\end{verbatim}
+\indentrel{-3}\end{paste}\end{patch}
+
+\begin{patch}{ugxIntegerBasicPageEmpty6}
+\begin{paste}{ugxIntegerBasicPageEmpty6}{ugxIntegerBasicPagePatch6}
+\pastebutton{ugxIntegerBasicPageEmpty6}{\showpaste}
+\tab{5}\spadcommand{x <= -1\free{x }}
+\end{paste}\end{patch}
+
+\begin{patch}{ugxIntegerBasicPagePatch7}
+\begin{paste}{ugxIntegerBasicPageFull7}{ugxIntegerBasicPageEmpty7}
+\pastebutton{ugxIntegerBasicPageFull7}{\hidepaste}
+\tab{5}\spadcommand{negative?(x)\free{x }}
+\indentrel{3}\begin{verbatim}
+   (7)  true
+                                          Type: Boolean
+\end{verbatim}
+\indentrel{-3}\end{paste}\end{patch}
+
+\begin{patch}{ugxIntegerBasicPageEmpty7}
+\begin{paste}{ugxIntegerBasicPageEmpty7}{ugxIntegerBasicPagePatch7}
+\pastebutton{ugxIntegerBasicPageEmpty7}{\showpaste}
+\tab{5}\spadcommand{negative?(x)\free{x }}
+\end{paste}\end{patch}
+
+\begin{patch}{ugxIntegerBasicPagePatch8}
+\begin{paste}{ugxIntegerBasicPageFull8}{ugxIntegerBasicPageEmpty8}
+\pastebutton{ugxIntegerBasicPageFull8}{\hidepaste}
+\tab{5}\spadcommand{x > 0\free{x }}
+\indentrel{3}\begin{verbatim}
+   (8)  false
+                                          Type: Boolean
+\end{verbatim}
+\indentrel{-3}\end{paste}\end{patch}
+
+\begin{patch}{ugxIntegerBasicPageEmpty8}
+\begin{paste}{ugxIntegerBasicPageEmpty8}{ugxIntegerBasicPagePatch8}
+\pastebutton{ugxIntegerBasicPageEmpty8}{\showpaste}
+\tab{5}\spadcommand{x > 0\free{x }}
+\end{paste}\end{patch}
+
+\begin{patch}{ugxIntegerBasicPagePatch9}
+\begin{paste}{ugxIntegerBasicPageFull9}{ugxIntegerBasicPageEmpty9}
+\pastebutton{ugxIntegerBasicPageFull9}{\hidepaste}
+\tab{5}\spadcommand{x >= 1\free{x }}
+\indentrel{3}\begin{verbatim}
+   (9)  false
+                                          Type: Boolean
+\end{verbatim}
+\indentrel{-3}\end{paste}\end{patch}
+
+\begin{patch}{ugxIntegerBasicPageEmpty9}
+\begin{paste}{ugxIntegerBasicPageEmpty9}{ugxIntegerBasicPagePatch9}
+\pastebutton{ugxIntegerBasicPageEmpty9}{\showpaste}
+\tab{5}\spadcommand{x >= 1\free{x }}
+\end{paste}\end{patch}
+
+\begin{patch}{ugxIntegerBasicPagePatch10}
+\begin{paste}{ugxIntegerBasicPageFull10}{ugxIntegerBasicPageEmpty10}
+\pastebutton{ugxIntegerBasicPageFull10}{\hidepaste}
+\tab{5}\spadcommand{positive?(x)\free{x }}
+\indentrel{3}\begin{verbatim}
+   (10)  false
+                                          Type: Boolean
+\end{verbatim}
+\indentrel{-3}\end{paste}\end{patch}
+
+\begin{patch}{ugxIntegerBasicPageEmpty10}
+\begin{paste}{ugxIntegerBasicPageEmpty10}{ugxIntegerBasicPagePatch10}
+\pastebutton{ugxIntegerBasicPageEmpty10}{\showpaste}
+\tab{5}\spadcommand{positive?(x)\free{x }}
+\end{paste}\end{patch}
+
+\begin{patch}{ugxIntegerBasicPagePatch11}
+\begin{paste}{ugxIntegerBasicPageFull11}{ugxIntegerBasicPageEmpty11}
+\pastebutton{ugxIntegerBasicPageFull11}{\hidepaste}
+\tab{5}\spadcommand{zero?(x)\free{x }}
+\indentrel{3}\begin{verbatim}
+   (11)  false
+                                          Type: Boolean
