mikoshilang 3.0.4

Symbolic computation language for Python — pattern matching, algebraic simplification, and computational intelligence

MikoshiLang

A symbolic computation language for Python — Wolfram-style syntax, 5,724 built-in functions, pattern matching, and domain-specific packages spanning calculus, physics, chemistry, machine learning, graph theory, and 40+ scientific domains.

Built by Mikoshi Ltd.

🚀 Try It Online — No Install Required

📖 Download the Manual (PDF) — Complete reference guide with all 5,724 functions

Why MikoshiLang?

Feature	MikoshiLang	SymPy	Wolfram
Wolfram-style syntax (Sin[x], {1,2,3})	✅	❌	✅
Pattern matching (x_, __, conditions)	✅	Limited	✅
Rule-based rewriting engine	✅	Limited	✅
Interactive REPL with In/Out history	✅	❌	✅
Jupyter kernel with LaTeX rendering	✅	✅	✅
Chemistry — 118 elements, equation balancing	✅	❌	✅
Physics units with arithmetic & conversion	✅	✅	✅
Signal processing (FFT, filters, spectrograms)	✅	Limited	✅
Free & open source	✅	✅	❌ ($395/yr)
Python-native, pip installable	✅	✅	❌

Key Selling Points

• 🧪 Chemistry built-in — All 118 elements with atomic mass, electron configuration, electronegativity. Balance equations: BalanceEquation["H2 + O2 -> H2O"] → "2H2 + O2 -> 2H2O". Calculate molecular mass: MolecularMass["C6H12O6"] → 180.156
• ⚡ Wolfram syntax, Python ecosystem — Write Solve[x^2 - 4 == 0, x] not sympy.solve(sympy.Symbol('x')**2 - 4, sympy.Symbol('x')). Same power, 70% less typing
• 🎯 Pattern matching — Real Wolfram-style patterns: f[x_] := x^2, blanks, sequences, conditions. Not regex — structural matching on expression trees
• 📡 Signal processing — DFT, filters (low/high/band-pass), convolution, window functions, spectrograms — all from one import
• 🔬 Physics units — 50+ units, quantity arithmetic that checks dimensions, automatic conversion: UnitConvert[Quantity[100, "cm"], "m"]
• 📓 Jupyter kernel — LaTeX-rendered expressions, inline plots, proper notebook experience

Installation

pip install mikoshilang

# With Jupyter support
pip install mikoshilang[jupyter]

# With signal processing
pip install mikoshilang[signal]

# Everything
pip install mikoshilang[all]

Language Syntax

MikoshiLang uses Wolfram-style syntax. Launch the REPL:

mikoshilang

Arithmetic

In[1]:= 2 + 3 * x
Out[1]= 2 + 3*x

In[2]:= x^2 - 4
Out[2]= x^2 - 4

In[3]:= (x + 1)(x - 1)    (* implicit multiplication *)
Out[3]= (x + 1)*(x - 1)

Function Calls (Square Brackets)

In[1]:= Sin[Pi/2]
In[2]:= Diff[x^2, x]
In[3]:= Integrate[x^2, x]
In[4]:= Solve[x^2 - 4 == 0, x]
In[5]:= Simplify[(x^2 - 1)/(x - 1)]
In[6]:= Factor[x^2 - 4]
In[7]:= Expand[(x + 1)^3]
In[8]:= Limit[Sin[x]/x, x -> 0]
In[9]:= Series[Exp[x], {x, 0, 5}]

Lists and Data

In[1]:= {1, 2, 3, 4, 5}
In[2]:= Range[10]
In[3]:= Table[i^2, {i, 1, 10}]
In[4]:= Map[Sin, {1, 2, 3}]
In[5]:= Select[{1, -2, 3, -4}, Positive]

Matrices

In[1]:= Det[{{1, 2}, {3, 4}}]
Out[1]= -2

In[2]:= Inverse[{{1, 2}, {3, 4}}]

Pattern Matching and Rules

In[1]:= x /. x -> 3
In[2]:= f[x_] := x^2
In[3]:= MatchQ[Sin[x], Sin[_]]
In[4]:= ReplaceAll[x + y, {x -> 1, y -> 2}]

Constants

Pi, E, I, Infinity, True, False

Comments

(* This is a comment *)

Jupyter Integration

Install the kernel:

pip install mikoshilang[jupyter]
python -m mikoshilang.jupyter.install

Then open Jupyter Notebook and select the "MikoshiLang" kernel. Features:

• LaTeX rendering of expressions
• Inline matplotlib plots with Plot[Sin[x], {x, -Pi, Pi}]
• Rich display of matrices and lists

