The calculator

RuiLoureiro · April 16, 2012, 06:48:32 PM

Hi all,
Here is calcula36, a new version of calcula35

We have the functions point(x1,y1; ... ;x6,y6)
to put that set of points into a table;
and the function f(x=a) or f(y=b)
to execute a linear interpolation.

When we execute a linear interpolation, the output is

X, Y, m and b (linear equation: y=mx+b)

Note that when we try f(x=a) the program sort the table by X
and use the nearest x point; when we try f(y=a) the program
sort the table by Y and use the nearest y point.

Example:
point(1,2 ; 3,5 ; 5,-1)

Sorting by X we have: (1,2), (3,5), (5,-1)

. To calculate f(x=0) it uses the points (1,2) and (3,5)
. To calculate f(x=2) it uses the points (1,2) and (3,5)
. To calculate f(x=4) it uses the points (3,5) and (5,-1)
. To calculate f(x=6) it uses the points (3,5) and (5,-1)

Sorting by Y we have: (5,-1), (1,2), (3,5)

. To calculate f(y=-2) it uses the points (5,-1) and (1,2)
. To calculate f(y=0) it uses the points (5,-1) and (1,2)
. To calculate f(y=3) it uses the points (1,2) and (3,5)
. To calculate f(y=6) it uses the points (1,2) and (3,5)

Note that, now, the point (5,-1) is near the point (1,2) !

Try it and say something.
If you have any idea or suggestion, please answer thsi post

Thanks
RuiLoureiro

dedndave · April 17, 2012, 12:00:42 AM

cool :U

RuiLoureiro · April 18, 2012, 02:45:04 PM

Dave,
one word to you: thanks ! :wink

Hi all,
Here is calcula37, a new version of calcula36

. The functions to do a linear interpolation are now
g(x=a) or g(y=b)or G(x=a) or G(y=b)
we can use x or X, y or Y;

. When the output is 1.000000000000, now it is only 1.0
if the result is 1.000000000000E+0045, now it is only 1.0E+0045

. sin(pi)=sin(0)= 0 not -0.0000000000000

error control

. division by 0:    1/0 is division by 0
. indeterminate form: 0/0 is an indeterminate form

functions

. Now we can define a function f(x) [ we must use F(x), F(X), f(X),f(x) ]

. To define a function we must write f(x)=...

To do it, we write something like this

f(x)=x/2-sin(x)/x [ENTER/COMPUTE]

To calculate f(0) or f(1.5) we must write

f(x=0) or f(x=1.5)

. With calcula37 we can define

. a set of 10 variables;    [type: t=12;s=5;f=1e3; ]
. a set of 6 points (x,y);    [type: point(1,2; 3,5; 4,8) ]
. a function f(x);       [type: f(x)=x+1 ]

* we can solve

. a quadratic equation;      [type: 2x^2+x-1=5 ]
. a system of 2 equations; [type: y+x=3; x-y=1; ]
. a system of 3 equations; [type: y+x+z=10; x-y=1; -z+y=5; ]
. any expression    [type: (3*15.5+2e3)/(1-5.14) ]

* we can do

. linear interpolation    [type point(1,2; 3,5) and g(x=2)]

* we can calculate

. the values of a function f(x)    [type: f(x=2) or f(x=-1) ]
. mean, variance, standard deviation, etc.
. factorial    [type: 6! ]
. k-combination of n [type: comb(10,6)]

* we have the system constants

. pi
. e

* we have 6 memories to save expressions

* we can enter an expression with 200 characters

What next ?

. surprise

Try it and say something.

Is there a bug ? please answer this post
If you have any idea or suggestion, please answer this post

Thanks
RuiLoureiro

RuiLoureiro · April 20, 2012, 03:46:03 PM

Hi all,
Here is calcula38

Now, we have 2 more functions:

. error()

The system error is 1e-3 if we dont use the function error
If we want the error equal 1e-5 (ERROR=1e-5) we do

error(1e-5) [ENTER/COMPUTE]

. root(x=a, x=b)
or
. root(x=a, x=b; n=...)