+\end{verbatim}
+\indentrel{-3}\end{paste}\end{patch}
+
+\begin{patch}{ugxIntegerBasicPageEmpty11}
+\begin{paste}{ugxIntegerBasicPageEmpty11}{ugxIntegerBasicPagePatch11}
+\pastebutton{ugxIntegerBasicPageEmpty11}{\showpaste}
+\tab{5}\spadcommand{zero?(x)\free{x }}
+\end{paste}\end{patch}
+
+\begin{patch}{ugxIntegerBasicPagePatch12}
+\begin{paste}{ugxIntegerBasicPageFull12}{ugxIntegerBasicPageEmpty12}
+\pastebutton{ugxIntegerBasicPageFull12}{\hidepaste}
+\tab{5}\spadcommand{one?(x)\free{x }}
+\indentrel{3}\begin{verbatim}
+   (12)  false
+                                          Type: Boolean
+\end{verbatim}
+\indentrel{-3}\end{paste}\end{patch}
+
+\begin{patch}{ugxIntegerBasicPageEmpty12}
+\begin{paste}{ugxIntegerBasicPageEmpty12}{ugxIntegerBasicPagePatch12}
+\pastebutton{ugxIntegerBasicPageEmpty12}{\showpaste}
+\tab{5}\spadcommand{one?(x)\free{x }}
+\end{paste}\end{patch}
+
+\begin{patch}{ugxIntegerBasicPagePatch13}
+\begin{paste}{ugxIntegerBasicPageFull13}{ugxIntegerBasicPageEmpty13}
+\pastebutton{ugxIntegerBasicPageFull13}{\hidepaste}
+\tab{5}\spadcommand{(x = -101)@Boolean\free{x }}
+\indentrel{3}\begin{verbatim}
+   (13)  true
+                                          Type: Boolean
+\end{verbatim}
+\indentrel{-3}\end{paste}\end{patch}
+
+\begin{patch}{ugxIntegerBasicPageEmpty13}
+\begin{paste}{ugxIntegerBasicPageEmpty13}{ugxIntegerBasicPagePatch13}
+\pastebutton{ugxIntegerBasicPageEmpty13}{\showpaste}
+\tab{5}\spadcommand{(x = -101)@Boolean\free{x }}
+\end{paste}\end{patch}
+
+\begin{patch}{ugxIntegerBasicPagePatch14}
+\begin{paste}{ugxIntegerBasicPageFull14}{ugxIntegerBasicPageEmpty14}
+\pastebutton{ugxIntegerBasicPageFull14}{\hidepaste}
+\tab{5}\spadcommand{odd?(x)\free{x }}
+\indentrel{3}\begin{verbatim}
+   (14)  true
+                                          Type: Boolean
+\end{verbatim}
+\indentrel{-3}\end{paste}\end{patch}
+
+\begin{patch}{ugxIntegerBasicPageEmpty14}
+\begin{paste}{ugxIntegerBasicPageEmpty14}{ugxIntegerBasicPagePatch14}
+\pastebutton{ugxIntegerBasicPageEmpty14}{\showpaste}
+\tab{5}\spadcommand{odd?(x)\free{x }}
+\end{paste}\end{patch}
+
+\begin{patch}{ugxIntegerBasicPagePatch15}
+\begin{paste}{ugxIntegerBasicPageFull15}{ugxIntegerBasicPageEmpty15}
+\pastebutton{ugxIntegerBasicPageFull15}{\hidepaste}
+\tab{5}\spadcommand{even?(x)\free{x }}
+\indentrel{3}\begin{verbatim}
+   (15)  false
+                                          Type: Boolean
+\end{verbatim}
+\indentrel{-3}\end{paste}\end{patch}
+
+\begin{patch}{ugxIntegerBasicPageEmpty15}
+\begin{paste}{ugxIntegerBasicPageEmpty15}{ugxIntegerBasicPagePatch15}
+\pastebutton{ugxIntegerBasicPageEmpty15}{\showpaste}
+\tab{5}\spadcommand{even?(x)\free{x }}
+\end{paste}\end{patch}
+
+\begin{patch}{ugxIntegerBasicPagePatch16}
+\begin{paste}{ugxIntegerBasicPageFull16}{ugxIntegerBasicPageEmpty16}
+\pastebutton{ugxIntegerBasicPageFull16}{\hidepaste}
+\tab{5}\spadcommand{gcd(56788,43688)}
+\indentrel{3}\begin{verbatim}
+   (16)  4
