AngouriMath
What's new
1.4preview.4 [in development]
Kernel functional and C#:
 Simplification a bit improved for sets
 ηreduction added for lambda calculs entities (simplification now triggers beta+eta reduction)
 Bug related to simplification of tangent fixed (it turned NaN when should be 0)
 A few xor simplification patterns thanks DavidBeh
 Now installing only AngouriMath (without interactive) still loads LaTeX in notebooks, thanks new dib kernel extension feature
 Matrix concatenation API
 Polar plot added, thanks cyberillithid
 Sliders for plotting added (2D and 3D)
 Spherical plotting
1.4preview.3
Kernel functional and C#:
 Imprecise equality from 1.4preview.2 implemented.
 Added compilation of Piecewise node, thanks @IlluminatiCRAZ.
 Division, logarithm, power, and trigonometric functions experienced a behavioural change: now, they upcast integer types to floating point.
 A few more default variables added to the terminal by default, thanks dogayalcin.
 PeterO.Numbers assembly gets loaded into the terminal too.
1.4preview.2
Kernel functional and C#:
 Application. It is a node, which represents one expression applied to another one. No parser support yet.
 Builtin functions will now be simplified from application of an expression applied to a known variable, for example, x applied to sin is sin of x. No parser support yet.
 Lambda. This node represents an abstraction working similarly to that in lambda calculus. It has one parameter, and when an expression is applied, this parameter is substituted with this expression. No parser support yet.
 Imprecise equality API added but not implemented.
 Bugs fixed. NaN is now returned when comparing NaN and a number with inequality signs.
 Now there is a package AngouriMath.Experimental.
 Entity, Complex, Real, Rational and Integer implement generic math from .NET 6.
 Fixed bug when crashed on too small sizes.
 Reduced the API calls to OSunsupported API.
 The terminal is now available as a .NET global tool, see NuGet.
1.4preview.1
F# and interactive:

Added plotting in
AngouriMath.Interactive namespace:Plot.linear ,Plot.scatter for 2D (functions over one variable), andPlot.surface ,Plot.scatter3D for 3D (functions over two variables). See visualization.  Formatters for PeterO Numbers added.
 Terminal repo merged into AngouriMath
 Complete redesign by using Spectre.Console and Radline. See more.
1.3
Kernel functional and C#:

No more
Tensor , we only work withMatrix now.  A few synonyms added for hyperbolic functions.
 Greek and cyrillic latters are now parsable. Symbols \n and \s are now ignored by the parser.
 Limits improved.
 Upcasts added to compilation, as well as many overloads and extension methods.

Latexise does not produce "\times" anymore (nothing or \cdot instead). It also now produces correct code in case when a variable has an index (both variable and index are latexised properly).  Tensors completely reconsidered. No more vectors or tensors. There are only matrices. Moreover, operators now, instead of being elementwise, are now matrixmeaningful. A vector is considered a onecolumn matrix. A lot of methods of matrices are now exposed.
 Rank of a matrix, Reduced row echelon form added.
 Max term count increased by a lot. No power limit in the expansion algorithm.
 Parentheses fixed in LaTeX for negative number cases (and negation sign).

A couple of bugs related to matrices fixed.
ReducedRowEchelonForm andRank added,GaussianEliminated replaced withRowEchelonForm (here we stick to the definition which implies that leading elements can differ from ones).  Piecewise now works correctly for cases when a node is applied to a whole piecewise.
 Implicit operators improved (one for BigInteger added).
 An important bug related to determinant fixed (determinant, which works via Gaussian elimination, did not take into account the number of swaps performed by the algorithm).
 Inverse and Adjugate are now properties. They do not throw exceptions. Instead, if they cannot be evaluated, a null is returned.
 No matrix division allowed anymore.

Taylor expansion of functions of several variables added:
MultivariableTaylorExpansionTerms (infinite generator of terms),MultivariableTaylorExpansion (returns an expression). 
Added a lot of numbertheory related methds, mostly in the UnsafeAndInternal and ExperimentalFeatures categories.
Added methods:
SymbolicFormOfSine ,SymbolicFormOfCosine ,ExpandSineOfSum ,ExpandConsineOfSum ,ExpandSineArgumentMultiplied ,ExpandCosineArgumentMultiplied ,GetSineOfHalvedAngle ,GetCosineOfHalvedAngle ,DecomposeRational ,GetSineOfHalvedAngle 
SymbolicFormOfSine andSymbolicFormOfCosine exposed inMathS.Compute . Use them to find the exact form of sines beyond basic table values like pi/3, pi/6, etc. These algorithms can decomposesin(17/42 pi) into the exact analytical form with roots and arithmetical operations only. They return null if cannot expand a sine or cosine into an exact form. 
Explicit parsing is now allowed with
MathS.ExplicitParsingOnly , so that omitted operators are not inserted automatically. 
MathS.Parse returns an Either of a successfully parsed entity or a failure of a few possible reasons of parsing failure. Close to some advanced Result type. 
Bugs related to
 imprecise computing of corner cases of tangent
 allocations on accessing a property
 integral of a piecewise
 F# wrapper significantly improved. Matrices, settings, intervals were added. Naming was reconsidered in favor of declarative programming. It also now has the same versioning as the kernel package.

