# Mathomatic Templates

donsauer\$ /sw/bin/mathomatic

1-> a=b-(c+2)
#1: a = b - c - 2
1-> b
#1: b = 2 + c + a

e# - the universal constant e (2.718281828...).
pi - the universal constant pi (3.1415926...).
i# - imaginary number (square root of -1).

1->  a=b+1/b
1
#1: a = b + -
b
1-> b ; solve for "b"
1
(a - ((((a^2) - 4)^-)*sign1))
2
#1: b = -----------------------------
2
1-> a ; solve for "a", to check the answer
Raising both sides to the power of 2 and unfactoring...
((b^2) + 1)
#1: a = -----------
b
1-> simplify
1
#1: a = b + -
b

1-> y=x^2+x ; the simplest quadratic equation
#2: y = (x^2) + x
2-> x ; solve for "x"
1
-1*(1 + (((1 + (4*y))^-)*sign1))
2
#2: x = --------------------------------
2
2-> calculate
Enter y: 0
Solution #1 with sign1 = 1:
x = -1
Solution #2 with sign1 = -1:
x = 0

2-> a=b+1 ; an example of iteration
#3: a = b + 1
3-> calculate b 10
Enter initial b: b
a = b + 10

3-> clear
3-> clear all

1-> x^3+x^2+x+1
#1: (x^3) + (x^2) + x + 1
1-> derivative x
Differentiating with respect to (x) and simplifying...
#2: (3*(x^2)) + (2*x) + 1

2->  a*x^n ; Show a general rule of differentiation.
#3: a*(x^n)
3-> derivative x
Differentiating with respect to (x) and simplifying...
#4: a*n*(x^(n - 1))

4->  divide
Enter dividend: (x^4) - (7*(x^3)) + (18*(x^2)) - (22*x) + 12
Enter divisor: (x^2) - (2*x) + 2
Polynomial division successful using base variable (x).
The quotient is:
6 + (x^2) - (5*x)
The remainder is:
0
Polynomial Greatest Common Divisor (iterations = 1):
(x^2) - (2*x) + 2

4-> l^2=(x1-x2)^2+(y1-y2)^2 ; Distance formula for 2D space.
#5: l^2 = ((x1 - x2)^2) + ((y1 - y2)^2)
5-> d^2=l^2+(z1-z2)^2 ; Add another leg.
#6: d^2 = (l^2) + ((z1 - z2)^2)
6-> eliminate l ; Combine the two equations.
Solving equation #5 for (l) and substituting into the current equation...
#6: d^2 = ((x1 - x2)^2) + ((y1 - y2)^2) + ((z1 - z2)^2)
6-> d ; Solve to get the distance formula for 3D space.
1
#6: d = ((((x1 - x2)^2) + ((y1 - y2)^2) + ((z1 - z2)^2))^-)*sign2
2
6-> ; The coordinate of point 1 is (x1, y1, z1) and point 2 is (x2, y2, z2).

6-> y=x^2
#7: y = x^2
7-> extrema x
#8: x = 0

8-> x^3+2x^2+3x+4
#9: (x^3) + (2*(x^2)) + (3*x) + 4
9-> factor
#9: (x*((x*(x + 2)) + 3)) + 4

9-> 1/x+1/y+1/z
1   1   1
#10: - + - + -
x   y   z
10-> fraction
(((y + x)*z) + (x*y))
#10: ---------------------
(x*y*z)
10-> simplify
1   1   1
#10: - + - + -
x   y   z

10-> (a+b*i#)/(c+d*i#)
(a + (b*i#))
#11: ------------
(c + (d*i#))
11-> imaginary
((b*i#*c) - (a*d*i#))
#12: ---------------------
((c^2) + (d^2))
12-> replace i# with 1
((b*c) - (a*d))
#12: ---------------
((c^2) + (d^2))

12-> x^3+x^2+x+1
#13: (x^3) + (x^2) + x + 1
13-> integrate x
(x^4)   (x^3)   (x^2)
#14: ----- + ----- + ----- + x
4       3       2
14-> derivative x ; Check the result.
Differentiating with respect to (x) and simplifying...
#15: (x^3) + (x^2) + x + 1

15-> y=a*x^n
#16: y = a*(x^n)
16-> laplace x
a*(n!)
#17: y = -----------
(x^(n + 1))
17-> laplace inverse x
#18: y = a*(x^n)

18-> ; Compute the derivative of (x^.5) using limits:
18-> a=((x+h)^.5-x^.5)/h
1       1
(((x + h)^-) - (x^-))
2       2
#19: a = ---------------------
h
19-> limit h 0
Raising both sides to the power of 2 and unfactoring...
1
#19: a = ---------
1
(2*(x^-))
2

19-> y=x+1
#20: y = x + 1
20-> nintegrate x
Enter lower bound: 0
Enter upper bound: x
Approximating the definite integral using Simpson's rule...
Integration successful.
(x^2)
#21: y = x + -----
2

21-> y=x^0.5/(1-x^3)
1
(x^-)
2
#22: y = -----------
(1 - (x^3))
22-> nintegrate x
Warning: Singularity detected, result of numerical integration may be wrong.
Enter lower bound: 2
Enter upper bound: 4
Approximating the definite integral using Simpson's rule...
Integration successful.
#23: y = -0.16256117185712

1-> y = (a+b+c+d)^(a+b+c+d)
#1: y = (a + b + c + d)^(a + b + c + d)
1-> optimize
#2: temp1 = a + b + c + d
#1: y = temp1^temp1
1-> eliminate temp1 ; undo the optimization
Solving equation #2 for (temp1) and substituting into the current equation...
#1: y = (a + b + c + d)^(a + b + c + d)

1-> y=a*x
#3: y = a*x
3-> product
Enter variable: x
x = 1
To: 10
#4: y = 3628800*(a^10)

1-> 10!

3-> (a+b*i#)/(c+d*i#)
(a + (b*i#))
#5: ------------
(c + (d*i#))
5-> real
((a*c) + (b*d))
#6: ---------------
((c^2) + (d^2))

6-> roots
Enter root (positive integer): 3
Enter real part (X): 8
Enter imaginary part (Y):
The polar coordinates are:
8 amplitude and 0 radians (0 degrees).
The 3 roots of 8^(1/3) are:
2
Inverse Check: 8
-1 +1.73205080757*i#
Inverse Check: 8
-1 -1.73205080757*i#
Inverse Check: 8

6-> y=a*x
#7: y = a*x
7-> sum
Enter variable: x
x = 1
To: 10
#8: y = 55*a

7-> e#^x
#9: e#^x
9-> taylor x
Taylor series expansion about (x) = point.
Enter point: 0
Enter order (number of derivatives to take): 10
(x^2)   (x^3)   (x^4)   (x^5)   (x^6)   (x^7)   (x^8)   (x^9)    (x^10)
#10: 1 + x + ----- + ----- + ----- + ----- + ----- + ----- + ----- + ------ + -------
2       6      24      120     720    5040    40320   362880   3628800

1-> a=b*(c+d)
#1: a = b*(c + d)
1-> z=(x+y)^2
#2: z = (x + y)^2
2->  unfactor all
#1: a = (b*c) + (b*d)
#2: z = (x^2) + (2*x*y) + (y^2)