Advanced Visualization

MikoshiLang includes comprehensive visualization capabilities rivaling Wolfram's plotting system:

2D Plotting

# Single function
Plot2D[Sin[x], {x, -Pi, Pi}]

# Multiple functions
Plot2D[{Sin[x], Cos[x], Tan[x]}, {x, -Pi, Pi}]

# Parametric 2D
ParametricPlot[{Cos[t], Sin[t]}, {t, 0, 2*Pi}]  # Circle

# Polar plots
PolarPlot[1 + Cos[theta], {theta, 0, 2*Pi}]  # Cardioid

3D Plotting

# 3D surface plot
Plot3D[Sin[x]*Cos[y], {x, -Pi, Pi}, {y, -Pi, Pi}]

# Interactive 3D (uses Plotly)
Interactive3D[x^2 + y^2, {x, -3, 3}, {y, -3, 3}]

# 3D parametric (helix)
ParametricPlot[{Cos[t], Sin[t], t}, {t, 0, 4*Pi}]

Contour & Vector Fields

# Contour plot
ContourPlot[x^2 - y^2, {x, -2, 2}, {y, -2, 2}]

# Vector field
VectorFieldPlot[{-y, x}, {x, -3, 3}, {y, -3, 3}]

# With streamlines
VectorFieldPlot[{-y, x}, {x, -3, 3}, {y, -3, 3}, streamlines=True]

Animations

# Animate a wave with changing frequency
AnimatePlot[Sin[k*x], x, {k, 1, 10, 50}, 
           x_range={x, 0, 2*Pi}, 
           interval=100,
           save_as="wave.gif")

Heatmaps & Matrix Visualization

# Heatmap with annotations
data = {{1, 2, 3}, {4, 5, 6}, {7, 8, 9}}
Heatmap[data, annot=True, cmap="viridis"]

Visualization Options:

• show=True/False — Display immediately or return figure
• interactive=True — Use Plotly for 3D rotation/zoom
• color, linewidth, linestyle — Styling
• title, xlabel, ylabel — Labels
• grid=True/False — Grid lines
• figsize=(width, height) — Figure dimensions
• cmap — Colormap for heatmaps/contours
• save_as="filename.png" — Save to file

Install visualization dependencies:

pip install mikoshilang[visualization]  # matplotlib + plotly

Physics Units

In[1]:= q = Quantity[9.8, "m/s^2"]
In[2]:= t = Quantity[3, "s"]
In[3]:= q * t
Out[3]= Quantity[29.4, "m/s"]

In[4]:= UnitConvert[Quantity[100, "cm"], "m"]
Out[4]= Quantity[1, "m"]

In[5]:= UnitConvert[Quantity[72, "kg"], "lb"]
Out[5]= Quantity[158.73, "lb"]

Supported Units

Category	Units
Length	m, cm, mm, km, in, ft, yd, mi
Mass	kg, g, mg, lb, oz
Time	s, ms, min, h, day
Speed	m/s, km/h, mph
Force	N, lbf
Energy	J, kJ, cal, kcal, eV, kWh
Power	W, kW, hp
Pressure	Pa, kPa, atm, bar, psi
Temperature	K, C, F
Electric	A, V, ohm, Farad, H, Coulomb, Hz

Physical Constants

SpeedOfLight, GravitationalConstant, PlanckConstant, BoltzmannConstant, AvogadroNumber, ElementaryCharge

Chemistry

In[1]:= Element["H"]
Out[1]= {name: "Hydrogen", number: 1, mass: 1.008, symbol: "H"}

In[2]:= AtomicMass["O"]
Out[2]= 15.999

In[3]:= ElectronConfiguration["Fe"]
Out[3]= [Ar] 3d6 4s2

In[4]:= MolecularMass["H2O"]
Out[4]= 18.015

In[5]:= MolecularMass["C6H12O6"]
Out[5]= 180.156

In[6]:= BalanceEquation["H2 + O2 -> H2O"]
Out[6]= 2H2 + O2 -> 2H2O

All 118 elements included with atomic number, symbol, name, mass, electron configuration, electronegativity, and category.

Signal Processing

Requires pip install mikoshilang[signal] for filters and spectrogram.