+                                  Type: PositiveInteger
+\end{verbatim}
+\indentrel{-3}\end{paste}\end{patch}
+
+\begin{patch}{ugxIntegerBasicPageEmpty16}
+\begin{paste}{ugxIntegerBasicPageEmpty16}{ugxIntegerBasicPagePatch16}
+\pastebutton{ugxIntegerBasicPageEmpty16}{\showpaste}
+\tab{5}\spadcommand{gcd(56788,43688)}
+\end{paste}\end{patch}
+
+\begin{patch}{ugxIntegerBasicPagePatch17}
+\begin{paste}{ugxIntegerBasicPageFull17}{ugxIntegerBasicPageEmpty17}
+\pastebutton{ugxIntegerBasicPageFull17}{\hidepaste}
+\tab{5}\spadcommand{lcm(56788,43688)}
+\indentrel{3}\begin{verbatim}
+   (17)  620238536
+                                  Type: PositiveInteger
+\end{verbatim}
+\indentrel{-3}\end{paste}\end{patch}
+
+\begin{patch}{ugxIntegerBasicPageEmpty17}
+\begin{paste}{ugxIntegerBasicPageEmpty17}{ugxIntegerBasicPagePatch17}
+\pastebutton{ugxIntegerBasicPageEmpty17}{\showpaste}
+\tab{5}\spadcommand{lcm(56788,43688)}
+\end{paste}\end{patch}
+
+\begin{patch}{ugxIntegerBasicPagePatch18}
+\begin{paste}{ugxIntegerBasicPageFull18}{ugxIntegerBasicPageEmpty18}
+\pastebutton{ugxIntegerBasicPageFull18}{\hidepaste}
+\tab{5}\spadcommand{max(678,567)}
+\indentrel{3}\begin{verbatim}
+   (18)  678
+                                  Type: PositiveInteger
+\end{verbatim}
+\indentrel{-3}\end{paste}\end{patch}
+
+\begin{patch}{ugxIntegerBasicPageEmpty18}
+\begin{paste}{ugxIntegerBasicPageEmpty18}{ugxIntegerBasicPagePatch18}
+\pastebutton{ugxIntegerBasicPageEmpty18}{\showpaste}
+\tab{5}\spadcommand{max(678,567)}
+\end{paste}\end{patch}
+
+\begin{patch}{ugxIntegerBasicPagePatch19}
+\begin{paste}{ugxIntegerBasicPageFull19}{ugxIntegerBasicPageEmpty19}
+\pastebutton{ugxIntegerBasicPageFull19}{\hidepaste}
+\tab{5}\spadcommand{min(678,567)}
+\indentrel{3}\begin{verbatim}
+   (19)  567
+                                  Type: PositiveInteger
+\end{verbatim}
+\indentrel{-3}\end{paste}\end{patch}
+
+\begin{patch}{ugxIntegerBasicPageEmpty19}
+\begin{paste}{ugxIntegerBasicPageEmpty19}{ugxIntegerBasicPagePatch19}
+\pastebutton{ugxIntegerBasicPageEmpty19}{\showpaste}
+\tab{5}\spadcommand{min(678,567)}
+\end{paste}\end{patch}
+
+\begin{patch}{ugxIntegerBasicPagePatch20}
+\begin{paste}{ugxIntegerBasicPageFull20}{ugxIntegerBasicPageEmpty20}
+\pastebutton{ugxIntegerBasicPageFull20}{\hidepaste}
+\tab{5}\spadcommand{reduce(max,[2,45,-89,78,100,-45])}
+\indentrel{3}\begin{verbatim}
+   (20)  100
+                                  Type: PositiveInteger
+\end{verbatim}
+\indentrel{-3}\end{paste}\end{patch}
+
+\begin{patch}{ugxIntegerBasicPageEmpty20}
+\begin{paste}{ugxIntegerBasicPageEmpty20}{ugxIntegerBasicPagePatch20}
+\pastebutton{ugxIntegerBasicPageEmpty20}{\showpaste}
+\tab{5}\spadcommand{reduce(max,[2,45,-89,78,100,-45])}
+\end{paste}\end{patch}
+
+\begin{patch}{ugxIntegerBasicPagePatch21}
+\begin{paste}{ugxIntegerBasicPageFull21}{ugxIntegerBasicPageEmpty21}
+\pastebutton{ugxIntegerBasicPageFull21}{\hidepaste}
+\tab{5}\spadcommand{reduce(min,[2,45,-89,78,100,-45])}
