Antique Notation
Author
Robby Villegas
Title
Antique Notation
Description
Function implementations for numerals in Roman, Greek, Diophantus polynomials, Viete quadratics, Harriot polynomials, Chuquet polynomials, and Leibniz notation.
Category
Working Material
Keywords
Roman, Greek, Diophantus polynomials, Viete quadratics, Harriot polynomials, Chuquet polynomials, Leibniz notation
URL
http://www.notebookarchive.org/2018-10-0yfrsz2/
DOI
https://notebookarchive.org/2018-10-0yfrsz2
Date Added
2018-10-02
Date Last Modified
2018-10-02
File Size
97.46 kilobytes
Supplements
Rights
Redistribution rights reserved
This notebook has not been updated since 2019. 
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Generic Definitions
Numeral Forms
Roman Numeral Form
Roman Numeral Form
Implementation
Implementation
Brief examples
Brief examples
Table[RomanNumeralForm[i],{i,77,7777,1000}]
{
,
,
,
,
,
,
,
}
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Table[i,{i,77,7777,1000}]//RomanNumeralForm
{
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,
,
,
,
,
}
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2^40//RomanNumeralForm
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Greek Numeral Form
Greek Numeral Form
Implementation
Implementation
Brief examples
Brief examples
Table[GreekNumeralForm[i],{i,77,7777,1000}]
{
,
,
,
,
,
,
,
}
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Table[i,{i,77,7777,1000}]//GreekNumeralForm
{
,
,
,
,
,
,
,
}
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2^40//GreekNumeralForm
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Polynomial Forms
Most of these polynomial forms assume a single variable, so it is wise to specify the intended variable in your input, i.e.
WhateverPolynomialForm[poly,x]
Diophantus' polynomial form (only up to 6x, unfortunately)
Diophantus' polynomial form (only up to , unfortunately)
6
x
Implementation
Implementation
Simple examples
Simple examples
In the Cajori discussion, Diophantus supplied ad hoc symbols for the first six (6) powers of a single unknown, with no apparent provision for higher powers or mixed products. Also, we require that the coefficients be integers, since our Greek numeral form works only on integers. Since Mathematica lacks the upside-down-flattened capital Psi character, I substituted a character that resembles it.
DiophantinePolynomialForm[x^3+13x^2+5x+2-7x^5,x]
Y
K
α
Y
Δ
ιγ
ϵ
°
M
β
Y
K
ζ
DiophantinePolynomialForm[x^2-1,x]
Y
Δ
α
°
M
α
DiophantinePolynomialForm[x^2-1,x^2]
ς↑
α
°
M
α
Although it is unwise not to provide the intended variable of the polynomial, this form will attempt to infer things, using the built-in PolynomialQ and Variables functions.
DiophantinePolynomialForm[x^3+13x^2+5x+2-7x^5]
Y
K
α
Y
Δ
ιγ
ϵ
°
M
β
Y
K
ζ
The following are not polynomials in the specified variable, thus they are left untouched.
DiophantinePolynomialForm[x^2-1,z]
-1+
2
x
DiophantinePolynomialForm[x^3-x^2-1,x^2]
-1-+
2
x
3
x
This polynomial has a degree too high (9) for the ad hoc list of symbols that Diophantus used, which go up to x^6 only.
DiophantinePolynomialForm[x^9-x^2-1,x]
-1-+
2
x
9
x
François Viète quadratic form
François Viète quadratic form
Remember to throw InterpretationBox around Roman and Greek numerals
Implementation
Implementation
Simple examples
Simple examples
This handles only quadratics (it is not clear from the web page how to generalize the notation beyond use of "Q" and "N"). It is wise to specify the intended variable.
VieteQuadraticForm[2x^2-7x+10,x]
2Q-7N+10
VieteQuadraticForm[-2x^2+7x-10,x]
-2Q+7N-10
VieteQuadraticForm[-2x^2+7x7x^2-3x+5,x]
-2Q+7N aequatis sit 7Q-3N+5
Harriot polynomial form
Harriot polynomial form
Implementation
Implementation
Simple examples
Simple examples
HarriotPolynomialForm[2x^2-7x+10,x]
2aa-7a+10
HarriotPolynomialForm[-2x^2+7x-10,x]
-2aa+7a-10
HarriotPolynomialForm[-2x^2+7x7x^2-3x+5,x]
-2aa+7a===7aa-3a+5
HarriotPolynomialForm[Sum[Random[Integer,{-4,4}]*x^i,{i,0,5}]Sum[Random[Integer,{-4,4}]*x^i,{i,0,5}],x]
4aaaaa+aaaa+3aaa+3aa-a===aaaaa-2aaaa+4aaa+aa+3a+1
Nicolas Chuquet polynomial form
Nicolas Chuquet polynomial form
Implementation
Implementation
Simple examples
Simple examples
ChuquetPolynomialForm[3x^3-4x+5,x]
3
3
m
1
4
0
5
ChuquetPolynomialForm[3x^3-4x+5-7x^-2,x]
3
3
m
1
4
0
5
m
2
m
7
ChuquetPolynomialForm[3x^3-4x+5-7x^-23x^3-4x+1,x]
3
3
m
1
4
0
5
m
2
m
7
3
3
m
1
4
0
1
Miscellaneous Notations
Leibniz function notation in Cajori Volume 2, page 193 (¶ 558)
Leibniz function notation in Cajori Volume 2, page 193 (¶ 558)
Implementation
Implementation
Simple examples
Simple examples
LeibnizForm[f[x]+g[x]+f[x,y]+h[u,v]]
f[x]+f[x,y]+g[x]+h[u,v]
{
+
+
+
,u[x]}
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{f[x]+f[x,y]+g[x]+h[u,v],u[x]}
LeibnizForm[f[x]+g[x]+f[x,y]+h[u,v]+h[x]+f[a,b,c]]
f[x]+f[x,y]+f[a,b,c]+g[x]+h[x]+h[u,v]
+
+
+
+
+
,v[a,b]
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{f[x]+f[x,y]+f[a,b,c]+g[x]+h[x]+h[u,v],v[a,b]}
Cite this as: Robby Villegas, "Antique Notation" from the Notebook Archive (2019), https://notebookarchive.org/2018-10-0yfrsz2
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