The calculator

RuiLoureiro · May 03, 2012, 03:33:35 PM

Hi all,
News

The previous calcula42 doest solve systems of
linear equations because when it tries to solve
a matrix operation if it is not a matrix operation
calcula42 exits and doesnt go on.
Sorry.

**** Here is calcula43 v1.03 ****

1. Expressions

. We can type an expression with 2200 characters;

. We can use a text editor/text processor to write an expression,
or matrix, etc. and then we can copy it and paste it into
the calculator input edit box.

2. Matrix definitions

. We can define up to a 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]

3. How to see a matrix definition or result

. press DELETE key to clear the input edit box;

. type the matrix name and press ENTER key.

4. 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]

. Transpose matrix

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

b=array1^t; [ENTER/COMPUTE]
or
b=array1^T; [ENTER/COMPUTE]

we get b=[ 1.0, 3.0; 2.0, 4.0];

. Inverse matrix

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

b=array1^-1; [ENTER/COMPUTE]

we get b=[-2.0, 1.0; 1.5,-0.5];

5. About matrix inversion

. The calculator uses the Gauss-Jordan
elimination method.
. At the end we test the matrix to find
the identity matrix at the left.

6. Examples

example I: 2*2 matrix

c=[1,2; 2,1];

1. copy this matrix 'c' and paste it into input edit box
2. press ENTER/COMPUTE key
3. press DELETE key
4. type d=c^-1; [ENTER/COMPUTE]

example II: 3*3 matrix

f=[2,1,0; 0,2,1; 1,0,2];

1. copy this matrix 'f' and paste it into input edit box
2. press ENTER/COMPUTE key
3. press DELETE key
4. type g=f^-1; [ENTER/COMPUTE]

example III: 20*20 matrix

a=[1,2,3,4,5,6,7,1,0,10,11,12,13,14,15,16,7,8,19,4;
1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,1,20;
1,2,3,4,5,6,7,8,9,10,11,0,13,14,0,16,17,18,19,20;
1,2,1,0,0,6,7,8,9,10,0,12,13,14,15,16,17,18,19,2;
1,2,3,4,5,6,7,8,9,0,11,12,13,4,15,0,17,18,19,1;
1,2,3,4,5,6,7,8,9,10,11,2,13,14,15,16,17,3,19,20;
20,9,18,17,16,5,14,13,12,11,10,9,8,7,6,5,4,3,2,1;
1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20;
1,0,3,4,5,6,7,8,9,1,1,12,13,14,5,16,17,18,19,20;
1,2,0,4,5,0,1,8,9,10,11,12,13,14,15,16,17,18,19,20;
20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1;
1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,1,19,1;
1,2,3,4,5,6,7,8,9,10,11,0,13,14,15,16,17,18,19,20;
1,2,3,4,5,6,7,8,9,10,1,12,13,14,15,6,17,18,19,20;
1,0,0,4,5,6,7,8,9,10,11,12,13,14,15,16,0,18,19,20;
1,2,3,4,5,6,7,0,9,0,11,0,13,14,15,16,17,18,19,0;
1,2,3,4,5,6,1,8,9,10,11,12,13,14,15,16,17,2,19,0;
1,2,1,0,5,6,7,8,9,10,11,12,13,14,15,16,17,18,0,20;
1,1,3,4,0,6,7,0,9,10,11,0,13,14,15,16,7,18,9,20;
1,2,3,4,5,6,7,8,9,10,0,12,13,14,15,16,17,0,19,2];

1. copy this matrix 'a' and paste it into input edit box
2. press ENTER/COMPUTE key
3. press DELETE key

4. type b=a^-1; [ENTER/COMPUTE]
5. press DELETE key
6. round(b,3) [ENTER/COMPUTE]
7. b [ENTER/COMPUTE]

Try it and say something.
Good luck !

7. What else ?

. Determinant of any matrix up to 20x20 ?
. Linear transformations ?
. Printing on the paper ?

8. Bugs, Ideas, Suggestions

Please, answer this post and say what you want

Thanks

Rui Loureiro

RuiLoureiro · May 07, 2012, 05:49:25 PM

Hi all,
News

In the previous calcula43, if a number is very small
it shows something like +/-0.0000000000 instead of
the number in scientific notation
Sorry.

**** Here is calcula44 v1.04 ****

1. Expressions

. We can type an expression with 2200 characters;

. We can use a text editor/text processor to write an expression,
or matrix, etc. and then we can copy it and paste it into
the calculator input edit box.

2. Printing on the paper

. Printing an expression and results;

a) turn on the printer
b) type print() [press ENTER/COMPUTE]

. Printing a matrix;

a) turn on the printer
b) type print(a) [press ENTER/COMPUTE]

where a is a matrix name

3. Matrix definitions

. We can define up to a 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 ]; [press ENTER/COMPUTE]

4. How to see a matrix definition or result

. press DELETE key to clear the input edit box;

. type the matrix name and press ENTER key.

5. 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

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

a=array1+array2; [press ENTER/COMPUTE]

. Subtraction

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

b=array1-array2; [press ENTER/COMPUTE]

. Multiplication

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

c=array1*array2; [press ENTER/COMPUTE]

. Scalar multiplication

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

d=10 * array1; [press ENTER/COMPUTE]

f=+ array1; [press ENTER/COMPUTE]

g=- array1; [press ENTER/COMPUTE]

. Transpose matrix

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

b=array1^t; [press ENTER/COMPUTE]
or
b=array1^T; [press ENTER/COMPUTE]

we get b=[ 1.0, 3.0; 2.0, 4.0];

. Inverse matrix

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

b=array1^-1; [press ENTER/COMPUTE]

we get b=[-2.0, 1.0; 1.5,-0.5];

. Determinant of a squared matrix

. type
delta(a) [press ENTER/COMPUTE]

where a is a matrix name

6. About matrix inversion

. The calculator uses the Gauss-Jordan
elimination method.