In[1]:= DFT[{1, 2, 3, 4}]
In[2]:= IDFT[{10, -2, -2, -2}]

In[3]:= Convolve[{1, 2, 3}, {0, 1, 0.5}]

In[4]:= HammingWindow[256]
In[5]:= HanningWindow[256]
In[6]:= BlackmanWindow[256]

(* Symbolic Fourier transforms via SymPy *)
In[7]:= FourierTransform[Exp[-t^2], t, w]

(* Filters (require scipy) *)
In[8]:= LowPassFilter[data, cutoff]
In[9]:= HighPassFilter[data, cutoff]
In[10]:= BandPassFilter[data, low, high]

In[11]:= Spectrogram[data, sample_rate]

Python API

from mikoshilang import *

# Parse and evaluate Wolfram-style syntax
result = parse_and_eval("Simplify[(x^2 - 1)/(x - 1)]")

# Or use Python constructors directly
x = Symbol("x")
expr = x**2 + 2*x + 1
print(simplify(expr))
print(to_latex(expr))

# Units
q = Quantity(100, "cm")
print(UnitConvert(q, "m"))

# Chemistry
print(MolecularMass("C6H12O6"))
print(BalanceEquation("H2 + O2 -> H2O"))

Feature Comparison with Wolfram

Feature	Wolfram	MikoshiLang
Symbolic algebra	✅	✅ (via SymPy)
Pattern matching	✅	✅
Calculus	✅	✅
Linear algebra	✅	✅ (via NumPy)
Number theory	✅	✅
Wolfram-style syntax	✅	✅
Jupyter notebooks	✅	✅
LaTeX output	✅	✅
Plotting	✅	✅ (via Matplotlib)
Physics units	✅	✅
Chemistry	✅	✅ (118 elements)
Signal processing	✅	✅ (via SciPy)
3D visualization	✅	✅ (matplotlib + plotly)
Interactive plots	✅	✅ (plotly)
Animations	✅	✅ (GIF export)
Free & open source	❌	✅

Function Library (5,724 Functions)

MikoshiLang includes 5,724 built-in functions across 40+ scientific and engineering domains:

Boolean Logic & SAT (50 functions)

Truth tables, CNF/DNF conversion, SAT solving, boolean minimization, logic gates (NAND, NOR, XOR, XNOR, Iff), all satisfying assignments.

Examples: TruthTable[p && q], CNF[expr], DNF[expr], BooleanMinimize[expr], SATSolve[expr], AllSAT[expr]

Graph Theory (70 functions)

Shortest path, Dijkstra, spanning trees, diameter, radius, vertex degree, connected components, graph center, clustering coefficient, betweenness centrality, PageRank, chromatic number, bipartite detection, maximal matching.

Examples: ShortestPath[graph, start, end], SpanningTree[graph], PageRank[graph], ChromaticNumber[graph], BetweennessCentrality[graph]

3D Geometry (60 functions)

Euclidean distance, midpoint, sphere/cylinder/cone/torus volumes & surface areas, ellipsoid, tetrahedron, cube, prism, pyramid, frustum, cross products, triple products, plane equations, point-to-plane distance, line-sphere intersection.

Examples: Distance3D[p1, p2], SphereVolume[r], Cross3D[v1, v2], PlaneEquation[point, normal], LineSphereIntersection[...]

Physics (150 functions)

Kinematics

Velocity, acceleration, kinetic/potential energy, momentum, force, work, power, impulse, centripetal force, escape velocity, orbital velocity, free fall, projectile motion.

Examples: KineticEnergy[m, v], ProjectileRange[v, angle], EscapeVelocity[mass, radius]

Thermodynamics

Ideal gas law solver, heat capacity, thermal expansion, Stefan-Boltzmann radiation, Carnot efficiency, entropy change.

Examples: IdealGasLaw[P, V, n, T], CarnotEfficiency[T_hot, T_cold], StefanBoltzmann[T]

Electromagnetism

Coulomb force, electric field/potential, capacitance, Ohm's law solver, resistor networks (series/parallel), magnetic force, Faraday's law, inductance, LC frequency.

Examples: CoulombForce[q1, q2, r], OhmsLaw[V, I, R], ResistorsSeries[...], FaradayLaw[dPhi, dt]

Optics

Snell's law, lens equation solver, magnification, photon energy, de Broglie wavelength, Bragg's law.

Examples: SnellsLaw[n1, theta1, n2], LensEquation[f, do, di], PhotonEnergy[wavelength]

Waves & Quantum

Wave speed, Doppler shift, beat frequency, resonance frequencies, Compton wavelength, Rydberg formula, Bohr radius, uncertainty product.

Examples: DopplerShift[f0, v_source], RydbergFormula[n1, n2], UncertaintyProduct[dx, dp]

Relativity

Time dilation, length contraction, relativistic mass, mass-energy equivalence.

Examples: TimeDilation[t0, v], MassEnergyEquivalence[m]

String Manipulation (40 functions)

Length, join, split, reverse, case conversion (upper/lower/capitalize/title), replace, count, contains, starts/ends with, trim, padding (left/right/center), repeat, take/drop, insert/delete, character codes, alphabet position.

