Z^3 Deeper Features - Revision history

Joseph: /* Function Composition */

2024-01-05T21:47:10Z

Function Composition

Joseph: /* Computation with Large Numbers, Decimals of Arbitrary Length, Fractions, Complex Numbers, etc. */

2024-01-05T20:24:53Z

Computation with Large Numbers, Decimals of Arbitrary Length, Fractions, Complex Numbers, etc.

Joseph: /* Computation with Large Numbers, Decimals of Arbitrary Length, Fractions, Complex Numbers, etc. */

2024-01-05T20:21:58Z

Computation with Large Numbers, Decimals of Arbitrary Length, Fractions, Complex Numbers, etc.

Joseph: /* Computation with Large Numbers, Decimals of Arbitrary Length, Fractions, Complex Numbers, etc. */

2024-01-05T19:58:20Z

Computation with Large Numbers, Decimals of Arbitrary Length, Fractions, Complex Numbers, etc.

Joseph: /* Computation with Large Numbers, Decimals of Arbitrary Length, Fractions, Complex Numbers, etc. */

2024-01-05T19:57:05Z

Computation with Large Numbers, Decimals of Arbitrary Length, Fractions, Complex Numbers, etc.

Joseph at 19:53, 5 January 2024

2024-01-05T19:53:18Z

Joseph: /* Function Composition */

2024-01-05T19:46:25Z

Function Composition

Joseph: Created page with " ==Function Composition== Functions can be composed using the @ operator. A chain of functions can also be composed using the same technique. Composed function works left to..."

2024-01-05T19:45:56Z

Created page with " ==Function Composition== Functions can be composed using the @ operator. A chain of functions can also be composed using the same technique. Composed function works left to..."

New page

==Function Composition==

Functions can be composed using the @ operator. A chain of functions can also be composed using the same technique. Composed function works left to right.

<pre>
a=(x=>x/3)@(x=>x+2);
a(3)
<pre>

gives 3.

First 3 is divided by 3, and then 2 is added to yield 3 as result.

<pre>
a=(x=>x+2)@(x=>x/3);
a(3)
<pre>
gives
1.6666666666666667

<pre>
a=(SIN@COS@TAN);
a(45)
<pre>

gives
0.7749904090605793

@@ Line 1: / Line 1: @@
 ==Function Composition==
@@ Line 27: / Line 31: @@
 gives
 .7749904090605793
 ==Computation with Large Numbers, Decimals of Arbitrary Length, Fractions, Complex Numbers, etc. ==

@@ Line 46: / Line 46: @@
 | Complex Number || x+yi || 3+4i
 |-
-| Fractions|| x.n%%nd || 1.4%%3 gives 2 1/3
+| Fractions|| x.n%%d || 1.4%%3 gives 2 1/3
 |}
@@ Line 69: / Line 67: @@
 .41421356237309504880168872420969807856967187537694807317667973799073247846210703885038753432764157273501384623091229702492483605585073721264412149709993583141322266592750559275579995050115278206057147010955997160597027453459686201472851741864088919860955232923048430871432145083976260362799525140799

@@ Line 42: / Line 42: @@
 | BigInt || n|| (60n)!
 |-
-| Floating Point|| fn.n || 23f5.2
+| Floating Point|| dn || SQRT(2d300)
 |-
 | Complex Number || x+yi || 3+4i
 |-
-| Fractions|| x%%n/d || 23%%5/2
+| Fractions|| x.n%%nd || 1.4%%3 gives 2 1/3
 |}
@@ Line 63: / Line 63: @@
 -156534884864787.47+246178250600375.44ⅈ

@@ Line 53: / Line 53: @@
 (60n)!
 gives
-8320987112741390144276341183223364380754172606361245952449277696409600000000000000
+-156534884864787.47+246178250600375.44ⅈ

← Older revision		Revision as of 19:57, 5 January 2024
Line 49:		Line 49:
	\|}		\|}

		+	// correct this


		+	(60n)!

−	~~(60n)!~~	+	gives
		+
		+	8320987112741390144276341183223364380754172606361245952449277696409600000000000000

← Older revision		Revision as of 19:53, 5 January 2024
Line 27:		Line 27:
	gives		gives
	0.7749904090605793		0.7749904090605793
		+
		+
		+	==Computation with Large Numbers, Decimals of Arbitrary Length, Fractions, Complex Numbers, etc. ==
		+
		+	Often the accuracy provided by the usual computational language is insufficient to handle more complex computations as well as type specific computations.
		+
		+	The following notations are used to indicate advanced numerical types in Z.
		+
		+	{\| class="wikitable"
		+	\|+ Advanced Types
		+	\|-
		+	! Type !! Notation !! Example
		+	\|-
		+	\| BigInt \|\| n\|\| (60n)!
		+	\|-
		+	\| Floating Point\|\| fn.n \|\| 23f5.2
		+	\|-
		+	\| Complex Number \|\| x+yi \|\| 3+4i
		+	\|-
		+	\| Fractions\|\| x%%n/d \|\| 23%%5/2
		+	\|}
		+
		+
		+
		+
		+	(60n)!

@@ Line 7: / Line 7: @@
 a=(x=>x/3)@(x=>x+2);
 a(3)
-<pre>
+</pre>
 gives 3.
@@ Line 16: / Line 16: @@
 a=(x=>x+2)@(x=>x/3);
 a(3)
-<pre>
+</pre>
 gives
 .6666666666666667
@@ Line 23: / Line 23: @@
 a=(SIN@COS@TAN);
 a(45)
-<pre>
+</pre>
 gives
 .7749904090605793