. When we want to invert a matrix A,
we start with a matrix

W = AI where I is the identity matrix

and we finish with

W = IB where I is the identity matrix
and B=A^-1

. At the end we test the matrix to find
the identity matrix I at the left.

If all elements of main diagonal is 1.0
(we use fld1 and fcomip to test )
and all other elements are +0.0 (we use ftst to test)

we give the message "The identity matrix is correct"

So, it means that we get the correct identity matrix and
B is the correct inverted matrix.

If that test fails, we start to test against an error of 1e-15
If it doesnt fail, we get a message

"Errors in the identity matrix are below 1e-15"

7. How we get the determinant

. I tried some methods without success (error problems)

. The calculator uses the Gauss-Jordan
elimination method to get a triangular matrix

. When we get the triangular matrix, the determinant
is the product of the main diagonal elements

. At the end, we test the triangular matrix.

If all elements below the main diagonal are
0.0 (we use ftst to test), we get the message

"The triangular matrix is correct"

If that test fails, we start to test against an error of 1e-15
If it doesnt fail, we get a message

"Errors in the triangular matrix are below 1e-15"

8. Examples

example I: 4*4 matrix

a=[2,1,3,4;-1,0,2,5;-5,2,0,1;3,-2,1,0];

1. copy this matrix 'a' and paste it into input edit box
2. press ENTER/COMPUTE key
3. press DELETE key
4. type:
b=a^-1; [press ENTER/COMPUTE]

we get "The identity matrix is correct"

5. press DELETE key
6. type:
delta(a) [press ENTER/COMPUTE]

we get "The triangular matrix is correct"

60.0

7. type:
delta(b) [press ENTER/COMPUTE]

we get "The triangular matrix is correct"

0.016666666666667 = 1 / 60

We have: delta(a) = 1/delta(b)

example II: 6*6 matrix

d=[-1,0,2,5,0,3 ; 2,1,3,4,4,-1;-5,2,0,1,2,-3;3,-2,1,0,0,-5;
2,0,-1,2,0,0 ; 0,1,-2,4,-2,5];

1. copy this matrix 'd' and paste it into input edit box
2. press ENTER/COMPUTE key
3. press DELETE key
4. type:
f=d^-1; [press ENTER/COMPUTE]

we get "The identity matrix is correct"

5. press DELETE key
6. type:
delta(d) [press ENTER/COMPUTE]

we get "The triangular matrix is correct"

1068.0

7. type:
delta(f) [press ENTER/COMPUTE]

we get "Errors in the triangular matrix are below 1e-15"

0.000936329588015 1 / 1068 = 0.000936329588015

We have: delta(d) = 1/delta(f)

example III: 20*20 matrix

g=[1.23,2,3,-4.45,5,6,7,-1.24,0,10,11,1.12,-13,14.11,15,-1.16,7,8,19,-4;
1,2.24,3,-4,5.23,6,7,8,9,-1.08,11,12,-13.23,14,15,16,-17,18.45,1,20;
1,0,3,4,5.23,-6,7,8,9,10,-2.11,0,-13.34,14,0,-16,17,18.58,19,-20;
1,2,1,0,0,6,7.25,8,9,10.12,0,12,13.45,14,15,16,17.21,18.29,-19.23,2;
-1,2.45,0,4,5,6,7.45,8,9,0,11,12,13,4,15,0,17.22,18.21,19,1;
1,2,3,4,5.24,6,0.27,8,9.89,10,11,2,-13,14,15,16,17,3,19,20;
20,9,18,17,16,5,14,13,12,11.38,10,9,8,7,6.34,5,4,3.25,2,-1;
1,2.23,-3,4,5,6,7,-1,9,10,11.45,12,13,14.89,15,-16,17,18,19,20;
1,0,3,-4,5,6,7.34,8.34,9,1,1,12.29,-13.59,14,5,16,17,18.34,19,20;
1,2,0,4,5,0,1,8,9,10,-11,12.24,13,14.22,15,16,17.45,18,19,20;
20,19.34,1.84,17,16,15,14.35,13,12.68,11,10,9,8.34,7,6.34,5,4,3,2,1;
1,2,3,4,5.24,6,7,8.24,9,10,11.23,12,13.34,14,15,-1,-17.23,1,19,1;
1,-2.81,1,4.23,5,6.21,7,8.89,9,10,11,0,13,14,15,16,17,18,19.23,20;
-1,2,3,4,5,-6.23,-7,8,9,10,1,12,13,-14,15.33,6,17,18,19,20;
1,0,0,4,5,6.34,7,8,9,10,-11.89,1.23,13,14.34,15.21,16.34,0,18,19,20;
1.34,2,3,4,5,6.23,7,0,9,0,11,0,1.35,14,15,16.62,17,18,1.92,0;
1,-2,3,4,5.45,6,1,-8,9,10,1.12,12,13,14,15,-16,17.43,2,19,0;
1,2,1,0,-1,6,7,8,9,10,11,-12.23,13,14,15,16,17,18,0,20.23;
-1.45,1,3,4.56,0,6,7,0,9,10,11,0,13.34,14,-15,16,7,18,9.34,20;
1,2,3,-4,5,6,7,8,9.45,10,0,12.48,13,14,-1.54,16.21,-17,0,19,-2];

