Hi all
This version is the result of what i learned
till now. Some procedures are now lighter.
Some strategies was corrected.
Now, we have not "division by 0" but infinity.
In this way, 1/(log(10)-1)* 0 gives "Indeterminate form"
and not "division by 0".
Now, it is time for corrections and improvements.
Meanwhile, the calculator should solve
any expression.
**** Here is calcula48 v1.08 **** Calculation rules 1. terms inside parentheses or brackets
2. functions
3. exponents or powers
4. multiplication and division
5. addition and subtraction
note 1: if we end a pair of brackets with
! we must have a positive integer inside: (12-3)!
note 2: the exponents are treated as
a) real: it is the general case
b) integer: enclosed by brackets (1-log(3))^(-2)
c) rational: enclosed by brackets (1-log(3))^(-2/3)
note 3: roots are calculated following this rule:
1. put the expression inside brackets: (log(3)-log(2)*2)
2. put the rational exponent inside brackets: (n/k)
3. use "^"
(log(3)-log(2)*2)^(n/k)
square root: sqr(2*log(2)-log(3))=(2*log(2)-log(3))^(1/2)
= 0.353466740455591 = 0.353466740455591
note 4: exponents or powers are calculated starting at the end
4^3^2: first: 3^2 = 9 second: 4^9 4^3^2 = 262144.0
(4^3)^2 = 64.0 ^2 = 4096.0
We can define:
1. a set of 10 constants: type t=10; s=2.25;u=-2.5e-3;
2. a function: type f(x)=x^2/(1-x)
3. a derivative: type df(x)=2*x-1
4. up to
20 matrices, up to a
20*20 matrix:
a=[1,2,2]; vector column 3 columns
b=[1;2;3]; " line 3 lines
c=[1,2;2,3]; squared matrix
We can solve:
1. Any expression
2. Mean(x1,...,xn): mean(12,13,12,13,14)
3. Factorial and k-combination of n: 12!, comb(12,3)
4. Logarithms of any base: logb(15.2, 5)
5. Quadratic equations: aX^2+bX+c=c0
6. Systems of 2 equations: type aX+bY=c
;fX+gY=h
; 7. Systems of 3 equations: type aX+bY+cZ=d
;fX+gY+hZ=i
; jX+kY+mZ=l
; 8. Systems of 4 equations: type aX+bY+cZ+dT=f
; gX+hY+iZ+jT=k
; lX+mY+nZ+oT=p
;qX+rY+sZ+tT=u
; (note: a,b,c, ... are real numbers)
9. Conversion decimal-binary-hexadecimal -
any 64-bit number conv(11000) = 00002AF8H
conv(11000b)= 24
conv(11000h)= 69632
10. Linear interpolation: type: point(1,2; 3,5) and g(x=2)
or g(y=2)
11. The equation f(x)=0
a) root(x=-20, x=20;
n=200)
b) root(x=-20, x=20;
d=0.01)
c) root(x=-20, x=20;
x=1.2)
note: in
root(x=a, x=b; x=X0 ) a, b, X0 can be
-9pi,...,-1pi, -pi, pi, 2pi, 3pi,...,9pi,
-9e,...,-1e, -e, e, 2e, 3e,...,9e.
Matrix operations .
Copy a=[1, 2; 3, 4]; [press ENTER/COMPUTE]
b=a; [press ENTER/COMPUTE]
Now we have a, b and a equal b
.
Addiction a1=[1, 2; 3, 4]; [press ENTER/COMPUTE]
a2=[5, 6; 7, 8]; [press ENTER/COMPUTE]
a=a1+a2; [press ENTER/COMPUTE]
.
Subtraction a1=[1, 2; 3, 4]; [press ENTER/COMPUTE]
a2=[5, 6; 7, 8]; [press ENTER/COMPUTE]
b=a1-a2; [press ENTER/COMPUTE]
.
