Brliant Calculator

Once you learn the syntax, Brliant Calculator becomes significantly faster than traditional GUI calculators or reaching for your mouse.

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Quick Start

Installation

pip install brliant_calc

Examples

bcalc basic add 5 10 15
bcalc adv sin 1.57
bcalc adv mean 10 20 30 40 50
bcalc eval "2**10 + sqrt(144) * sin(pi/2)"
bcalc nt is_prime 17
bcalc g circle_area 5

Create a Custom Alias

Make it even faster by creating a short alias:

bcalc -changeCall bc

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Core Features

Comprehensive Mathematics

Basic Arithmetic

bcalc basic add 10 5 3         
bcalc basic mul 2 3 4         
bcalc basic div 100 4        

Trigonometry & Hyperbolic Functions

bcalc adv sin 1.57           
bcalc adv arcsin 0.5          
bcalc adv sinh 1              

Logarithms & Exponentials

bcalc adv log 100              
bcalc adv log10 1000          
bcalc adv log2 256            
bcalc adv exp 2               

Statistics

bcalc adv mean 10 20 30 40     
bcalc adv std 2 4 6 8 10       
bcalc adv median 1 3 5 7 9   
bcalc adv max 15 42 8 23        

Rounding & Precision

bcalc adv floor 3.7             
bcalc adv ceil 3.2              
bcalc adv round 3.14159 2       
bcalc adv sqrt 256              

Matrix Operations

bcalc matrix mul "[[1,2],[3,4]]" --m2 "[[5,6],[7,8]]"
bcalc matrix det "[[1,2],[3,4]]"
bcalc matrix inv "[[1,2],[3,4]]"
bcalc matrix eig "[[1,2],[3,4]]"

Complex Numbers

bcalc complex add "1+2j" --c2 "3+4j"        
bcalc complex mul "2+3j" --c2 "1-1j"        
bcalc complex polar "1+1j"                   
bcalc complex mag "3+4j"                     

Function Plotting

Visualize mathematical functions with secure AST parsing:

bcalc plot "sin(x)" --range "0,6.28"
bcalc plot "sin(x**2 + pi)" --range "0,10"
bcalc plot "exp(-x) * cos(2*pi*x)" --range "0,5"
bcalc plot "x**3 - 2*x**2 + x" --range "-2,3"

Supported Functions: sin, cos, tan, exp, log, sqrt, abs, and all hyperbolic variants
Constants: pi, e

Symbolic Mathematics

bcalc symbolic diff "x**2 + 2*x + 1" --variable x
bcalc symbolic integrate "sin(x)" --variable x
bcalc symbolic solve "x**2 - 4" --variable x
bcalc symbolic simplify "(x+1)**2"

Unit Conversions

bcalc units length 1000 meter kilometer     
bcalc units temperature 100 celsius fahrenheit 
bcalc units mass 1 kilogram pound           

Currency Conversion

bcalc curr upd
bcalc convert USD EUR 100

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New Features (v4.1)

1. Number Theory (numtheory / nt)

Primality, factorization, and integer math:

bcalc nt is_prime 17              # True
bcalc nt prime_factors 60          # [2, 2, 3, 5]
bcalc nt gcd 12 18 24             # 6
bcalc nt lcm 4 6 8                # 24
bcalc nt fibonacci 10             # 55
bcalc nt nth_prime 5              # 11
bcalc nt euler_totient 12         # 4
bcalc nt catalan 5                # 42
bcalc nt binomial 10 3           # 120
bcalc nt mod_inverse 3 11         # 4
bcalc nt prime_sieve 50           # all primes up to 50
bcalc nt digit_sum 12345          # 15
bcalc nt is_palindrome 12321      # True
bcalc nt collatz_steps 27         # 111
bcalc nt perfect_number_check 28  # True
bcalc nt goldbach_partitions 10   # [(3, 7), (5, 5)]