The root function try to find the value X where f(X)<= ERROR
starting at x=a and end at x=b.

The number of sampled points used by the system is n=200.
If we want n=1000 we use

root(x=a, x=b; n=1000)

Example:

f(x)=3*x^3-x^2+2*x-1

root(x=-1, x=2; n=200)

Xc= 0.455; f(Xc)= -0.014435875 (f(Xc) is the closest value)
Xmin= -1.0
f(Xmin)= -5.0
Xmax= 2.0
f(Xmax)= 23.0

root(x=0, x=1; n=200)
X= 0.46
f(X)= 0.000408

error(1e-5)

root(x=0.4454, x=1; n=1000)
Xc= 0.4598196; f(Xc)= -0.00013028358895

Try it and say something.

Is there a bug ? please answer this post
If you have any idea or suggestion, please answer this post

Thanks
RuiLoureiro

dedndave · April 20, 2012, 03:52:29 PM

you write code faster than i do, Rui :P
i can't keep up with you - lol

jj2007 · April 20, 2012, 05:31:12 PM

Quote from: dedndave on April 20, 2012, 03:52:29 PM
i can't keep up with you - lol

Same for me - just incredible ::)
:U

RuiLoureiro · April 21, 2012, 01:28:52 PM

Dave,

Quote
you write code faster than i do, Rui
i can't keep up with you

Thanks for reply
The calculator is faster than me !
Jochen,

Quote
Same for me - just incredible

Thanks for reply
It is not fast. It is normal

Here is calcula39

Now, we have 2 more functions:

. df(x)=expression to define the derivative of the
function f(x) (used to solve the equation f(x)=0)

. root(x=a, x=b; x=X0 ) to solve f(X)=0 (<= ERROR)
using the Newton method

Examples 1:
f(x) =3*x^3-x^2+2*x-1
df(x)=9*x^2-2*x+2

error(1e-5)

root(x=0,x=1;x=0.46)

X=0.459863289103337
f(X)=0.000000058678523

error(1e-9)

root(x=0,x=1; x=0.46)

X= 0.459863269435932
f(X)= 0.000000000000003

error(1e-15)

root( x=-20, x=20; x=-10 )
X= 0.459863269435931
f(X)= 0

Now, we can start to find the roots of f(x)
using, for instance, root(x=-20, x=20; n=200)
root(x=-20, x=20; n=1000), root(x=-20, x=20; n=10000)

If we find one closest value X0, we define the derivative
and then we use something like this

root(x=-20, x=20; x=X0).

note: I corrected a bug in the previous calcula38

EDIT: In root(x=a, x=b; x=X0 ) a, b, X0 can be
-9pi,...,-1pi, -pi, pi, 2pi, 3pi,...,9pi.
The same for e

Try it and say something.

Is there a bug ? please answer this post
If you have any idea or suggestion, please answer this post

Thanks
RuiLoureiro

dedndave · April 21, 2012, 02:51:06 PM

Rui - you are a math monster !
i bet you would like this site...
http://projecteuler.net/index.php

i have solved about 20 problems so far :P

RuiLoureiro · April 25, 2012, 10:34:15 AM

Hi all

Here is calcula40

Now, we have 2 more functions:

. df(x=a)=expression

. root(x=a, x=b) n is = 200
root(x=a, x=b; n=integer) n from 200 to 1000000

root(x=a, x=b; d=delta ) d = increment (delta=0.1, 0.01, ...)
root(x=a, x=b; x= X0 ) X0 =starting point

. Calcula40 doest accept some typing errors
when we want to save f(x) or df(x),
and show the error

Example:
f(x)=2x^2+sen(x)+1 [ENTER/COMPUTE]
Error= x^2+sen

f(x)=2x^2+sin(x)+1 [ENTER/COMPUTE]
Error= 2x^2+sin(x)+1

f(x)=2*x^2+sin(x)+1 [ENTER/COMPUTE]
The function is defined

. With calcula40

* we can define

. a set of 10 variables; [type: t=12;s=5;f=1e3; ]
. a set of 6 points (x,y); [type: point(1,2; 3,5; 4,8) ]
. a function f(x); [type: f(x)=x+1 ]

* we can define the error to use with root(...)