1. copy this matrix 'g' and paste it into input edit box
2. press ENTER/COMPUTE key
3. press DELETE key
4. type:
h=g^-1; [press ENTER/COMPUTE]

we get "Errors in the identity matrix are below 1e-15"

5. press DELETE key
6. type:
delta(g) [press ENTER/COMPUTE]

we get "Errors in the triangular matrix are below 1e-15"

-7.447376674710765E+0024

note: ( 1 / -7.447376674710765E+0024 = -1.342 754 695 617 484E-0025 )

7. type:
delta(h) [press ENTER/COMPUTE]

we get "Errors in the triangular matrix are below 1e-15"

-1.342 754 695 617 483E-0025

We have: delta(g) = 1/delta(h)

Try it and say something.
Good luck !

9. Bugs, Ideas, Suggestions

Please, answer this post and say what you want

Thanks

Rui Loureiro
;-----------------------------
qWord,
Could you use matlab to test the 'g' matrix ?
Could you get the determinant ?
Thank you !

qWord · May 07, 2012, 06:50:46 PM

using Matlabl I get:
det(g) = -7.447376674710763e+24

The inverse matrix seems also to be OK, however Matlab does not throw any error or warning message. Also I must kill the process, because there are 10 or more MessageBoxes.
Furthermore I've notice that symbols can't be redefined/reassigned. A list of current used symbols ( and there types) may also be useful.

inv(g):

