JBCL Algebraic Calculator Help

Kotuku


Topics are:
Overview Examples of Calculations Punctuation
How to use Advanced Features How to And Common Questions
Scientific Functions Mathematics Constants Physics Constants
Credits


Overview

Calc3

JBCL Calculator


This is a different form of calculator.  For those used to algebra or some advanced calculators like the Sharp Scientific calculator it is a much simpler way to work.

For instance you can enter calculations like

17*142
-or-
(1+2+3)*(4+5+6)
and then just click the Calculate button

Note for those who didn't know, most of these kinds of calculations can be done on Google's home page - if it detects a calculation like this it prints the answer.
However one is not always online, and this program adds ability to record and save calculation histories, and 10 memories.



Main Screen

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Example Calculations

17*142
-or-
(1+2+3)*(4+5+6)

-or-
67.5*67.75*1.125

Punctuation


Note you do have to be a little careful entering calculations.

-You have to enter decimal numbers with a leading digit, eg 12.345 or 0.0123
-If you use brackets you have to have matching ones, eg (((1+2+3)*(4+5)+6)/7)
-if you use invalid syntax or functions you will get an error message!
-if you see a message "access violation" then usually its a syntax error causing this


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How to Use JBCLCalc

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Advanced Options

Using Memories

To use a memory, double click the memory.  This brings up a menu of what you can do:

You can also use the memory directly in the calculation window by giving typing the name Mem1 or  Mem2 or  Mem3  etc.   This will insert the value currently in that memory into the calculation when the Calculate button is clicked.


Using Memory

Using Result

Similar to memories - if you type Result in a calculation this will be replaced by the current value in the Result.   Note this is the result before the calculation takes place - afterwards it will be a different number of course).

Tips


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How-To and Common Questions


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Scientific Functions

works with real numbers;
accepts operators:
             + - * / ^
accepts functions:
 cos, sin, tg, ctg, abs, sgn or sign, sqrt, ln,
 exp, arcsin, arccos, arctg or arctan, arcctg,
sh or sinh, ch or cosh, th or tanh,
cth or coth, heaviside
supports unlimited number of user defined variables

Notes:

Examples:

sqrt(1/(mu0*e0))     This gives an answer of  299792458.014787   which happens to be the speed of light

       G*EarthMass/((EarthDiameter/2)^2)
Result = 9.8016820520445                    this figure 9.8 m/Sec^2     is the gravitational acceleration of anything  at the Earth's surface.


More Constants

Note - some of these below are already in the constants list in the Program - most are not.

Any values you wish to use can be copied into the calculation window by copying the number.

If you wish more of these values in the predefined constants list, contact JBCL

Reference - Mathematical Constants

there are many inbuilt constants,  such as pi and e and c
(click the constants button to see a list of these)

pi = 3.141592653589793238  for calculator
pi = 3.141592653589793238462643383279502884197169399375105820974944   more accurate value not for calculator
e = 2.71828182845905   = exp(1)
c = 2.99792458e8  [m/s]

Mathematical constants from http://www.ebyte.it/library/educards/constants/MathConstants.html