+\indentrel{3}\begin{verbatim}
+   (21)  - 89
+                                          Type: Integer
+\end{verbatim}
+\indentrel{-3}\end{paste}\end{patch}
+
+\begin{patch}{ugxIntegerBasicPageEmpty21}
+\begin{paste}{ugxIntegerBasicPageEmpty21}{ugxIntegerBasicPagePatch21}
+\pastebutton{ugxIntegerBasicPageEmpty21}{\showpaste}
+\tab{5}\spadcommand{reduce(min,[2,45,-89,78,100,-45])}
+\end{paste}\end{patch}
+
+\begin{patch}{ugxIntegerBasicPagePatch22}
+\begin{paste}{ugxIntegerBasicPageFull22}{ugxIntegerBasicPageEmpty22}
+\pastebutton{ugxIntegerBasicPageFull22}{\hidepaste}
+\tab{5}\spadcommand{reduce(gcd,[2,45,-89,78,100,-45])}
+\indentrel{3}\begin{verbatim}
+   (22)  1
+                                  Type: PositiveInteger
+\end{verbatim}
+\indentrel{-3}\end{paste}\end{patch}
+
+\begin{patch}{ugxIntegerBasicPageEmpty22}
+\begin{paste}{ugxIntegerBasicPageEmpty22}{ugxIntegerBasicPagePatch22}
+\pastebutton{ugxIntegerBasicPageEmpty22}{\showpaste}
+\tab{5}\spadcommand{reduce(gcd,[2,45,-89,78,100,-45])}
+\end{paste}\end{patch}
+
+\begin{patch}{ugxIntegerBasicPagePatch23}
+\begin{paste}{ugxIntegerBasicPageFull23}{ugxIntegerBasicPageEmpty23}
+\pastebutton{ugxIntegerBasicPageFull23}{\hidepaste}
+\tab{5}\spadcommand{reduce(lcm,[2,45,-89,78,100,-45])}
+\indentrel{3}\begin{verbatim}
+   (23)  1041300
+                                  Type: PositiveInteger
+\end{verbatim}
+\indentrel{-3}\end{paste}\end{patch}
+
+\begin{patch}{ugxIntegerBasicPageEmpty23}
+\begin{paste}{ugxIntegerBasicPageEmpty23}{ugxIntegerBasicPagePatch23}
+\pastebutton{ugxIntegerBasicPageEmpty23}{\showpaste}
+\tab{5}\spadcommand{reduce(lcm,[2,45,-89,78,100,-45])}
+\end{paste}\end{patch}
+
+\begin{patch}{ugxIntegerBasicPagePatch24}
+\begin{paste}{ugxIntegerBasicPageFull24}{ugxIntegerBasicPageEmpty24}
+\pastebutton{ugxIntegerBasicPageFull24}{\hidepaste}
+\tab{5}\spadcommand{13 / 4}
+\indentrel{3}\begin{verbatim}
+         13
+   (24)  ÄÄ
+          4
+                                 Type: Fraction Integer
+\end{verbatim}
+\indentrel{-3}\end{paste}\end{patch}
+
+\begin{patch}{ugxIntegerBasicPageEmpty24}
+\begin{paste}{ugxIntegerBasicPageEmpty24}{ugxIntegerBasicPagePatch24}
+\pastebutton{ugxIntegerBasicPageEmpty24}{\showpaste}
+\tab{5}\spadcommand{13 / 4}
+\end{paste}\end{patch}
+
+\begin{patch}{ugxIntegerBasicPagePatch25}
+\begin{paste}{ugxIntegerBasicPageFull25}{ugxIntegerBasicPageEmpty25}
+\pastebutton{ugxIntegerBasicPageFull25}{\hidepaste}
+\tab{5}\spadcommand{13 quo 4}
+\indentrel{3}\begin{verbatim}
+   (25)  3
+                                  Type: PositiveInteger
+\end{verbatim}
+\indentrel{-3}\end{paste}\end{patch}
+
+\begin{patch}{ugxIntegerBasicPageEmpty25}
+\begin{paste}{ugxIntegerBasicPageEmpty25}{ugxIntegerBasicPagePatch25}
+\pastebutton{ugxIntegerBasicPageEmpty25}{\showpaste}
+\tab{5}\spadcommand{13 quo 4}
+\end{paste}\end{patch}
+
+\begin{patch}{ugxIntegerBasicPagePatch26}
+\begin{paste}{ugxIntegerBasicPageFull26}{ugxIntegerBasicPageEmpty26}