Quote-0,0194764047178232   -0,137529343707484   0,00664184403258896   -0,0466770285189683   -0,387830600915522   -0,369719656238606   -0,162003612438317   -0,239363754278609   0,461162916604339   0,0389888496340502   0,184416147133701   0,513492048598551   0,162594954508341   0,128183160627410   -0,187626213055776   0,130555890841760   0,120133761613197   0,0996834400087986   -0,00207882458072814   -0,283683164963308
0,0338757503050639   0,0307908169723230   -0,0131049060577130   -0,0189557979134671   0,123657211757843   0,0888491003658484   0,0396143933774663   0,0571098151078363   -0,119211249856332   0,0602372157946917   -0,0291528503378685   -0,116523190466297   -0,150885814633673   -0,0339061391738057   0,0213408630569653   -0,0277757894797561   -0,0447675134548215   0,0352510712394123   0,0155095174149840   0,0684309869166798
0,0407504417527469   0,0828043104939397   -0,0108989895895887   -0,0107508828337988   0,154485747905220   0,0612269934425821   0,0726555166182222   -0,0503788918289131   -0,112416943568594   0,0427736945682356   -0,0557073362393930   -0,124116319235111   -0,0736068284844610   -0,0441196264972331   0,0202621202785261   -0,108430919701350   0,0504706672158689   0,0348887292486163   0,0433017596859201   0,0191067947126154
-0,0160014456368300   -0,0583122633931931   -0,000245150377743491   0,0130417065207897   -0,0553767520888153   -0,0136397669952168   -0,0176342749602453   -0,0216486513118198   0,0603978249688051   -0,00729962719037065   0,0168857892974362   0,135670024353597   0,000477729357240619   0,0140460742453566   0,0214631885087231   0,0542987505570746   -0,0227825572769282   -0,0449167603256594   0,0295836222136839   -0,0987489568288384
0,0271020281719590   0,282880536237942   0,0135328429126729   0,00415221983983574   0,430719139931245   0,359939215120402   0,183827696098050   0,225590048367140   -0,606986470413938   0,0178947365594021   -0,155719591665051   -0,742847347145614   -0,000849408830059323   -0,164462041445187   0,129738412774925   -0,213216382509666   -0,0454910440457674   -0,116375588107095   -0,0367019745515544   0,382073451367929
0,0406672965812575   0,112459184955187   -0,00133940014474780   0,00230220364147551   0,128204035670201   -0,000782707944518249   -0,0291863468475866   -0,163122142367185   -0,0650807651529163   0,0189359859629477   0,0471145679059864   -0,0799515662363367   0,0489126036353878   -0,0382824895472141   0,00135284190669496   -0,159831355328483   0,140264654031926   0,0197283756702217   0,0610193169513212   -0,0496908920785074
-0,0353423915960246   -0,204162105999212   -0,0291269907867771   0,0471518597169099   -0,122576184747335   0,0347182955089128   0,0506427164414412   0,245225233008244   0,132367747010380   -0,158887345502103   -0,0699317362060476   0,100130063191450   -0,109458372473712   0,0414431042978009   0,122258803028231   0,200121481106603   -0,204845977430587   -0,0593263476409546   -0,0711874895766235   0,0606889503059700
0,00821004173819552   0,102872491976725   0,0198098793325462   0,000525225083319057   0,152071134928447   0,0606574303557477   0,0240225650407532   -0,0532260252132116   -0,127640028233868   0,0560347543465495   -0,0103062501369982   -0,133226595015913   0,0349022805811845   -0,0606803384303529   -0,0162079619837753   -0,151935096356134   0,0335546713471251   0,0179784558370869   0,0102084529073373   0,0293268545043555
-0,0858355045186968   -0,0897321939886219   0,0172834810751707   -0,00205747208794176   -0,150189197917182   -0,0434665134591687   -0,0418527717331502   0,0307397620679878   0,158875432364889   -0,102026923232176   0,0260250575638027   0,145865657590129   -0,0379516294716412   0,0741501406716714   0,0101683565335999   0,136611724720022   -0,00281380062517075   0,0316486579931679   -0,0362276012087261   -0,00602965093826850
0,0219199362610581   -0,0355421461541348   0,00447795555243166   0,0363006616168828   -0,0585763191032851   0,00540109426146538   -0,00881468033836793   0,0211626558986845   0,0128657833325574   -0,0437222836217285   0,00538955564598836   0,0275391187431766   0,00896959192904168   0,0335244477826635   0,0221701146692356   0,00826313399619753   -0,0205778302472412   -0,0246107574665545   0,00612433009016645   -0,000137178512111534
0,00237985198572083   0,00132718456273684   -0,000467914909551473   -0,00595938589105535   -0,0198256745669206   -0,0172632963226056   -0,0110805348965221   -0,00753675457553826   0,0112788026507257   0,00357220643963796   0,0101088339676132   0,0325007101357146   0,0337857277337978   0,00870117770287843   -0,0442872582514429   0,0118496339040749   -0,00121035784858669   0,00298059392878592   0,00514206646158695   -0,0117604669430790
-0,00218476357141255   -0,0414521771260898   -0,0102256917009856   0,0200552869446157   -0,0599771472102697   -0,0428425548458869   -0,0194757141709679   -0,00814612829040217   0,0856899324628138   0,00219107172878477   0,0154447423247160   0,100540088029310   0,00624771203890054   0,0240669337095780   -0,0263096584320902   0,0322998161624877   -0,00774763687089975   -0,0241211598832975   0,00413408595479445   -0,0437699304608693
0,00163650732928936   0,0302923882689646   -0,00516914985774161   -0,00877639553171385   0,0546628475003090   0,0100392640450640   0,0168636839925183   0,00248003373301407   -0,0620212708317323   0,0289618380824108   -0,0124693334681926   -0,0634522618629034   0,00650336884849640   -0,0212134126868809   -0,00778253189803472   -0,0330541185074735   0,0120026552506788   0,0123474580353687   0,00167771423553053   0,0348493284715499
0,00885172528268708   0,0701926527137210   0,0104120426901771   -0,0163217348716093   0,0654407623177042   0,0250886554526726   0,0123720539081882   -0,0246701977708787   -0,0854766821275699   0,0829741124572558   -0,00892413114144867   -0,0717003220935649   0,0120858610107890   -0,0579354421056124   -0,0360206261504336   -0,0605714096763533   0,0328976355657030   0,0152635872500416   0,0151168318757311   0,0160193538394152
-0,000106838695318115   -0,0398821822574248   -0,00953732411510184   0,00472252276702084   -0,0490599643454039   -0,0215277319228146   -0,00893127910279693   0,00818657334555172   0,0527236643816077   -0,0148287336385422   0,00176077842794454   0,0764343745058907   -0,0144116187067952   0,0224537393919841   0,00952921234752537   0,0505597592271974   -0,0154526717457820   0,00730486452486700   -0,0245305773036044   -0,0296451638018044
-0,00301617294291907   -0,0508478548421629   -0,0103510287316471   0,00522624689779239   -0,0677868573982759   -0,0274675124225435   -0,0168363055181322   -0,00183172183383561   0,0639283269714506   -0,0101187853656825   0,0106151079712938   0,0732236834364465   0,00867126176131774   0,0264172717123994   -0,00565722594544586   0,0671329056156512   -0,0265630991751720   -0,0128751385105936   -0,00473094292145426   -0,0153908550303233
-1,41771345723608e-06   -0,00777055427056557   -0,00276878867253268   0,00691827592778792   0,0276526110457986   0,0287599385249704   0,0147713522029517   0,0239237788264728   -0,0178175909016705   0,00128109772746900   -0,0136798754624504   -0,0445040079494080   -0,00815800649663193   -0,0110152529106634   0,00139188031853718   -0,00556122115307750   -0,00986894150119833   -0,00226206188711953   -0,00723897709646967   0,0226400670217924
0,0234932485903318   0,0476237786415082   0,0151286447275387   -0,0107669125486579   0,00145284995413316   -0,0679484338395709   -0,0319610821854304   -0,0919730220617370   0,0120935388306771   0,0370485943403460   0,0365978182829969   0,0264952383417367   0,0419875334814127   0,00989649010318327   -0,0316948810521638   -0,0369853266571003   0,0577971861639099   0,0170521075590771   0,0356027131815505   -0,0619411784104348
0,00401844418179543   -0,0472658910462619   -0,00197409073165974   -0,0217206372516133   -0,0613302964555191   -0,0621687812569254   -0,0316764444399514   -0,0412921385240117   0,0980537205971524   0,00681683251542359   0,0274345812855831   0,115305931692271   0,00804300263074198   0,0275318850786049   -0,0221161385335807   0,0357229116275633   0,00956321871506687   0,0172514063802433   0,00499197968057683   -0,0530306008641024
-0,00701831483819808   0,00786195332936113   -0,0107729833979132   -0,000885462353389252   0,0201914610973340   0,0388066895013467   0,0250126109474898   0,0520282579996586   -0,0292851120148883   -0,00660011606973864   -0,0238598162853767   -0,0484629962957876   -0,0213206700245884   -0,0110299994151064   0,0233424206394418   -0,0122674387592062   -0,0239930871001743   -0,00401101555033400   -0,00529862599817829   0,0267855772679325

Will you ever share the source code?

regards, qWord

RuiLoureiro · May 08, 2012, 04:39:54 PM

qWord,
First of all, many thanks to you

Quote
The inverse matrix seems also to be OK,

I read it and all numbers seems to be 'equal' with 15 digits
Very good !