Basic math constants 
π, Archimedes' constant  3.141 592 653 589 793 238 462 643 ...  Circumference of a disc with unit diameter. 
√2, Pythagora's constant  1.414 213 562 373 095 048 801 688 ...  Diagonal of a square with unit side. 
e, Euler number  2.718 281 828 459 045 235 360 287 ...  Base of natural logarithms. 
γ, Euler-Mascheroni constant  0.577 215 664 901 532 860 606 512 ...  limit of [(1+1/2+1/3+...1/n)-ln(n)]. 
ln(2), Natural logarithm of 2  0.693 147 180 559 945 309 417 232 ...  eln(2) = 2
φ, Golden ratio  0.618 033 988 749 894 848 204 586 ...  φ = (1-φ)/φ or φ = (√5 -1)/2. 
Conversion constants 
1 rad, Radian in degrees  57.295 779 513 082 320 876 798 154 ...  180/π 
1°, Degree in radians  0.017 453 292 519 943 295 769 237 ...  π/180 
Math constants with particular physical significance 
ρ2, 2D close packing ratio  0.906 899 682 117 089 252 970 392 ...  ρ2 = π / 2√3. Best covering of 2D plane by circles. 
ρ3, 3D close packing ratio  0.740 480 489 693 061 041 169 313 ...  ρ3 = π / 3√2. Best covering of 3D space by spheres. 
ξ0, First root of Bessel J0(x)  2.404 825 557 695 ...  Also first root of sinc(0,x). 
ξ2, First root of Bessel J1(x)  3.831 705 970 207 ...  Also first root of sinc(2,x). 
ξ3, First root of [sin(x)/x - cos(x)]  4.493 409 457 909 ...  Also first root of sinc(3,x). 
ξ4, First root of [2J1(x)/x - J0(x)]  5.135 622 301 840 ...  Also first root of sinc(4,x). 
Various math constants 
ζ(3), Apery' constant  1.202 056 903 159 59 ...  Special value of the Riemann function ζ(x). 
B, Brun' constant  1.902 160 58 ...  Sum of the reciprocals of twin primes 
C, Catalan's constant  0.915 965 594 177 219 015 ...  C = Sum(n=0,1,2,...)[(-1)^/(2n+1)^2] 
α, Feigenbaum constant  2.502 907 875 0 ...  Appears in the theory of chaos. 
δ, Feigenbaum constant  4.669 201 609 1 ...  Appears in the theory of chaos. 
M, Gauss' lemniscate constant  1.198 140 234 735 59...  Length of lemniscate [r2=cos(2θ)] is 2π/M.
A, Gleisher-Kinkelin constant  1.282 427 129 ...  Appears in number theory. 
λ, Golomb-Dickman constant  0.624 329 989 ...  Longest cycle distribution in random permutations. 
λ, Laplace limit constant  0.662 743 419 3...  Let η = √(1+λ2); then λeη = 1+η.
M3, Madelung's constant  -1.747 564 594 633 ...  M3 = Sum(i,j,k)[(-1)^(i+j+k)/sqr(i^2+j^2+k^2)] 
A, Moving sofa constant  2.219 531 668 871 ...  Greatest sofa that can turn a hallway corner. 
α, Otter's constant  2.955 765 285 652 ...  Appears in tree enumeration. 
β, Otter's constant  0.534 949 606 142 ...  Appears in tree enumeration. 
p3, Polya's random-walk constant  0.340 537 339 287 ...  Probability to return back in a 3D-lattice random walk. 
m, Rényi's parking constant  0.747 597 920 253 ...  Density of randomly parked cars in a street. 
G, Wilbraham-Gibbs constant  1.851 937 051 982 466 170 4...  G = Integral of sin(θ)/θ from 0 to π 

Reference - Physics Constants

Physics constants from  http://www.ebyte.it/library/educards/constants/ConstantsOfPhysicsAndMath.html

Note: If you copy and paste physics constants from the section below, remove the parts in square brackets,  these are the uncertainties and cannot be used in the calculator

