TI-84+ and Casio (fx-CG 50) Micropython: Simplifying Nested Radicals
Introduction
The following program will simplifying the following expression:
√(x + y) = √a + √b
The input is x and y, with output a and b. The following conditions are implied: x > y and x > 0.
To see the derivation of simplification and examples, please check out this blog entry:
https://edspi31415.blogspot.com/2018/11/simplifying-nested-radicals.html
TI 84 Plus Program: DENEST
"EWS 2018-11-12"
Disp "√(X+Y)=√(A)+√(B)","X>Y","X>0"
Prompt X,Y
X/2+1/2*√(X^2-Y^2)→A
X/2-1/2*√(X^2-Y^2) →B
√(A)→Z
round(Z,9)→Z
Disp " "
If Y<0 font="">
Then
If fPart(Z)=0
Then
Disp √(A),"- √(",B,")"
Else
Disp "√(",A,")- √(",B,")"
End
Else
If fPart(Z)=0
Then
Disp √(A),"+ √(",B,")"
Else
Disp "√(",A,")+ √(",B,")"
End
End
Casio Micropython (fx-CG 50) Script denest.py
Input is the form of:
√(x1 * √x2 + y1 * √y2) = √a + √b
import math
print("sqrt(x+y)=")
print("sqrt(a)+sqrt(b)")
print("x>y","x>0")
print(" ")
print("x1*sqrt(x2)")
x1=float(input("x1:"))
x2=float(input("x2:"))
x=x1*math.sqrt(x2)
print(" ")
print("y1*sqrt(y2)")
y1=float(input("y1:"))
y2=float(input("y2:"))
y=y1*math.sqrt(y2)
a=x/2+math.sqrt(x**2-y**2)
b=x/2-math.sqrt(x**2-y**2)
z=math.sqrt(a)
z=round(z,10)
a=round(a,10)
b=round(b,10)
if y<0: font="">
if z-int(z)==0:
print(z,"-sqrt(")
print(b,"?")
else:
print("sqrt(",a)
print("-sqrt(")
print(b,")")
else:
if z-int(z)==0:
print(z,"+sqrt(")
print(b,")")
else:
print("sqrt(",a)
print("+sqrt(")
print(b,")")
Source:
Michael J. Wester, Editor. Computer Algebra Systems: A Practical Guide John Wiley & Sons: Chichester 1999. ISBN 978-0-471-983538
Eddie
All original content copyright, © 2011-2018. Edward Shore. Unauthorized use and/or unauthorized distribution for commercial purposes without express and written permission from the author is strictly prohibited. This blog entry may be distributed for noncommercial purposes, provided that full credit is given to the author. Please contact the author if you have questions.
Introduction
The following program will simplifying the following expression:
√(x + y) = √a + √b
The input is x and y, with output a and b. The following conditions are implied: x > y and x > 0.
To see the derivation of simplification and examples, please check out this blog entry:
https://edspi31415.blogspot.com/2018/11/simplifying-nested-radicals.html
TI 84 Plus Program: DENEST
"EWS 2018-11-12"
Disp "√(X+Y)=√(A)+√(B)","X>Y","X>0"
Prompt X,Y
X/2+1/2*√(X^2-Y^2)→A
X/2-1/2*√(X^2-Y^2) →B
√(A)→Z
round(Z,9)→Z
Disp " "
If Y<0 font="">
Then
If fPart(Z)=0
Then
Disp √(A),"- √(",B,")"
Else
Disp "√(",A,")- √(",B,")"
End
Else
If fPart(Z)=0
Then
Disp √(A),"+ √(",B,")"
Else
Disp "√(",A,")+ √(",B,")"
End
End
Casio Micropython (fx-CG 50) Script denest.py
Input is the form of:
√(x1 * √x2 + y1 * √y2) = √a + √b
import math
print("sqrt(x+y)=")
print("sqrt(a)+sqrt(b)")
print("x>y","x>0")
print(" ")
print("x1*sqrt(x2)")
x1=float(input("x1:"))
x2=float(input("x2:"))
x=x1*math.sqrt(x2)
print(" ")
print("y1*sqrt(y2)")
y1=float(input("y1:"))
y2=float(input("y2:"))
y=y1*math.sqrt(y2)
a=x/2+math.sqrt(x**2-y**2)
b=x/2-math.sqrt(x**2-y**2)
z=math.sqrt(a)
z=round(z,10)
a=round(a,10)
b=round(b,10)
if y<0: font="">
if z-int(z)==0:
print(z,"-sqrt(")
print(b,"?")
else:
print("sqrt(",a)
print("-sqrt(")
print(b,")")
else:
if z-int(z)==0:
print(z,"+sqrt(")
print(b,")")
else:
print("sqrt(",a)
print("+sqrt(")
print(b,")")
Source:
Michael J. Wester, Editor. Computer Algebra Systems: A Practical Guide John Wiley & Sons: Chichester 1999. ISBN 978-0-471-983538
Eddie
All original content copyright, © 2011-2018. Edward Shore. Unauthorized use and/or unauthorized distribution for commercial purposes without express and written permission from the author is strictly prohibited. This blog entry may be distributed for noncommercial purposes, provided that full credit is given to the author. Please contact the author if you have questions.