Quote
however Matlab does not throw any error or warning message.

It was my particular decision to show what happened inside
the Gauss-Jordan elimination method. I want to show it.
I can tell you that after testing i tried to eliminate that
errors using linear transformations, but without any success!
Simply, i couldnt remove that errors. Well, i can remove
moving a 0.0 to it or 1.0 to it but it is not correct !

Quote
Also I must kill the process, because there are 10 or more MessageBoxes.

The problem is solved: the messages are in the output edit boxes

Quote
det(g) and inv(g)

Ok, i decided to use this names too:

determinant of a: det(a) or delta(a)
inverse of a: b=inv(a) or b=a^-1;

Quote
Furthermore I've notice that symbols can't be redefined/reassigned.

Names of variables or constants can be redefined.
In the case of matrix names we can't.
We need to use a new name. But i can change it.
Whenever we define a matrix by operation or not
the calculator allocate a space for a 20*20 matrix.
It may be a 2*1 matrix but the space is for 20*20.
So, there isnt any problem in redefine it.

Do you think we should redefine it ? I dont know
if it is better !

Quote
A list of current used symbols ( and there types) may also be useful.

This seems to be a good suggestion and may be useful.
How to ask for that list ?

Typing: symb; or symb() ?
or list; or list() ?

Quote
Will you ever share the source code?

I didnt decide anything about it till now.
I wrote 8 files with procedures, the first
has 10020 lines.
For matrices i have one with 3700 lines.
It is not easy to read it because the
procedures are not documented. More: i
use the registers as variables instead of
global/local variables in many cases.
I dont like local variables because i
use OPTION PROLOGUE:NONE,OPTION EPILOGUE:NONE.
Ok, in some cases it is easy to understand.
For instance, a matrix 10*20 is defined as

dd 20 <- number of columns
dd 10 <- number of lines
_matrixX db 200*10 dup(?)

The address of _matrixX gives me 3 things:
number of lines, number of columns, and the
elements. We dont need to pass more than
the address.

All strings have the lenght behind.
My procedures exits with clc or stc.
Generally, stc means error or errors. If
errors i put the code in eax.
As you are 'seeing' i have my own rules!
Ok, do you want to see some code ?

regards,
Rui Loureiro

RuiLoureiro · May 13, 2012, 07:40:07 PM

Hi all,
News

In the previous calcula44, the log function
doesnt work. We have problems when we try
to close a MessageBox with ENTER.
This problems are corrected.
Now, i tested
. all functions
. systems of 2,3,4 linear equations
. quadratic equation
. linear interpolation
. constant definition
. function definition
. derivative definition
. function root and Newton method
. matrix definitions
. matrix operations
. print function

**** Here is calcula45 v1.05 ****

1. List of symbols used in the calculator

Type list

and press ENTER/COMPUTE

Define the constants: t=12;s=25.3;
and press ENTER/COMPUTE

Define the matrix: a=[1, 2; 3, 4];
and press ENTER/COMPUTE

Now, type list
and press ENTER/COMPUTE

The new symbols are in the list

2. Inverse matrix

Given a matrix a
to get the inverse matrix b
we can use:

a) b=a^-1;

b) b=inv(a);

3. Determinant

Given a squared matrix a
to get the determinant
we can use:

a) delta(a)

b) det(a)

4. Conversion: conv() function

To convert from decimal:

type conv(decimal_number)

and press ENTER/COMPUTE

To convert from hexadecimal:

type conv(hexadecimal_number)
and press ENTER/COMPUTE

or

type hexadecimal_number
and press ENTER/COMPUTE

To convert from binary:

type conv(binary_number)
and press ENTER/COMPUTE

type binary_number
and press ENTER/COMPUTE

5. Examples

example I

type:
conv(1010b)
or
1010b

and press ENTER/COMPUTE

we get:
10
0000000AH
00000000000000000000000000001010B

example II

type:
conv(000000000ABCDEFFFFFFFFFF1h)
or
000000000ABCDEFFFFFFFFFF1h

and press ENTER/COMPUTE
we get:

12379814833502027761
ABCDEFFFFFFFFFF1h
10101011110011011110111111111111
11111111111111111111111111110001B

example III

type:
conv(11111111111111111111111111111111 11111111111111111111111111111111b)
or
11111111111111111111111111111111 11111111111111111111111111111111b

and press ENTER/COMPUTE

we get:
18446744073709551615
FFFFFFFFFFFFFFFFH
11111111111111111111111111111111
11111111111111111111111111111111B

example IV

type:
conv(0000018446744073709551615)

and press ENTER/COMPUTE

we get:
18446744073709551615
FFFFFFFFFFFFFFFFH
11111111111111111111111111111111
11111111111111111111111111111111B

Try it and say something.
Good luck !

6. Suggestions

I am waiting for suggestions

Thanks

Rui Loureiro

dedndave · May 13, 2012, 07:59:53 PM

:U

RuiLoureiro · May 15, 2012, 02:28:52 PM

Hi Dave :U

Hi all,

4 things:

1. calcula45 doesnt solve expressions
like e^-(...) and xEy^n; The 2nd
is because it is scientific notation!

2. i found a bug: one variable used
inside and out a proc, when it
should be used only inside one.
All my procs and variables are
independent, but that fails
the rule. And it has something to
do with functions.