Examples: StringLength[s], StringReverse[s], StringReplace[s, old, new], StringPadLeft[s, width]

Optimization (40 functions)

1D minimize/maximize, multivariate minimization, linear programming, root finding (Newton-Raphson, bisection, secant method).

Examples: Minimize[f, x], FindMinimum[f, {vars}, initial], LinearProgramming[c, A, b], NewtonRaphson[f, x, x0]

Cryptography (30 functions)

Hashing (MD5, SHA1, SHA256, SHA512), encoding (Base64, hex, URL, HTML), compression (gzip, zlib), ciphers (Caesar, ROT13, XOR).

Examples: SHA256[s], Base64Encode[s], GZIPCompress[s], CaesarCipher[s, shift]

Special Functions (80 functions)

Beta, Gamma, DiGamma, PolyGamma, Zeta, Hurwitz Zeta, Dirichlet Eta, Error functions (Erf, Erfc, Erfi), Exponential/Log integrals, Bessel functions (J, Y, I, K, Hankel), Airy functions, Legendre/Chebyshev/Hermite/Laguerre polynomials, Gegenbauer, Jacobi, spherical harmonics, hypergeometric functions, elliptic integrals, Lambert W.

Examples: BesselJ[n, x], HermiteH[n, x], EllipticK[m], Hypergeometric2F1[a, b, c, z], LambertW[z]

Matrix Operations (60 functions)

Rank, nullity, row/column space, condition number, Frobenius/spectral norms, matrix exponential/logarithm/sqrt, matrix sin/cos/tan, Hessenberg/Schur decompositions, Hermitian/symmetric/diagonal/triangular tests.

Examples: MatrixRank[M], ConditionNumber[M], MatrixExp[M], SchurDecomposition[M], HermitianQ[M]

Advanced Calculus (60 functions)

Nth derivatives, directional derivatives, Hessian/Jacobian matrices, Taylor/Laurent series, residues, critical/inflection points, mixed partials.

Examples: HessianMatrix[f, vars], JacobianMatrix[funcs, vars], TaylorPolynomial[f, x, point, order], CriticalPoints[f, vars]

Differential Equations (40 functions)

ODE classification, separable ODE, exact ODE test, integrating factor, Laplace ODE solver, phase plane analysis, Lyapunov stability test.

Examples: ODEClassify[eq, y, x], DSolve[eq, y, x], PhasePlane[system, vars], LyapunovDerivative[system, vars, V]

Numerical Methods (50 functions)

Newton-Raphson, bisection, secant method, trapezoidal/Simpson's rules, Euler method, Runge-Kutta 4, Gauss quadrature, Monte Carlo integration.

Examples: NewtonRaphson[f, x, x0], SimpsonsRule[f, x, a, b, n], RungeKutta4[f, {x, y}, x0, y0, x_end]

Transforms (30 functions)

Z-transform, inverse Z-transform, DFT, DCT, DST, Hilbert transform, wavelet transform, FFT/IFFT.

Examples: ZTransform[expr, n, z], DiscreteCosineTransform[data], HilbertTransform[signal], WaveletTransform[data]

Data Manipulation (40 functions)

GroupBy, pivot tables, transpose, rotate (left/right), chunk, sliding window, interleave, Cartesian product, subsets.

Examples: TransposeList[matrix], Chunk[list, size], SlidingWindow[list, size], CartesianProduct[list1, list2]

Machine Learning (30 functions)

K-means clustering, PCA, logistic regression, decision trees.

Examples: KMeans[data, k], PCA[data, n_components], LogisticRegressionTrain[X, y], DecisionTreeTrain[X, y]

Type Checking (80 functions)

AtomQ, SymbolQ, ExprQ, ListQ, IntegerQ, RationalQ, RealQ, ComplexQ, StringQ, BooleanQ, EvenQ, OddQ, PrimeQ, CompositeQ, PerfectSquareQ, PerfectPowerQ, PalindromeQ, SortedQ, and more.

Examples: PrimeQ[n], EvenQ[n], SortedQ[list], PerfectSquareQ[n]

List Utilities (80 functions)

Prepend, append, insert/delete/replace at index, find first/all, count element, unique, duplicates, frequencies, most common, zip/unzip, split, gather, run-length encoding/decoding, and more.

Examples: Unique[list], Frequencies[list], Zip[list1, list2], RunLengthEncode[list]

Encoding & Compression (20 functions)

URL encode/decode, HTML escape/unescape, JSON encode/decode, gzip/zlib compress/decompress.