. error()

The system error is 1e-3.
If we want the error equal 1e-5 (ERROR=1e-5) we do

error(1e-5)

* we can solve

. a quadratic equation; [type: 2x^2+x-1=5 ]
. a system of 2 equations; [type: y+x=3; x-y=1; ]
. a system of 3 equations; [type: y+x+z=10; x-y=1; -z+y=5; ]
. any expression [type: (3*15.5+2e3)/(1-5.14) ]

* we can solve

. the equation f(x)=0 using root(...)

* we can do

. linear interpolation [type: point(1,2; 3,5) and g(x=2)]

* we can calculate

. the values of a function f(x) [type: f(x=2) or f(x=-1) ]
. the values of a derivative df(x) [type: df(x=2) or df(x=-1) ]

. mean, variance, standard deviation, etc.
. factorial [type: 6! ]
. k-combination of n [type: comb(10,6)]

* we have the system constants

. pi
. e

* we have 6 memories to save expressions

* we can enter an expression with 200 characters

What next ?

. May be to solve a system of 4 linear equations
showing the determinant (solved by determinants)

Try it and say something.

Is there a bug ? please answer this post
If you have any idea or suggestion, please answer this post

Thanks
RuiLoureiro

RuiLoureiro · April 26, 2012, 02:40:42 PM

Hi all,

***Here is calcula41 v1.01***

1. 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 )

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 * )

If we type 120pi [ENTER/COMPUTE] we get 376.9911184307752

r may be a scientific notation

-2e3pi [ENTER/COMPUTE] we get -6283.185307179586

the same as -2e3*pi [ENTER/COMPUTE]

2. System of 4 linear equations

. Now we can solve a system of 4 linear equations

. We must use x,y,z,t or X,Y,Z,T in any order.

Examples:

x+y-Z=4; z-T+y=-2; 2x+2t+z=-3; Y-z=5; [ENTER/COMPUTE]

X=-1.0 Y=2.0 Z=-3.0 T=1.0 Determinant=5.0

Bugs

If i find a bug, i will post the next calcula42

What next ?

I am waiting for suggestions

Try it and say something.

Is there a bug ? please answer this post
If you have any idea or suggestion, please answer this post

Thanks
RuiLoureiro

EDIT: qWord, and Dave,
Thanks for reply
I am thinking about your suggestions :bg

qWord · April 26, 2012, 03:24:37 PM

generalize the parser thus working with vectors/matrices is possible. Even scalar values could be represented as a 1x1 array:

Code Select

a = [1,2,3;4,5,6;7,8,9];
b = [10;11;12];
c = a * b;
x = 123  % = [123]

(like matlab :bg)

dedndave · April 26, 2012, 04:03:48 PM

i was trying to think of ideas :P

base conversion
prime numbers
fibonacci sequences
taylor and other series (perhaps overdoing it a bit)

if you look at the problems on Project Euler, you may get some ideas
http://projecteuler.net/problems

Farabi · April 27, 2012, 06:09:37 AM

:U Hey, that was cool, how do you create the parser ??

RuiLoureiro · April 27, 2012, 05:41:40 PM

Hi all :bg

Farabi,
Hello !
Thanks for reply

Quote
how do you create the parser ??

It's just the problem !
But the basic answer is this: thinking and doing
If you want i can tell you my basic ideas.
Is simple but i wrote too many procedures to do
that.

Dave,

Quote
prime numbers

Thank you for reply
My problem is how to show a lot of output !
Give me one suggestion.

qWord,

Quote
generalize the parser thus working with vectors/matrices is possible.
a = [1,2,3;4,5,6;7,8,9];
b = [10;11;12];
c = a * b;

Thank you for reply
For now, i decided to follow your suggestion just as you type.