2. Combinatorics (combo / cb)

Counting, arrangements, and partitions:

bcalc cb permutation 5 3           # 60
bcalc cb combination 10 4          # 210
bcalc cb multiset_combination 3 5  # 35
bcalc cb derangement 4             # 9
bcalc cb stirling_second_kind 5 3  # 25
bcalc cb bell_number 5             # 52
bcalc cb partition_count 5         # 7
bcalc cb stars_and_bars 10 3       # 66
bcalc cb catalan_number 4          # 14
bcalc cb lah_number 5 3            # 120

3. Extended Statistics (stats / st)

Advanced descriptive and inferential stats:

bcalc st mode 1 2 2 3 4                    # 2
bcalc st percentile 1 2 3 4 5 75            # 75th percentile
bcalc st correlation 1 2 3 4 5 2 4 5 4 5   # Pearson r
bcalc st covariance 1 2 3 2 4 6             # sample covariance
bcalc st skewness 1 2 3 4 5                # distribution skewness
bcalc st kurtosis 1 2 3 4 5 6              # excess kurtosis
bcalc st geometric_mean 2 4 8              # 4.0
bcalc st harmonic_mean 1 2 4               # 1.714
bcalc st z_score 85 75 10                  # (85-75)/10 = 1.0
bcalc st chi_square 10 20 30 15 25 35      # chi-squared statistic
bcalc st iqr 1 2 3 4 5 6 7                 # interquartile range
bcalc st range_val 3 7 2 9 5               # 7
bcalc st coefficient_of_variation 10 12 14 16
bcalc st weighted_mean 80 90 70 0.3 0.5 0.2
bcalc st moving_average 1 2 3 4 5 3        # 3-period moving avg
bcalc st confidence_interval 10 12 14 16 18 # 95% CI

4. Geometry (geo / g)

Shapes, distances, and spatial calculations:

bcalc g circle_area 5                # 78.54
bcalc g circle_circumference 5       # 31.42
bcalc g sphere_volume 3              # 113.1
bcalc g sphere_surface_area 3        # 113.1
bcalc g rectangle_area 5 10          # 50
bcalc g rectangle_perimeter 5 10     # 30
bcalc g triangle_area 6 4            # 12
bcalc g triangle_area_sss 3 4 5      # 6 (Heron's formula)
bcalc g cylinder_volume 3 10         # 282.7
bcalc g cylinder_surface_area 3 10
bcalc g cone_volume 3 5
bcalc g cone_surface_area 3 5
bcalc g pyramid_volume 20 10
bcalc g torus_volume 5 2
bcalc g torus_surface_area 5 2
bcalc g ellipse_area 5 3
bcalc g ellipse_perimeter 5 3
bcalc g distance_2d 0 0 3 4          # 5.0
bcalc g distance_3d 0 0 0 1 2 2      # 3.0
bcalc g midpoint_2d 0 0 6 8          # (3, 4)
bcalc g arc_length 5 90
bcalc g sector_area 5 90

5. Financial Math (fin / f)

Interest, loans, investments, and depreciation:

bcalc f compound_interest 1000 5 3        # compound interest
bcalc f simple_interest 1000 5 3          # simple interest
bcalc f emi 100000 8 12                   # monthly EMI
bcalc f present_value 1000 5 3            # PV of future amount
bcalc f future_value 1000 5 3             # FV of present amount
bcalc f depreciation_straight_line 10000 2000 5
bcalc f npv 10 -1000 300 400 500          # net present value
bcalc f roi 1000 1500                      # return on investment
bcalc f payback_period -5000 1000 1500 2000 2500
bcalc f inflation_adjusted_return 8 3
bcalc f doubling_time 7                    # years to double
bcalc f annuity_payment 10000 5 12