All modules are moved to the
AngouriMath.FSharp namespace. ForInteractive , there is now namespaceInteractive . There is also no need to call magic commands to bind latex to rendering. 
Overload for
** added as a power operator. 
Overload for
***. added as a tensor multiplication. 
Overload for
****. added as a tensor power. 
Interactive.AggressiveOperators module allows for arithmetic operators overloaded for a pair of object and object. The reason is to avoid using additional methods to parse an expression while performing some computations. 
There are now matrix operators, which unconditionally return a matrix.
Here is the list of them:
+. ,. ,*. ,/. ,**. . Module:AngouriMath.FSharp.MatrixOperators . 
There is also function
asMatrix .  Now there are also operators less, greater, less or equal, greater or equal which create entities.
 Functions det, inverse, adjugate added for matices.
 Conjugate of a complex is now a property.
 All nodecreating functions now apply InnerSimplified automatically, unless explicitly specified otherwise.
 Functions to compile expressions added.
 Parsing, to string, latex, basic calculus, solvers, properties are exposed.
 Visit the lab to see samples.
 See the instructions how to get it, if you want to participate in the project or experiment with that.
 Honk# is shipped with AngouriMath instead of FieldCache and a few other packages. Not only some internal functions of AM are rewritten in it, but AM adopts fluent style of using it natively, for example, by having API exposing Either (anonymous type union).
 AngouriMath now multitargets netstandard2.1 (which does not require System.Memory dependency) and .NET Framework 4.7.2 (which also loads such dependencies as System.Numerics), so now it should be more convenient to use from legacy apps.
1.3preview.4
Kernel functional and C#:
 Implicit operators improved (one for BigInteger added).
 An important bug related to determinant fixed (determinant, which works via Gaussian elimination, did not take into account the number of swaps performed by the algorithm).
 Inverse and Adjugate are now properties. They do not throw exceptions. Instead, if they cannot be evaluated, a null is returned.
 No matrix division allowed anymore.

There are now matrix operators, which unconditionally return a matrix.
Here is the list of them:
+ , ,* ,/ ,** . Module:AngouriMath.FSharp.MatrixOperators . 
There is also function
asMatrix .
 Visit the lab to see samples.
 See the instructions how to get it, if you want to participate in the project or experiment with that.
1.3preview.3
Kernel functional and C#:
 Max term count increased by a lot. No power limit in the expansion algorithm.
 Parentheses fixed in LaTeX for negative number cases (and negation sign).

A couple of bugs related to matrices fixed.
ReducedRowEchelonForm andRank added,GaussianEliminated replaced withRowEchelonForm (here we stick to the definition which implies that leading elements can differ from ones).  Piecewise now works correctly for cases when a node is applied to a whole piecewise.

All modules are moved to the
AngouriMath.FSharp namespace. ForInteractive , there is now namespaceInteractive . There is also no need to call magic commands to bind latex to rendering. 
Overload for
** added as a power operator. 
Interactive.AggressiveOperators module allows for arithmetic operators overloaded for a pair of object and object. The reason is to avoid using additional methods to parse an expression while performing some computations.
1.3preview.2
Kernel functional and C#:
 Upcasts added to compilation, as well as many overloads and extension methods.