Universal constants 
Speed of light c  2.997 924 580 e+8  m.s-1 m/s  Now assigned (see SI units) 
Gravitation constant G  6.67428[67] e-11  kg-1.m3.s-2   force = G M1M2 / r122
Planck constant h  6.626 068 96[33] e-34  kg.m2.s-1 J.s  = energy quantum / frequency
Angular Planck constant  1.054 571 628[53] e-34  kg.m2.s-1 J.s  h/2π
Planck mass mp  2.176 44[11] e-8  kg  kg  mp2 = (h/2π) c / G 
Planck time tp  5.391 24[27] e-44  s  s  = (h/2π) / (mpc2)
Planck length lp  1.616 252[81] e-35  m  m  = ctp 
Planck temperature  1.416 785[71] e+32  K  K  = mpc2 / k
Hubble constant  2.26[23] e-18  s-1   Universe expansion rate
Electromagnetic constants 
Permeability of vacuum μ0  12.566 370 614... e-7  kg.m.s-2.A-2 H/m | N/A2 = 4π.10-7. Assigned.
Permittivity of vacuum ε0  8.854 187 817... e-12  kg-1.m-3.s4.A2 F/m  = 1 / (c2 μ0). Assigned.
Impedance of vacuum Z0  376.730 313 461 ...  kg.m2.s-3.A-2 Ω  Assigned by Z02 = μ0/ε0.
Elementary charge e  1.602 176 487[40] e-19  s.A  C   
Charge/Quantum ratio  2.417 989 454[60] e14  kg-1.m-2.s2.A A/J  = e / h 
Quantum/Charge ratio  4.135 667 33[10] e-15  kg.m2.s-2.A-1 J/A  = h / e 
Fine structure constant α  7.297 352 5376[50] e-3  Dimensionless    = μ0 c e2 / 2h. July 2006 [1].
Inverse of  
fine structure constant		 137.035 999 679[94]  Dimensionless    = 1/α = 2h / (μ0 c e2).
Updated July 2006 [1].
Magnetic flux quantum Φ0  2.067 833 667[52] e-15  kg.m2.s-2.A-1 Wb  = h / 2e 
Conductance quantum G0  7.748 091 7004[53] e-5  kg-1.m-2.s3.A2 S  = 2e2 / h
Inverse of conductance quantum  1.290 640 377 87[88] e+4  kg.m2.s-3.A-2 Ω  = RK / 2 
Josephson constant KJ  4.835 978 91[12] e14  kg-1.m-2.s2.A Hz/V  = 2e / h 
conventional: 483597.9 GHz/V
von Klitzing constant RK  2.581 280 755 7[18] e+4  kg.m2.s-3.A-2 Ω  = h / e2 
conventional: 25812.807 Ω
Electron and atomic physics constants 
Electron rest mass me  9.109 382 15[45] e-31  kg  kg  0.510 998 910[13] MeV 
5.485 799 094 2[23] e-4 u
Electron charge/mass ratio  - 1.758 820 150[44] e11  kg-1.s.A C/kg  = e / me 
Compton wavelength of electron  2.426 310 217 5[33] e-12  m  m  λC,e = h / c me 
Classical electron radius re  2.817 940 289 4[58] e-15  m  m  = e2 / (4πε0mec2 )
Thomson cross section σe  0.665 245 855 8[27] e-28  m2 m2 = (8π/3) re2
Quantum of circulation  3.636 947 519 9[50] e-4  m2.s-1 m2/s = h / 2me 
Bohr magneton μB  9.274 009 15[23] e-24  m2.A J/T  = 2π h e / me 
Electron spin Se  1/2  Dimensionless     
Electron magnetic moment μe  - 9.284 763 77[23] e-24  m2.A J/T  Last update July 2006 [2] 
Electron g-factor  - 2.002 319 304 362 2[15]  Dimensionless    = μe / (Se μB). 
Electron/Proton  
magnetic moments ratio		 - 658.210 684 8[54]  Dimensionless     
Electron/Shieled proton  
magnetic moments ratio		 - 658.227 597 1[72]  Dimensionless    In water; standard conditions
Electron gyromagnetic ratio γe  28.024 953 64[70] e+9  kg-1.s.A Hz/T  γe = μe / h Se 
Rydberg constant R∞  1.097 373 156 852 7[73] e+7  m-1 m-1 = c α2 me / 2h 
Hartree energy EH  4.359 743 94[22] e-18  kg.m2.s-2 J  = α2 me c2 = 2h c R∞ 
Bohr radius  5.291 772 08 59[36] e-11  m  m  = α / (4π R∞) 
Physico-chemical constants 
Atomic mass constant u  1.660 538 782[83] e-27  kg  kg  Mass of 12C nuclide / 12
Molar mass of  12C  12 e-3  kg  kg  Assigned 
Molar mass constant  1 e-3  kg.mol-1 kg/mol  Assigned 
Boltzman constant k  1.380 6504[24] e-23  kg.m2.s-2.K-1 J/K  Sets thermodynamic temp. 
Boltzman constant in eV/K  86.173 43[15] e-6  kg.m2.s-3.A-1.K-1 V/K  = k/e.   Electrochemical
potential is ~ (k/e)T ln(c1/c2)
Avogadro's number NA  6.022 141 79[30] e+23  mol-1 mol-1 Particles in a mole of substance 
Molar Planck constant  3.990 312 682 1[57] e-10  kg.m2.s-1.mol-1 J.s/mol  = h NA 
Molar Planck constant by c  0.119 626 564 72[17]  kg.m3.s-2.mol-1 J.m/mol  = h c NA 
Electron molar mass  5.485 799 094 3[23] e-7  kg.mol-1 kg/mol  = me NA 