6. Signal Processing (signal / sig)

FFT, correlations, windows, and spectral analysis:

bcalc sig fft 1 2 3 4                      # Fast Fourier Transform
bcalc sig ifft 10 0 0 0                    # Inverse FFT
bcalc sig moving_average 1 2 3 4 5 --args 3
bcalc sig power_spectrum 1 2 3 4           # frequency vs power
bcalc sig autocorrelation 1 2 3 4          # self-correlation
bcalc sig cross_correlation 1 2 3 --signal2 2 3 4
bcalc sig hamming_window --args 8           # Hamming window
bcalc sig hanning_window --args 8           # Hanning window
bcalc sig blackman_window --args 8          # Blackman window
bcalc sig spectrogram_data 1 2 3 4 5 6 7 8 --args 4 2

7. Calculus (calc / cl)

Taylor series, numerical methods, limits, and multivariate:

bcalc cl taylor_series "sin(x)" --variable x --point 0 --order 6
bcalc cl numerical_diff "x**2+1" --point 3 --h 0.0001
bcalc cl numerical_integrate "x**2" --a 0 --b 1
bcalc cl series_sum "1/n**2" --start 1 --end 100 --variable n
bcalc cl limit "sin(x)/x" --point 0
bcalc cl partial_diff "x**2*y+y**3" --variables x,y
bcalc cl double_integrate "x*y" --var1 x --var2 y
bcalc cl maclaurin_series "exp(x)" --order 8
bcalc cl gradient "x**2+y**2+z**2" --variables x,y,z
bcalc cl jacobian "x*y,y*z" --variables x,y,z

8. Equation Solver (eqn / eq)

Algebraic and numerical root finding:

bcalc eq quadratic 1 -3 2                    # x²-3x+2=0 → x=1,2
bcalc eq cubic 1 -6 11 -6                    # x³-6x²+11x-6=0
bcalc eq polynomial_roots 1 -6 11 -6         # from coefficients
bcalc eq linear_system_2d 2 3 8 5 1 11      # 2x+3y=8, 5x+y=11
bcalc eq simultaneous_2d 1 1 3 2 1 5        # x+y=3, 2x+y=5
bcalc eq linear_system_3d 1 1 1 6 0 2 5 -4 2 5 3 27
bcalc eq bisection "x**3-x-2" --point 1     # numerical root
bcalc eq newton_raphson "x**2-2" --point 1.5
bcalc eq secant_method "x**3-x-2" --x0 1 --x1 2

9. Expression Evaluator (eval / ev)

Direct math expression evaluation with safe AST parsing:

bcalc ev "2**10 + sqrt(144) * sin(pi/2)"     # 1024 + 12 = 1036
bcalc ev "factorial(5) + comb(10,3)"          # 120 + 120 = 240
bcalc ev "log(e) + log10(100)"                # 1 + 2 = 3
bcalc ev "gcd(12,8) * lcm(4,6)"              # 4 * 12 = 48

Supported: All standard math functions (sin, cos, sqrt, log, exp, ...), constants (pi, e, tau), operators (+, -, *, /, **, //, %), and factorial, gcd, comb, perm.

10. Calculation History (history / hi)

Persistent history with search, export, and stats:

bcalc hi list --limit 10          # show last 10 entries
bcalc hi recall --index 1        # recall specific entry
bcalc hi search --query "add"     # search by keyword
bcalc hi export --filepath out.json  # export to JSON
bcalc hi clear                    # wipe history
bcalc hi stats                    # usage statistics

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New in v3.1 — Scientific Expansion

11. Probability & Distributions (prob / pb)

PDFs, CDFs, and statistical tests:

bcalc pb normal_pdf 0 --mu 0 --sigma 1     # standard normal PDF
bcalc pb normal_cdf 1.96                   # ~0.975
bcalc pb binomial_pmf 5 10 0.5            # 5 heads in 10 flips
bcalc pb poisson_pmf 2 3                   # k=2, lambda=3
bcalc pb exponential_pdf 1 2               # x=1, lambda=2
bcalc pb t_test_1samp 1 2 3 4 5 3.0        # data... popmean
bcalc pb t_test_ind 1 2 3 2 3 4            # group1... group2
bcalc pb sample_normal 10 0 1              # 10 random samples

