😍 💼 🚶🏾 What's new in AngouriMath 1.2? ♌️ 🏦 👩🏽

Greetings. For the last 7 months I have been working on the biggest AngouriMath update . And there is something to tell about.

What is happening in a nutshell

In November 2019, I realized that this world, more precisely the world of the dotnet, lacks a symbolic algebra library for simplifying expressions, solving equations, for deriving latex, and so on. So I decided to create one.

But there is ...

Hearing what I am doing, different people come up with different solutions. Rewrite SymPy, make a wrapper over SageMath for dotnet, spiral Wolfram | Alpha, use primitive mathnet.symbolics (they themselves speak of primitiveness).

But all this has either limitations or difficulties. The same I am working on is a very lightweight library written and optimized for .NET. Open source, of course. (under MIT)

Update 1.2

In August, one of the main contributors @ HappyPig375 helped to rewrite a significant part of the library to the normal type hierarchy. Now there is a separate type for each operator or function. It was a tipping point, before which the library was slow, clumsy, and completely non-obvious. Now let's go over what has been done since then.

An expression is a record

For example, this is how the declaration of the sum operator looks like

public sealed partial record Sumf(Entity Augend, Entity Addend) : NumericNode

Thanks to this, we can easily apply the new pattern matching:

internal static Entity CommonRules(Entity x) => x switch
{
    // (a * f(x)) * g(x) = a * (f(x) * g(x))
    Mulf(Mulf(Number const1, Function func1), Function func2) => func1 * func2 * const1,

    // (a/b) * (c/d) = (a*c)/(b*d)
    Mulf(Divf(var any1, var any2), Divf(var any3, var any4)) => any1 * any3 / (any2 * any4),

    // a / (b / c) = a * c / b
    Divf(var any1, Divf(var any2, var any3)) => any1 * any3 / any2,

(this is an example of patterns that work when simplifying an expression)

Maths

, .

, , , .

12 , (sinh(x)

(e.Pow(x) - e.Pow(-x)) / 2

).

Abs Signum. abs : (|x|)

. , , ( | , ).

Phi ( ).

WriteLine(@"phi(8)".EvalNumerical());
WriteLine(@"(|-3 + 4i|)".EvalNumerical());
WriteLine(@"sinh(3)".Simplify());
WriteLine(@"sec(0.5)".Simplify());

4
5
(e ^ 3 - 1 / e ^ 3) / 2
sec(1/2)

. , NaN, . - SpecialSet, .

- . - , - , . : not

, or

, xor

, and

, implies

.

, Boolean

, EvaluableBoolean

. , EvaluableNumerical

, Number

.

WriteLine(@"(true or b) implies c".Simplify());

( c

)

Boolean

, . : =

, <

, >

, <=

, >=

.

. , a > b > c

, (a > b > c

, a > b and b > c

).

WriteLine(@"a < b >= c".Simplify());

( a < b and b >= c

)

. .

- FiniteSet, , . . : { 1, 2, 3 }

.

/ : [1; 2]

, (1; 2)

, [1; 2)

, (1; 2]

. .

SpecialSet

"" . CC

, RR

, QQ

, ZZ

, BB

, , , , .

ConditionalSet

set-builder notation, : { x : x > 0 and x^2 = y }

( x

, y

).

WriteLine(@"({ 1, 2 } \/ { 5 }) /\ { x : x in [2; 3] and x > 0 } ".Simplify());

( { 2 }

)

, . .

WriteLine("tan(a x) / (b x)".Limit("x", 0));
WriteLine("(sin(t) - t) / t3".Limit("t", 0));

( a / b

-1/6

)

"Provided"

, . , sqrt(x) provided x >= 0

. x, NaN.

, NaN, . , NaN NaN.

-

Piecewise

- Provided

. -, , Piecewise

, Provided

, .

, Piecewise

:

Entity abs = "piecewise(x provided x > 0, -x provided x <= 0)";
WriteLine(abs.Substitute("x", 3).EvalNumerical());
WriteLine(abs.Substitute("x", -3).EvalNumerical());

( 3 )

, / .

, , AngouriMathBaseException

. p/invoke

- - , , , AngouriMathBaseException

, . , , catch- ( ).

, . , 1.1.0.5. .

F#

API AngouriMath F#. , , F# . - , .

Interactive

, AngouriMath Jupyter. AngouriMath.Interactive ILatexiseable

LaTeX- MathJax ( ).

. , ? , . ([ThreadStatic]

), .

- , Solve

Simplify

, .

, . , , . ,

using var _ = MaxExpansionTermCount.Set(10);
// -

(, Set

, IDisposable

).

. , . , . , .

- , ( ).

What's new in AngouriMath 1.2?