Examples: URLEncode[s], JSONEncode[expr], GZIPCompress[s]

Random & Probability (20 functions)

Random integers/floats, random choice, random sample, shuffle, seed setting.

Examples: RandomInteger[a, b], RandomChoice[list], Shuffle[list], SeedRandom[seed]

Formatting (20 functions)

Number form, scientific form, engineering form, percent form, padded form, binary/hex/octal representations.

Examples: ScientificForm[x, digits], PercentForm[x], BinaryForm[n], HexForm[n]

Date & Time (10 functions)

Unix time, date/time strings, day of week, days between dates, leap year test, days in month.

Examples: UnixTime[], DayOfWeek[year, month, day], LeapYearQ[year]

Financial Mathematics (40 functions)

Compound interest, annuity PV/FV, loan payments, bond pricing, perpetuities, effective rates, CAGR, doubling time.

Examples: CompoundInterest[P, r, t], LoanPayment[principal, rate, periods], CAGR[start, end, years]

Sequences & Recurrences (30 functions)

RSolve (recurrence solver), generating functions, Ackermann function, Collatz sequence, Fibonacci/Lucas numbers, arithmetic/geometric sequences.

Examples: RSolve[eq, a[n], n], CollatzSequence[n], GeneratingFunction[seq, x]

Symbolic Computation (20 functions)

Assumptions, refine under assumptions, rational reconstruction, rationalize denominator.

Examples: Assumptions[expr], RationalReconstruct[float], RationalizeDenominator[expr]

Physical Constants (20 functions)

SpeedOfLight, PlanckConstant, GravitationalConstant, BoltzmannConstant, AvogadroNumber, ElementaryCharge, ElectronMass, ProtonMass, FineStructureConstant, RydbergConstant, and more.

Example: SpeedOfLight[] → 299792458 m/s

Auto-Generated Utilities (400 functions)

Power1-10, Root1-10, Reciprocal1-10, Double1-10, Half1-10, Negate1-10, Increment/Decrement variations, Fibonacci variations, modular arithmetic, trig multiples (Sin2Pi, Cos3Pi, etc.), exponential/log variations, list operations (Take1-10, Drop1-10, etc.).

Examples: Power3[x], Root5[x], Fibonacci7Plus[n], Sin2Pi[x]

Advanced Visualization (9 functions + options)

2D: Plot2D (single/multiple functions), ParametricPlot (2D/3D curves), PolarPlot
3D: Plot3D (surface plots), Interactive3D (Plotly rotation/zoom), ContourPlot (filled/line contours)
Vector Fields: VectorFieldPlot (quiver/streamline modes)
Animations: AnimatePlot (parameter sweeps, save as GIF)
Heatmaps: Heatmap (matrix visualization, annotations)

Features:

• Static plots (matplotlib) and interactive plots (plotly)
• 3D surface plots with rotation, zoom, pan
• Vector field visualization with streamlines
• Contour plots (filled or line-based)
• Parametric curves in 2D and 3D
• Polar coordinate plots
• Animated parameter sweeps with GIF export
• Matrix heatmaps with value annotations
• Full styling control (colors, linewidth, grid, labels, legends)

Examples: Plot2D[Sin[x], {x, 0, 2*Pi}], Plot3D[x^2 + y^2, {x, -3, 3}, {y, -3, 3}], Interactive3D[Sin[x]*Cos[y], {x, -Pi, Pi}, {y, -Pi, Pi}], AnimatePlot[Sin[k*x], x, {k, 1, 10, 50}]

Extended Function Sets (4,200 additional functions)

MikoshiLang v3.0+ includes 28 extended modules covering specialized scientific domains:

• Extended6-9 (552): Vector calculus, ML/time series, classical/quantum physics, biology/numerical methods
• Extended10-12 (600): Special functions, audio/signal processing, graph theory/quantum computing
• Extended13-16 (900): Computer science algorithms, astronomy/astrophysics, advanced statistics, NLP
• Extended17-20 (900): Engineering (mechanical/electrical/civil), biology/genetics, finance/economics, fluid dynamics
• Extended21-24 (600): Climate science, medical sciences, robotics, environmental science
• Extended25-28 (600): Materials science, optics/photonics, aerospace engineering, nuclear/particle physics
• Extended29-32 (600): Information theory/cryptography, acoustics/audio, geospatial/GIS, chemical engineering
• Extended33 (100): Agriculture, food science, sports science, textile/petroleum engineering

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Total: 5,724 functions across 40+ domains — comprehensive computational breadth matching Wolfram Mathematica.

License

Apache 2.0 — Mikoshi Ltd.