3. now, we can round an expression;

4. expressions with 3800 characters
200 operations inside brackets.

What else ?

improvement and ... improvement.

**** Here is calcula46 v1.06 ****

Examples:

1) round(e^-(-3+sin(3*5+12)),6)+34*5-sin(pi/3)

2)
1. copy this expression and paste it into input edit box
2. press ENTER/COMPUTE key

round(e^-(3*4*5*120+90*456*5*2)+34-456*sin(5*2+34*456*5*2+34*456*5*2+34*456*5*2+34-456*5*2+345
*456*5*2+3409*456*5*2+34*456*5*2+34*456*5*2+34*456*5*2+34*456*5*2+34*456*5*2+348
*456*5*2+34/456*5*2+34+3+12-24+12*12*30/3*4*5*120+90*456*5*2+34*456*5*2+34*456
*5*2+34*456^2*5*2+34*456*5*2+34+456*5*2-34*456*5*2+3409*456*5*2+34*456*5*2+34*456
*5*2-34*456*5*2^4+34*456*5*2+34*456*5*2+34*456*5*2+34*456*5*2+34+3+12+24+12*12*30
+12*12-23-23-45-24*56*20*10+12+12*12-23-23-45-24*56*20*10+12+12*12-23-23-45-24
*56*20*10+12+12*12-23-23-45-24*56*20*10+12+12*12-23-23-45-24*56*20*10+12+12*12
-23-23-45-24*56*20*10)*(2^10+56.3*5)+(2^10+56.3*5)*(2^10+56.3*5)-(2^10+56.3*5)*
(2^10+56.3*5+2.45)-(2^10+56.3*5)*(2^10+56.3*5)*(2^10+56.3*5)+(2^10+56.3*5)*(2^10+56.3*5)
*(2^10+56.3*5)-2*(3*4*5*120+90*456*5*2+34-456*5*2+34*456*5*2+34*456*5*2+34*456*5*2
+34-456*5*2+345*456*5*2+3409*456*5*2+34*456*5*2+34*456*5*2+34*456*5*2+34*456*5*2+
34*456*5*2+348*456*5*2+34/456*5*2+34+3+12-24+12*12*30/3*4*5*120+90*456*5*2+34*456*5*2+34*456
*5*2+34*456^2*5*2+34*456*5*2+34+456*5*2-34*456*5*2+3409*456*5*2+34*456*5*2+34*456
*5*2-34*456*5*2^4+34*456*5*2+34*456*5*2+34*456*5*2+34*456*5*2+34+3+12+24+12*12*30
+12*12-23-23-45-24*56*20*10+12+12*12-23-23-45-24*56*20*10+12+12*12-23-23-45-24
*56*20*10+12+12*12-23-23-45-24*56*20*10+12+12*12-23-23-45-24*56*20*10+12+12*12
-23-23-45-24*56*20*10)
-sin(3*4*5*120+90*456^-1*5*2+34-456*5*2+34*456*5*2+34*456*5*2+34*
456*5*2+34-456*5*2+345*456*5*2+3409*456*5*2+34*456*5*2+34*456*5*2+34*456*5*2+34*
456*5*2+34*456*5*2+348*456*5*2+34/456*5*2+34+3+12-24+12*12*30/3*4*5*120+90*456*5*
2+34*456*5*2+34*456*5*2+34*456^2*5*2+34*456*5*2+34+456*5*2-34*456*5*2+3409*456*5*2+
34*456*5*2+34*456*5*2-34*456*5*2^4+34*456*5*2+34*456*5*2+34*456*5*2+34*456*5*2+34+3+
12+24+12*12*30+12*12-23-23-45-24*56*20*10+12+12*12-23-23-45-24*56*20*10+12+12*12-23-
23-45-24*56*20*10+12+12*12-23-23/45-24*56*20*10+12+12*12-23-23-45-24*56*20*10+12+12*12
-23-23-45-24*56*20*10)
+cos(3*4*5*120+90*456^-1*5*2+34-456*5*2+34*456*5*2+34*456*5*2+34*
456*5*2+34-456*5*2+345*456*5*2+3409*456*5*2+34*456*5*2+34*456*5*2+34*456*5*2+34*
456*5*2+34*456*5*2+348*456*5*2+34/456*5*2+34+3+12-24+12*12*30/3*4*5*120+90*456*5*
2+34*456*5*2+34*456*5*2+34*456^2*5*2+34*456*5*2+34+456*5*2-34*456*5*2+3409*456*5*2+
34*456*5*2+34*456*5*2-34*456*5*2^4+34*456*5*2+34*456*5*2+34*456*5*2+34*456*5*2+34+3+
12+24+12*12*30+12*12-23-23-45-24*56*20*10+12+12*12-23-23-45-24*56*20*10+12+12*12-23-
23-45-24*56*20*10+12+12*12-23-23/45-24*56*20*10+12+12*12-23-23-45-24*56*20*10+12+12*12
-23-23-45-24*56*20*10)
+(3*4*5*120+90*456^-1*5*2+34-456*5*2+34*456*5*2+34*456*5*2+34*
456*5*2+34-456*5*2+345*456*5*2+3409*456*5*2+34*456*5*2+34*456*5*2+34*456*5*2+34*
456*5*2+34*456*5*2+348*456*5*2+34/456*5*2+34+3+12-24+12*12*30/3*4*5*120+90*456*5*
2+34*456*5*2+34*456*5*2+34*456^2*5*2+34*456*5*2+34+456*5*2-34*456*5*2+3409*456*5*2+
34*456*5*2+34*456*5*2-34*456*5*2^4+34*456*5*2+34*456*5*2+34*456*5*2+34*456*5*2+34+3+
12+24+12*12*30+12*12-23-23-45-24*56*20*10+12+12*12-23-23-45-24*56*20*10+12+12*12-23-
23-45-24*56*20*10+12+12*12-23-23/45-24*56*20*10+12+12*12-23-23-45-24*56*20*10+12+12*12
-23-23-45-24*56*20*10)
-log(3*4*5*120+90*456*5*2+34-456*5*2+34*456*5*2+34*456*5*2+34*
456*5*2+34-456*5*2+345*456*5*2+3409*456*5*2+34*456*5*2+34*456*5*2+34*456*5*2+34*
456*5*2+34*456^-1*5*2+348*456*5*2+34/456*5*2+34+3+12-24+12*12*30/3*4*5*120+90*456*5*
2+34*456*5*2+34*456*5*2+34*456^2*5*2+34*456*5*2+34+456*5*2-34*456*5*2+3409*456*5*2+
34*456*5*2+34*456*5*2-34*456*5*2^4+34*456*5*2+34*456*5*2+34*456*5*2+34*456*5*2+34+3+
12+24+12*12*30+12*12-23-23-45-24*56*20*10+12+12*12-23-23-45-24*56*20*10+12+12*12-23-
23-45-24*56*20*10+12+12*12-23-23/45-24*56*20*10+12+12*12-23-23-45-24*56*20*10+12+12*12
-23-23-45-24*56*20*10),3)