12. Digital Logic (logic / lg)

Base conversions and boolean algebra:

bcalc lg base_convert 255 10 16            # FF
bcalc lg base_convert 1010 2 10            # 10
bcalc lg truth_table "A & (B | C)"         # generate full table
bcalc lg simplify_boolean "A & A | B"      # A | B
bcalc lg bitwise_and 12 7                  # 4
bcalc lg bitwise_xor 12 7                  # 11

13. Information Theory (info / it)

Entropy and distance metrics:

bcalc it shannon_entropy 0.5 0.5           # 1.0 bit
bcalc it kl_divergence 0.5 0.5 0.1 0.9     # relative entropy
bcalc it hamming_distance 1011 1101        # 2
bcalc it levenshtein_distance kitten sitting # 3
bcalc it cross_entropy 0.5 0.5 0.4 0.6
bcalc it mutual_information "[[0.25, 0.25], [0.25, 0.25]]"

14. Numerical Analysis (numerical / nm)

Interpolation and ODE solvers:

bcalc nm polynomial_fit 1 2 3 1 4 9 2      # x... y... degree
bcalc nm lagrange_interpolation 1 2 3 1 4 9 2.5
bcalc nm cubic_spline_interpolation 1 2 3 4 1 8 27 64 2.5
bcalc nm rk4_solve --func_str "t*y" --y0 1 --t_start 0 --t_end 1 --steps 10
bcalc nm newton_interpolation 1 2 3 1 4 9 2.5

15. Chemistry (chemistry / ch)

Molar mass and gas laws:

bcalc ch molar_mass H2O                    # 18.015
bcalc ch molar_mass H2SO4                  # 98.079
bcalc ch ideal_gas_law --p 1 --v 22.4 --n 1 # Solve for T
bcalc ch molarity 0.5 2.0                  # 0.25 M
bcalc ch ph_from_h 1e-7                    # 7.0
bcalc ch h_from_ph 3.0                     # 0.001

# Solution chemistry, stoichiometry & kinetics
bcalc ch dilution 6 0.5 1.5                # M1V1=M2V2 → V2 = 2.0
bcalc ch molality 2 0.5                    # 4.0 mol/kg
bcalc ch mole_fraction 2 3                 # 0.4
bcalc ch limiting_reagent 10 2 6 1         # reagent 1 limiting
bcalc ch percent_yield 8 10                # 80.0%
bcalc ch boiling_point_elevation 0.5 0.512 # 0.256 °C
bcalc ch freezing_point_depression 0.5 1.86
bcalc ch osmotic_pressure 0.1 298          # Π = MRT (atm)
bcalc ch henderson_hasselbalch 4.76 10     # pH = pKa + log10(ratio)
bcalc ch half_life 0.1                     # t½ = ln(2)/k
bcalc ch radioactive_decay 100 0.1 5       # N = N₀·e^(-kt)
bcalc ch density 50 25                     # 2.0 g/mL
bcalc ch ppm_to_concentration 100 58.44    # 0.001711 mol/L
bcalc ch molarity_to_ppm 0.1 58.44         # 5844 ppm

Note: limiting_reagent takes alternating (amount, coefficient) pairs, e.g. 10 2 6 1 means reagent 1 has 10 mol with coefficient 2, reagent 2 has 6 mol with coefficient 1. osmotic_pressure expects temperature in Kelvin.