+\pastebutton{ugxIntegerBasicPageFull26}{\hidepaste}
+\tab{5}\spadcommand{13 rem 4}
+\indentrel{3}\begin{verbatim}
+   (26)  1
+                                  Type: PositiveInteger
+\end{verbatim}
+\indentrel{-3}\end{paste}\end{patch}
+
+\begin{patch}{ugxIntegerBasicPageEmpty26}
+\begin{paste}{ugxIntegerBasicPageEmpty26}{ugxIntegerBasicPagePatch26}
+\pastebutton{ugxIntegerBasicPageEmpty26}{\showpaste}
+\tab{5}\spadcommand{13 rem 4}
+\end{paste}\end{patch}
+
+\begin{patch}{ugxIntegerBasicPagePatch27}
+\begin{paste}{ugxIntegerBasicPageFull27}{ugxIntegerBasicPageEmpty27}
+\pastebutton{ugxIntegerBasicPageFull27}{\hidepaste}
+\tab{5}\spadcommand{zero?(167604736446952 rem 2003644)}
+\indentrel{3}\begin{verbatim}
+   (27)  true
+                                          Type: Boolean
+\end{verbatim}
+\indentrel{-3}\end{paste}\end{patch}
+
+\begin{patch}{ugxIntegerBasicPageEmpty27}
+\begin{paste}{ugxIntegerBasicPageEmpty27}{ugxIntegerBasicPagePatch27}
+\pastebutton{ugxIntegerBasicPageEmpty27}{\showpaste}
+\tab{5}\spadcommand{zero?(167604736446952 rem 2003644)}
+\end{paste}\end{patch}
+
+\begin{patch}{ugxIntegerBasicPagePatch28}
+\begin{paste}{ugxIntegerBasicPageFull28}{ugxIntegerBasicPageEmpty28}
+\pastebutton{ugxIntegerBasicPageFull28}{\hidepaste}
+\tab{5}\spadcommand{d := divide(13,4)\bound{d }}
+\indentrel{3}\begin{verbatim}
+   (28)  [quotient= 3,remainder= 1]
+     Type: Record(quotient: Integer,remainder: Integer)
+\end{verbatim}
+\indentrel{-3}\end{paste}\end{patch}
+
+\begin{patch}{ugxIntegerBasicPageEmpty28}
+\begin{paste}{ugxIntegerBasicPageEmpty28}{ugxIntegerBasicPagePatch28}
+\pastebutton{ugxIntegerBasicPageEmpty28}{\showpaste}
+\tab{5}\spadcommand{d := divide(13,4)\bound{d }}
+\end{paste}\end{patch}
+
+\begin{patch}{ugxIntegerBasicPagePatch29}
+\begin{paste}{ugxIntegerBasicPageFull29}{ugxIntegerBasicPageEmpty29}
+\pastebutton{ugxIntegerBasicPageFull29}{\hidepaste}
+\tab{5}\spadcommand{d.quotient\free{d }}
+\indentrel{3}\begin{verbatim}
+   (29)  3
+                                  Type: PositiveInteger
+\end{verbatim}
+\indentrel{-3}\end{paste}\end{patch}
+
+\begin{patch}{ugxIntegerBasicPageEmpty29}
+\begin{paste}{ugxIntegerBasicPageEmpty29}{ugxIntegerBasicPagePatch29}
+\pastebutton{ugxIntegerBasicPageEmpty29}{\showpaste}
+\tab{5}\spadcommand{d.quotient\free{d }}
+\end{paste}\end{patch}
+
+\begin{patch}{ugxIntegerBasicPagePatch30}
+\begin{paste}{ugxIntegerBasicPageFull30}{ugxIntegerBasicPageEmpty30}
+\pastebutton{ugxIntegerBasicPageFull30}{\hidepaste}
+\tab{5}\spadcommand{d.remainder\free{d }}
+\indentrel{3}\begin{verbatim}
+   (30)  1
+                                  Type: PositiveInteger
+\end{verbatim}
+\indentrel{-3}\end{paste}\end{patch}
+
+\begin{patch}{ugxIntegerBasicPageEmpty30}
+\begin{paste}{ugxIntegerBasicPageEmpty30}{ugxIntegerBasicPagePatch30}
+\pastebutton{ugxIntegerBasicPageEmpty30}{\showpaste}
+\tab{5}\spadcommand{d.remainder\free{d }}
+\end{paste}\end{patch}
+