# Personalized Polynomial

```Personalized Polynomial
Creating the polynomial that passes through a set of letter-points from a word.
x-cordinate of a letter-point is the position of the letter in the word.
The first letter has a position of one, the second letter has a position of two...
The y-cordinate of the letter-point is the depth of the letter in the alphabet.
A has a depth of 1, B has a depth of two...
The word for this personalized polynomial is “SAMUEL”.
ClearAll;
Defining the Polynomial
The word “SAMUEL” is six letters long.
Part S
Defining the part of the polynomial for “S”.
“S” is the first letter in “SAMUEL” and the 19th letter of the alphabet.
[email protected]_D:=19*[email protected], 8i, 2, 6<D
[email protected], 8i, 2, 6<D;
Part A
Defining the part of the polynomial for “A”.
“A” is the second letter in “SAMUEL” and the 1st letter of the alphabet.
[email protected]_D:=1*[email protected], 8i, 1, 1<D*[email protected], 8i, 3, 6<D
[email protected], 8i, 1, 1<D*[email protected], 8i, 3, 6<DL;
Part M
Defining the part of the polynomial for “M”.
“M” is the third letter in “SAMUEL” and the 13th letter of the alphabet.
[email protected]_D:=13*[email protected], 8i, 1, 2<D*[email protected], 8i, 4, 6<D
[email protected], 8i, 1, 2<D*[email protected], 8i, 4, 6<DL;
Part U
Defining the part of the polynomial for “U”.
“U” is the forth letter in “SAMUEL” and the 21st letter of the alphabet.
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B Group
[email protected]_D:=21*[email protected], 8i, 1, 3<D*[email protected], 8i, 5, 6<D
[email protected], 8i, 1, 3<D*[email protected], 8i, 5, 6<DL;
Part E
Defining the part of the polynomial for “E”.
“E” is the fifth letter in “SAMUEL” and the fifth letter of the alphabet.
[email protected]_D:=5*[email protected], 8i, 1, 4<D*[email protected], 8i, 6, 6<D
[email protected], 8i, 1, 4<D*[email protected], 8i, 6, 6<DL;
Part L
Defining the part of the polynomial for “L”.
“L” is the sixth letter in “SAMUEL” and the twelveth letter of the alphabet.
[email protected]_D:=12*[email protected], 8i, 1, 5<D
[email protected], 8i, 1, 5<D;
Tying It Together
Defining the polynomial as the sum of all of its parts.
In[938]:=
[email protected]_D:= [email protected] + [email protected] [email protected] [email protected] + [email protected] + [email protected];
[email protected]@xDD
1
Out[939]=
120
I7440 - 4018 x - 3595 x2 + 3125 x3 - 725 x4 + 53 x5 M
Displaying the Polynomial
Displaying the Polynomial in a Chart
In[940]:=
[email protected], 8i, 6<D;
[email protected]@iD, 8i,6<D;
TableData= [email protected], Outputs1<D;
[email protected], TableHeadings® 8None, 8"Input", "Output"<<D
Out[943]//TableForm=
Input
1
2
3
4
5
6
Output
19
1
13
21
5
12
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Weaver
Personalized Polynomial.nb |
Displaying the Polynomial in a Graph
The Points and Their Labels
[email protected]@8Orange, [email protected],19<, 8.04,1<D<D,
[email protected]@[email protected]"S", Large, Bold, BlueD, 81.07, 21.5<DDD;
[email protected]@8Orange, [email protected],1<, 8.04,1<D<D,
[email protected]@[email protected]"A", Large, Bold, BlueD, 82, 4<DDD;
[email protected]@8Orange, [email protected],13<, 8.04,1<D<D,
[email protected]@[email protected]"M", Large, Bold, BlueD, 82.9, 15.8<DDD;
[email protected]@8Orange, [email protected],21<, 8.04,1<D<D,
[email protected]@[email protected]"U", Large, Bold, BlueD, 84.05, 23.5<DDD;
[email protected]@8Orange, [email protected],5<, 8.04,1<D<D,
[email protected]@[email protected]"E", Large, Bold, BlueD, 85.07, 8<DDD;
[email protected]@8Orange, [email protected],12<, 8.04,1<D<D,
[email protected]@[email protected]"L", Large, Bold, BlueD, 85.95, 14.8<DDD;
[email protected], A2, M2, U2, E2, L2D;
The Domain and Range
In[951]:=
MinDomain=0;
MaxDomain=7;
[email protected]@i1000D, 8i, 1000*MinDomain, 1000*MaxDomain<D;
[email protected]@Outputs2DD;
[email protected]@Outputs2DD;
[email protected];
The Function
In[961]:=
[email protected]@xD, 8x, MinDomain, MaxDomain<,
AxesLabel® 8"Input", "Output"<, PlotStyle®Blue,
PlotRange® 8MinRange-10100*Range1, MaxRange-60100*Range1<,
PlotLabel® "Personalized Polynomial"D;
3
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B Group
Weaver
Tying It Together
In[962]:=
[email protected], DataPointsAndLabelsD
Personalized Polynomial
Output
80
60
40
Out[962]=
20
U
S
M
L
E
A
1
2
Input
3
4
-20
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5
6
7
```