Multiplication a1=[1, 2; 3, 4]; [press ENTER/COMPUTE]
a2=[5, 6; 7, 8]; [press ENTER/COMPUTE]
c=a1*a2; [press ENTER/COMPUTE]
.
Scalar multiplication a1=[1, 2; 3, 4]; [press ENTER/COMPUTE]
d=10 * a1; [press ENTER/COMPUTE]
f=+ a1; [press ENTER/COMPUTE]
g=- a1; [press ENTER/COMPUTE]
.
Transpose matrix a1=[1, 2; 3, 4]; [press ENTER/COMPUTE]
b=a1^t; [press ENTER/COMPUTE]
or
b=a1^T; [press ENTER/COMPUTE]
we get b=[ 1.0, 3.0; 2.0, 4.0];
.
Inverse matrix a1=[1, 2; 3, 4]; [press ENTER/COMPUTE]
b=a1^-1; [press ENTER/COMPUTE]
b=inv(a1)
we get b=[-2.0, 1.0; 1.5,-0.5];
.
Determinant of a square matrix . type
delta(a) [press ENTER/COMPUTE]
det(a)
where
a is a matrix name
INFINITY and Indeterminate forms Use 1/0 or (1/0) for generate the infinity
arcsec(1/0)= 1.570796326794897 arctan(1/0)= 1.570796326794897
arctan(1/0)= 1.570796326794897 arccot(1/0)= 0
1.570796326794897 = pi/2
0/0 = Indeterminate form
0^0 = Indeterminate form
(1/0)/(1/0) = Indeterminate form
(1/0)* 0 = Indeterminate form
Detailed questions about pi Now, when we use
pi we dont need to use
* In this way, we can type any expression with
pi like
n pi OR +n pi OR -n pi ( n integer )
r pi OR +r pi OR -r pi ( r real, scientific notation)
It is the same as
n*pi, +n*pi, -n*pi ( we dont need to type * )
r*pi, +r*pi, -r*pi ( we dont need to type * )
Symbols Type
list and press ENTER/COMPUTE
Length of an expression or matrix The calculator supports any expression or
matrix up to 3800 characters.
Memories The calculator has 6 memories to save any
expression or matrix in the input box.
error function Some functions use the system error = 1e-3
To set it to 1e-5, type
error(1e-5) and press ENTER/COMPUTE
printing on the paper . print() prints the last results
. print(a) prints the matrix
a Constant name or Matrix name . It must start with a letter and it can have
up to 8 characters;
. Type
the constant name or
the matrix name and press ENTER/COMPUTE to see its definition or value.
Constants Any integer or real number, scientific notation
e, +e, -e, pi, +pi, -pi
Keys . ENTER to compute
. DELETE to clean the input box
. Use Home, End, Ctrl+Home, Ctrl+End etc.
when we have the focus in the input box.
Big expressions... or not We can use a
text editor to type it.
Then
we copy and paste it into the edit box.
Some numbers 1700! = 2.99835320555842E+4755
e^10000 = 8.806818225662921E+4342
Try it and say something. Good luck ! Thanks
Rui Loureiro
EDIT: i decided to replace calcula50 by the new
calcula51 See the last post
I made some corrections in Calcula50
calcula51 has a new look
Good luck
Rui Loureiro
EDIT: now we have Calcula55 the
version 3.00.1 with new functions and the file of rules
RulesV2_20.txtPlease, see the last post
EDIT: I replaced Calcula58 by the new
powerful Calcula59 It works with complex numbers. Please
see the last postEDIT: I replaced Calcula59 by
the new powerful Calcula60 It works with complex numbers and complex functions.
Please see the last post note: RulesV3_10_2I - rules in English
RulesV3_10_2P - regras em Português
EDIT: I replaced Calcula62 by
the new powerful Calcula63 Please see the last post to get the examples EDIT: I replaced
calcula66 by
calcula67 to correct some problems DERIVATIVES : compute a derivative of any function
See the link in the last post