16. Date & Time (datetime / dt)

Date arithmetic, weekdays, and calendar math:

bcalc dt add_days 2024-01-15 30            # 2024-02-14
bcalc dt add_days today -7                 # one week ago
bcalc dt add_months 2024-01-31 1           # 2024-02-29 (clamped)
bcalc dt diff_days 2024-01-01 2024-12-31   # 365 (date2 - date1)
bcalc dt day_of_week 2024-07-04            # Thursday
bcalc dt age 2000-01-01                    # age in whole years
bcalc dt julian_day 2000-01-01              # 2451545
bcalc dt is_leap_year 2024                 # True
bcalc dt week_number 2024-01-01            # 1 (ISO week)

Date formats: YYYY-MM-DD (also YYYY/MM/DD, DD-MM-YYYY, DD/MM/YYYY, MM/DD/YYYY) or the keyword today.

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Interactive Shell Mode

bcalc sel basic
basic > x = 5
Variable 'x' set to 5.0
basic > y = 120
Variable 'y' set to 120.0
basic > mul x y
600
basic > div x y
0.0416667
basic > vars
Stored Variables:
  x = 5.0
  y = 120.0
basic > exit

Variable Storage

Define variables once, use them everywhere:

bcalc sel plot
plot > a = 2
plot > b = 3.14
plot > plot sin(a*x + b) --range 0,10
Plot displayed.

Variables work in all modes:

• Arithmetic: mul x y, add a b c
• Advanced math: sin x, pow x 2
• Plotting: sin(a*x), x**2 + b*x + c

Advanced Examples

Physics Calculations

bcalc physics force 10 9.8              
bcalc physics kinetic_energy 5 10       
bcalc physics ohms_law 2 10             

Vector Operations

bcalc vector dot_product 1 2 3 4 5 6    
bcalc vector cross_product 1 0 0  0 1 0 
bcalc vector magnitude 3 4             

Dimensional Analysis

bcalc dim evaluate_dim "5 * meter + 30 * centimeter"
bcalc dim convert_dim --value 100 --from_unit "km/h" --to_unit "m/s"

Arbitrary Precision

bcalc precise add_fraction "1/3" "1/6" 
bcalc precise div_decimal "1" "3" --precision 50

Convolutions

bcalc convolve 1 2 3 -k 0.5 0.5

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Command Aliases

Create shorter commands:

bcalc -changeCall bc
bc basic add 5 10
bc adv sin 1.57
bcalc -listAliases
bcalc -removeAlias bc

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Shortcuts

Command	Shortcut
basic	b
adv	a
matrix	m
complex	cx
symbolic	s
plot	pl
vector	v
physics	p
units	u
dim	d
precise	pr
curr	cr
convolve	cnv
numtheory	nt
combo	cb
stats	st
geo	g
fin	f
signal	sig
calc	cl
eqn	eq
eval	ev
history	hi
prob	pb
logic	lg
info	it
numerical	nm
chemistry	ch
datetime	dt
sel	sh

Example: bcalc b add 5 10 instead of bcalc basic add 5 10

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Full Operation Reference

Basic Arithmetic

add, sub, mul, div, mod

Advanced Math

Trigonometric: sin, cos, tan, arcsin, arccos, arctan
Hyperbolic: sinh, cosh, tanh, arcsinh, arccosh, arctanh
Logarithms: log, log10, log2
Powers: exp, pow, nth, sqrt
Rounding: floor, ceil, round, trunc, abs, sign
Statistics: mean, median, std, var, min, max, sum, prod
Other: fact

Probability & Distributions

normal_pdf, normal_cdf, normal_ppf, binomial_pmf, binomial_cdf, poisson_pmf, poisson_cdf, exponential_pdf, t_test_1samp, t_test_ind, sample_normal, sample_binomial

Digital Logic

base_convert, truth_table, simplify_boolean, bitwise_and, bitwise_or, bitwise_xor, bitwise_not

Information Theory

shannon_entropy, kl_divergence, hamming_distance, levenshtein_distance, cross_entropy, mutual_information

Numerical Analysis

polynomial_fit, lagrange_interpolation, cubic_spline_interpolation, rk4_solve, newton_interpolation