Electron molar charge  -9.648 533 99[24] e+4  s.A.mol-1 C/mol  = e NA. 
Faraday constant F  9.648 533 99[24] e+4  s.A.mol-1 C/mol  = |electron molar charge|. 
Molar gas constant R  8.314 472[15]  kg.m2.s-2.K-1.mol-1 J/K.mol  = k NA 
Molar volume  
of ideal gas Vm		 22.413 996[39] e-3  m3.mol-1 m3/mol = (RT/p) 
at T=273.15 K, p=101325 Pa 
Loschmidt constant n0  2.686 777 4[47] e25  m-3 m-3 = NA / Vm 
at T=273.15 K, p=101325 Pa
Sackur-Tetrode constant S0/R  - 1.151 704 7[44]  Dimensionless    (5/2)+ln[(2πmukT/h2)3/2(kT/p)]
at T=1K, p=100 kPa.
Radiation constants 
Stefan-Boltzmann const. σ  5.670 400[40] e-8  kg.s-3.K-4 W/m2.K4 = 2 π5 k4 / 15 h3 c2 
1st radiation constant c1  3.741 771 18[19] e-16  kg.m4.s-3 W.m2 = 2 π h c2 
2nd radiation constant c2  1.438 775 2[25] e-2  m.K  m.K  = h c / k 
Wien displacement const.  2.897 768 5[51] e-3  m.K  m.K  = λmaxT = c2 / 4.9651423... 
Conventional constants 
Standard gravity acceleration  9.806 65  m.s-2 m/s2 Assigned. Called 1 g (gee).
Standard atmosphere  101 325  Pa    Assigned. Called 1 atm.
Molar mass constant  0.001  kg.mol-1 kg/mol  Assigned (exact) 
Molar mass of  12C  0.012  kg  kg  Assigned (exact) 
SI conversion factors 
Electron volt  1.602 176 487[40] e-19  kg.m2.s-2 J   
Astronomical unit ua, au  1.495 978 70[30] e+11  m  m  Mean Earth-to-Sun distance 
Atomic mass constant u, mu  1.660 538 782[83] e-27  kg  kg  Mass of 12C nuclide / 12 
Nuclear and particle physics constants 
Fermi coupling GF/(hc/2π)3 3.670 336[31] e+48  kg-2   = (1.026 8365[88] e-5) / mp2
Fermi coupling in eV-2  1.166 37[1] e+4  eV-2    
Weak mixing angle sin2θW  0.222 55[56]  Dimensionless    = 1- (mW/mZ)2
Proton rest mass mp  1.672 621 637[83] e-27  kg  kg  938.272 013[23] MeV 
1.007 276 466 77[10] u
Nuclear magneton μN  5.050 783 24[13] e-27  m2.A J/T  = 2π h e / mp 
Nuclear magneton in Hz/T  7.622 593 84[19] e+6  kg-1.s.A Hz/T  = μN/h = [Larmor freq.]/[g-factor]. 
Compton wavelength of proton  1.321 409 844 6[19] e-15  m  m  λC,p = h / c mp 
Proton magnetic moment  1.410 606 662[37] e-26  m2.A J/T  μp 
Proton g-factor  5.585 694 713[46]  Dimensionless    = μp / (Sp μN) 
Proton gyromagnetic ratio  42.577 482 1[11] e+6  kg-1.s.A Hz/T  γp = μp / h Sp. 
Proton gyromagnetic ratio shielded 42.576 388 1[12] e+6  kg-1.s.A Hz/T  In H2O,  standard conditions
Proton magnetic shielding  25.694[14] e-6  Dimensionless    Relative value 
Proton rms charge radius  0.8768[69] e-15  m  m   
Neutron rest mass mn  1.674 927 211[84] e-27  kg  kg  939.565 346[23] MeV 
1.008 664 915 97[43] u
Compton wavelength of neutron  1.319 590 895 1[20] e-15  m  m  λC,n = h / c mn 
Neutron magnetic moment  - 0.966 236 41[23] e-26  m2.A J/T  μn 
Neutron g-factor  -3.826 085 45[90]  Dimensionless    = μn / (Sn μN) 
Neutron gyromagnetic ratio  29.164 695 4[69] e+6  kg-1.s.A Hz/T  γn = μn / h Sn 
Muon rest mass  1.883 531 30[11] e-28  kg  kg  105.658 3668[38] MeV 
0.113 428 925 6[29] u
Muon magnetic moment  -4.490 447 86[16] e-26  m2.A J/T   
Muon g-factor  -2.002 331 841 4[12]  Dimensionless     
Muon gyromagnetic ratio  135.538 817[12] e+6  kg-1.s.A Hz/T  = μn / h Sn 
Tau rest mass  3.167 77[52] e-27  kg  kg  1776.99[29] MeV, 
1.907 68[31] u
Deuteron rest mass  3.343 583 20[17] e-27  kg  kg  1875.612 793[47] MeV 
2.013 553 212 724[78] u
Deuteron magnetic moment  0.433 073 465[11] e-26  m2.A J/T   
Deuteron g-factor  0.857 438 2308[72]  Dimensionless     
Deuteron gyromagnetic ratio  6.535903 e+6  kg-1.s.A Hz/T   
Helion rest mass  5.006 411 92[25] e-27  kg  kg  2808.391 383[70] MeV 
3.014 932 247 3[26] u
Helion magnetic moment  -1.074 5532 982[30] e-26  m2.A J/T  Shielded 
Helion gyromagnetic ratio  32.434 101 98[90] e+6  kg-1.s.A Hz/T  Shielded 
α-particle rest mass  6.644 656 20[33] e-27  kg  kg  3727.379 109[93] MeV 
4.001 506 179 127[62] u