Latexise does not produce "\times" anymore (nothing or \cdot instead). It also now produces correct code in case when a variable has an index (both variable and index are latexised properly).  Tensors completely reconsidered. No more vectors or tensors. There are only matrices. Moreover, operators now, instead of being elementwise, are now matrixmeaningful. A vector is considered a onecolumn matrix. A lot of methods of matrices are now exposed.
 C++ wrapper (under development): parsing, to string, latex, basic calculus, solvers, properties are exposed.
 F# wrapper significantly improved. Matrices, settings, intervals were added. Naming was reconsidered in favor of declarative programming. It also now has the same versioning as the kernel package.
1.3preview.1
 A few synonyms added for hyperbolic functions.
 Greek and cyrillic latters are now parsable.
 Limits improved.
1.2
1.2 brings us incredibly many features, completely reconsidering all patterns. Number of nodes was doubled, a lot of syntax related to solvers, building an expression tree, performance improved.
Not only that, we added AngouriMath.FSharp and AngouriMath.Interactive packages for working in F# and Jupyter respectively.
1.2 is not backward compatible with 1.1.0.5.
We highly recommend reading this if you plan to migrate from 1.1.0.5 to 1.2, as tons of concepts from 1.1.0.5 were reconsidered and rewritten.
General structure
Now there's no operator's name. Moreover, there's no operator anymore. There are records for each separate
logical action, be than a sum operator or sine function. They all are inside
Active functions like renamed
ToSymPy fixed, as well as many other bugs. Solvers and simplificators improved.
Math features
How the math of AM is improved.
Secant, Cosecant, Arcsecant, Arccosecant
Are now available as nodes with the obvious syntax and their synonyms.
Secant:
Cosecant:
Arcsecant:
Arccosecant:
Hyberbolic trigonometric functions
All trigonometric functions (sin, cos, ..., arcsecant) now have their "h" pair. For example,
Abs and Signum and Phi nodes
Abs always returns a real nonnegative number for a numerical argument. Signum always returns a complex number such that its absolute value is 1 for a numerical argument. One exception for signum is 0: for 0 it returns 0. Phi returns an integer (where Phi is the Euler's totient function).
Syntax for abs:
Syntax for signum:
Syntax for phi:
Domains
Now every node is constrained within a domain. This initgetonly property is called
Syntax:
Note: since domain is not a node, it is true that
Boolean algebra
Now there are many boolean operators added and they are nodes. Instead of
Available operators and their syntaxes:
Syntax of boolean constants:
Equality and inequality nodes
Those return a
Syntax for equal, greater, less, greater or equal, less or equal:
There's also compositional syntax separately for inequalities and inequalities, e. g.
Sets
Sets are now entities. There're
Syntax for finite set:
Syntax for interval:
Syntax for SpecialSet:
Syntax for ConditionalSet:
The
Limits improved
Added some patterns for nondefined expressions, for instance, the first and the second
remarkable limits and a few more. L'Hopital's rule added as well.
Provided
Provided is a node, which turns into NaN if the predicate is false, turns into Expression if the predicate is true. For example,
you may write
Exception: when a provided is in a finite set. Then,
Syntax:
Piecewise
Piecewisedefined functions are finally added too. They allow you to define conditions under which different expressions will be substituted. For example, that is how we can define abs function for real x:
Entity abs = "piecewise(x provided x > 0, x provided x <= 0)";
WriteLine(abs.Substitute("x", 3).EvalNumerical());
WriteLine(abs.Substitute("x", 3).EvalNumerical());
When a piecewise takes part in an expression, the expression will usually be expanded to piecewise, for example,
piecewise(a provided b, c provided d, ...) + 3
>
piecewise(a + 3 provided b, c + 3 provided d, ...)
IMPORTANT. The definition of AM's piecewise differs from the classical one. For the classical math one, piecewise turns into some case if this case's condition is true and all others are false. In AM's definition, piecewise turns into some case if this case's condition is true and all those *before* the considered case are false.
Syntax:
Industrial features
Features, related to industrial integration, production, researches. Usually, improved convenience or stability.
Ultimate exception class added
It is called
Performance improved
F# in AngouriMath
Now you can work with AngouriMath from F# without writing your own wrapper and work with AM's types directly. Check samples
and readme to get more information
Interactive
Now you can work in Jypyter with expressions being rendered directly to the output. See samples and readme for more information
Multithreading
Some methods like
New settings
Now, you don't have to pass a lambda. Instead, use syntax
using var _ = MaxExpansionTermCount.Set(10);
// do what is needed
1.2preview.6
Multithreading, casts for numbers added. AngouriMathBaseException is now root of all AM's exceptions. FieldCache moved to alpha.3, which is strongly named1.2preview.5
Hyberbolic functions are now parsable, Phi node added, a few vulnerabilities fixed1.2preview.4
A few security issues fixed, a few simple rules added, sorter refactored, ToSymPy fixed, Arcsecant & Arccosecant1.2preview.3
Derive > Differentiate, now all calculus functions apply InnerSimplified automatically, naive set solver, bugs fixed1.2preview.2
A lot of patterns for sets added, bugs fixed, extensions for integrate, limit added1.2preview.1
Sets, domains, booleans, signum and abs1.1.0.5
Limits improved & some bugs fixed & nodes for limits, derivatives, integral1.1.0.4beta
Limits & gamma & factorial1.1.0.1
Bugs fixed + smart expansion + solver improved + EDecimal and EInteger instead of decimal and BigInteger1.1.0
Added Numerix module, and this version is not compatible to all previous versions, migrate changes see in https://github.com/asccommunity/AngouriMath/blob/master/CHANGELOG.md1.0.20
Added Tensor, system of equations, polynom divisions, periodic roots for solvers, compilation boosted, simplification improved, LaTeX formatting improved, cache for compiled functions added, search boosted, tons of bugs fixedAngouri © 20192022 · Project's repo · Site's repo · Octicons · Transparency · 1533 pages online