It is easy to integrate it in the calculator.
Just now, it is possible to define a vector line,
vector column or matrix.
The max number of lines or columns is 20 (very big !)
We can define a max number of 20 vectors/matrices
(i think it is enough).

But ...! There is a problem !
How to show 400 numbers ? Opening a new window ?

Quote
Even scalar values could be represented as a 1x1 array:

I decided to reject the case 1x1.
We can define 10 constants, so it is not needed

RuiLoureiro · April 30, 2012, 04:31:30 PM

Hi all,

**** Here is calcula42 v1.02 ****

1. expressions

. The lenght of each expression can be 1200 characters

2. round(a,n)

. n must be one digit 0,1,2,...,9

. new function to round

a) a real number a

round(23.51982,2) [ENTER/COMPUTE]

b) each element of a matrix

array1=[2.456, 1.382, 0.89459]; [ENTER/COMPUTE]

round(array1,2) [ENTER/COMPUTE]

3. matrix names

. Any name starting with a letter with up to 8 characters;

. We can define up to 20 matrices names;

4. matrix definitions

. We can define up to 20x20 matrix

. Now we can define a matrix a
column 1 column 2 column 3
line 1: 1 , 2 , 3 -> 1 2 3
line 2: 4 , 5 , 6 -> 4 5 6
line 3: 7 , 8 , 9 -> 7 8 9

TYPE:
a=[1,2,3 ; 4,5,6 ; 7,8,9 ]; [ENTER/COMPUTE]

Now, press DELETE KEY and
type: a press ENTER/COMPUTE to see the matrix a

. vector column
column 1
line 1: 1 ; -> 1
line 2: 4 ; -> 4
line 3: 7 -> 7

b=[1 ; 4 ; 7 ]; [ENTER/COMPUTE]

. vector line
column 1 column 2 column 3
line 1: 1 , 2 , 3 -> 1 2 3

b=[1 , 2 , 3 ]; [ENTER/COMPUTE]

5. matrix operations

. Addiction

array1=[1, 2; 3, 4]; [ENTER/COMPUTE]
array2=[5, 6; 7, 8]; [ENTER/COMPUTE]

a=array1+array2; [ENTER/COMPUTE]

. Subtraction

array1=[1, 2; 3, 4]; [ENTER/COMPUTE]
array2=[5, 6; 7, 8]; [ENTER/COMPUTE]

b=array1-array2; [ENTER/COMPUTE]

. Multiplication

array1=[1, 2; 3, 4]; [ENTER/COMPUTE]
array2=[5, 6; 7, 8]; [ENTER/COMPUTE]

c=array1*array2; [ENTER/COMPUTE]

. Scalar multiplication

array1=[1, 2; 3, 4]; [ENTER/COMPUTE]

d=10 * array1; [ENTER/COMPUTE]

f=+ array1; [ENTER/COMPUTE]

g=- array1; [ENTER/COMPUTE]

note: f=+array1 is <=> f=array1 and
f=-array1 is <=> f=-1*array1

6. matrix output

We show the matrix in the input edit box
and
in one messagebox

Have you any suggestion to show a big 20x20 matrix ?
Please, let me know

What next ?

. transpose of a matrix
. matrix inverse

Suggestions ?

How to write to do a transpose of a matrix ?

b=a^T; ?????????? (a=matrix m*n)

How to write to do a matrix inverse ?

b=a^-1; ?????????? (a=matrix m*n)

Try it and say something.

Is there a bug ? please answer this post
If you have any idea or suggestion, please answer this post

Thanks to you

Rui Loureiro

EDIT: Copy this 20*20 matrix 'a' and paste it into the edit box and PRESS ENTER
Then, try b=a*a; c=b*b; d=c*c; .... etc

a=[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20;
1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20;
1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20;
1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20;
1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20;
1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20;
1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20;
1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20;
1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20;
1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20;
1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20;
1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20;
1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20;
1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20;
1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20;
1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20;
1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20;
1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20;
1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20;
1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20];

News:

The calculator