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Future Ideas

1 - Adding more constants to the program.   If you want to extend the list of Constants the program knows about - this is awkward at present, I will add a function to make this easy and standard.   Note there is no limit to the number of constants that the program can store.

2 - If it is useful to have a memory able to use a different name then I could add this.   For example, in calculating the GST Tax on $10000 where the GST rate is 12.5%,

10000 * 0.125 = 1125   could be put into Mem1 and called GST
10000 + GST could be evaluated and put into Mem2 and called Inclusive

This would mean you could use in calculations the words GST and INCLUSIVE instead of Mem1 and Mem2.   (The names Mem1 and Mem2 could still be used as well for these memories).

Let JBCL know of which of these ideas you like, and any others that you have!


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Credits

The ideas for this Calculator have come from many places: 
Sharp Scientific Calculators
Even in the 1970s there were Sharp calculators that entered calculations similar to this
Sharp Scientific Calculator

It allowed algebraic entry like in this program.
JBCalc was an original version of this as a DOS program

Aidaim Software for the parsing of text.
I would have written this myself, but they also provided all the scientific functions
so I have used their library to interpret these expressions
//==============================================================================
// Product name: CalcExpress
// Copyright 2000-2002 AidAim Software.
// Description:
// CalcExpress is an interpreter for quick and easy
// evaluation of mathematical expressions.
// It is a smart tool easy in use.
// Supports 5 operators, parenthesis, 18 mathematical functions and
// user-defined variables.
// Date: 06/14/2001
//==============================================================================