Chemistry

molar_mass, ideal_gas_law, molarity, ph_from_h, h_from_ph, dilution, molality, mole_fraction, limiting_reagent, percent_yield, boiling_point_elevation, freezing_point_depression, osmotic_pressure, henderson_hasselbalch, half_life, radioactive_decay, density, ppm_to_concentration, molarity_to_ppm

Date & Time

add_days, add_months, diff_days, day_of_week, age, julian_day, is_leap_year, week_number

Number Theory

is_prime, prime_factors, gcd, lcm, fibonacci, nth_prime, euler_totient, catalan, binomial, mod_inverse, prime_sieve, digit_sum, reverse_number, is_palindrome, collatz_steps, perfect_number_check, goldbach_partitions

Combinatorics

permutation, combination, multiset_combination, derangement, stirling_second_kind, bell_number, partition_count, stars_and_bars, catalan_number, lah_number

Extended Statistics

mode, percentile, correlation, covariance, skewness, kurtosis, geometric_mean, harmonic_mean, z_score, chi_square, iqr, range_val, coefficient_of_variation, weighted_mean, moving_average, confidence_interval

Geometry

circle_area, circle_circumference, sphere_volume, sphere_surface_area, rectangle_area, rectangle_perimeter, triangle_area, triangle_area_sss, cylinder_volume, cylinder_surface_area, cone_volume, cone_surface_area, pyramid_volume, torus_volume, torus_surface_area, ellipse_area, ellipse_perimeter, distance_2d, distance_3d, midpoint_2d, arc_length, sector_area

Financial Math

compound_interest, simple_interest, emi, present_value, future_value, depreciation_straight_line, npv, roi, payback_period, inflation_adjusted_return, doubling_time, annuity_payment

Signal Processing

fft, ifft, moving_average, power_spectrum, autocorrelation, cross_correlation, hamming_window, hanning_window, blackman_window, spectrogram_data

Calculus

taylor_series, numerical_diff, numerical_integrate, series_sum, limit, partial_diff, double_integrate, maclaurin_series, gradient, jacobian

Equation Solver

quadratic, cubic, polynomial_roots, linear_system_2d, simultaneous_2d, linear_system_3d, bisection, newton_raphson, secant_method

Expression Evaluator

evaluate

History

list, recall, search, export, clear, stats

Matrix Operations

mul, det, inv, eig, transpose, rank, lu, qr, cholesky, svd, solve, least_squares, null_space, condition_number, exp, sylvester, generalized_eigen, power, det_via_lu, inv_via_lu, log, sqrt, polar, solve_triangular

Complex Numbers

add, sub, mul, div, mag, phase, polar, rect

Symbolic Math

simplify, diff, integrate, solve, expand, factor

Vector Operations

dot_product, cross_product, magnitude, normalize, angle_between

Physics

force, kinetic_energy, potential_energy, ohms_law, work, speed, acceleration

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Contributing

Feel free to submit a Pull Request!

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Advanced Matrix Solvers

The CLI supports 24 advanced matrix solvers:

LU Decomposition

bcalc matrix lu "[[4,3],[6,3]]"

QR Decomposition

bcalc matrix qr "[[1,2],[3,4]]"

Cholesky Decomposition

bcalc matrix cholesky "[[4, 12], [12, 37]]"

Singular Value Decomposition (SVD)

bcalc matrix svd "[[1, 0], [0, 1]]"

Solve Linear Systems

bcalc matrix solve "[[3, 1], [1, 2]]" --b "[9, 8]"

Matrix Exponential

bcalc matrix exp "[[0, 1], [-1, 0]]"

Generalized Eigenvalues

bcalc matrix generalized_eigen "[[1, 2], [3, 4]]" --b "[[5, 6], [7, 8]]"

Polar Decomposition

bcalc matrix polar "[[1, 2], [3, 4]]"