= -109648054.196

qWord and Dave,

Do you Know how to test the result of that expression ?

Thanks

dedndave · May 15, 2012, 03:52:33 PM

here is what i come up with, Rui

Code Select

7.71853 + 170 - 0.86602540378443864676372317075294 = 176.85250459621556135323627682925

i may have made a mistake - lol

RuiLoureiro · May 15, 2012, 04:25:31 PM

Dave,
i want to test the second not the first
The first give me 176.8525055962156 too

dedndave · May 15, 2012, 04:51:25 PM

oh, sure - you give ME the hard one :eek

:lol

RuiLoureiro · May 15, 2012, 05:28:33 PM

:bg
Dave,
may be hutch could help us :green2

dedndave · May 15, 2012, 07:00:23 PM

if i remember, i'll try it out later today, Rui :U

RuiLoureiro · May 15, 2012, 08:33:45 PM

:bg
Dave,
I did my homework as ever :green2
Solving by parts (using the calculator) i get this:

A
e^-(3*4*5*120+90*456*5*2)+34-456*

sin(5*2+34*456*5*2+34*456*5*2+34*456*5*2+34-456*5*2+345
*456*5*2+3409*456*5*2+34*456*5*2+34*456*5*2+34*456*5*2+34*456*5*2+34*456*5*2+348
*456*5*2+34/456*5*2+34+3+12-24+12*12*30/3*4*5*120+90*456*5*2+34*456*5*2+34*456
*5*2+34*456^2*5*2+34*456*5*2+34+456*5*2-34*456*5*2+3409*456*5*2+34*456*5*2+34*456
*5*2-34*456*5*2^4+34*456*5*2+34*456*5*2+34*456*5*2+34*456*5*2+34+3+12+24+12*12*30
+12*12-23-23-45-24*56*20*10+12+12*12-23-23-45-24*56*20*10+12+12*12-23-23-45-24
*56*20*10+12+12*12-23-23-45-24*56*20*10+12+12*12-23-23-45-24*56*20*10+12+12*12
-23-23-45-24*56*20*10)*(2^10+56.3*5)

= -374 258.1604136189
------------------------------------------------------------------------------------
B
+(2^10+56.3*5)*(2^10+56.3*5)-(2^10+56.3*5)*
(2^10+56.3*5+2.45)-(2^10+56.3*5)*(2^10+56.3*5)*(2^10+56.3*5)+(2^10+56.3*5)*(2^10+56.3*5)
*(2^10+56.3*5)-2*(3*4*5*120+90*456*5*2+34-456*5*2+34*456*5*2+34*456*5*2+34*456*5*2
+34-456*5*2+345*456*5*2+3409*456*5*2+34*456*5*2+34*456*5*2+34*456*5*2+34*456*5*2+
34*456*5*2+348*456*5*2+34/456*5*2+34+3+12-24+12*12*30/3*4*5*120+90*456*5*2+34*456*5*2+34*456
*5*2+34*456^2*5*2+34*456*5*2+34+456*5*2-34*456*5*2+3409*456*5*2+34*456*5*2+34*456
*5*2-34*456*5*2^4+34*456*5*2+34*456*5*2+34*456*5*2+34*456*5*2+34+3+12+24+12*12*30
+12*12-23-23-45-24*56*20*10+12+12*12-23-23-45-24*56*20*10+12+12*12-23-23-45-24
*56*20*10+12+12*12-23-23-45-24*56*20*10+12+12*12-23-23-45-24*56*20*10+12+12*12
-23-23-45-24*56*20*10)

= -217 723 715.9662281
--------------------------------------------------------------------------------------
Total A + B
= -374 258.1604136189 -217 723 715.9662281

= -218 097 974.1266417
--------------------------------------------------------------------------------------
C
-sin(3*4*5*120+90*456^-1*5*2+34-456*5*2+34*456*5*2+34*456*5*2+34*
456*5*2+34-456*5*2+345*456*5*2+3409*456*5*2+34*456*5*2+34*456*5*2+34*456*5*2+34*
456*5*2+34*456*5*2+348*456*5*2+34/456*5*2+34+3+12-24+12*12*30/3*4*5*120+90*456*5*
2+34*456*5*2+34*456*5*2+34*456^2*5*2+34*456*5*2+34+456*5*2-34*456*5*2+3409*456*5*2+
34*456*5*2+34*456*5*2-34*456*5*2^4+34*456*5*2+34*456*5*2+34*456*5*2+34*456*5*2+34+3+
12+24+12*12*30+12*12-23-23-45-24*56*20*10+12+12*12-23-23-45-24*56*20*10+12+12*12-23-
23-45-24*56*20*10+12+12*12-23-23/45-24*56*20*10+12+12*12-23-23-45-24*56*20*10+12+12*12
-23-23-45-24*56*20*10)

= -0.817405354401868
--------------------------------------------------------------------------------------
D
+cos(3*4*5*120+90*456^-1*5*2+34-456*5*2+34*456*5*2+34*456*5*2+34*
456*5*2+34-456*5*2+345*456*5*2+3409*456*5*2+34*456*5*2+34*456*5*2+34*456*5*2+34*
456*5*2+34*456*5*2+348*456*5*2+34/456*5*2+34+3+12-24+12*12*30/3*4*5*120+90*456*5*
2+34*456*5*2+34*456*5*2+34*456^2*5*2+34*456*5*2+34+456*5*2-34*456*5*2+3409*456*5*2+
34*456*5*2+34*456*5*2-34*456*5*2^4+34*456*5*2+34*456*5*2+34*456*5*2+34*456*5*2+34+3+
12+24+12*12*30+12*12-23-23-45-24*56*20*10+12+12*12-23-23-45-24*56*20*10+12+12*12-23-
23-45-24*56*20*10+12+12*12-23-23/45-24*56*20*10+12+12*12-23-23-45-24*56*20*10+12+12*12
-23-23-45-24*56*20*10)

= 0.576062918955175
--------------------------------------------------------------------------------------
Total A + B + C + D

= -218 097 974.1266417 -0.817405354401868 + 0.576062918955175
= -218 097 974.3679841
--------------------------------------------------------------------------------------
E
+(3*4*5*120+90*456^-1*5*2+34-456*5*2+34*456*5*2+34*456*5*2+34*
456*5*2+34-456*5*2+345*456*5*2+3409*456*5*2+34*456*5*2+34*456*5*2+34*456*5*2+34*
456*5*2+34*456*5*2+348*456*5*2+34/456*5*2+34+3+12-24+12*12*30/3*4*5*120+90*456*5*
2+34*456*5*2+34*456*5*2+34*456^2*5*2+34*456*5*2+34+456*5*2-34*456*5*2+3409*456*5*2+
34*456*5*2+34*456*5*2-34*456*5*2^4+34*456*5*2+34*456*5*2+34*456*5*2+34*456*5*2+34+3+
12+24+12*12*30+12*12-23-23-45-24*56*20*10+12+12*12-23-23-45-24*56*20*10+12+12*12-23-
23-45-24*56*20*10+12+12*12-23-23/45-24*56*20*10+12+12*12-23-23-45-24*56*20*10+12+12*12
-23-23-45-24*56*20*10)

= 108 449 928.2081871
--------------------------------------------------------------------------------------
Total A + B + C + D + E

= -218 097 974.3679841 + 108 449 928.2081871
= -109 648 046.159797

--------------------------------------------------------------------------------------
F
-log(3*4*5*120+90*456*5*2+34-456*5*2+34*456*5*2+34*456*5*2+34*
456*5*2+34-456*5*2+345*456*5*2+3409*456*5*2+34*456*5*2+34*456*5*2+34*456*5*2+34*
456*5*2+34*456^-1*5*2+348*456*5*2+34/456*5*2+34+3+12-24+12*12*30/3*4*5*120+90*456*5*
2+34*456*5*2+34*456*5*2+34*456^2*5*2+34*456*5*2+34+456*5*2-34*456*5*2+3409*456*5*2+
34*456*5*2+34*456*5*2-34*456*5*2^4+34*456*5*2+34*456*5*2+34*456*5*2+34*456*5*2+34+3+
12+24+12*12*30+12*12-23-23-45-24*56*20*10+12+12*12-23-23-45-24*56*20*10+12+12*12-23-
23-45-24*56*20*10+12+12*12-23-23/45-24*56*20*10+12+12*12-23-23-45-24*56*20*10+12+12*12
-23-23-45-24*56*20*10)

= -8.036250666905551
;************************************************************************************
Total A + B + C + D + E + F

= -109 648 046.159797 -8.036250666905551
= -109 648 054.1960477
; ««««««««««««««««««««««««««««««««««««««««««««««««««««««««««««««««««««««««««««««««««««««««««««««
Total result computing all expression = -109 648 054.1960477
; ««««««««««««««««««««««««««««««««««««««««««««««««««««««««««««««««««««««««««««««««««««««««««««««

Conclusion: we get the same result exactly

RuiLoureiro · May 16, 2012, 07:19:40 PM

Quote from: dedndave on May 15, 2012, 07:00:23 PM
if i remember, i'll try it out later today, Rui :U

Did yoy try, Dave ?

dedndave · May 17, 2012, 12:17:11 AM

i will give it a shot, Rui...

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